From a1da0105cacb1e816ddd4bd696a3c3b4ad600182 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Sep 2020 16:27:14 -0400 Subject: [PATCH 01/55] bug fixes for small no-split initial sets --- nnenum/nnenum/enumerate.py | 9 ++++++--- nnenum/nnenum/lp_star.py | 2 +- nnenum/nnenum/overapprox.py | 25 +++++++++++-------------- nnenum/nnenum/timerutil.py | 3 +++ nnenum/nnenum/util.py | 3 ++- 5 files changed, 23 insertions(+), 19 deletions(-) diff --git a/nnenum/nnenum/enumerate.py b/nnenum/nnenum/enumerate.py index b96638e..fd84564 100644 --- a/nnenum/nnenum/enumerate.py +++ b/nnenum/nnenum/enumerate.py @@ -89,6 +89,10 @@ def enumerate_network(init, network, spec=None): check_openblas_threads() Timers.reset() + + if not Settings.TIMING_STATS: + Timers.disable() + Timers.tic('enumerate_network') start = time.perf_counter() @@ -101,9 +105,6 @@ def enumerate_network(init, network, spec=None): assert not Settings.RESULT_SAVE_TIMERS or Settings.TIMING_STATS, \ "RESULT_SAVE_TIMERS cannot be used if TIMING_STATS is False" - if not Settings.TIMING_STATS: - Timers.disable() - # adversarial generation process and queue concrete_io_tuple = None q = None @@ -665,6 +666,8 @@ def worker_func(worker_index, shared): # fix timers while Timers.stack and Timers.stack[-1].name != timer_name: + print(f".enumerate popping timer {Timers.stack[-1].name}, stack len {len(Timers.stack)}") + Timers.toc(Timers.stack[-1].name) Timers.toc(timer_name) diff --git a/nnenum/nnenum/lp_star.py b/nnenum/nnenum/lp_star.py index 81df393..ea27899 100644 --- a/nnenum/nnenum/lp_star.py +++ b/nnenum/nnenum/lp_star.py @@ -113,7 +113,7 @@ def to_full_input(self, compressed_input): return rv def input_box_bounds(self, cur_box, max_dim=np.inf, count_lps=True): - '''get input box bounds on this set, compared with the current bounds using lp + '''compute new input box bounds on this set, compared with the current bounds using lp returns a list of 3-tuples for each of the bounds that was adjusted: (dim, lb, ub) diff --git a/nnenum/nnenum/overapprox.py b/nnenum/nnenum/overapprox.py index cd2a160..c891015 100644 --- a/nnenum/nnenum/overapprox.py +++ b/nnenum/nnenum/overapprox.py @@ -69,13 +69,14 @@ def make_prerelu_sims(ss, network): state = ss.prefilter.simulation[1].copy() layer_num = ss.cur_layer - layer = network.layers[layer_num] - rv[layer_num] = state + if layer_num < len(network.layers): + layer = network.layers[layer_num] + rv[layer_num] = state - # current layer may be partially processed - if isinstance(layer, ReluLayer): - state = np.clip(state, 0, np.inf) + # current layer may be partially processed + if isinstance(layer, ReluLayer): + state = np.clip(state, 0, np.inf) while layer_num + 1 < len(network.layers): layer_num += 1 @@ -301,7 +302,9 @@ def do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=None print(f"Overapprox Round {round_num+1}/{len(overapprox_types)} has {len(sets)} set(s)") try: - run_overapprox_round(network, ss, sets, prerelu_sims, check_cancel_func) + if ss.cur_layer < len(network.layers): + run_overapprox_round(network, ss, sets, prerelu_sims, check_cancel_func) + diff = time.perf_counter() - start if Settings.SAVE_BRANCH_TUPLES_TIMES else 0 except OverapproxCanceledException as e: diff = time.perf_counter() - start if Settings.SAVE_BRANCH_TUPLES_TIMES else 0 @@ -310,7 +313,6 @@ def do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=None raise OverapproxCanceledException(f"{e}; {rv}, {msg}") - gens = [s.get_num_gens() for s in sets] rv.round_generators.append(gens) rv.round_ms.append(diff * 1000) @@ -408,7 +410,7 @@ def run_overapprox_round(network, ss_init, sets, prerelu_sims, check_cancel_func split_indices = sort_splits(layer_bounds, split_indices) zero_indices = np.nonzero(layer_bounds[:, 1] < -Settings.SPLIT_TOLERANCE)[0] - + for s in sets: s.execute_with_bounds(layer_num, layer_bounds, split_indices, zero_indices) else: @@ -482,17 +484,12 @@ def tighten_bounds(self, layer_bounds, split_indices, sim, check_cancel_func, de returns (layer_bounds, split_indices), split_indices can be None ''' - #print(f". split_indices on call (star): {split_indices}") - #print(f". layer_bounds on call (star): {layer_bounds[:3]}") - if layer_bounds is None: num_neurons = self.star.a_mat.shape[0] layer_bounds = np.array([[-np.inf, np.inf] for _ in range(num_neurons)], dtype=float) elif split_indices is None: split_indices = make_split_indices(layer_bounds) - #print(f". split_indices (Before lp): {split_indices}") - if self.do_lp: both_bounds = Settings.OVERAPPROX_BOTH_BOUNDS @@ -553,7 +550,7 @@ def execute_with_bounds(self, _layer_num, layer_bounds, split_indices, zero_indi if self.get_num_gens() + len(split_indices) > self.max_gens: raise OverapproxCanceledException(f'{self.type_string} gens exceeds limit (> {self.max_gens})') - + update_zono(self.zono, self.relu_update_func, layer_bounds, split_indices, zero_indices) def transform_linear(self, layer): diff --git a/nnenum/nnenum/timerutil.py b/nnenum/nnenum/timerutil.py index 0bf607f..6b7ca03 100644 --- a/nnenum/nnenum/timerutil.py +++ b/nnenum/nnenum/timerutil.py @@ -152,6 +152,9 @@ def toc(name): Timers.stack[-1].toc() Timers.stack.pop() + else: + assert not Timers.stack, "Timers.enabled was False but Timers.stack non-empty: " + \ + f"{[t.name for t in Timers.stack]}" @staticmethod def print_stats(name=None, short=False): diff --git a/nnenum/nnenum/util.py b/nnenum/nnenum/util.py index 3e98ab9..119abab 100644 --- a/nnenum/nnenum/util.py +++ b/nnenum/nnenum/util.py @@ -146,6 +146,7 @@ def compress_init_box(input_box, tol=1e-9): inputs = len(input_box) dtype = type(input_box[0][0]) + assert dtype in [float, np.float64, np.float32], f"input_box dtype should be float32/64, got {dtype}" cur_bias = np.array([0] * inputs, dtype=dtype) cur_bm_transpose = [] @@ -153,7 +154,7 @@ def compress_init_box(input_box, tol=1e-9): for dim, (lb, ub) in enumerate(input_box): mid = (lb + ub) / 2.0 - + if abs(ub-lb) < tol: # equal, update cur_bias cur_bias[dim] = mid From 1a87804f85dcb166f65e97ff280c33892d984779 Mon Sep 17 00:00:00 2001 From: "dependabot[bot]" <49699333+dependabot[bot]@users.noreply.github.com> Date: Fri, 25 Sep 2020 21:00:48 +0000 Subject: [PATCH 02/55] Bump tensorflow from 2.2.0 to 2.2.1 Bumps [tensorflow](https://github.com/tensorflow/tensorflow) from 2.2.0 to 2.2.1. - [Release notes](https://github.com/tensorflow/tensorflow/releases) - [Changelog](https://github.com/tensorflow/tensorflow/blob/master/RELEASE.md) - [Commits](https://github.com/tensorflow/tensorflow/compare/v2.2.0...v2.2.1) Signed-off-by: dependabot[bot] --- requirements.txt | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/requirements.txt b/requirements.txt index 3cfff89..d447b10 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,4 +1,4 @@ -tensorflow==2.2.0 +tensorflow==2.2.1 numpy==1.17.4 scipy==1.4.1 foolbox==2.4.0 From a909af9f56cd80940856f5517ece0326b927b36d Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 2 Nov 2020 11:57:52 -0500 Subject: [PATCH 03/55] updated lp star and lpi --- nnenum/nnenum/lp_star.py | 20 +++++++++---- nnenum/nnenum/lpinstance.py | 53 ++++++++++++++++++++++++++++------ nnenum/nnenum/specification.py | 12 ++++---- 3 files changed, 65 insertions(+), 20 deletions(-) diff --git a/nnenum/nnenum/lp_star.py b/nnenum/nnenum/lp_star.py index ea27899..e83ec41 100644 --- a/nnenum/nnenum/lp_star.py +++ b/nnenum/nnenum/lp_star.py @@ -117,6 +117,8 @@ def input_box_bounds(self, cur_box, max_dim=np.inf, count_lps=True): returns a list of 3-tuples for each of the bounds that was adjusted: (dim, lb, ub) + + note: lb may be -np.inf and ub may be np.inf ''' Timers.tic("star.input_box_bounds") @@ -132,6 +134,7 @@ def input_box_bounds(self, cur_box, max_dim=np.inf, count_lps=True): while True: vec = np.array([1 if not should_skip[i, 0] else 0 for i in range(dims)], dtype=float) + Timers.tic('lpi.minimize pre') res = self.lpi.minimize(vec) Timers.toc('lpi.minimize pre') @@ -179,36 +182,43 @@ def input_box_bounds(self, cur_box, max_dim=np.inf, count_lps=True): # adjust lb if not should_skip[dim, 0]: + # possible optimization: this may be solving an extra lp if the above loops only involved a single dim + vec = np.array([1 if i == dim else 0 for i in range(dims)], dtype=float) Timers.tic('lpi.minimize post') - res = self.lpi.minimize(vec) + min_val = self.lpi.minimize(vec)[dim] Timers.toc('lpi.minimize post') if count_lps: self.num_lps += 1 + max_val = cur_box[dim][1] if cur_box is not None else np.inf + if cur_box is None or abs(res[dim] - cur_box[dim][0]) >= tol: assert not should_skip[dim, 0] - rv.append([dim, res[dim], np.inf]) + rv.append([dim, min_val, max_val]) # adjust ub if not should_skip[dim, 1]: vec = np.array([-1 if i == dim else 0 for i in range(dims)], dtype=float) Timers.tic('lpi.minimize post') - res = self.lpi.minimize(vec) + max_val = self.lpi.minimize(vec)[dim] Timers.toc('lpi.minimize post') if count_lps: self.num_lps += 1 + min_val = cur_box[dim][0] if cur_box is not None else -np.inf + if cur_box is None or abs(res[dim] - cur_box[dim][1]) >= tol: assert not should_skip[dim, 1] if not rv or rv[-1][0] != dim: - rv.append([dim, -np.inf, res[dim]]) + rv.append([dim, min_val, max_val]) else: - rv[-1][2] = res[dim] + # both bounds changed, update previous val + rv[-1][2] = max_val Timers.toc("star.input_box_bounds") diff --git a/nnenum/nnenum/lpinstance.py b/nnenum/nnenum/lpinstance.py index b37d979..16e7717 100644 --- a/nnenum/nnenum/lpinstance.py +++ b/nnenum/nnenum/lpinstance.py @@ -132,9 +132,11 @@ def set_col_bounds(self, col, lb, ub): 'set double-bounded column bounds' col_type = glpk.glp_get_col_type(self.lp, col + 1) - assert col_type == glpk.GLP_DB - glpk.glp_set_col_bnds(self.lp, col + 1, glpk.GLP_DB, lb, ub) # double-bounded variable + if col_type != glpk.GLP_DB: + print(f"Warning: Contract col {col} to {lb, ub} skipped (col type is not GLP_DB):\n{self}") + else: + glpk.glp_set_col_bnds(self.lp, col + 1, glpk.GLP_DB, lb, ub) # double-bounded variable def get_col_bounds(self): 'get column bounds' @@ -208,7 +210,7 @@ def deserialize(self): def _column_names_str(self): 'get the line in __str__ for the column names' - rv = " " + rv = " " dbl_max = sys.float_info.max for col, name in enumerate(self.names): @@ -233,12 +235,12 @@ def _opt_dir_str(self, zero_print): lp = self.lp cols = self.get_num_cols() - rv = "min" + rv = "min " for col in range(1, cols + 1): val = glpk.glp_get_obj_coef(lp, col) - num = str(val) + num = f"{val:.6f}" num = num.rjust(6)[:6] # fix width to exactly 6 if val == 0: @@ -275,7 +277,7 @@ def _constraints_str(self, zero_print): cols = self.get_num_cols() stat_labels = ["?(0)?", "BS", "NL", "NU", "NF", "NS"] - inds =SwigArray.get_int_array(cols + 1) + inds = SwigArray.get_int_array(cols + 1) vals = SwigArray.get_double_array(cols + 1) for row in range(1, rows + 1): @@ -293,7 +295,7 @@ def _constraints_str(self, zero_print): val = vals[index] break - num = str(val) + num = f"{val:.6f}" num = num.rjust(6)[:6] # fix width to exactly 6 rv += (zero_print(num) if val == 0 else num) + " " @@ -304,7 +306,7 @@ def _constraints_str(self, zero_print): val = glpk.glp_get_row_ub(lp, row) rv += " <= " - num = str(val) + num = f"{val:.6f}" num = num.rjust(6)[:6] # fix width to exactly 6 rv += (zero_print(num) if val == 0 else num) + " " @@ -464,7 +466,7 @@ def add_double_bounded_cols(self, names, lb, ub): assert lb < ub glpk.glp_set_col_bnds(self.lp, num_cols + i + 1, glpk.GLP_DB, lb, ub) # double-bounded variable - def add_dense_row(self, vec, rhs): + def add_dense_row(self, vec, rhs, normalize=True): ''' add a row from a dense nd.array, row <= rhs ''' @@ -475,6 +477,13 @@ def add_dense_row(self, vec, rhs): assert len(vec.shape) == 1 or vec.shape[0] == 1 assert len(vec) == self.get_num_cols(), f"vec had {len(vec)} values, but lpi has {self.get_num_cols()} cols" + if normalize: + norm = np.linalg.norm(vec) + assert norm > 0 + + vec = vec / norm + rhs = rhs / norm + rows_before = self.get_num_rows() self.add_rows_less_equal([rhs]) @@ -486,6 +495,29 @@ def add_dense_row(self, vec, rhs): Timers.toc('add_dense_row') + def del_cols(self, cols): + ''' + delete columns. passed in cols is python index (not glpk index) + ''' + + i_vec = SwigArray.get_int_array(len(cols) + 1) + + print(f".lpi del cols debug assert b_. names before = {self.names}, del_cols = {cols}") + + #for i, c in enumerate(reversed(sorted(cols))): + for i, c in enumerate(cols): + assert self.names[c].startswith('b_') + del self.names[c] + + i_vec[1 + i] = c + 1 + + print(f". names after: {self.names}") + + for name in self.names: + assert not name.startswith('b_') + + glpk.glp_del_cols(self.lp, len(cols), i_vec) + def set_constraints_csr(self, data, glpk_indices, indptr, shape): ''' set the constrains row by row to be equal to the passed-in csr matrix attribues @@ -701,6 +733,9 @@ def minimize(self, direction_vec, fail_on_unsat=True): rv = result_nodir else: print("Error: No-dir result was also infeasible!") + + if self.get_num_rows() < 50 and self.get_num_cols() < 50: + print(f"{self}") else: print("Using result after reset basis (soltion was now feasible)") diff --git a/nnenum/nnenum/specification.py b/nnenum/nnenum/specification.py index 63ad0d2..64a9a41 100644 --- a/nnenum/nnenum/specification.py +++ b/nnenum/nnenum/specification.py @@ -83,7 +83,7 @@ def zono_might_violate_spec(self, zono): return rv - def get_violation_star(self, lp_star, safe_spec_list=None): + def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): '''does this lp_star violate the spec? if so, return a new, non-empty star object with the violation region @@ -98,7 +98,7 @@ def get_violation_star(self, lp_star, safe_spec_list=None): # skip parts of the disjunctive spec that are already safe continue - res = spec.get_violation_star(lp_star) + res = spec.get_violation_star(lp_star, normalize=normalize) if res is not None: break @@ -197,7 +197,7 @@ def zono_might_violate_spec(self, zono): return might_violate - def get_violation_star(self, lp_star, safe_spec_list=None): + def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): '''does this lp_star violate the spec? if so, return a new, non-empty star object with the violation region @@ -210,7 +210,7 @@ def get_violation_star(self, lp_star, safe_spec_list=None): # constructing a new star and do exact check copy = lp_star.copy() - + # add constraints on the outputs # output = a_mat.tranpose * input_col @@ -224,8 +224,8 @@ def get_violation_star(self, lp_star, safe_spec_list=None): init_bias = np.dot(self.mat, copy.bias) for i, row in enumerate(init_spec): - lpi.add_dense_row(row, self.rhs[i] - init_bias[i]) - + lpi.add_dense_row(row, self.rhs[i] - init_bias[i], normalize=normalize) + winput = lpi.minimize(None, fail_on_unsat=False) if winput is None: From 00d6cf0ac24c047a3efd2d48ce11665e463fc04a Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 9 Nov 2020 13:59:41 -0500 Subject: [PATCH 04/55] removed delcols --- nnenum/nnenum/lpinstance.py | 23 ----------------------- 1 file changed, 23 deletions(-) diff --git a/nnenum/nnenum/lpinstance.py b/nnenum/nnenum/lpinstance.py index 16e7717..5e52c6d 100644 --- a/nnenum/nnenum/lpinstance.py +++ b/nnenum/nnenum/lpinstance.py @@ -495,29 +495,6 @@ def add_dense_row(self, vec, rhs, normalize=True): Timers.toc('add_dense_row') - def del_cols(self, cols): - ''' - delete columns. passed in cols is python index (not glpk index) - ''' - - i_vec = SwigArray.get_int_array(len(cols) + 1) - - print(f".lpi del cols debug assert b_. names before = {self.names}, del_cols = {cols}") - - #for i, c in enumerate(reversed(sorted(cols))): - for i, c in enumerate(cols): - assert self.names[c].startswith('b_') - del self.names[c] - - i_vec[1 + i] = c + 1 - - print(f". names after: {self.names}") - - for name in self.names: - assert not name.startswith('b_') - - glpk.glp_del_cols(self.lp, len(cols), i_vec) - def set_constraints_csr(self, data, glpk_indices, indptr, shape): ''' set the constrains row by row to be equal to the passed-in csr matrix attribues From 010c1c49a361c38fcac0c00fbc7cbcb6f7628208 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sat, 12 Dec 2020 21:31:21 -0500 Subject: [PATCH 05/55] minor for nfm --- nnenum/nnenum/enumerate.py | 2 - nnenum/nnenum/lp_star.py | 278 ++++++++++++++++++++++++--------- nnenum/nnenum/lp_star_state.py | 2 +- nnenum/nnenum/prefilter.py | 11 +- nnenum/nnenum/settings.py | 2 + nnenum/nnenum/zonotope.py | 4 +- 6 files changed, 220 insertions(+), 79 deletions(-) diff --git a/nnenum/nnenum/enumerate.py b/nnenum/nnenum/enumerate.py index fd84564..e37798f 100644 --- a/nnenum/nnenum/enumerate.py +++ b/nnenum/nnenum/enumerate.py @@ -666,8 +666,6 @@ def worker_func(worker_index, shared): # fix timers while Timers.stack and Timers.stack[-1].name != timer_name: - print(f".enumerate popping timer {Timers.stack[-1].name}, stack len {len(Timers.stack)}") - Timers.toc(Timers.stack[-1].name) Timers.toc(timer_name) diff --git a/nnenum/nnenum/lp_star.py b/nnenum/nnenum/lp_star.py index e83ec41..b8f0f63 100644 --- a/nnenum/nnenum/lp_star.py +++ b/nnenum/nnenum/lp_star.py @@ -8,6 +8,7 @@ from nnenum.lpinstance import LpInstance from nnenum.util import Freezable +from nnenum.settings import Settings from nnenum.timerutil import Timers from nnenum import kamenev @@ -33,6 +34,8 @@ def __init__(self, a_mat, bias, box_bounds=None): self.init_bm = None self.init_bias = None + self.input_bounds_witnesses = None # a list of min, max for each dim + # cached lp result self.last_lp_result = None @@ -40,6 +43,15 @@ def __init__(self, a_mat, bias, box_bounds=None): # box_bounds may be None if we're initializing in lp_star.copy() if box_bounds is not None: + if Settings.CONTRACT_LP_TRACK_WITNESSES: + min_pt = np.array([a for a, b in box_bounds], dtype=float) + max_pt = np.array([b for a, b in box_bounds], dtype=float) + + self.input_bounds_witnesses = [] + + for _ in range(len(box_bounds)): + self.input_bounds_witnesses.append([min_pt, max_pt]) + self.lpi = LpInstance() for i, (lb, ub) in enumerate(box_bounds): @@ -83,6 +95,12 @@ def copy(self): Timers.tic('copy init bm bias') + if self.input_bounds_witnesses is not None: + rv.input_bounds_witnesses = [] + + for a, b in self.input_bounds_witnesses: + rv.input_bounds_witnesses.append([a, b]) + if self.init_bm is None: rv.init_bm = None else: @@ -111,8 +129,97 @@ def to_full_input(self, compressed_input): rv = rv.astype(self.a_mat.dtype) return rv + + def input_box_bounds_old(self, cur_box, should_skip, count_lps=True): + '''get input box bounds on this set, compared with the current bounds using lp + returns a list of 3-tuples for each of the bounds that was adjusted: + (dim, lb, ub) + ''' + + dims = self.lpi.get_num_cols() + rv = [] + tol = 1e-8 + + Timers.tic("star.input_box_bounds_old") + + for dim in range(dims): - def input_box_bounds(self, cur_box, max_dim=np.inf, count_lps=True): + if not should_skip[dim, 0]: + # adjust lb + vec = np.array([1 if i == dim else 0 for i in range(dims)], dtype=float) + Timers.tic('lpi.minimize') + res = self.lpi.minimize(vec) + Timers.toc('lpi.minimize') + + if self.input_bounds_witnesses: + self.input_bounds_witnesses[dim][0] = res + + if count_lps: + self.num_lps += 1 + + if cur_box is None or abs(res[dim] - cur_box[dim][0]) >= tol: + rv.append([dim, res[dim], np.inf]) + + if not should_skip[dim, 1]: + # adjust ub + vec = np.array([-1 if i == dim else 0 for i in range(dims)], dtype=float) + + Timers.tic('lpi.minimize') + res = self.lpi.minimize(vec) + Timers.toc('lpi.minimize') + + if self.input_bounds_witnesses: + self.input_bounds_witnesses[dim][1] = res + + if count_lps: + self.num_lps += 1 + + if cur_box is None or abs(res[dim] - cur_box[dim][1]) >= tol: + if not rv or rv[-1][0] != dim: + rv.append([dim, -np.inf, res[dim]]) + else: + rv[-1][2] = res[dim] + + Timers.toc("star.input_box_bounds_old") + + return rv + + def input_box_bounds(self, cur_box, hyperplane_vec, rhs, count_lps=True): + 'compute input box bounds on the set' + + dims = self.lpi.get_num_cols() + should_skip = np.zeros((dims, 2), dtype=bool) + + if self.input_bounds_witnesses is not None: + for d in range(dims): + min_wit, max_wit = self.input_bounds_witnesses[d] + + assert abs(min_wit[d] - cur_box[d][0]) < 1e-5 + assert abs(max_wit[d] - cur_box[d][1]) < 1e-5 + + if np.dot(hyperplane_vec, min_wit) <= rhs: + should_skip[d, 0] = True + + if np.dot(hyperplane_vec, max_wit) <= rhs: + should_skip[d, 1] = True + + if Settings.CONTRACT_LP_OPTIMIZED and cur_box is not None: + rv = self.input_box_bounds_new(cur_box, should_skip, count_lps) + else: + rv = self.input_box_bounds_old(cur_box, should_skip, count_lps) + + #print("debug check") + #should_skip = np.zeros((dims, 2), dtype=bool) + #rv2 = self.input_box_bounds_old(cur_box, should_skip, count_lps) + #if len(rv) != len(rv2): + + # print(f"hyperplane_vec <= rhs was {hyperplane_vec} <= {rhs}") + # print(f"box was {cur_box}\nrv was {rv}\nrv2 was {rv2}") + # assert False + + return rv + + def input_box_bounds_new(self, cur_box, should_skip, count_lps=True): '''compute new input box bounds on this set, compared with the current bounds using lp returns a list of 3-tuples for each of the bounds that was adjusted: @@ -121,62 +228,48 @@ def input_box_bounds(self, cur_box, max_dim=np.inf, count_lps=True): note: lb may be -np.inf and ub may be np.inf ''' - Timers.tic("star.input_box_bounds") + assert cur_box is not None - dims = min(max_dim, self.lpi.get_num_cols()) + Timers.tic("star.input_box_bounds_new") + + dims = self.lpi.get_num_cols() rv = [] - should_skip = np.zeros((dims, 2), dtype=bool) tol = 1e-8 + num_lps = 0 - if cur_box is not None: - #vec = np.ones(dims) + vec = np.ones((dims, ), dtype=float) - while True: - vec = np.array([1 if not should_skip[i, 0] else 0 for i in range(dims)], dtype=float) + for d in range(dims): + if should_skip[d, 0]: + vec[d] = 0 - Timers.tic('lpi.minimize pre') - res = self.lpi.minimize(vec) - Timers.toc('lpi.minimize pre') + while True: + Timers.tic('lpi.minimize pre1') + res = self.lpi.minimize(vec) + num_lps += 1 + Timers.toc('lpi.minimize pre1') - skipped_all = True - skipped_some = False - - for dim in range(dims): - if should_skip[dim, 0]: - continue - - if abs(res[dim] - cur_box[dim][0]) < tol: - should_skip[dim, 0] = True - skipped_some = True - else: - skipped_all = False + skipped_all = True + skipped_some = False - if skipped_all or not skipped_some: - break + for dim in range(dims): + if should_skip[dim, 0]: + continue - # other side - while True: - vec = np.array([-1 if not should_skip[i, 1] else 0 for i in range(dims)], dtype=float) - Timers.tic('lpi.minimize pre') - res = self.lpi.minimize(vec) - Timers.toc('lpi.minimize pre') - - skipped_all = True - skipped_some = False - - for dim in range(dims): - if should_skip[dim, 1]: - continue - - if abs(res[dim] - cur_box[dim][1]) < tol: - should_skip[dim, 1] = True - skipped_some = True - else: - skipped_all = False + if abs(res[dim] - cur_box[dim][0]) < tol: + + if self.input_bounds_witnesses is not None: + self.input_bounds_witnesses[dim][0] = res + + vec[dim] = 0 + should_skip[dim, 0] = True + skipped_some = True + else: + skipped_all = False - if skipped_all or not skipped_some: - break + if skipped_all or not skipped_some: + break for dim in range(dims): @@ -184,43 +277,86 @@ def input_box_bounds(self, cur_box, max_dim=np.inf, count_lps=True): if not should_skip[dim, 0]: # possible optimization: this may be solving an extra lp if the above loops only involved a single dim - vec = np.array([1 if i == dim else 0 for i in range(dims)], dtype=float) - Timers.tic('lpi.minimize post') - min_val = self.lpi.minimize(vec)[dim] - Timers.toc('lpi.minimize post') + vec = np.zeros((dims, ), dtype=float) + vec[dim] = 1 + + Timers.tic('lpi.minimize post1') + res = self.lpi.minimize(vec) + min_val = res[dim] + num_lps += 1 + Timers.toc('lpi.minimize post1') - if count_lps: - self.num_lps += 1 + if self.input_bounds_witnesses is not None: + self.input_bounds_witnesses[dim][0] = res - max_val = cur_box[dim][1] if cur_box is not None else np.inf + if abs(min_val - cur_box[dim][0]) >= tol: + rv.append([dim, min_val, np.inf]) - if cur_box is None or abs(res[dim] - cur_box[dim][0]) >= tol: - assert not should_skip[dim, 0] - rv.append([dim, min_val, max_val]) + # other side + vec = -1 * np.ones((dims, ), dtype=float) + + for d in range(dims): + if should_skip[d, 1]: + vec[d] = 0 + + while True: + Timers.tic('lpi.minimize pre2') + res = self.lpi.minimize(vec) + num_lps += 1 + Timers.toc('lpi.minimize pre2') + + skipped_all = True + skipped_some = False + + for dim in range(dims): + if should_skip[dim, 1]: + continue + + if abs(res[dim] - cur_box[dim][1]) < tol: + if self.input_bounds_witnesses is not None: + self.input_bounds_witnesses[dim][1] = res + + vec[dim] = 0 + should_skip[dim, 1] = True + skipped_some = True + else: + skipped_all = False + + if skipped_all or not skipped_some: + break + for dim in range(dims): # adjust ub if not should_skip[dim, 1]: - vec = np.array([-1 if i == dim else 0 for i in range(dims)], dtype=float) + vec = np.zeros((dims, ), dtype=float) + vec[dim] = -1 - Timers.tic('lpi.minimize post') - max_val = self.lpi.minimize(vec)[dim] - Timers.toc('lpi.minimize post') + Timers.tic('lpi.minimize post2') + res = self.lpi.minimize(vec) + max_val = res[dim] + num_lps += 1 + Timers.toc('lpi.minimize post2') - if count_lps: - self.num_lps += 1 + if self.input_bounds_witnesses is not None: + self.input_bounds_witnesses[dim][1] = res - min_val = cur_box[dim][0] if cur_box is not None else -np.inf + if abs(max_val - cur_box[dim][1]) >= tol: - if cur_box is None or abs(res[dim] - cur_box[dim][1]) >= tol: - assert not should_skip[dim, 1] + found = False - if not rv or rv[-1][0] != dim: - rv.append([dim, min_val, max_val]) - else: - # both bounds changed, update previous val - rv[-1][2] = max_val + for index, (rv_dim, _rv_min, _rv_max) in enumerate(rv): + if rv_dim == dim: + found = True + rv[index][2] = max_val + break + + if not found: + rv.append([dim, -np.inf, max_val]) + + if count_lps: + self.num_lps += num_lps - Timers.toc("star.input_box_bounds") + Timers.toc("star.input_box_bounds_new") return rv diff --git a/nnenum/nnenum/lp_star_state.py b/nnenum/nnenum/lp_star_state.py index 1a424f3..932aa21 100644 --- a/nnenum/nnenum/lp_star_state.py +++ b/nnenum/nnenum/lp_star_state.py @@ -59,7 +59,7 @@ def __init__(self, uncompressed_init_box=None, spec=None, safe_spec_list=None): def __del__(self): # delete the circular reference which would prevent the memory from being freed - if self.prefilter.output_bounds: + if self.prefilter is not None and self.prefilter.output_bounds: self.prefilter.output_bounds.prefilter = None def __str__(self): diff --git a/nnenum/nnenum/prefilter.py b/nnenum/nnenum/prefilter.py index 2cfa44d..3429002 100644 --- a/nnenum/nnenum/prefilter.py +++ b/nnenum/nnenum/prefilter.py @@ -309,8 +309,13 @@ def split_relu(self, neuron_index, pos_star, neg_star, self_gets_positive, start Timers.toc("contract_zonotope") if Settings.CONTRACT_ZONOTOPE_LP: - pos.zono.contract_lp(pos_star) - neg.zono.contract_lp(neg_star) + row = pos_star.a_mat[i] + bias = pos_star.bias[i] + + Timers.tic("contract_zonotope_lp") + pos.zono.contract_lp(pos_star, -row, bias) + neg.zono.contract_lp(neg_star, row, -bias) + Timers.toc("contract_zonotope_lp") if Settings.EAGER_BOUNDS: ### RECOMPUTE LAYER BOUNDS eagerly (for remaining neurons) (and witnesses) @@ -318,7 +323,7 @@ def split_relu(self, neuron_index, pos_star, neg_star, self_gets_positive, start neg.domain_shrank(neg_star, start_time, depth) # tolerance for lp solver is about 1e-6 - assert pos.simulation[1][i] >= -1e-4, f"pos sim for {i} was {pos.simulation[1][i]}" + assert pos.simulation[1][i] >= -1e-3, f"pos sim for {i} was {pos.simulation[1][i]}" # neg should exactly be equal to zero, since we assigned a_mat and bias to zero assert abs(neg.simulation[1][i]) <= Settings.SPLIT_TOLERANCE, f"neg sim for {i} was {neg.simulation[1][i]}" diff --git a/nnenum/nnenum/settings.py b/nnenum/nnenum/settings.py index 1e1230b..a40701d 100644 --- a/nnenum/nnenum/settings.py +++ b/nnenum/nnenum/settings.py @@ -57,6 +57,8 @@ def reset(cls): cls.CONTRACT_ZONOTOPE = False # try domain contraction on zonotopes (more accurate prefilter, but slower) cls.CONTRACT_ZONOTOPE_LP = False # contract zonotope using LPs (even more accurate prefilter, but even slower) + cls.CONTRACT_LP_OPTIMIZED = True # use optimized lp contraction + cls.CONTRACT_LP_TRACK_WITNESSES = True # track box bounds witnesses to reduce LP solving cls.CONTRACT_OVERAPPROX_VIOLATION = False # contract from overapproximation violation? diff --git a/nnenum/nnenum/zonotope.py b/nnenum/nnenum/zonotope.py index 29124fc..a9ea56a 100644 --- a/nnenum/nnenum/zonotope.py +++ b/nnenum/nnenum/zonotope.py @@ -111,7 +111,7 @@ def get_domain_center(self): return rv - def contract_lp(self, star): + def contract_lp(self, star, hyperplane_vec, rhs): '''do lp zonotope contraction returns True if domain was tightened @@ -121,7 +121,7 @@ def contract_lp(self, star): cur_box = self.init_bounds - new_bounds_list = star.input_box_bounds(cur_box, count_lps=True) + new_bounds_list = star.input_box_bounds(cur_box, hyperplane_vec, rhs, count_lps=True) for dim, lb, ub in new_bounds_list: self.update_init_bounds(dim, (lb, ub)) From 9597fb507950901b4241e582c3038d6381ce7cbd Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 14 Dec 2020 22:42:18 -0500 Subject: [PATCH 06/55] NFM version, added comment about one-norm name --- nnenum/nnenum/settings.py | 1 + 1 file changed, 1 insertion(+) diff --git a/nnenum/nnenum/settings.py b/nnenum/nnenum/settings.py index a40701d..15d81ad 100644 --- a/nnenum/nnenum/settings.py +++ b/nnenum/nnenum/settings.py @@ -19,6 +19,7 @@ class Settings(metaclass=FreezableMeta): BRANCH_OVERAPPROX, BRANCH_EGO, BRANCH_EGO_LIGHT, BRANCH_EXACT = range(4) # used for BRANCH_MODE SPLIT_LARGEST, SPLIT_ONE_NORM, SPLIT_SMALLEST, SPLIT_INORDER = range(4) # used for SPLIT_ORDER + #TODO: one norm should acutally be called inf norm @classmethod def reset(cls): From f1344b3822e8187020389b51012c25128ffd1928 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 21 Dec 2020 11:33:18 -0500 Subject: [PATCH 07/55] added get_input_box_bounds to star --- nnenum/nnenum/lp_star.py | 61 ++++++++++++++++++++++++---------- nnenum/nnenum/lp_star_state.py | 45 ------------------------- nnenum/nnenum/overapprox.py | 8 ++--- nnenum/nnenum/settings.py | 2 -- nnenum/nnenum/specification.py | 10 ++++++ nnenum/nnenum/zonotope.py | 5 ++- 6 files changed, 57 insertions(+), 74 deletions(-) diff --git a/nnenum/nnenum/lp_star.py b/nnenum/nnenum/lp_star.py index b8f0f63..0a5dbb0 100644 --- a/nnenum/nnenum/lp_star.py +++ b/nnenum/nnenum/lp_star.py @@ -130,7 +130,7 @@ def to_full_input(self, compressed_input): return rv - def input_box_bounds_old(self, cur_box, should_skip, count_lps=True): + def update_input_box_bounds_old(self, cur_box, should_skip, count_lps=True): '''get input box bounds on this set, compared with the current bounds using lp returns a list of 3-tuples for each of the bounds that was adjusted: (dim, lb, ub) @@ -140,7 +140,7 @@ def input_box_bounds_old(self, cur_box, should_skip, count_lps=True): rv = [] tol = 1e-8 - Timers.tic("star.input_box_bounds_old") + Timers.tic("star.update_input_box_bounds_old") for dim in range(dims): @@ -180,37 +180,62 @@ def input_box_bounds_old(self, cur_box, should_skip, count_lps=True): else: rv[-1][2] = res[dim] - Timers.toc("star.input_box_bounds_old") + Timers.toc("star.update_input_box_bounds_old") return rv - def input_box_bounds(self, cur_box, hyperplane_vec, rhs, count_lps=True): - 'compute input box bounds on the set' + def get_input_box_bounds(self): + 'gets the input box bounds from witnesses' + + assert self.input_bounds_witnesses is not None + dims = self.lpi.get_num_cols() + + rv = [] + + for d in range(dims): + min_wit, max_wit = self.input_bounds_witnesses[d] + rv.append((min_wit[d], max_wit[d])) + + return rv + + def update_input_box_bounds(self, hyperplane_vec_list, rhs_list, count_lps=True): + '''update the input box bounds on the set after some constaints are added + + hyperplane_vec_list and rhs_list (can also be individual items) + define the new constraint that was added (optimized bounds using witnesses) + ''' dims = self.lpi.get_num_cols() should_skip = np.zeros((dims, 2), dtype=bool) + # TODO: check if cur_box is the same as get_input_box_bounds + cur_box = self.get_input_box_bounds() + + if not isinstance(hyperplane_vec_list, list): + hyperplane_vec_list = [hyperplane_vec_list] + + assert not isinstance(rhs_list, list) + rhs_list = [rhs_list] + if self.input_bounds_witnesses is not None: for d in range(dims): min_wit, max_wit = self.input_bounds_witnesses[d] - assert abs(min_wit[d] - cur_box[d][0]) < 1e-5 - assert abs(max_wit[d] - cur_box[d][1]) < 1e-5 - - if np.dot(hyperplane_vec, min_wit) <= rhs: - should_skip[d, 0] = True + for hyperplane_vec, rhs in zip(hyperplane_vec_list, rhs_list): + if not should_skip[d, 0] and np.dot(hyperplane_vec, min_wit) <= rhs: + should_skip[d, 0] = True - if np.dot(hyperplane_vec, max_wit) <= rhs: - should_skip[d, 1] = True + if should_skip[d, 1] and np.dot(hyperplane_vec, max_wit) <= rhs: + should_skip[d, 1] = True if Settings.CONTRACT_LP_OPTIMIZED and cur_box is not None: - rv = self.input_box_bounds_new(cur_box, should_skip, count_lps) + rv = self.update_input_box_bounds_new(cur_box, should_skip, count_lps) else: - rv = self.input_box_bounds_old(cur_box, should_skip, count_lps) + rv = self.update_input_box_bounds_old(cur_box, should_skip, count_lps) #print("debug check") #should_skip = np.zeros((dims, 2), dtype=bool) - #rv2 = self.input_box_bounds_old(cur_box, should_skip, count_lps) + #rv2 = self.update_input_box_bounds_old(cur_box, should_skip, count_lps) #if len(rv) != len(rv2): # print(f"hyperplane_vec <= rhs was {hyperplane_vec} <= {rhs}") @@ -219,7 +244,7 @@ def input_box_bounds(self, cur_box, hyperplane_vec, rhs, count_lps=True): return rv - def input_box_bounds_new(self, cur_box, should_skip, count_lps=True): + def update_input_box_bounds_new(self, cur_box, should_skip, count_lps=True): '''compute new input box bounds on this set, compared with the current bounds using lp returns a list of 3-tuples for each of the bounds that was adjusted: @@ -230,7 +255,7 @@ def input_box_bounds_new(self, cur_box, should_skip, count_lps=True): assert cur_box is not None - Timers.tic("star.input_box_bounds_new") + Timers.tic("star.update_input_box_bounds_new") dims = self.lpi.get_num_cols() rv = [] @@ -356,7 +381,7 @@ def input_box_bounds_new(self, cur_box, should_skip, count_lps=True): if count_lps: self.num_lps += num_lps - Timers.toc("star.input_box_bounds_new") + Timers.toc("star.update_input_box_bounds_new") return rv diff --git a/nnenum/nnenum/lp_star_state.py b/nnenum/nnenum/lp_star_state.py index 932aa21..5c540dd 100644 --- a/nnenum/nnenum/lp_star_state.py +++ b/nnenum/nnenum/lp_star_state.py @@ -124,51 +124,6 @@ def from_init_box(self, uncompressed_init_box): self.prefilter = Prefilter() self.prefilter.init_from_uncompressed_box(uncompressed_init_box, self.star, init_box) - def contract_from_violation(self, violation_stars): - '''contract from a list of violation stars - - returns True if contracted - ''' - - Timers.tic('contract_from_violation') - - max_dim = self.star.a_mat.shape[1] - - #self_box = self.star.input_box_bounds(None) - - zono_box = self.prefilter.zono.init_bounds - -# print(f"prefilter box bounds: {}") - print(f"\nnum violation stars: {len(violation_stars)}") - - vio_box = [[np.inf, -np.inf] for _ in range(max_dim)] - - for star in violation_stars: - single_vio_box = star.input_box_bounds(None, max_dim=max_dim) - - for dim, lb, ub in single_vio_box: - vio_box[dim][0] = min(vio_box[dim][0], lb) - vio_box[dim][1] = max(vio_box[dim][1], ub) - - tol = 1e-7 - - contracted = False - - for i, (lb, ub) in enumerate(vio_box): - if lb > zono_box[i][0] + tol or ub < zono_box[i][1] - tol: - print(f"contracting {i} from {zono_box[i]} to {lb, ub}") - - self.prefilter.zono.update_init_bounds(i, (lb, ub)) - self.star.lpi.set_col_bounds(i, lb, ub) - contracted = True - - Timers.toc('contract_from_violation') - - if contracted: - self.prefilter.domain_shrank(self.star) - - return contracted - def is_finished(self, network): 'is the current star finished?' diff --git a/nnenum/nnenum/overapprox.py b/nnenum/nnenum/overapprox.py index c891015..5436bae 100644 --- a/nnenum/nnenum/overapprox.py +++ b/nnenum/nnenum/overapprox.py @@ -145,9 +145,8 @@ def check_round(ss, sets, spec_arg, check_cancel_func=None): unsafe_violation_stars.append(violation_star) unsafe_violation_indices.append(i) - if not Settings.CONTRACT_OVERAPPROX_VIOLATION: - # if contracting violation, we need all violation stars - break + # just need one violation star + break Timers.toc('overapprox_check_round') @@ -333,9 +332,6 @@ def do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=None and Settings.ADVERSARIAL_ONNX_PATH and try_seeded_adversarial: rv.concrete_io_tuple = try_seeded_adversarial(dims, abstract_ios) - if vstars and Settings.CONTRACT_OVERAPPROX_VIOLATION: - ss.contract_from_violation(vstars) - if first_round: first_round = False diff --git a/nnenum/nnenum/settings.py b/nnenum/nnenum/settings.py index 15d81ad..43905a6 100644 --- a/nnenum/nnenum/settings.py +++ b/nnenum/nnenum/settings.py @@ -61,8 +61,6 @@ def reset(cls): cls.CONTRACT_LP_OPTIMIZED = True # use optimized lp contraction cls.CONTRACT_LP_TRACK_WITNESSES = True # track box bounds witnesses to reduce LP solving - cls.CONTRACT_OVERAPPROX_VIOLATION = False # contract from overapproximation violation? - # the types of overapproximation to use in each round cls.OVERAPPROX_TYPES = [['zono.area'], ['zono.area', 'zono.ybloat', 'zono.interval'], diff --git a/nnenum/nnenum/specification.py b/nnenum/nnenum/specification.py index 64a9a41..fa24af1 100644 --- a/nnenum/nnenum/specification.py +++ b/nnenum/nnenum/specification.py @@ -237,6 +237,16 @@ def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): #woutput = np.dot(copy.a_mat, winput) + copy.bias #assert self.is_violation(woutput), f"witness output {woutput} was not a violation of {self}" + # also comput input box bounds + Timers.tic('violation_input_box_bounds') + #for i, row in enumerate(init_spec): + # row + # rhs = self.rhs[i] - init_bias[i] + + # rv.input_box_bounds(HERE + + Timers.toc('violation_input_box_bounds') + Timers.toc('get_violation_star') return rv if is_violation else None diff --git a/nnenum/nnenum/zonotope.py b/nnenum/nnenum/zonotope.py index a9ea56a..bd91eef 100644 --- a/nnenum/nnenum/zonotope.py +++ b/nnenum/nnenum/zonotope.py @@ -119,9 +119,8 @@ def contract_lp(self, star, hyperplane_vec, rhs): Timers.tic("contract_lp") - cur_box = self.init_bounds - - new_bounds_list = star.input_box_bounds(cur_box, hyperplane_vec, rhs, count_lps=True) + #cur_box = self.init_bounds + new_bounds_list = star.update_input_box_bounds(hyperplane_vec, rhs, count_lps=True) for dim, lb, ub in new_bounds_list: self.update_init_bounds(dim, (lb, ub)) From 7b54456af79002b93f49a01cb5bf68a9522b4868 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Tue, 22 Dec 2020 14:48:31 -0500 Subject: [PATCH 08/55] minor --- nnenum/nnenum/lp_star.py | 51 ++++++++++++++++++++++++++-------- nnenum/nnenum/overapprox.py | 7 +---- nnenum/nnenum/settings.py | 3 +- nnenum/nnenum/specification.py | 25 +++++++++-------- 4 files changed, 55 insertions(+), 31 deletions(-) diff --git a/nnenum/nnenum/lp_star.py b/nnenum/nnenum/lp_star.py index 0a5dbb0..4ebf6c8 100644 --- a/nnenum/nnenum/lp_star.py +++ b/nnenum/nnenum/lp_star.py @@ -184,17 +184,46 @@ def update_input_box_bounds_old(self, cur_box, should_skip, count_lps=True): return rv + def check_input_box_bounds_slow(self): + ''' + run a sanity check that the input box bounds witnesses are correct + this uses LP and is slow, so it's meant to help with debugging + ''' + + dims = self.lpi.get_num_cols() + should_skip = np.zeros((dims, 2), dtype=bool) + correct_bounds_list = self.update_input_box_bounds_old(None, should_skip) + + cur_bounds = self.get_input_box_bounds() + + for d, min_val, max_val in correct_bounds_list: + + assert abs(min_val - cur_bounds[d][0]) < 1e-5 + assert abs(max_val - cur_bounds[d][1]) < 1e-5 + def get_input_box_bounds(self): 'gets the input box bounds from witnesses' - assert self.input_bounds_witnesses is not None - dims = self.lpi.get_num_cols() - rv = [] - for d in range(dims): - min_wit, max_wit = self.input_bounds_witnesses[d] - rv.append((min_wit[d], max_wit[d])) + if self.input_bounds_witnesses is not None: + dims = self.lpi.get_num_cols() + + assert len(self.input_bounds_witnesses) == dims, \ + f"dims:{dims}, num witneses: {len(self.input_bounds_witnesses)}" + + for d in range(dims): + min_wit, max_wit = self.input_bounds_witnesses[d] + rv.append((min_wit[d], max_wit[d])) + else: + Timers.tic('full input bounds') + should_skip = np.zeros((dims, 2), dtype=bool) + correct_bounds_list = self.update_input_box_bounds_old(None, should_skip) + + for _d, lb, ub in correct_bounds_list: + rv.append((lb, ub)) + + Timers.toc('full input bounds') return rv @@ -206,7 +235,7 @@ def update_input_box_bounds(self, hyperplane_vec_list, rhs_list, count_lps=True) ''' dims = self.lpi.get_num_cols() - should_skip = np.zeros((dims, 2), dtype=bool) + should_skip = np.ones((dims, 2), dtype=bool) # TODO: check if cur_box is the same as get_input_box_bounds cur_box = self.get_input_box_bounds() @@ -222,11 +251,11 @@ def update_input_box_bounds(self, hyperplane_vec_list, rhs_list, count_lps=True) min_wit, max_wit = self.input_bounds_witnesses[d] for hyperplane_vec, rhs in zip(hyperplane_vec_list, rhs_list): - if not should_skip[d, 0] and np.dot(hyperplane_vec, min_wit) <= rhs: - should_skip[d, 0] = True + if should_skip[d, 0] and np.dot(hyperplane_vec, min_wit) > rhs: + should_skip[d, 0] = False - if should_skip[d, 1] and np.dot(hyperplane_vec, max_wit) <= rhs: - should_skip[d, 1] = True + if should_skip[d, 1] and np.dot(hyperplane_vec, max_wit) > rhs: + should_skip[d, 1] = False if Settings.CONTRACT_LP_OPTIMIZED and cur_box is not None: rv = self.update_input_box_bounds_new(cur_box, should_skip, count_lps) diff --git a/nnenum/nnenum/overapprox.py b/nnenum/nnenum/overapprox.py index 5436bae..0f01630 100644 --- a/nnenum/nnenum/overapprox.py +++ b/nnenum/nnenum/overapprox.py @@ -277,11 +277,6 @@ def do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=None first_round = True sets = [] - if Settings.OVERAPPROX_CONTRACT_ZONO_LP: - #if len(ss.branch_tuples) % 10 == 0: - # print(f"contracting lp randomly in overapprox") - ss.prefilter.zono.contract_lp(ss.star) - for round_num, types in enumerate(overapprox_types): assert isinstance(types, list), f"types was not list: {types}" sets.clear() @@ -500,7 +495,7 @@ def check_spec(self, spec, check_cancel_func): # todo: evaluate whether this helps check_cancel_func() - self.violation_star = spec.get_violation_star(self.star) + self.violation_star = spec.get_violation_star(self.star, domain_contraction=False) return self.violation_star is None diff --git a/nnenum/nnenum/settings.py b/nnenum/nnenum/settings.py index 43905a6..c7b51b3 100644 --- a/nnenum/nnenum/settings.py +++ b/nnenum/nnenum/settings.py @@ -57,7 +57,7 @@ def reset(cls): cls.EAGER_BOUNDS = True cls.CONTRACT_ZONOTOPE = False # try domain contraction on zonotopes (more accurate prefilter, but slower) - cls.CONTRACT_ZONOTOPE_LP = False # contract zonotope using LPs (even more accurate prefilter, but even slower) + cls.CONTRACT_ZONOTOPE_LP = True # contract zonotope using LPs (even more accurate prefilter, but even slower) cls.CONTRACT_LP_OPTIMIZED = True # use optimized lp contraction cls.CONTRACT_LP_TRACK_WITNESSES = True # track box bounds witnesses to reduce LP solving @@ -69,7 +69,6 @@ def reset(cls): cls.OVERAPPROX_NEAR_ROOT_MAX_SPLITS = 2 cls.OVERAPPROX_TYPES_NEAR_ROOT = cls.OVERAPPROX_TYPES - cls.OVERAPPROX_CONTRACT_ZONO_LP = True # contract LP during overapproximation steps? cls.OVERAPPROX_GEN_LIMIT_MULTIPLIER = 1.5 # don't try approx star if multizono.gens > THIS * last_safe_gens cls.OVERAPPROX_MIN_GEN_LIMIT = 50 # minimum generators to use as cap cls.OVERAPPROX_LP_TIMEOUT = 1.0 # timeout for LP part of overapproximation, use np.inf for unbounded diff --git a/nnenum/nnenum/specification.py b/nnenum/nnenum/specification.py index fa24af1..af330aa 100644 --- a/nnenum/nnenum/specification.py +++ b/nnenum/nnenum/specification.py @@ -83,7 +83,7 @@ def zono_might_violate_spec(self, zono): return rv - def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): + def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False, domain_contraction=True): '''does this lp_star violate the spec? if so, return a new, non-empty star object with the violation region @@ -98,7 +98,7 @@ def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): # skip parts of the disjunctive spec that are already safe continue - res = spec.get_violation_star(lp_star, normalize=normalize) + res = spec.get_violation_star(lp_star, normalize=normalize, domain_contraction=domain_contraction) if res is not None: break @@ -197,7 +197,7 @@ def zono_might_violate_spec(self, zono): return might_violate - def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): + def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False, domain_contraction=True): '''does this lp_star violate the spec? if so, return a new, non-empty star object with the violation region @@ -222,9 +222,14 @@ def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): lpi = copy.lpi init_bias = np.dot(self.mat, copy.bias) + hs_list = [] + rhs_list = [] for i, row in enumerate(init_spec): - lpi.add_dense_row(row, self.rhs[i] - init_bias[i], normalize=normalize) + rhs = self.rhs[i] - init_bias[i] + hs_list.append(row) + rhs_list.append(rhs) + lpi.add_dense_row(row, rhs, normalize=normalize) winput = lpi.minimize(None, fail_on_unsat=False) @@ -238,14 +243,10 @@ def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False): #assert self.is_violation(woutput), f"witness output {woutput} was not a violation of {self}" # also comput input box bounds - Timers.tic('violation_input_box_bounds') - #for i, row in enumerate(init_spec): - # row - # rhs = self.rhs[i] - init_bias[i] - - # rv.input_box_bounds(HERE - - Timers.toc('violation_input_box_bounds') + if domain_contraction: + Timers.tic('violation_update_input_box_bounds') + rv.update_input_box_bounds(hs_list, rhs_list) + Timers.toc('violation_update_input_box_bounds') Timers.toc('get_violation_star') From 5e8f23838cc34804cf16047ffab436ed07e83b11 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 28 Dec 2020 15:14:02 -0500 Subject: [PATCH 09/55] renamed to src --- {nnenum => src}/nnenum/agen.py | 0 {nnenum => src}/nnenum/enumerate.py | 0 {nnenum => src}/nnenum/kamenev.py | 0 {nnenum => src}/nnenum/lp_star.py | 11 ++--------- {nnenum => src}/nnenum/lp_star_state.py | 0 {nnenum => src}/nnenum/lpinstance.py | 26 ++++++++++++++----------- {nnenum => src}/nnenum/lpplot.py | 0 {nnenum => src}/nnenum/lputil.py | 0 {nnenum => src}/nnenum/network.py | 0 {nnenum => src}/nnenum/onnx_network.py | 0 {nnenum => src}/nnenum/overapprox.py | 0 {nnenum => src}/nnenum/prefilter.py | 2 +- {nnenum => src}/nnenum/result.py | 0 {nnenum => src}/nnenum/settings.py | 0 {nnenum => src}/nnenum/specification.py | 0 {nnenum => src}/nnenum/timerutil.py | 0 {nnenum => src}/nnenum/util.py | 0 {nnenum => src}/nnenum/worker.py | 0 {nnenum => src}/nnenum/zonotope.py | 0 19 files changed, 18 insertions(+), 21 deletions(-) rename {nnenum => src}/nnenum/agen.py (100%) rename {nnenum => src}/nnenum/enumerate.py (100%) rename {nnenum => src}/nnenum/kamenev.py (100%) rename {nnenum => src}/nnenum/lp_star.py (98%) rename {nnenum => src}/nnenum/lp_star_state.py (100%) rename {nnenum => src}/nnenum/lpinstance.py (97%) rename {nnenum => src}/nnenum/lpplot.py (100%) rename {nnenum => src}/nnenum/lputil.py (100%) rename {nnenum => src}/nnenum/network.py (100%) rename {nnenum => src}/nnenum/onnx_network.py (100%) rename {nnenum => src}/nnenum/overapprox.py (100%) rename {nnenum => src}/nnenum/prefilter.py (99%) rename {nnenum => src}/nnenum/result.py (100%) rename {nnenum => src}/nnenum/settings.py (100%) rename {nnenum => src}/nnenum/specification.py (100%) rename {nnenum => src}/nnenum/timerutil.py (100%) rename {nnenum => src}/nnenum/util.py (100%) rename {nnenum => src}/nnenum/worker.py (100%) rename {nnenum => src}/nnenum/zonotope.py (100%) diff --git a/nnenum/nnenum/agen.py b/src/nnenum/agen.py similarity index 100% rename from nnenum/nnenum/agen.py rename to src/nnenum/agen.py diff --git a/nnenum/nnenum/enumerate.py b/src/nnenum/enumerate.py similarity index 100% rename from nnenum/nnenum/enumerate.py rename to src/nnenum/enumerate.py diff --git a/nnenum/nnenum/kamenev.py b/src/nnenum/kamenev.py similarity index 100% rename from nnenum/nnenum/kamenev.py rename to src/nnenum/kamenev.py diff --git a/nnenum/nnenum/lp_star.py b/src/nnenum/lp_star.py similarity index 98% rename from nnenum/nnenum/lp_star.py rename to src/nnenum/lp_star.py index 4ebf6c8..6df781a 100644 --- a/nnenum/nnenum/lp_star.py +++ b/src/nnenum/lp_star.py @@ -190,6 +190,8 @@ def check_input_box_bounds_slow(self): this uses LP and is slow, so it's meant to help with debugging ''' + print("Warning: check_input_box_bounds_slow called") + dims = self.lpi.get_num_cols() should_skip = np.zeros((dims, 2), dtype=bool) correct_bounds_list = self.update_input_box_bounds_old(None, should_skip) @@ -262,15 +264,6 @@ def update_input_box_bounds(self, hyperplane_vec_list, rhs_list, count_lps=True) else: rv = self.update_input_box_bounds_old(cur_box, should_skip, count_lps) - #print("debug check") - #should_skip = np.zeros((dims, 2), dtype=bool) - #rv2 = self.update_input_box_bounds_old(cur_box, should_skip, count_lps) - #if len(rv) != len(rv2): - - # print(f"hyperplane_vec <= rhs was {hyperplane_vec} <= {rhs}") - # print(f"box was {cur_box}\nrv was {rv}\nrv2 was {rv2}") - # assert False - return rv def update_input_box_bounds_new(self, cur_box, should_skip, count_lps=True): diff --git a/nnenum/nnenum/lp_star_state.py b/src/nnenum/lp_star_state.py similarity index 100% rename from nnenum/nnenum/lp_star_state.py rename to src/nnenum/lp_star_state.py diff --git a/nnenum/nnenum/lpinstance.py b/src/nnenum/lpinstance.py similarity index 97% rename from nnenum/nnenum/lpinstance.py rename to src/nnenum/lpinstance.py index 5e52c6d..0c58c44 100644 --- a/nnenum/nnenum/lpinstance.py +++ b/src/nnenum/lpinstance.py @@ -120,7 +120,7 @@ def serialize(self): rhs.append(glpk.glp_get_row_ub(self.lp, row + 1)) - col_bounds = self.get_col_bounds() + col_bounds = self._get_col_bounds() # remember to free lp object before overwriting with tuple glpk.glp_delete_prob(self.lp) @@ -128,18 +128,22 @@ def serialize(self): Timers.toc('serialize') - def set_col_bounds(self, col, lb, ub): - 'set double-bounded column bounds' + # removed this, as get_col_bounds shouldn't be used externally + #def set_col_bounds(self, col, lb, ub): + # 'set double-bounded column bounds' - col_type = glpk.glp_get_col_type(self.lp, col + 1) + # col_type = glpk.glp_get_col_type(self.lp, col + 1) - if col_type != glpk.GLP_DB: - print(f"Warning: Contract col {col} to {lb, ub} skipped (col type is not GLP_DB):\n{self}") - else: - glpk.glp_set_col_bnds(self.lp, col + 1, glpk.GLP_DB, lb, ub) # double-bounded variable + # if col_type != glpk.GLP_DB: + # print(f"Warning: Contract col {col} to {lb, ub} skipped (col type is not GLP_DB):\n{self}") + # else: + # glpk.glp_set_col_bnds(self.lp, col + 1, glpk.GLP_DB, lb, ub) # double-bounded variable + + def _get_col_bounds(self): + '''get column bounds - def get_col_bounds(self): - 'get column bounds' + for external use use star's get_input_bounds which may be tighter + ''' lp_cols = self.get_num_cols() @@ -160,7 +164,7 @@ def get_col_bounds(self): elif col_type == glpk.GLP_FX: lb = ub = glpk.glp_get_col_lb(self.lp, col + 1) else: - assert col_type == glpk.GLP_FR, "unsupported col type in get_col_bounds()" + assert col_type == glpk.GLP_FR, "unsupported col type in _get_col_bounds()" col_bounds.append((lb, ub)) diff --git a/nnenum/nnenum/lpplot.py b/src/nnenum/lpplot.py similarity index 100% rename from nnenum/nnenum/lpplot.py rename to src/nnenum/lpplot.py diff --git a/nnenum/nnenum/lputil.py b/src/nnenum/lputil.py similarity index 100% rename from nnenum/nnenum/lputil.py rename to src/nnenum/lputil.py diff --git a/nnenum/nnenum/network.py b/src/nnenum/network.py similarity index 100% rename from nnenum/nnenum/network.py rename to src/nnenum/network.py diff --git a/nnenum/nnenum/onnx_network.py b/src/nnenum/onnx_network.py similarity index 100% rename from nnenum/nnenum/onnx_network.py rename to src/nnenum/onnx_network.py diff --git a/nnenum/nnenum/overapprox.py b/src/nnenum/overapprox.py similarity index 100% rename from nnenum/nnenum/overapprox.py rename to src/nnenum/overapprox.py diff --git a/nnenum/nnenum/prefilter.py b/src/nnenum/prefilter.py similarity index 99% rename from nnenum/nnenum/prefilter.py rename to src/nnenum/prefilter.py index 3429002..dd15fee 100644 --- a/nnenum/nnenum/prefilter.py +++ b/src/nnenum/prefilter.py @@ -176,7 +176,7 @@ def init_from_star(self, star): self.simulation = star.minimize_vec(None, return_io=True) - box_bounds = star.lpi.get_col_bounds() + box_bounds = star.get_input_box_bounds() self.zono = Zonotope(star.bias, star.a_mat, box_bounds) diff --git a/nnenum/nnenum/result.py b/src/nnenum/result.py similarity index 100% rename from nnenum/nnenum/result.py rename to src/nnenum/result.py diff --git a/nnenum/nnenum/settings.py b/src/nnenum/settings.py similarity index 100% rename from nnenum/nnenum/settings.py rename to src/nnenum/settings.py diff --git a/nnenum/nnenum/specification.py b/src/nnenum/specification.py similarity index 100% rename from nnenum/nnenum/specification.py rename to src/nnenum/specification.py diff --git a/nnenum/nnenum/timerutil.py b/src/nnenum/timerutil.py similarity index 100% rename from nnenum/nnenum/timerutil.py rename to src/nnenum/timerutil.py diff --git a/nnenum/nnenum/util.py b/src/nnenum/util.py similarity index 100% rename from nnenum/nnenum/util.py rename to src/nnenum/util.py diff --git a/nnenum/nnenum/worker.py b/src/nnenum/worker.py similarity index 100% rename from nnenum/nnenum/worker.py rename to src/nnenum/worker.py diff --git a/nnenum/nnenum/zonotope.py b/src/nnenum/zonotope.py similarity index 100% rename from nnenum/nnenum/zonotope.py rename to src/nnenum/zonotope.py From 06fdebea2c062145e98732ccb7690e541ae1acb3 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 31 Dec 2020 16:13:02 -0500 Subject: [PATCH 10/55] fixed conrete counterexample input shape when pre-overapprox sim is unsafe --- src/nnenum/enumerate.py | 14 +++++++++----- src/nnenum/lp_star.py | 2 ++ src/nnenum/lpinstance.py | 2 +- src/nnenum/overapprox.py | 4 +++- src/nnenum/worker.py | 5 ++--- 5 files changed, 17 insertions(+), 10 deletions(-) diff --git a/src/nnenum/enumerate.py b/src/nnenum/enumerate.py index e37798f..0dedc00 100644 --- a/src/nnenum/enumerate.py +++ b/src/nnenum/enumerate.py @@ -44,16 +44,15 @@ def make_init_ss(init, network, spec, start_time): ss = LpStarState(init_box, spec=spec) elif isinstance(init, LpStar): - assert isinstance(init, LpStar), 'init must be box or star' - - assert len(init.bias) == network_inputs - ss = LpStarState(spec=spec) ss.from_init_star(init) else: - assert isinstance(init, LpStarState) + assert isinstance(init, LpStarState), f"unsupported init type: {type(init)}" ss = init + assert len(ss.star.init_bias) == network_inputs, f"init_bias len: {len(ss.star.init_bias)}" + \ + f", network inputs: {network_inputs}" + ss.should_try_overapprox = False # propagate the initial star up to the first split @@ -208,6 +207,7 @@ def enumerate_network(init, network, spec=None): Timers.toc('run workers') + rv = shared.result rv.total_secs = time.perf_counter() - start process_result(shared) @@ -299,6 +299,10 @@ def process_result(shared): if enum_ended_early and shared.result.polys: print(f"Warning: result polygons / stars is incomplete, since the enumeration ended early") + # if unsafe, convert concrete inputs / outputs to regular lists + shared.result.cinput = list(shared.result.cinput) + shared.result.coutput = list(shared.result.coutput) + # deserialize stars if saved if shared.result.stars: shared.result.stars = list(shared.result.stars) # convert to normal list diff --git a/src/nnenum/lp_star.py b/src/nnenum/lp_star.py index 6df781a..5a47616 100644 --- a/src/nnenum/lp_star.py +++ b/src/nnenum/lp_star.py @@ -117,6 +117,8 @@ def copy(self): def to_full_input(self, compressed_input): 'convert possibly compressed input to full input' + #print(f".to_full_input, init_bm = {self.init_bm}\ninit_bias = {self.init_bias}") + if self.init_bm is None: rv = compressed_input.copy() else: diff --git a/src/nnenum/lpinstance.py b/src/nnenum/lpinstance.py index 0c58c44..6c781d2 100644 --- a/src/nnenum/lpinstance.py +++ b/src/nnenum/lpinstance.py @@ -599,7 +599,7 @@ def is_feasible(self): return self.minimize(None, fail_on_unsat=False) is not None - def contains_point(self, pt): + def contains_point(self, pt, tol=1e-9): '''does this lpi contain the point? this is slow, will pull the constraints and check them ''' diff --git a/src/nnenum/overapprox.py b/src/nnenum/overapprox.py index 0f01630..4ca7779 100644 --- a/src/nnenum/overapprox.py +++ b/src/nnenum/overapprox.py @@ -41,7 +41,7 @@ def check_cancel_func(): print(f"Doing quick overapprox with {len(overapprox_types)} rounds...") rr = do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=check_cancel_func, - overapprox_types=overapprox_types) + overapprox_types=overapprox_types) rv = rr.is_safe, rr.concrete_io_tuple except OverapproxCanceledException as e: @@ -221,6 +221,7 @@ def test_abstract_violation(dims, vstars, vindices, network, spec): assert cur_spec.is_violation(coutput, tol_rhs=1e-4) trimmed_input = cinput[:dims] + full_input = vstar.to_full_input(trimmed_input) exec_output = network.execute(full_input) flat_output = np.ravel(exec_output) @@ -361,6 +362,7 @@ def run_overapprox_round(network, ss_init, sets, prerelu_sims, check_cancel_func layer_bounds = ss_init.prefilter.output_bounds.layer_bounds #print(f". layer bounds {layer_num}:\n{layer_bounds}") + print(f".overapprox, star set input bounds: {ss_init.star.get_input_box_bounds()}") # run first layer with existing bounds for s in sets: diff --git a/src/nnenum/worker.py b/src/nnenum/worker.py index 2a096b2..c5fc37d 100644 --- a/src/nnenum/worker.py +++ b/src/nnenum/worker.py @@ -239,17 +239,16 @@ def check_cancel_func(): if spec.is_violation(sim_out): sim_in_flat = ss.prefilter.simulation[0] sim_in = ss.star.to_full_input(sim_in_flat) - sim_in = sim_in.astype(ss.star.a_mat.dtype) # run through complete network in to out before counting it sim_out = network.execute(sim_in) sim_out = nn_flatten(sim_out) if spec.is_violation(sim_out): - concrete_io_tuple = [sim_in_flat, sim_out] + concrete_io_tuple = [sim_in, sim_out] if Settings.PRINT_OUTPUT: - print("\nOverapproximation found was a confirmed counterexample.") + print("\nPre-overapproximation simulation found a confirmed counterexample.") print(f"\nUnsafe Base Branch: {self.priv.ss.branch_str()} (Mode: {Settings.BRANCH_MODE})") self.found_unsafe(concrete_io_tuple) From 16ed7b04f8ab016c045cf1dbaca1d6109587096f Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sat, 2 Jan 2021 16:25:29 -0500 Subject: [PATCH 11/55] removed debug printing --- src/nnenum/lp_star.py | 8 ++++++++ src/nnenum/lpinstance.py | 2 +- src/nnenum/overapprox.py | 2 +- 3 files changed, 10 insertions(+), 2 deletions(-) diff --git a/src/nnenum/lp_star.py b/src/nnenum/lp_star.py index 5a47616..2053f73 100644 --- a/src/nnenum/lp_star.py +++ b/src/nnenum/lp_star.py @@ -218,6 +218,14 @@ def get_input_box_bounds(self): for d in range(dims): min_wit, max_wit = self.input_bounds_witnesses[d] + + if min_wit[d] > max_wit[d]: + # can happen due to numerical error + assert min_wit[d] - 1e-5 < max_wit[d] + + mid = (min_wit[d] + max_wit[d]) / 2 + min_wit[d] = max_wit[d] = mid + rv.append((min_wit[d], max_wit[d])) else: Timers.tic('full input bounds') diff --git a/src/nnenum/lpinstance.py b/src/nnenum/lpinstance.py index 6c781d2..ed18ff5 100644 --- a/src/nnenum/lpinstance.py +++ b/src/nnenum/lpinstance.py @@ -452,7 +452,7 @@ def add_double_bounded_cols(self, names, lb, ub): lb = float(lb) ub = float(ub) - assert lb <= ub + assert lb <= ub, f"lb ({lb}) <= ub ({ub}). dif: {ub - lb}" assert isinstance(names, list) num_vars = len(names) diff --git a/src/nnenum/overapprox.py b/src/nnenum/overapprox.py index 4ca7779..0c7e668 100644 --- a/src/nnenum/overapprox.py +++ b/src/nnenum/overapprox.py @@ -362,7 +362,7 @@ def run_overapprox_round(network, ss_init, sets, prerelu_sims, check_cancel_func layer_bounds = ss_init.prefilter.output_bounds.layer_bounds #print(f". layer bounds {layer_num}:\n{layer_bounds}") - print(f".overapprox, star set input bounds: {ss_init.star.get_input_box_bounds()}") + #print(f".overapprox, star set input bounds: {ss_init.star.get_input_box_bounds()}") # run first layer with existing bounds for s in sets: From b3899d69aba39a5b911335d1f0f1e62d0e76e1fb Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 24 Jan 2021 15:58:51 -0500 Subject: [PATCH 12/55] default normalize and fixed bounds check order in lp_star --- src/nnenum/lp_star.py | 9 ++++----- src/nnenum/lpinstance.py | 17 +++++++++++++---- src/nnenum/specification.py | 4 ++-- 3 files changed, 19 insertions(+), 11 deletions(-) diff --git a/src/nnenum/lp_star.py b/src/nnenum/lp_star.py index 2053f73..3dd886d 100644 --- a/src/nnenum/lp_star.py +++ b/src/nnenum/lp_star.py @@ -194,16 +194,15 @@ def check_input_box_bounds_slow(self): print("Warning: check_input_box_bounds_slow called") + cur_bounds = self.get_input_box_bounds() + dims = self.lpi.get_num_cols() should_skip = np.zeros((dims, 2), dtype=bool) correct_bounds_list = self.update_input_box_bounds_old(None, should_skip) - cur_bounds = self.get_input_box_bounds() - for d, min_val, max_val in correct_bounds_list: - - assert abs(min_val - cur_bounds[d][0]) < 1e-5 - assert abs(max_val - cur_bounds[d][1]) < 1e-5 + assert abs(min_val - cur_bounds[d][0]) < 1e-5, f"dim {d} min was {cur_bounds[d][0]}, should be {min_val}" + assert abs(max_val - cur_bounds[d][1]) < 1e-5, f"dim {d} max was {cur_bounds[d][1]}, should be {max_val}" def get_input_box_bounds(self): 'gets the input box bounds from witnesses' diff --git a/src/nnenum/lpinstance.py b/src/nnenum/lpinstance.py index ed18ff5..89613df 100644 --- a/src/nnenum/lpinstance.py +++ b/src/nnenum/lpinstance.py @@ -450,6 +450,8 @@ def add_cols(self, names): def add_double_bounded_cols(self, names, lb, ub): 'add a certain number of columns to the LP with the given lower and upper bound' + assert lb != -np.inf + lb = float(lb) ub = float(ub) assert lb <= ub, f"lb ({lb}) <= ub ({ub}). dif: {ub - lb}" @@ -466,6 +468,8 @@ def add_double_bounded_cols(self, names, lb, ub): for i in range(num_vars): if lb == ub: glpk.glp_set_col_bnds(self.lp, num_cols + i + 1, glpk.GLP_FX, lb, ub) # fixed variable + elif ub == np.inf: + glpk.glp_set_col_bnds(self.lp, num_cols + i + 1, glpk.GLP_LO, lb, ub) # lower-bounded variable else: assert lb < ub glpk.glp_set_col_bnds(self.lp, num_cols + i + 1, glpk.GLP_DB, lb, ub) # double-bounded variable @@ -510,6 +514,9 @@ def set_constraints_csr(self, data, glpk_indices, indptr, shape): assert shape[0] <= self.get_num_rows() assert shape[1] <= self.get_num_cols() + if glpk_indices: + assert isinstance(glpk_indices[0], int), f"indices type was not int: {type(glpk_indices[0])}" + # actually set the constraints row by row assert isinstance(data, list), "data was not a list" @@ -517,9 +524,8 @@ def set_constraints_csr(self, data, glpk_indices, indptr, shape): # we must copy the indices since glpk is offset by 1 :( count = int(indptr[row + 1] - indptr[row]) - #indices_list = glpk_indices[indptr[row]:indptr[row+1]] - #indices_vec = SwigArray.as_int_array(indices_list) - indices_vec = SwigArray.as_int_array(glpk_indices[indptr[row]:indptr[row+1]], count) + indices_list = glpk_indices[indptr[row]:indptr[row+1]] + indices_vec = SwigArray.as_int_array(indices_list, count) #data_row_list = [float(d) for d in data[indptr[row]:indptr[row+1]]] #data_vec = SwigArray.as_double_array(data_row_list) @@ -871,7 +877,9 @@ def get_int_array(cls, size): cls.int_array_size = 2**math.ceil(math.log(size, 2)) # allocate in multiples of two cls.int_array = glpk.intArray(cls.int_array_size) - #print(f"allocated int array of size {cls.int_array_size} (requested {size})") + #print(f".allocated int array of size {cls.int_array_size} (requested {size})") + + #print(f".returning {cls.int_array} of size {cls.int_array_size} (requested {size})") return cls.int_array @@ -895,6 +903,7 @@ def as_int_array(cls, list_data, size): arr = cls.get_int_array(size + 1) for i, val in enumerate(list_data): + #print(f"setting {i+1} <- val: {val} ({type(val)}") arr[i+1] = val return arr diff --git a/src/nnenum/specification.py b/src/nnenum/specification.py index af330aa..5d8bdb0 100644 --- a/src/nnenum/specification.py +++ b/src/nnenum/specification.py @@ -83,7 +83,7 @@ def zono_might_violate_spec(self, zono): return rv - def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False, domain_contraction=True): + def get_violation_star(self, lp_star, safe_spec_list=None, normalize=True, domain_contraction=True): '''does this lp_star violate the spec? if so, return a new, non-empty star object with the violation region @@ -197,7 +197,7 @@ def zono_might_violate_spec(self, zono): return might_violate - def get_violation_star(self, lp_star, safe_spec_list=None, normalize=False, domain_contraction=True): + def get_violation_star(self, lp_star, safe_spec_list=None, normalize=True, domain_contraction=True): '''does this lp_star violate the spec? if so, return a new, non-empty star object with the violation region From 81178bc14916a026b7225975b449fbdcadf0fa91 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sat, 13 Feb 2021 13:33:42 -0500 Subject: [PATCH 13/55] removed extra printing --- src/nnenum/overapprox.py | 2 +- src/nnenum/worker.py | 3 +-- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/src/nnenum/overapprox.py b/src/nnenum/overapprox.py index 0c7e668..d4d9e64 100644 --- a/src/nnenum/overapprox.py +++ b/src/nnenum/overapprox.py @@ -216,7 +216,7 @@ def test_abstract_violation(dims, vstars, vindices, network, spec): rows.append(sum_row) for row in rows: - # this one is alsmost free since objective direction is None + # this one is almost free since objective direction is None cinput, coutput = vstar.minimize_vec(None, return_io=True) assert cur_spec.is_violation(coutput, tol_rhs=1e-4) diff --git a/src/nnenum/worker.py b/src/nnenum/worker.py index c5fc37d..6a37932 100644 --- a/src/nnenum/worker.py +++ b/src/nnenum/worker.py @@ -16,7 +16,6 @@ from nnenum.settings import Settings from nnenum.util import Freezable, to_time_str from nnenum.network import nn_unflatten, nn_flatten -from nnenum.specification import DisjunctiveSpec from nnenum.prefilter import LpCanceledException from nnenum.agen import AgenState @@ -734,7 +733,7 @@ def find_concrete_io(self, star, branch_tuples): if branch_list_in_branch_tuples(exec_branch_list, branch_tuples): rv = full_cinput_flat, exec_output else: - print(". weakly-tested code: couldn't confirm countereample... tightening constraints") + #print(". weakly-tested code: couldn't confirm countereample... tightening constraints") # try to make each of the constraints a little tighter star_copy = star.copy() From 138d1e48503be17bba6244472279f0e316ef3f3c Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 31 May 2021 12:30:56 -0400 Subject: [PATCH 14/55] added underflow settings and fixed unsat counterexample --- src/nnenum/enumerate.py | 2 +- src/nnenum/lp_star.py | 36 ++++++++++++++++++++---------------- src/nnenum/settings.py | 2 ++ src/nnenum/worker.py | 3 +-- 4 files changed, 24 insertions(+), 19 deletions(-) diff --git a/src/nnenum/enumerate.py b/src/nnenum/enumerate.py index 0dedc00..dc81e90 100644 --- a/src/nnenum/enumerate.py +++ b/src/nnenum/enumerate.py @@ -504,7 +504,7 @@ def __init__(self, worker_index): def worker_func(worker_index, shared): 'worker function during verification' - np.seterr(all='raise') # raise exceptions on floating-point errors instead of printing warnings + np.seterr(all='raise', under=Settings.UNDERFLOW_BEHAVIOR) # raise exceptions on floating-point errors if shared.multithreaded: reinit_onnx_sessions(shared.network) diff --git a/src/nnenum/lp_star.py b/src/nnenum/lp_star.py index 3dd886d..7fe64b6 100644 --- a/src/nnenum/lp_star.py +++ b/src/nnenum/lp_star.py @@ -464,7 +464,7 @@ def construct_last_io(self): return [i, o] - def minimize_vec(self, vec, return_io=False): + def minimize_vec(self, vec, return_io=False, fail_on_unsat=True): '''optimize over this set vec is the vector of outputs we're optimizing over, None means use zero vector @@ -502,25 +502,29 @@ def minimize_vec(self, vec, return_io=False): #Timers.toc('setup') #Timers.tic('lpi.minimize') - lp_result = self.lpi.minimize(lp_vec) - if lp_result.dtype != dtype: - lp_result = lp_result.astype(dtype) - - self.last_lp_result = lp_result - - self.num_lps += 1 - #Timers.toc('lpi.minimize') - assert len(lp_result) == num_init_vars + lp_result = self.lpi.minimize(lp_vec, fail_on_unsat=fail_on_unsat) + + if lp_result is None: + rv = None + else: + if lp_result.dtype != dtype: + lp_result = lp_result.astype(dtype) + + self.last_lp_result = lp_result + + self.num_lps += 1 + #Timers.toc('lpi.minimize') + assert len(lp_result) == num_init_vars - #print("--------") - #print(f"lp_result: {lp_result}") + #print("--------") + #print(f"lp_result: {lp_result}") - #Timers.tic('a_mat mult') - rv = np.dot(self.a_mat, lp_result) + self.bias - #Timers.toc('a_mat mult') + #Timers.tic('a_mat mult') + rv = np.dot(self.a_mat, lp_result) + self.bias + #Timers.toc('a_mat mult') # return input as well - if return_io: + if rv is not None and return_io: rv = [lp_result, rv] Timers.toc('star.minimize_vec') diff --git a/src/nnenum/settings.py b/src/nnenum/settings.py index c7b51b3..306056d 100644 --- a/src/nnenum/settings.py +++ b/src/nnenum/settings.py @@ -103,6 +103,8 @@ def reset(cls): cls.GLPK_RESET_BEFORE_MINIMIZE = False # reset the lp basis before minimize cls.SKIP_COMPRESSED_CHECK = False # sanity check for compressed inputs when COMPRESS_INIT_BOX is False + #### + cls.UNDERFLOW_BEHAVIOR = 'raise' # np.seterr behavior for floating-point underflow #### cls.NUM_LP_PROCESSES = 1 # if > 1, then force multiprocessing during lp step diff --git a/src/nnenum/worker.py b/src/nnenum/worker.py index 6a37932..867c210 100644 --- a/src/nnenum/worker.py +++ b/src/nnenum/worker.py @@ -751,9 +751,8 @@ def find_concrete_io(self, star, branch_tuples): rhs[i] = val - tighten_factor star_copy.lpi.set_rhs(rhs) - - res = star_copy.minimize_vec(None, return_io=True) + res = star_copy.minimize_vec(None, return_io=True, fail_on_unsat=False) if res is None: # infeasible From 4018cc026274e4ee580fc215b342ad39fb42c0f4 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 31 May 2021 15:53:17 -0400 Subject: [PATCH 15/55] updated normalization logic --- src/nnenum/lpinstance.py | 10 +++++----- src/nnenum/settings.py | 1 + 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/src/nnenum/lpinstance.py b/src/nnenum/lpinstance.py index 89613df..432e9a8 100644 --- a/src/nnenum/lpinstance.py +++ b/src/nnenum/lpinstance.py @@ -485,12 +485,12 @@ def add_dense_row(self, vec, rhs, normalize=True): assert len(vec.shape) == 1 or vec.shape[0] == 1 assert len(vec) == self.get_num_cols(), f"vec had {len(vec)} values, but lpi has {self.get_num_cols()} cols" - if normalize: + if normalize and not Settings.SKIP_CONSTRAINT_NORMALIZATION: norm = np.linalg.norm(vec) - assert norm > 0 - - vec = vec / norm - rhs = rhs / norm + + if norm > 1e-9: + vec = vec / norm + rhs = rhs / norm rows_before = self.get_num_rows() diff --git a/src/nnenum/settings.py b/src/nnenum/settings.py index 306056d..9c05a8d 100644 --- a/src/nnenum/settings.py +++ b/src/nnenum/settings.py @@ -105,6 +105,7 @@ def reset(cls): cls.SKIP_COMPRESSED_CHECK = False # sanity check for compressed inputs when COMPRESS_INIT_BOX is False #### cls.UNDERFLOW_BEHAVIOR = 'raise' # np.seterr behavior for floating-point underflow + cls.SKIP_CONSTRAINT_NORMALIZATION = False # disable constraint normalization in LP (may reduce stability) #### cls.NUM_LP_PROCESSES = 1 # if > 1, then force multiprocessing during lp step From 8e161d0edf9b2be1782602edff9b5807235bec3a Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 14:54:19 -0400 Subject: [PATCH 16/55] working on adding vnnlib support --- .gitignore | 2 + .travis.yml | 19 ++ Dockerfile | 7 +- README.md | 32 +- examples/acasxu/README.md | 2 +- examples/acasxu/acasxu_all.py | 73 ++--- examples/acasxu/acasxu_single.py | 265 ---------------- .../data/ACASXU_run2a_1_1_batch_2000.mat | Bin 108240 -> 0 bytes examples/acasxu/data/prop_1.vnnlib | 36 +++ examples/acasxu/data/prop_10.vnnlib | 41 +++ examples/acasxu/data/prop_2.vnnlib | 39 +++ examples/acasxu/data/prop_3.vnnlib | 39 +++ examples/acasxu/data/prop_4.vnnlib | 39 +++ examples/acasxu/data/prop_5.vnnlib | 41 +++ examples/acasxu/data/prop_6.vnnlib | 39 +++ examples/acasxu/data/prop_7.vnnlib | 39 +++ examples/acasxu/data/prop_8.vnnlib | 40 +++ examples/acasxu/data/prop_9.vnnlib | 41 +++ src/nnenum/nnenum.py | 130 ++++++++ src/nnenum/vnnlib.py | 290 ++++++++++++++++++ 20 files changed, 898 insertions(+), 316 deletions(-) create mode 100644 .travis.yml delete mode 100644 examples/acasxu/acasxu_single.py delete mode 100644 examples/acasxu/data/ACASXU_run2a_1_1_batch_2000.mat create mode 100644 examples/acasxu/data/prop_1.vnnlib create mode 100644 examples/acasxu/data/prop_10.vnnlib create mode 100644 examples/acasxu/data/prop_2.vnnlib create mode 100644 examples/acasxu/data/prop_3.vnnlib create mode 100644 examples/acasxu/data/prop_4.vnnlib create mode 100644 examples/acasxu/data/prop_5.vnnlib create mode 100644 examples/acasxu/data/prop_6.vnnlib create mode 100644 examples/acasxu/data/prop_7.vnnlib create mode 100644 examples/acasxu/data/prop_8.vnnlib create mode 100644 examples/acasxu/data/prop_9.vnnlib create mode 100644 src/nnenum/nnenum.py create mode 100644 src/nnenum/vnnlib.py diff --git a/.gitignore b/.gitignore index 3682077..fbe45dd 100644 --- a/.gitignore +++ b/.gitignore @@ -13,3 +13,5 @@ __pycache__ *branch_str.txt *.mypy_cache .coverage +examples/acasxu/out.txt +examples/acasxu/results/* diff --git a/.travis.yml b/.travis.yml new file mode 100644 index 0000000..9e2b4c4 --- /dev/null +++ b/.travis.yml @@ -0,0 +1,19 @@ + +# configuration file for continuous integration testing using travis-ci.org + +dist: xenial + +language: python + +dist: + - trusty + +services: + - docker + +script: +# build Docker container +- docker build -t nnenum . + +# run tests +- docker run nnenum diff --git a/Dockerfile b/Dockerfile index 8d27e99..17dfe1a 100644 --- a/Dockerfile +++ b/Dockerfile @@ -6,7 +6,7 @@ # To get a shell after building the image: # docker run -ir nnenum_image bash -FROM tensorflow/tensorflow:2.2.0 +FROM python:3.6 COPY ./requirements.txt /work/requirements.txt @@ -22,4 +22,7 @@ ENV OPENBLAS_NUM_THREADS=1 ENV OMP_NUM_THREADS=1 # copy remaining files to docker -COPY . /work \ No newline at end of file +COPY . /work + +# cmd, run one of each benchmark +CMD cd /work && ./run_tests.sh diff --git a/README.md b/README.md index 142c2de..533f1be 100644 --- a/README.md +++ b/README.md @@ -4,14 +4,38 @@ The tool is written by Stanley Bak ([homepage](http://stanleybak.com), [twitter](https://twitter.com/StanleyBak)). ### Getting Started -The `Dockerfile` shows how to install all the dependencies (mostly python packages) and set up the environment. Although the tool loads neural networks directly from ONNX files, the properties and initial sets and verification settings must be defined in python scripts. +The `Dockerfile` shows how to install all the dependencies (mostly python packages) and set up the environment. The tool loads neural networks directly from ONNX files and properties from vnnlib files. +For example, try running: -The best way to get started is to look at some of the examples. For example, in the `examples/acasxu` directory you can try to verify property 9 of network 3-3 of the [well-studied ACAS Xu neural network verification benchmarks](https://arxiv.org/abs/1702.01135) by running the command: +'python3 -m nnenum.nnenum examples/acasxu/data/ACASXU_run2a_3_3_batch_2000.onnx examples/acasxu/data/prop_9.vnnlib' -```python3 acasxu_single.py 3 3 9``` ### VNN 2020 Neural Network Verification Competition (VNN-COMP) Version -The nnenum tool performed well in VNN-COMP 2020, being the only tool to verify all the ACAS-Xu benchmarks (each in under 10 seconds), as well as one of the best on the MNIST and CIFAR-10 benchmarks. The version used for the competition as well as model files and scripts to run the compeition benchmarks are in the `vnn2020` branch. +The nnenum tool performed well in VNN-COMP 2020, being the only tool to verify all the ACAS-Xu benchmarks (each in under 10 seconds). The version used for the competition as well as model files and scripts to run the compeition benchmarks are in the `vnn2020` branch. ### CAV 2020 Paper Version The CAV 2020 paper ["Improved Geometric Path Enumeration for Verifying ReLU Neural Networks"](http://stanleybak.com/papers/bak2020cav.pdf) by S. Bak, H.D Tran, K. Hobbs and T. T. Johnson corresponds to optimizations integrated into the exact analysis mode of nnenum, which also benefits overapproximative analysis. The paper version and repeatability evaluation package instructions are available [here](http://stanleybak.com/papers/bak2020cav_repeatability.zip). + +### Citing ### +The following citations can be used for nnenum: + +``` +@inproceedings{bak2021nfm, + title={nnenum: Verification of ReLU Neural Networks with Optimized Abstraction Refinement}, + author={Bak, Stanley}, + booktitle={NASA Formal Methods Symposium}, + pages={19--36}, + year={2021}, + organization={Springer} +} +``` + +``` +@inproceedings{bak2020cav, + title={Improved Geometric Path Enumeration for Verifying ReLU Neural Networks}, + author={Bak, Stanley and Tran, Hoang-Dung and Hobbs, Kerianne and Johnson, Taylor T.}, + booktitle={Proceedings of the 32nd International Conference on Computer Aided Verification}, + year={2020}, + organization={Springer} +} +``` diff --git a/examples/acasxu/README.md b/examples/acasxu/README.md index bb082c1..54542e1 100644 --- a/examples/acasxu/README.md +++ b/examples/acasxu/README.md @@ -1,5 +1,5 @@ These are the well-studied ACAXU benchmarks from "Reluplex: An efficient SMT solver for verifying deep neural networks" by Katz, Guy, et al., CAV 2017. -To run a specific bencmark, such as network 3-3 with property 9, execute 'python3 acasxu_single.py 3 3 9' +To run a specific bencmark, such as network 3-3 with property 9, execute 'python3 -m nnenum.nnenum data/ACASXU_run2a_3_3_batch_2000.onnx data/prop_9.vnnlib' To run all the benchmarks, run acasxu_all.py (results summary file is placed in results folder). diff --git a/examples/acasxu/acasxu_all.py b/examples/acasxu/acasxu_all.py index 008e715..4294695 100644 --- a/examples/acasxu/acasxu_all.py +++ b/examples/acasxu/acasxu_all.py @@ -4,32 +4,25 @@ Stanley Bak, 2020 ''' -import os import sys import time from pathlib import Path +import subprocess from termcolor import cprint -from nnenum.settings import Settings -from acasxu_single import verify_acasxu - def main(): 'main entry point' start = time.time() - Settings.TIMING_STATS = False - Settings.PARALLEL_ROOT_LP = False - Settings.SPLIT_IF_IDLE = False - Settings.PRINT_OVERAPPROX_OUTPUT = False - full_filename = 'results/full_acasxu.dat' hard_filename = 'results/hard_acasxu.dat' + timeout = 600.0 if len(sys.argv) > 1: - Settings.TIMEOUT = 60 * float(sys.argv[1]) - print(f"Running measurements with timeout = {Settings.TIMEOUT} secs") + timeout = 60.0 * float(sys.argv[1]) + print(f"Running measurements with timeout = {timeout} secs") instances = [] @@ -69,39 +62,7 @@ def main(): cprint(f"\nRunning net {a_prev}-{tau} with spec {spec}", "grey", "on_green") - if spec == "7": - # ego / 10 processes is beter for deep counterexamples in prop 7 - Settings.BRANCH_MODE = Settings.BRANCH_EGO - Settings.NUM_PROCESSES = 10 - - # property 7 is nondeterministic due to work sharing among processes... use median of 10 runs - pretimeout = Settings.TIMEOUT - Settings.TIMEOUT = min(5, pretimeout) # smaller timeout to make it go faster - runs = 10 - print(f"\nTrying median of {runs} quick runs") - results = [] - - for i in range(runs): - print(f"\nTrial {i+1}/{runs}:") - res_str, secs = verify_acasxu(net_pair, spec) - results.append((secs, res_str)) - - results.sort() - print(f"results: {results}") - secs, res_str = results[runs // 2] # median - - print(f"Median: {secs}, {res_str}") - - Settings.TIMEOUT = pretimeout - - if res_str == "timeout": - # median was timeout; run full - res_str, secs = verify_acasxu(net_pair, spec) - else: - Settings.BRANCH_MODE = Settings.BRANCH_OVERAPPROX - Settings.NUM_PROCESSES = len(os.sched_getaffinity(0)) - - res_str, secs = verify_acasxu(net_pair, spec) + res_str, secs = verify_acasxu(net_pair, spec, timeout) s = f"{a_prev}_{tau}\t{spec}\t{res_str}\t{secs}" f.write(s + "\n") @@ -116,5 +77,29 @@ def main(): print(f"Completed all measurements in {round(mins, 2)} minutes") +def verify_acasxu(net_pair, spec, timeout): + 'returns res_str, secs' + + prev, tau = net_pair + + onnx_path = f'./data/ACASXU_run2a_{prev}_{tau}_batch_2000.onnx' + spec_path = f'./data/prop_{spec}.vnnlib' + + args = [sys.executable, '-m', 'nnenum.nnenum', onnx_path, spec_path, f'{timeout}', 'out.txt'] + + start = time.perf_counter() + + result = subprocess.run(args, check=False) + + if result.returncode == 0: + with open('out.txt', 'r') as f: + res_str = f.readline() + else: + res_str = 'error_exit_code_{result.returncode}' + + diff = time.perf_counter() - start + + return res_str, diff + if __name__ == '__main__': main() diff --git a/examples/acasxu/acasxu_single.py b/examples/acasxu/acasxu_single.py deleted file mode 100644 index ed63ca3..0000000 --- a/examples/acasxu/acasxu_single.py +++ /dev/null @@ -1,265 +0,0 @@ -''' -Stanley Bak - -generic ACAS-Xu analyis script for onnx networks - -Determines network and property from command-line parameters. -''' - -import sys - -import numpy as np - -from nnenum.enumerate import enumerate_network -from nnenum.settings import Settings -from nnenum.onnx_network import load_onnx_network_optimized -from nnenum.specification import Specification, DisjunctiveSpec - -def get_init_box(property_str): - 'get lb, ub lists for the given property' - - if property_str in ("1", "2"): - init_lb = [55947.691, -3.141592, -3.141592, 1145, 0] - init_ub = [60760, 3.141592, 3.141592, 1200, 60] - elif property_str == "3": - init_lb = [1500, -0.06, 3.1, 980, 960] - init_ub = [1800, 0.06, 3.141592, 1200, 1200] - elif property_str == "4": - init_lb = [1500, -0.06, 0, 1000, 700] - init_ub = [1800, 0.06, 0, 1200, 800] - elif property_str == "5": - init_lb = [250, 0.2, -3.141592, 100, 0] - init_ub = [400, 0.4, -3.141592 + 0.005, 400, 400] - elif property_str == "6.1": - init_lb = [12000, 0.7, -3.141592, 100, 0] - init_ub = [62000, 3.141592, -3.141592 + 0.005, 1200, 1200] - elif property_str == "6.2": - init_lb = [12000, -3.141592, -3.141592, 100, 0] - init_ub = [62000, -0.7, -3.141592 + 0.005, 1200, 1200] - elif property_str == "7": - init_lb = [0, -3.141592, -3.141592, 100, 0] - init_ub = [60760, 3.141592, 3.141592, 1200, 1200] - elif property_str == "8": - init_lb = [0, -3.141592, -0.1, 600, 600] - init_ub = [60760, -0.75*3.141592, 0.1, 1200, 1200] - elif property_str == "9": - init_lb = [2000, -0.4, -3.141592, 100, 0] - init_ub = [7000, -0.14, -3.141592 + 0.01, 150, 150] - elif property_str == "10": - init_lb = [36000, 0.7, -3.141592, 900, 600] - init_ub = [60760, 3.141592, -3.141592 + 0.01, 1200, 1200] - else: - raise RuntimeError(f"init_box undefined for property {property_str}") - - # scaling inputs - means_for_scaling = [19791.091, 0.0, 0.0, 650.0, 600.0, 7.5188840201005975] - range_for_scaling = [60261.0, 6.28318530718, 6.28318530718, 1100.0, 1200.0] - - num_inputs = len(init_lb) - - # normalize input - for i in range(num_inputs): - #print(f"unscaled Input {i}: {init_lb[i], init_ub[i]}") - init_lb[i] = (init_lb[i] - means_for_scaling[i]) / range_for_scaling[i] - init_ub[i] = (init_ub[i] - means_for_scaling[i]) / range_for_scaling[i] - #print(f"scaled Input {i}: {init_lb[i], init_ub[i]}") - - return init_lb, init_ub - -def is_minimal_spec(indices): - 'create a disjunctive spec that a specific set of outputs is minimal' - - if isinstance(indices, int): - indices = [indices] - - spec_list = [] - - for i in range(5): - if i in indices: # index 3 is strong left - continue - - mat = [] - rhs = [] - - for index in indices: - l = [0, 0, 0, 0, 0] - l[index] = -1 - l[i] = 1 - - mat.append(l) - rhs.append(0) - - spec_list.append(Specification(mat, rhs)) - - return DisjunctiveSpec(spec_list) - -def get_spec(property_str): - 'get the specification' - - #labels = ['Clear of Conflict (COC)', 'Weak Left', 'Weak Right', 'Strong Left', 'Strong Right'] - - if property_str == "1": - # unsafe if COC >= 1500 - - # Output scaling is 373.94992 with a bias of 7.518884 - output_scaling_mean = 7.5188840201005975 - output_scaling_range = 373.94992 - - # (1500 - 7.518884) / 373.94992 = 3.991125 - threshold = (1500 - output_scaling_mean) / output_scaling_range - spec = Specification([[-1, 0, 0, 0, 0]], [-threshold]) - - elif property_str == "2": - # unsafe if COC is maximal: - # y0 > y1 and y0 > y1 and y0 > y2 and y0 > y3 and y0 > y4 - spec = Specification([[-1, 1, 0, 0, 0], - [-1, 0, 1, 0, 0], - [-1, 0, 0, 1, 0], - [-1, 0, 0, 0, 1]], [0, 0, 0, 0]) - elif property_str in ("3", "4"): - # unsafe if COC is minimal score - spec = Specification([[1, -1, 0, 0, 0], - [1, 0, -1, 0, 0], - [1, 0, 0, -1, 0], - [1, 0, 0, 0, -1]], [0, 0, 0, 0]) - elif property_str == "5": - # strong right should be minimal - spec = is_minimal_spec(4) - elif property_str in ["6.1", "6.2", "10"]: - # coc should be minimal - spec = is_minimal_spec(0) - elif property_str == "7": - # unsafe if strong left is minimial or strong right is minimal - spec_left = Specification([[-1, 0, 0, 1, 0], - [0, -1, 0, 1, 0], - [0, 0, -1, 1, 0]], [0, 0, 0]) - - spec_right = Specification([[-1, 0, 0, 0, 1], - [0, -1, 0, 0, 1], - [0, 0, -1, 0, 1]], [0, 0, 0]) - - spec = DisjunctiveSpec([spec_left, spec_right]) - elif property_str == "8": - # weak left is minimal or COC is minimal - spec = is_minimal_spec([0, 1]) - elif property_str == "9": - # strong left should be minimal... - spec = is_minimal_spec(3) - else: - raise RuntimeError(f"spec undefined for property {property_str}") - - return spec - -def load_init_network(net_pair, property_str): - '''load the network / spec and return it - - the network is based on the net_pair, using specification spec - - returns (init_box, network, spec) - ''' - - # load the network and prepare input / output specs - n1, n2 = net_pair - - init_lb, init_ub = get_init_box(property_str) - init_box = list(zip(init_lb, init_ub)) - - spec = get_spec(property_str) - - #network = weights_biases_to_nn(weights, biases) - onnx_filename = (f'data/ACASXU_run2a_{n1}_{n2}_batch_2000.onnx') - network = load_onnx_network_optimized(onnx_filename) - - return init_box, network, spec - -def verify_acasxu(net, spec_str): - ''''verify a system, - - returns result_str, runtime (secs) - ''' - - required_spec_net_list = [ - ["5", (1, 1)], - ["6", (1, 1)], -# ["6.1", (1, 1)], -# ["6.2", (1, 1)], - ["7", (1, 9)], - ["8", (2, 9)], - ["9", (3, 3)], - ["10", (4, 5)]] - - for req_spec, tup in required_spec_net_list: - if spec_str == req_spec: - assert net == tup, f"spec {spec_str} should only be run on net {tup}" - - result_str = None - runtime = None - - if spec_str == "6": - # disjunctive spec - print("Running first part of spec 6") - - init_box, network, spec = load_init_network(net, "6.1") - init_box = np.array(init_box, dtype=float) - - res = enumerate_network(init_box, network, spec) - result_str = res.result_str - runtime = res.total_secs - print(f"First part of spec 6 finished in {runtime}") - - if result_str == "safe": - print("Running second part of spec 6") - init_box, network, spec = load_init_network(net, "6.2") - init_box = np.array(init_box, dtype=float) - - res = enumerate_network(init_box, network, spec) - result_str = res.result_str - runtime += res.total_secs - print(f"Second part of spec 6 finished in {res.total_secs}") - else: - init_box, network, spec = load_init_network(net, spec_str) - init_box = np.array(init_box, dtype=float) - - res = enumerate_network(init_box, network, spec) - result_str = res.result_str - runtime = res.total_secs - - return result_str, runtime - -def main(): - 'main entry point' - - # change default settings for improved speed with ACAS Xu - Settings.SPLIT_IF_IDLE = False - Settings.PARALLEL_ROOT_LP = False - Settings.PRINT_OVERAPPROX_OUTPUT = False - - if len(sys.argv) < 4: - print("expected at least 3 args: net1 net2 spec_num ") - sys.exit(1) - - net1 = int(sys.argv[1]) - net2 = int(sys.argv[2]) - spec_str = sys.argv[3] - - if spec_str == "7": - # ego is better at finding deep counterexamples - Settings.BRANCH_MODE = Settings.BRANCH_EGO - Settings.NUM_PROCESSES = 10 - else: - Settings.BRANCH_MODE = Settings.BRANCH_OVERAPPROX - - if len(sys.argv) > 4: - cores = int(sys.argv[4]) - - Settings.NUM_PROCESSES = cores - print(f"Override num cores: {cores}") - - print(f"\nRunning with network {net1}-{net2} and spec {spec_str}") - - result_str, runtime = verify_acasxu((net1, net2), spec_str) - - print(f"Result for {net1}-{net2} and spec {spec_str}: {result_str}. Total runtime: {round(runtime, 2)} sec") - -if __name__ == "__main__": - main() diff --git a/examples/acasxu/data/ACASXU_run2a_1_1_batch_2000.mat b/examples/acasxu/data/ACASXU_run2a_1_1_batch_2000.mat deleted file mode 100644 index d9e6b982de4b64d6b330592dfcba448ce297479f..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 108240 zcmbTe1yogi^esw|2^DepR?WkcCR(poO2zSbMjZuNpK$%Jj^X~PX5qi&1a9e z<({ePKYp&OeTw_Vb3M)10^H|yAF1j;Qs;iIbBbI3i2?UH0}XDGBizCwr-*+dC%Huq z3!k9)A54^&WLStlJHbRjK}ReZh?(-=Ftq>McY5-AN(wb%N!mV>*yz9QNlVi7-}WNJ zXVMt|jl)QMwj;jC-7KkJ*j)zN-1nZ{Iar7%H@j|rb2|*K<|+?#2sWZyqeulsSsXIM z39nQ2-Dn&3{hlU!EOeSse%`RJ2}Rp?v4@q_V_u>CNoT`6y!NoZ|IUVA&|1IM^M_>t z(40uOn(xVkkE(yCwXyk0TzR@oQSOx2)H_51iZbuYMWyQnad zn}weRyDF7W*JIPx$eeByUDT+*A>O>&h|w(?POjBSpq{be(!M>P!8?f3)c=|T%56L7 zXck$9(Y|ywhu@WBpOA$gonQ=vUYhuFlrI|@eofJ2%eJER#2hzGZx;+KZ7wiT%z{%R zH*Jc#8?ebxY66{_kJfX+}5kx&!5~QOW>_);5Yby?xCcwTrUdL(WaF~<>1qi$!`S;5eT>Qzv#@R z;+dyG=LF__;STNFdzIh9;7gHwR&8v{iC-()jMJ1 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zLWi0`xw0!0{H`czDZM8CZ_UT(`@FBinjyN`3KK7!6C;U(%|LM=cPMSJnRRM)h-C|? zh{RM;p^2ympcx&gssWd0zaBg6x&ug>ZV!hFlKKu8)_pn)YcmSN-9l16AGHPfg``9hJ*i%btONQ4kzrDJfe!IxH)Hki|8x^GSxLFqu;dyb1^=kv#k@9 zxDAD!AeY;}wWYV2$Lad12};2`@7R?{IB&8c{o1}%*iY$qS@mli&<4ZhZ1O!I*&{At zTUH3rddwGPlM}JEm`wDIw$V_$ zJ=S!1ekK-Bv@KdMCjt+Y{QBeDNjDr?*cjITS2A{+znnj~lniW%_>^mMOr%YBj{J-{ zFsd(+qCb`m>*Up0)f(B*R=e$O^;odd18vJ)cy6uhHH3V^dfN9UY-ZlEdtm1*RCNhlk5zT?v{ z<0&^vWx9Z_kYO6-K_W0pe9bJF;h2^%vB~y$3gJ1IU2|C{0xjP(gd3{5L8uRV(}bWk z%9-1iZrWu7GUx9;RaRtTMUQ_&#VIEMX=A&)b`aaZCO7XHq;tv!TjsliEetWxiaHO|1W| zu3Pj^ibfze{N0xb;x$_W$F?)TC&8()dOH(TKa2MTQWAmJ-_C+RNZqOq10IY~*cGuf zSg#(W4Sp%GL-D1F)-tj0f3%nH=rKBIaRKQ`pdr3>xc!j{el2zyFuPccdWS9daV+e> z*I(^Kxk>RD>44xK7hRblY0Sj z79++l*4_?Io=z8BY%frpT|KXQ5bu!(xj)#+eMUT#%;^R-G>0xJi2QHne#D{a{&)Tl Dj4TN4 diff --git a/examples/acasxu/data/prop_1.vnnlib b/examples/acasxu/data/prop_1.vnnlib new file mode 100644 index 0000000..8b40838 --- /dev/null +++ b/examples/acasxu/data/prop_1.vnnlib @@ -0,0 +1,36 @@ +; ACAS Xu property 1 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (55947.691, 60760) +(assert (<= X_0 0.679857769)) +(assert (>= X_0 0.6)) + +; Unscaled Input 1: (-3.141592653589793, 3.141592653589793) +(assert (<= X_1 0.5)) +(assert (>= X_1 -0.5)) + +; Unscaled Input 2: (-3.141592653589793, 3.141592653589793) +(assert (<= X_2 0.5)) +(assert (>= X_2 -0.5)) + +; Unscaled Input 3: (1145, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 0.45)) + +; Unscaled Input 4: (0, 60) +(assert (<= X_4 -0.45)) +(assert (>= X_4 -0.5)) + +; Unsafe if COC >= 1500. Output scaling is 373.94992 with a bias of 7.518884: (1500 - 7.518884) / 373.94992 = 3.991125 +(assert (>= Y_0 3.991125645861615)) diff --git a/examples/acasxu/data/prop_10.vnnlib b/examples/acasxu/data/prop_10.vnnlib new file mode 100644 index 0000000..bec2cdc --- /dev/null +++ b/examples/acasxu/data/prop_10.vnnlib @@ -0,0 +1,41 @@ +; ACAS Xu property 10 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (36000, 60760) +(assert (<= X_0 0.679857769)) +(assert (>= X_0 0.268978427)) + +; Unscaled Input 1: (0.7, 3.141592) +(assert (<= X_1 0.499999896)) +(assert (>= X_1 0.11140846)) + +; Unscaled Input 2: (-3.141592, -3.1315920000000004) +(assert (<= X_2 -0.498408347)) +(assert (>= X_2 -0.499999896)) + +; Unscaled Input 3: (900, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 0.227272727)) + +; Unscaled Input 4: (600, 1200) +(assert (<= X_4 0.5)) +(assert (>= X_4 0.0)) + +; unsafe if coc is not minimal +(assert (or + (and (<= Y_1 Y_0)) + (and (<= Y_2 Y_0)) + (and (<= Y_3 Y_0)) + (and (<= Y_4 Y_0)) +)) diff --git a/examples/acasxu/data/prop_2.vnnlib b/examples/acasxu/data/prop_2.vnnlib new file mode 100644 index 0000000..c823019 --- /dev/null +++ b/examples/acasxu/data/prop_2.vnnlib @@ -0,0 +1,39 @@ +; ACAS Xu property 2 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (55947.691, 60760) +(assert (<= X_0 0.679857769)) +(assert (>= X_0 0.6)) + +; Unscaled Input 1: (-3.141592653589793, 3.141592653589793) +(assert (<= X_1 0.5)) +(assert (>= X_1 -0.5)) + +; Unscaled Input 2: (-3.141592653589793, 3.141592653589793) +(assert (<= X_2 0.5)) +(assert (>= X_2 -0.5)) + +; Unscaled Input 3: (1145, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 0.45)) + +; Unscaled Input 4: (0, 60) +(assert (<= X_4 -0.45)) +(assert (>= X_4 -0.5)) + +; Unsafe if COC is maximal +(assert (<= Y_1 Y_0)) +(assert (<= Y_2 Y_0)) +(assert (<= Y_3 Y_0)) +(assert (<= Y_4 Y_0)) diff --git a/examples/acasxu/data/prop_3.vnnlib b/examples/acasxu/data/prop_3.vnnlib new file mode 100644 index 0000000..d3ba649 --- /dev/null +++ b/examples/acasxu/data/prop_3.vnnlib @@ -0,0 +1,39 @@ +; ACAS Xu property 3 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (1500, 1800) +(assert (<= X_0 -0.298552812)) +(assert (>= X_0 -0.303531156)) + +; Unscaled Input 1: (-0.06, 0.06) +(assert (<= X_1 0.009549297)) +(assert (>= X_1 -0.009549297)) + +; Unscaled Input 2: (3.1, 3.141592653589793) +(assert (<= X_2 0.5)) +(assert (>= X_2 0.493380324)) + +; Unscaled Input 3: (980, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 0.3)) + +; Unscaled Input 4: (960, 1200) +(assert (<= X_4 0.5)) +(assert (>= X_4 0.3)) + +; Unsafe if COC is minimal +(assert (<= Y_0 Y_1)) +(assert (<= Y_0 Y_2)) +(assert (<= Y_0 Y_3)) +(assert (<= Y_0 Y_4)) diff --git a/examples/acasxu/data/prop_4.vnnlib b/examples/acasxu/data/prop_4.vnnlib new file mode 100644 index 0000000..278651b --- /dev/null +++ b/examples/acasxu/data/prop_4.vnnlib @@ -0,0 +1,39 @@ +; ACAS Xu property 4 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (1500, 1800) +(assert (<= X_0 -0.298552812)) +(assert (>= X_0 -0.303531156)) + +; Unscaled Input 1: (-0.06, 0.06) +(assert (<= X_1 0.009549297)) +(assert (>= X_1 -0.009549297)) + +; Unscaled Input 2: (0, 0) +(assert (<= X_2 0.0)) +(assert (>= X_2 0.0)) + +; Unscaled Input 3: (1000, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 0.318181818)) + +; Unscaled Input 4: (700, 800) +(assert (<= X_4 0.166666667)) +(assert (>= X_4 0.083333333)) + +; Unsafe if COC is minimal +(assert (<= Y_0 Y_1)) +(assert (<= Y_0 Y_2)) +(assert (<= Y_0 Y_3)) +(assert (<= Y_0 Y_4)) diff --git a/examples/acasxu/data/prop_5.vnnlib b/examples/acasxu/data/prop_5.vnnlib new file mode 100644 index 0000000..3f1e03e --- /dev/null +++ b/examples/acasxu/data/prop_5.vnnlib @@ -0,0 +1,41 @@ +; ACAS Xu property 5 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (250, 400) +(assert (<= X_0 -0.321785085)) +(assert (>= X_0 -0.324274257)) + +; Unscaled Input 1: (0.2, 0.4) +(assert (<= X_1 0.063661977)) +(assert (>= X_1 0.031830989)) + +; Unscaled Input 2: (-3.141592, -3.1365920000000003) +(assert (<= X_2 -0.499204121)) +(assert (>= X_2 -0.499999896)) + +; Unscaled Input 3: (100, 400) +(assert (<= X_3 -0.227272727)) +(assert (>= X_3 -0.5)) + +; Unscaled Input 4: (0, 400) +(assert (<= X_4 -0.166666667)) +(assert (>= X_4 -0.5)) + +; unsafe if strong right is not minimal +(assert (or + (and (<= Y_0 Y_4)) + (and (<= Y_1 Y_4)) + (and (<= Y_2 Y_4)) + (and (<= Y_3 Y_4)) +)) diff --git a/examples/acasxu/data/prop_6.vnnlib b/examples/acasxu/data/prop_6.vnnlib new file mode 100644 index 0000000..1cc4f30 --- /dev/null +++ b/examples/acasxu/data/prop_6.vnnlib @@ -0,0 +1,39 @@ +; ACAS Xu property 6 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Spec 6 +; unsafe if coc is not minimal +; Unscaled Input 0: (12000, 62000) +; Unscaled Input 1: (0.7, 3.141592) +; Unscaled Input 2: (-3.141592, -3.1365920000000003) +; Unscaled Input 3: (100, 1200) +; Unscaled Input 4: (0, 1200) +;;;; or ;;;; +; Unscaled Input 0: (12000, 62000) +; Unscaled Input 1: (-3.141592, -0.7) +; Unscaled Input 2: (-3.141592, -3.1365920000000003) +; Unscaled Input 3: (100, 1200) +; Unscaled Input 4: (0, 1200) +(assert (or + (and (<= X_0 0.700434925) (>= X_0 -0.129289109) (<= X_1 0.499999896) (>= X_1 0.11140846) (<= X_2 -0.499204121) (>= X_2 -0.499999896) (<= X_3 0.5) (>= X_3 -0.5) (<= X_4 0.5) (>= X_4 -0.5)) + (and (<= X_0 0.700434925) (>= X_0 -0.129289109) (<= X_1 -0.11140846) (>= X_1 -0.499999896) (<= X_2 -0.499204121) (>= X_2 -0.499999896) (<= X_3 0.5) (>= X_3 -0.5) (<= X_4 0.5) (>= X_4 -0.5)) +)) + +; unsafe if coc is not minimal +(assert (or + (and (<= Y_1 Y_0)) + (and (<= Y_2 Y_0)) + (and (<= Y_3 Y_0)) + (and (<= Y_4 Y_0)) +)) diff --git a/examples/acasxu/data/prop_7.vnnlib b/examples/acasxu/data/prop_7.vnnlib new file mode 100644 index 0000000..55552a2 --- /dev/null +++ b/examples/acasxu/data/prop_7.vnnlib @@ -0,0 +1,39 @@ +; ACAS Xu property 7 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (0, 60760) +(assert (<= X_0 0.679857769)) +(assert (>= X_0 -0.328422877)) + +; Unscaled Input 1: (-3.141592, 3.141592) +(assert (<= X_1 0.499999896)) +(assert (>= X_1 -0.499999896)) + +; Unscaled Input 2: (-3.141592, 3.141592) +(assert (<= X_2 0.499999896)) +(assert (>= X_2 -0.499999896)) + +; Unscaled Input 3: (100, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 -0.5)) + +; Unscaled Input 4: (0, 1200) +(assert (<= X_4 0.5)) +(assert (>= X_4 -0.5)) + +; unsafe if strong left is minimial or strong right is minimal +(assert (or + (and (<= Y_3 Y_0) (<= Y_3 Y_1) (<= Y_3 Y_2)) + (and (<= Y_4 Y_0) (<= Y_4 Y_1) (<= Y_4 Y_2)) +)) diff --git a/examples/acasxu/data/prop_8.vnnlib b/examples/acasxu/data/prop_8.vnnlib new file mode 100644 index 0000000..9eda965 --- /dev/null +++ b/examples/acasxu/data/prop_8.vnnlib @@ -0,0 +1,40 @@ +; ACAS Xu property 8 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (0, 60760) +(assert (<= X_0 0.679857769)) +(assert (>= X_0 -0.328422877)) + +; Unscaled Input 1: (-3.141592, -2.3561940000000003) +(assert (<= X_1 -0.374999922)) +(assert (>= X_1 -0.499999896)) + +; Unscaled Input 2: (-0.1, 0.1) +(assert (<= X_2 0.015915494)) +(assert (>= X_2 -0.015915494)) + +; Unscaled Input 3: (600, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 -0.045454545)) + +; Unscaled Input 4: (600, 1200) +(assert (<= X_4 0.5)) +(assert (>= X_4 0.0)) + +; weak left is minimal or COC is minimal +(assert (or + (and (<= Y_2 Y_0) (<= Y_2 Y_1)) + (and (<= Y_3 Y_0) (<= Y_3 Y_1)) + (and (<= Y_4 Y_0) (<= Y_4 Y_1)) +)) diff --git a/examples/acasxu/data/prop_9.vnnlib b/examples/acasxu/data/prop_9.vnnlib new file mode 100644 index 0000000..8d20d03 --- /dev/null +++ b/examples/acasxu/data/prop_9.vnnlib @@ -0,0 +1,41 @@ +; ACAS Xu property 9 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; Unscaled Input 0: (2000, 7000) +(assert (<= X_0 -0.212261512)) +(assert (>= X_0 -0.295233916)) + +; Unscaled Input 1: (-0.4, -0.14) +(assert (<= X_1 -0.022281692)) +(assert (>= X_1 -0.063661977)) + +; Unscaled Input 2: (-3.141592, -3.1315920000000004) +(assert (<= X_2 -0.498408347)) +(assert (>= X_2 -0.499999896)) + +; Unscaled Input 3: (100, 150) +(assert (<= X_3 -0.454545455)) +(assert (>= X_3 -0.5)) + +; Unscaled Input 4: (0, 150) +(assert (<= X_4 -0.375)) +(assert (>= X_4 -0.5)) + +; strong left should be minimal +(assert (or + (and (<= Y_0 Y_3)) + (and (<= Y_1 Y_3)) + (and (<= Y_2 Y_3)) + (and (<= Y_4 Y_3)) +)) diff --git a/src/nnenum/nnenum.py b/src/nnenum/nnenum.py new file mode 100644 index 0000000..1c01edb --- /dev/null +++ b/src/nnenum/nnenum.py @@ -0,0 +1,130 @@ +''' +nnenum vnnlib front end + +usage: "python3 nnenum.py [timeout=None]" + +Stanley Bak +June 2021 +''' + +import sys + +import numpy as np + +from nnenum.enumerate import enumerate_network +from nnenum.settings import Settings +from nnenum.result import Result +from nnenum.onnx_network import load_onnx_network_optimized +from nnenum.specification import Specification, DisjunctiveSpec +from nnenum.vnnlib import get_num_inputs_outputs, read_vnnlib_simple + +def make_spec(vnnlib_filename, onnx_filename): + '''make Specification + + returns a pair: (list of [box, Specification], inp_dtype) + ''' + + num_inputs, num_outputs, inp_dtype = get_num_inputs_outputs(onnx_filename) + vnnlib_spec = read_vnnlib_simple(vnnlib_filename, num_inputs, num_outputs) + + rv = [] + + for box, spec_list in vnnlib_spec: + if len(spec_list) == 1: + mat, rhs = spec_list[0] + spec = Specification(mat, rhs) + else: + spec_obj_list = [Specification(mat, rhs) for mat, rhs in spec_list] + spec = DisjunctiveSpec(spec_obj_list) + + rv.append((box, spec)) + + return rv, inp_dtype + +def set_control_settings(): + 'set settings for smaller control benchmarks' + + Settings.reset() + Settings.TIMING_STATS = False + Settings.PARALLEL_ROOT_LP = False + Settings.SPLIT_IF_IDLE = False + Settings.PRINT_OVERAPPROX_OUTPUT = False + Settings.TRY_QUICK_OVERAPPROX = True + + Settings.CONTRACT_ZONOTOPE_LP = True + Settings.CONTRACT_LP_OPTIMIZED = True + Settings.CONTRACT_LP_TRACK_WITNESSES = True + + Settings.OVERAPPROX_BOTH_BOUNDS = False + + Settings.BRANCH_MODE = Settings.BRANCH_OVERAPPROX + Settings.OVERAPPROX_GEN_LIMIT_MULTIPLIER = 1.5 + Settings.OVERAPPROX_LP_TIMEOUT = 0.02 + Settings.OVERAPPROX_MIN_GEN_LIMIT = 70 + +def set_image_settings(): + 'set settings for larger image benchmarks' + + pass + +def main(): + 'main entry point' + + if len(sys.argv) < 3: + print('usage: "python3 nnenum.py [timeout=None] [outfile=None]"') + sys.exit(1) + + onnx_filename = sys.argv[1] + vnnlib_filename = sys.argv[2] + timeout = None + outfile = None + + if len(sys.argv) >= 4: + timeout = float(sys.argv[3]) + + if len(sys.argv) >= 5: + outfile = sys.argv[4] + + # + spec_list, input_dtype = make_spec(vnnlib_filename, onnx_filename) + + network = load_onnx_network_optimized(onnx_filename) + result_str = 'none' # gets overridden + + num_inputs = len(spec_list[0][0]) + + if num_inputs < 700: + set_control_settings() + else: + set_image_settings() + + for init_box, spec in spec_list: + init_box = np.array(init_box, dtype=input_dtype) + + if timeout is not None: + if timeout <= 0: + result_str = 'timeout' + break + + Settings.TIMEOUT = timeout + + res = enumerate_network(init_box, network, spec) + result_str = res.result_str + + if timeout is not None: + # reduce timeout by the runtime + timeout -= res.total_secs + + if result_str != "safe": + break + + if outfile is not None: + with open(outfile, 'w') as f: + f.write(result_str) + + if result_str == 'error': + sys.exit(Result.results.index('error')) + + +if __name__ == '__main__': + main() diff --git a/src/nnenum/vnnlib.py b/src/nnenum/vnnlib.py new file mode 100644 index 0000000..c3fe1c7 --- /dev/null +++ b/src/nnenum/vnnlib.py @@ -0,0 +1,290 @@ +''' +vnnlib simple utilities + +Stanley Bak +June 2021 +''' + +from copy import deepcopy +import re + +import numpy as np + +import onnxruntime as ort +import onnx + +def read_statements(vnnlib_filename): + '''process vnnlib and return a list of strings (statements) + + useful to get rid of comments and blank lines and combine multi-line statements + ''' + + with open(vnnlib_filename, 'r') as f: + lines = f.readlines() + + lines = [line.strip() for line in lines] + assert len(lines) > 0 + + # combine lines if case a single command spans multiple lines + open_parentheses = 0 + statements = [] + current_statement = '' + + for line in lines: + comment_index = line.find(';') + + if comment_index != -1: + line = line[:comment_index].rstrip() + + if not line: + continue + + new_open = line.count('(') + new_close = line.count(')') + + open_parentheses += new_open - new_close + + assert open_parentheses >= 0, "mismatched parenthesis in vnnlib file" + + # add space + current_statement += ' ' if current_statement else '' + current_statement += line + + if open_parentheses == 0: + statements.append(current_statement) + current_statement = '' + + if current_statement: + statements.append(current_statement) + + # remove repeated whitespace characters + statements = [" ".join(s.split()) for s in statements] + + # remove space after '(' + statements = [s.replace('( ', '(') for s in statements] + + # remove space after ')' + statements = [s.replace(') ', ')') for s in statements] + + return statements + +def update_rv_tuple(rv_tuple, op, first, second, num_inputs, num_outputs): + 'update tuple from rv in read_vnnlib_simple, with the passed in constraint "(op first second)"' + + if first.startswith("X_"): + # Input constraints + index = int(first[2:]) + + assert not second.startswith("X") and not second.startswith("Y"), \ + f"input constraints must be box ({op} {first} {second})" + assert 0 <= index < num_inputs + + limits = rv_tuple[0][index] + + if op == "<=": + limits[1] = min(float(second), limits[1]) + else: + limits[0] = max(float(second), limits[0]) + + assert limits[0] <= limits[1], f"{first} range is empty: {limits}" + + else: + # output constraint + if op == ">=": + # swap order if op is >= + first, second = second, first + + row = [0.0] * num_outputs + rhs = 0.0 + + # assume op is <= + if first.startswith("Y_") and second.startswith("Y_"): + index1 = int(first[2:]) + index2 = int(second[2:]) + + row[index1] = 1 + row[index2] = -1 + elif first.startswith("Y_"): + index1 = int(first[2:]) + row[index1] = 1 + rhs = float(second) + else: + assert second.startswith("Y_") + index2 = int(second[2:]) + row[index2] = -1 + rhs = -1 * float(first) + + mat, rhs_list = rv_tuple[1], rv_tuple[2] + mat.append(row) + rhs_list.append(rhs) + +def make_input_box_dict(num_inputs): + 'make a dict for the input box' + + rv = {i: [-np.inf, np.inf] for i in range(num_inputs)} + + return rv + +def get_io_nodes(onnx_model): + 'returns 3 -tuple: input node, output nodes, input dtype' + + sess = ort.InferenceSession(onnx_model.SerializeToString()) + inputs = [i.name for i in sess.get_inputs()] + assert len(inputs) == 1, f"expected single onnx network input, got: {inputs}" + input_name = inputs[0] + + outputs = [o.name for o in sess.get_outputs()] + assert len(outputs) == 1, f"expected single onnx network output, got: {outputs}" + output_name = outputs[0] + + g = onnx_model.graph + inp = [n for n in g.input if n.name == input_name][0] + out = [n for n in g.output if n.name == output_name][0] + + input_type = g.input[0].type.tensor_type.elem_type + + assert input_type in [onnx.TensorProto.FLOAT, onnx.TensorProto.DOUBLE] + + dtype = np.float32 if input_type == onnx.TensorProto.FLOAT else np.float64 + + return inp, out, dtype + +def get_num_inputs_outputs(onnx_filename): + 'get num inputs, num outputs, and input dtype of an onnx file' + + onnx_model = onnx.load(onnx_filename) + inp, out, inp_dtype = get_io_nodes(onnx_model) + + inp_shape = tuple(d.dim_value if d.dim_value != 0 else 1 for d in inp.type.tensor_type.shape.dim) + out_shape = tuple(d.dim_value if d.dim_value != 0 else 1 for d in out.type.tensor_type.shape.dim) + + num_inputs = 1 + num_outputs = 1 + + for n in inp_shape: + num_inputs *= n + + for n in out_shape: + num_outputs *= n + + return num_inputs, num_outputs, inp_dtype + +def read_vnnlib_simple(vnnlib_filename, num_inputs, num_outputs): + '''process in a vnnlib file. You can get num_inputs and num_outputs using get_num_inputs_outputs(). + + this is not a general parser, and assumes files are provided in a 'nice' format. Only a single disjunction + is allowed + + output a list containing 2-tuples: + 1. input ranges (box), list of pairs for each input variable + 2. specification, provided as a list of pairs (mat, rhs), as in: mat * y <= rhs, where y is the output. + Each element in the list is a term in a disjunction for the specification. + ''' + + # example: "(declare-const X_0 Real)" + regex_declare = re.compile(r"^\(declare-const (X|Y)_(\S+) Real\)$") + + # comparison sub-expression + # example: "(<= Y_0 Y_1)" or "(<= Y_0 10.5)" + comparison_str = r"\((<=|>=) (\S+) (\S+)\)" + + # example: "(and (<= Y_0 Y_2)(<= Y_1 Y_2))" + dnf_clause_str = r"\(and (" + comparison_str + r")+\)" + + # example: "(assert (<= Y_0 Y_1))" + regex_simple_assert = re.compile(r"^\(assert " + comparison_str + r"\)$") + + # disjunctive-normal-form + # (assert (or (and (<= Y_3 Y_0)(<= Y_3 Y_1)(<= Y_3 Y_2))(and (<= Y_4 Y_0)(<= Y_4 Y_1)(<= Y_4 Y_2)))) + regex_dnf = re.compile(r"^\(assert \(or (" + dnf_clause_str + r")+\)\)$") + + rv = [] # list of 3-tuples, (box-dict, mat, rhs) + rv.append((make_input_box_dict(num_inputs), [], [])) + + lines = read_statements(vnnlib_filename) + + for line in lines: + #print(f"Line: {line}") + + if len(regex_declare.findall(line)) > 0: + continue + + groups = regex_simple_assert.findall(line) + + if groups: + assert len(groups[0]) == 3, f"groups was {groups}: {line}" + op, first, second = groups[0] + + for rv_tuple in rv: + update_rv_tuple(rv_tuple, op, first, second, num_inputs, num_outputs) + + continue + + ################ + groups = regex_dnf.findall(line) + assert groups, f"failed parsing line: {line}" + + tokens = line.replace("(", " ").replace(")", " ").split() + tokens = tokens[2:] # skip 'assert' and 'or' + + conjuncts = " ".join(tokens).split("and")[1:] + + old_rv = rv + rv = [] + + for rv_tuple in old_rv: + for c in conjuncts: + rv_tuple_copy = deepcopy(rv_tuple) + rv.append(rv_tuple_copy) + + c_tokens = [s for s in c.split(" ") if len(s) > 0] + + count = len(c_tokens) // 3 + + for i in range(count): + op, first, second = c_tokens[3*i:3*(i+1)] + + update_rv_tuple(rv_tuple_copy, op, first, second, num_inputs, num_outputs) + + # merge elements of rv with the same input spec + merged_rv = {} + + for rv_tuple in rv: + boxdict = rv_tuple[0] + matrhs = (rv_tuple[1], rv_tuple[2]) + + key = str(boxdict) # merge based on string representation of input box... accurate enough for now + + if key in merged_rv: + merged_rv[key][1].append(matrhs) + else: + merged_rv[key] = (boxdict, [matrhs]) + + # finalize objects (convert dicts to lists and lists to np.array) + final_rv = [] + + for rv_tuple in merged_rv.values(): + box_dict = rv_tuple[0] + + box = [] + + for d in range(num_inputs): + r = box_dict[d] + + assert r[0] != -np.inf and r[1] != np.inf, f"input X_{d} was unbounded: {r}" + box.append(r) + + spec_list = [] + + for matrhs in rv_tuple[1]: + mat = np.array(matrhs[0], dtype=float) + rhs = np.array(matrhs[1], dtype=float) + spec_list.append((mat, rhs)) + + final_rv.append((box, spec_list)) + + #for i, (box, spec_list) in enumerate(final_rv): + # print(f"-----\n{i+1}. {box}\nspec:{spec_list}") + + return final_rv + From 96e446fd79ce52be6e31f7af8b8ce81a9a53139f Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 15:10:44 -0400 Subject: [PATCH 17/55] removing adversarial counterexmaples --- src/nnenum/agen.py | 348 --------------------------------------- src/nnenum/enumerate.py | 136 +-------------- src/nnenum/overapprox.py | 18 +- src/nnenum/settings.py | 16 -- src/nnenum/worker.py | 65 +------- 5 files changed, 10 insertions(+), 573 deletions(-) delete mode 100644 src/nnenum/agen.py diff --git a/src/nnenum/agen.py b/src/nnenum/agen.py deleted file mode 100644 index 39aced0..0000000 --- a/src/nnenum/agen.py +++ /dev/null @@ -1,348 +0,0 @@ -''' -adversarial generation for nnenum - -Stanley Bak, 2020 -''' - -import os -import logging -import time -import warnings - -import numpy as np - -import onnx - -import tensorflow as tf -import foolbox as fb - -from nnenum.util import Freezable -from nnenum.timerutil import Timers -from nnenum.network import nn_unflatten -from nnenum.settings import Settings - -class AgenState(Freezable): - 'adversarial image generation container' - - def __init__(self, onnx_filename, orig_image, label, epsilon, bounds=(0.0, 1.0)): - '''initialize a session''' - - warnings.filterwarnings("ignore", category=UserWarning) - logging.basicConfig(level=logging.ERROR) - #warnings.filterwarnings("ignore", message='exponential search failed') - - # turn of logging errors - #tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR) - os.environ['TF_CPP_MIN_LOG_LEVEL'] = '3' # FATAL - logging.getLogger('tensorflow').setLevel(logging.FATAL) - - # disable eager execution - tf.compat.v1.disable_eager_execution() - - # slightly hack... onnx model is used only to get input / output names - assert onnx_filename.endswith(".onnx") - model = onnx.load(onnx_filename) - self.output_name = f"{model.graph.output[0].name}:0" - self.input_name = f"{model.graph.input[0].name}:0" - - filename = f'{onnx_filename}.pb' - graph_def = None - - with tf.io.gfile.GFile(filename, 'rb') as f: - graph_def = tf.compat.v1.GraphDef() - graph_def.ParseFromString(f.read()) - - assert graph_def is not None - - self.graph_def = graph_def - self.orig_image = orig_image - self.epsilon = epsilon - self.bounds = bounds - self.labels = np.array([label]) - - self.sess = tf.compat.v1.Session() - - with self.sess.as_default(): - tf.import_graph_def(self.graph_def, name='') - graph = self.sess.graph - - input_tensor = graph.get_tensor_by_name(self.input_name) - output_tensor = graph.get_tensor_by_name(self.output_name) - - self.fmodel = fb.models.TensorFlowModel(input_tensor, output_tensor, bounds=self.bounds) - - self.freeze_attrs() - - def __del__(self): - if self.sess is not None: - self.sess.close() - self.sess = None - - def try_mixed_adversarial(self, iteration, random_only): - ''' - try generating an adversarial using a mixed strategy, depending on the iteration - - returns [adversarial image, epsilon], if found, else None - ''' - - rv = None - - classes = [fb.attacks.FGSM, # 0.057 in 41ms - fb.attacks.ContrastReductionAttack, # 0.05 in 64 ms - fb.attacks.BlendedUniformNoiseAttack, # 0.09 in 93ms - fb.attacks.DecoupledDirectionNormL2Attack, # 0.074 in 124ms - fb.attacks.BIM, # 0.044 in 300 ms - fb.attacks.PGD, # 0.05 in 1302 ms - fb.attacks.MomentumIterativeAttack, # 0.04 in 300 ms - fb.attacks.AdamPGD, #0.055 in 800ms - fb.attacks.AdamRandomPGD, # 0.042 in 700ms - fb.attacks.RandomPGD # best - ] - - # pick the attack class... - attack_class = None - - if not random_only and iteration < len(classes): - attack_class = classes[iteration] - - t = Settings.ADVERSARIAL_TARGET - criterion = fb.criteria.Misclassification() if t is None else fb.criteria.TargetClass(t) - - with self.sess.as_default(): - if attack_class is None: - attack_class = SingleEpsilonRPGD - attack = SingleEpsilonRPGD(self.fmodel, distance=fb.distances.Linfinity, criterion=criterion) - - # subtract a small amount since attack was overshooting by numerical precision - SingleEpsilonRPGD.set_epsilon(self.epsilon - 1e-6) - else: - attack = attack_class(self.fmodel, distance=fb.distances.Linfinity, criterion=criterion) - - Timers.tic('attack') - a = attack(self.orig_image, self.labels, unpack=False)[0] - Timers.toc('attack') - - dist = a.distance.value - - #print(f"attack class: {attack_class}, ep: {dist}, iteration {iteration}") - - if dist <= Settings.ADVERSARIAL_EPSILON: - rv = a.perturbed - rv.shape = self.orig_image.shape - - if rv is not None: - print(f"try_mixed_adversarial found violation image on iteration {iteration} with ep={dist} and " + \ - f"attack class: {attack_class}") - - return rv - - def try_single(self): - '''try to generate an adversarial image for the single value of epsilon (quick) - - returns [adversarial image, epsilon], if found, else None - ''' - - Timers.tic('try_single') - - rv = None - - t = Settings.ADVERSARIAL_TARGET - criterion = fb.criteria.Misclassification() if t is None else fb.criteria.TargetClass(t) - - with self.sess.as_default(): - attack = SingleEpsilonRPGD(self.fmodel, distance=fb.distances.Linfinity, criterion=criterion) - - # subtract a small amount since attack was overshooting by numerical precision - SingleEpsilonRPGD.set_epsilon(self.epsilon - 1e-6) - - Timers.tic('attack') - a = attack(self.orig_image, self.labels, unpack=False)[0] - Timers.toc('attack') - - dist = a.distance.value - - if dist != np.inf: - rv = [a.perturbed, dist] - rv[0].shape = self.orig_image.shape - - Timers.toc('try_single') - - return rv - - def try_seeded(self, seed_image): - '''try to generate the closest adversarial image from a given seed image, and check if it's within - the desired epsilon from the original image - - returns [adversarial image, epsilon], if found, else None - ''' - - Timers.tic('try_seeded') - - assert seed_image.shape == self.orig_image.shape - - rv = None - - closest_status = "" - closest_dist = np.inf - - classes = [ - #fb.attacks.FGSM, # 0.057 in 41ms - #fb.attacks.ContrastReductionAttack, # 0.05 in 64 ms - #fb.attacks.BlendedUniformNoiseAttack, # 0.09 in 93ms - #fb.attacks.NewtonFoolAttack, # 0.11 in 93ms - #fb.attacks.DecoupledDirectionNormL2Attack, # 0.074 in 124ms - fb.attacks.BIM, # 0.044 in 300 ms - #fb.attacks.PGD, # 0.05 in 1302 ms - #fb.attacks.MomentumIterativeAttack, # 0.04 in 300 ms - #fb.attacks.AdamPGD, #0.055 in 800ms - #fb.attacks.AdamRandomPGD, # 0.042 in 700ms - #fb.attacks.RandomPGD # best - ] - - t = Settings.ADVERSARIAL_TARGET - criterion = fb.criteria.Misclassification() if t is None else fb.criteria.TargetClass(t) - - with self.sess.as_default(): - for attack_class in classes: - - #if rv is not None: - # break - - attack = attack_class(self.fmodel, distance=fb.distances.Linfinity, criterion=criterion) - - factor = 0.65 # sweet spot - - blended_image = factor * seed_image + (1.0 - factor) * self.orig_image - - # clip to fix floating-point out of bounds - blended_image = np.clip(blended_image, self.bounds[0], self.bounds[1]) - - #blended_ep = np.linalg.norm(np.ravel(self.orig_image - blended_image), ord=np.inf) - - #if blended_ep > Settings.ADVERSARIAL_EPSILON: - # break - - start = time.perf_counter() - Timers.tic('attack') - a = attack(blended_image, self.labels, unpack=False)[0] - Timers.toc('attack') - - diff = time.perf_counter() - start - - if a.distance.value != np.inf: - # compute the distance from the original imag - aimage = a.perturbed - aimage.shape = self.orig_image.shape - - diff_image = self.orig_image - aimage - - dist = np.linalg.norm(np.ravel(diff_image), ord=np.inf) - - status = f"({factor}) {round(diff * 1000, 1)}ms, {round(a.distance.value, 5)} from " + \ - f"blended and {round(dist, 5)} from orig with attack class: {attack_class.__name__}" - - #print(f".agen {status}") - - if dist < closest_dist: - closest_dist = dist - closest_status = status - - tol = 1e-6 - - if dist <= self.epsilon + tol: - rv = [aimage, dist] - - print(f"SUCCESS: seed succeeded with factor {factor}.") - break - - label = "SEED-SUCCESS" if rv is not None else "SEED-FAILED" - print(f"{label}: {closest_status}", flush=True) - - Timers.toc('try_seeded') - - return rv - -class SingleEpsilonRPGD( - fb.attacks.iterative_projected_gradient.LinfinityGradientMixin, - fb.attacks.iterative_projected_gradient.LinfinityClippingMixin, - fb.attacks.iterative_projected_gradient.LinfinityDistanceCheckMixin, - fb.attacks.iterative_projected_gradient.GDOptimizerMixin, - fb.attacks.iterative_projected_gradient.IterativeProjectedGradientBaseAttack, -): - 'random projected gradient descent with custom parameters' - - epsilon = 0 # bad... storing in class variable - - @classmethod - def set_epsilon(cls, epsilon): - 'set epsilon value' - cls.epsilon = epsilon - - @fb.attacks.base.generator_decorator - def as_generator( - self, - a, - binary_search=False, - epsilon=None, # use from constructor - stepsize=0.01, - iterations=50, - random_start=True, - return_early=True, - ): - epsilon = SingleEpsilonRPGD.epsilon - assert epsilon > 0 - - yield from self._run( - a, binary_search, epsilon, stepsize, iterations, random_start, return_early - ) - -def try_quick_adversarial(num_attempts, remaining_secs=None): - '''try a quick adversarial example using Settings - - returns AgenState instance, aimage (may be None) - ''' - - start = time.perf_counter() - - onnx_path = Settings.ADVERSARIAL_ONNX_PATH - ep = Settings.ADVERSARIAL_EPSILON - im = Settings.ADVERSARIAL_ORIG_IMAGE - l = Settings.ADVERSARIAL_ORIG_LABEL - - agen = AgenState(onnx_path, im, l, ep) - a = None - - for i in range(num_attempts): - - if remaining_secs is not None: - diff = time.perf_counter() - start - - if diff > remaining_secs: - break # timeout! - - a = agen.try_single() - - if a is not None: - break - - if a is not None: - aimage, ep = a - - if Settings.PRINT_OUTPUT and num_attempts > 0: - print(f"try_quick_adversarial found violation image on iteration {i} with ep={ep}") - - else: - aimage = None - - #with agen.sess.as_default(): - # attack = fb.attacks.RandomPGD(agen.fmodel, distance=fb.distances.Linfinity) - - # Timers.tic('attack') - # a = attack(agen.orig_image, agen.labels, unpack=False)[0] - # Timers.toc('attack') - - # dist = a.distance.value - - # print(f"\nDist of random PGD adversarial: {dist}") - - return agen, aimage diff --git a/src/nnenum/enumerate.py b/src/nnenum/enumerate.py index dc81e90..9f95dcc 100644 --- a/src/nnenum/enumerate.py +++ b/src/nnenum/enumerate.py @@ -23,7 +23,6 @@ from nnenum.worker import Worker from nnenum.overapprox import try_quick_overapprox from nnenum.onnx_network import reinit_onnx_sessions -from nnenum.agen import try_quick_adversarial from nnenum.prefilter import LpCanceledException @@ -104,33 +103,19 @@ def enumerate_network(init, network, spec=None): assert not Settings.RESULT_SAVE_TIMERS or Settings.TIMING_STATS, \ "RESULT_SAVE_TIMERS cannot be used if TIMING_STATS is False" - # adversarial generation process and queue - concrete_io_tuple = None - q = None - p = None - found_adv = None - - if Settings.ADVERSARIAL_ONNX_PATH is not None and Settings.ADVERSARIAL_TRY_QUICK: - q = multiprocessing.Queue() - found_adv = multiprocessing.Value('i', 0) - - p = multiprocessing.Process(target=gen_adv, args=(q, found_adv, network, Settings.TIMEOUT)) - p.start() - # don't wait for result... run safety check in parallel - init_ss = None - if concrete_io_tuple is None and time.perf_counter() - start < Settings.TIMEOUT: + if time.perf_counter() - start < Settings.TIMEOUT: init_ss = make_init_ss(init, network, spec, start) # returns None if timeout proven_safe = False try_quick = Settings.TRY_QUICK_OVERAPPROX or Settings.SINGLE_SET if init_ss is not None and try_quick and spec is not None: - proven_safe, concrete_io_tuple = try_quick_overapprox(init_ss, network, spec, start, found_adv) + proven_safe, concrete_io_tuple = try_quick_overapprox(init_ss, network, spec, start) if concrete_io_tuple is not None: - # non-parallel adversarial example was generated + # try_quick_overapprox found error if Settings.PRINT_OUTPUT: print("Proven unsafe before enumerate") @@ -152,26 +137,7 @@ def enumerate_network(init, network, spec=None): rv = Result(network, quick=True) rv.result_str = 'safe' else: - concrete_io_tuple = None - - if p is not None and q is not None: - concrete_io_tuple = q.get() - p.join() - p.terminate() - q.cancel_join_thread() - p = None - q = None - - if concrete_io_tuple is not None: - if Settings.PRINT_OUTPUT: - print("Initial quick adversarial search found unsafe image.") - - rv = Result(network, quick=True) - rv.result_str = 'unsafe' - - rv.cinput = concrete_io_tuple[0] - rv.coutput = concrete_io_tuple[1] - elif Settings.SINGLE_SET: + if Settings.SINGLE_SET: if Settings.PRINT_OUTPUT: print("SINGLE_SET analysis inconclusive.") @@ -212,12 +178,6 @@ def enumerate_network(init, network, spec=None): rv.total_secs = time.perf_counter() - start process_result(shared) - if p is not None and q is not None: - q.cancel_join_thread() - p.terminate() - p = None - q = None - if rv.total_secs is None: rv.total_secs = time.perf_counter() - start @@ -465,8 +425,6 @@ def __init__(self, worker_index): self.stars_in_progress = 0 - self.agen = None # adversarial example generator - if Settings.SHUFFLE_TIME is not None: self.next_shuffle_step = Settings.SHUFFLE_TIME self.next_shuffle_time = time.time() + self.next_shuffle_step @@ -521,44 +479,6 @@ def worker_func(worker_index, shared): priv.start_time = shared.start_time w = Worker(shared, priv) - if worker_index == 1 and Settings.ADVERSARIAL_IN_WORKERS and Settings.ADVERSARIAL_ONNX_PATH: - # while worker 0 does overapproximation, worker 1 - priv.agen, aimage = try_quick_adversarial(1) - - for i in range(Settings.ADVERSARIAL_WORKERS_MAX_ITER): - - if aimage is not None: - if Settings.PRINT_OUTPUT: - print(f"mixed_adversarial worker {worker_index} found unsafe image after on iteration {i}") - - flat_image = nn_flatten(aimage) - - output = w.shared.network.execute(flat_image) - flat_output = np.ravel(output) - - olabel = np.argmax(output) - confirmed = olabel != Settings.ADVERSARIAL_ORIG_LABEL - - if Settings.PRINT_OUTPUT: - print(f"Original label: {Settings.ADVERSARIAL_ORIG_LABEL}, output argmax: {olabel}") - print(f"counterexample was confirmed: {confirmed}") - - if confirmed: - concrete_io_tuple = (flat_image, flat_output) - w.found_unsafe(concrete_io_tuple) - break - - if shared.should_exit.value != 0: - break - - #if shared.finished_initial_overapprox.value == 1 and worker_index != 1: - # worker 1 finishes all attempts, other works help with enumeration - # break - - # try again using a mixed strategy - random_attacks_only = False - aimage = priv.agen.try_mixed_adversarial(i, random_attacks_only) - try: w.main_loop() @@ -674,52 +594,4 @@ def worker_func(worker_index, shared): Timers.toc(timer_name) -def gen_adv(q, found_adv, network, remaining_secs): - '''try a quick adversarial - - puts concrete_io_tuple or None into the queue - - when it's found, the multiprocessing.value (found_adv) is set to 1 - ''' - - concrete_io_tuple = gen_adv_single_threaded(network, remaining_secs) - - if concrete_io_tuple is not None: - found_adv.value = 1 - - q.put(concrete_io_tuple) - q.close() - -def gen_adv_single_threaded(network, remaining_secs): - 'gen adversarial without multiprocessing interface' - - concrete_io_tuple = None - - start = time.perf_counter() - _, aimage = try_quick_adversarial(Settings.ADVERSARIAL_QUICK_NUM_ATTEMPTS, remaining_secs) - gen_time = time.perf_counter() - start - - if aimage is not None: - if Settings.PRINT_OUTPUT: - print("try_quick_adversarial found unsafe image") - - start = time.perf_counter() - - output = network.execute(aimage) - flat_output = np.ravel(output) - - olabel = np.argmax(output) - confirmed = olabel != Settings.ADVERSARIAL_ORIG_LABEL - exec_time = time.perf_counter() - start - - if Settings.PRINT_OUTPUT: - print(f"Original label: {Settings.ADVERSARIAL_ORIG_LABEL}, output argmax: {olabel}") - - gen_ms = f"{round(1000*gen_time, 1)}ms" - exec_ms = f"{round(1000*exec_time, 1)}ms" - print(f"counterexample was confirmed: {confirmed}. Gen: {gen_ms}, Exec: {exec_ms}") - - if confirmed: - concrete_io_tuple = (nn_flatten(aimage), flat_output) - return concrete_io_tuple diff --git a/src/nnenum/overapprox.py b/src/nnenum/overapprox.py index d4d9e64..ffeb057 100644 --- a/src/nnenum/overapprox.py +++ b/src/nnenum/overapprox.py @@ -12,8 +12,8 @@ from nnenum.specification import DisjunctiveSpec from nnenum.network import ReluLayer, FullyConnectedLayer, nn_flatten, nn_unflatten -def try_quick_overapprox(ss, network, spec, start_time, found_adv): - 'try a quick overapproximation, return True if safe' +def try_quick_overapprox(ss, network, spec, start_time): + 'try a quick overapproximation, return is_safe, concrete_io_tuple' Timers.tic('try_quick_overapprox') @@ -26,9 +26,6 @@ def check_cancel_func(): if diff > Settings.TIMEOUT: raise OverapproxCanceledException('timeout exceeded') - - if found_adv is not None and found_adv.value != 0: - raise OverapproxCanceledException('found_adv was set') try: check_cancel_func() @@ -259,7 +256,7 @@ def test_abstract_violation(dims, vstars, vindices, network, spec): return abstract_ios, concrete_io_tuple def do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=None, gen_limit=np.inf, - overapprox_types=None, try_seeded_adversarial=None): + overapprox_types=None): '''do the multi-round overapproximation analysis returns an instance of RoundsResult: @@ -318,15 +315,10 @@ def do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=None if rv.is_safe: break - if vstars and (Settings.ADVERSARIAL_TEST_ABSTRACT_VIO or Settings.ADVERSARIAL_SEED_ABSTRACT_VIO): + if vstars: dims = ss.star.lpi.get_num_cols() - if Settings.ADVERSARIAL_TEST_ABSTRACT_VIO: - abstract_ios, rv.concrete_io_tuple = test_abstract_violation(dims, vstars, vindices, network, spec) - - if rv.concrete_io_tuple is None and Settings.ADVERSARIAL_SEED_ABSTRACT_VIO \ - and Settings.ADVERSARIAL_ONNX_PATH and try_seeded_adversarial: - rv.concrete_io_tuple = try_seeded_adversarial(dims, abstract_ios) + abstract_ios, rv.concrete_io_tuple = test_abstract_violation(dims, vstars, vindices, network, spec) if first_round: first_round = False diff --git a/src/nnenum/settings.py b/src/nnenum/settings.py index 9c05a8d..7396c1d 100644 --- a/src/nnenum/settings.py +++ b/src/nnenum/settings.py @@ -117,19 +117,3 @@ def reset(cls): 'Gemm', 'MatMul', 'Mul', 'Reshape', 'Relu', 'Shape', 'Sub', 'Unsqueeze'] cls.ONNX_BLACKLIST = ['Atan', 'MaxPool', 'Sigmoid', 'Tanh'] # unsupported nonlinear laters - - ### - # settings for adversarial generation - cls.ADVERSARIAL_TRY_QUICK = True # if settings are provided, try quick adversrial generation at start - cls.ADVERSARIAL_QUICK_NUM_ATTEMPTS = 10 # how many attempts - cls.ADVERSARIAL_IN_WORKERS = True # do lots of attempted adversarial generation until more work is produced - cls.ADVERSARIAL_WORKERS_MAX_ITER = 100 # how many attempts workers should make - cls.ADVERSARIAL_TEST_ABSTRACT_VIO = True # try executing abstract violations - cls.ADVERSARIAL_SEED_ABSTRACT_VIO = False # try adversarial examples seeded from abstract violations - - - cls.ADVERSARIAL_ONNX_PATH = None # path to .onnx file with corresponidng .onnx.pb file - cls.ADVERSARIAL_EPSILON = None - cls.ADVERSARIAL_ORIG_IMAGE = None - cls.ADVERSARIAL_ORIG_LABEL = None - cls.ADVERSARIAL_TARGET = None # can optionally be set to specific class, default: any misclassification diff --git a/src/nnenum/worker.py b/src/nnenum/worker.py index 867c210..877e364 100644 --- a/src/nnenum/worker.py +++ b/src/nnenum/worker.py @@ -18,7 +18,6 @@ from nnenum.network import nn_unflatten, nn_flatten from nnenum.prefilter import LpCanceledException -from nnenum.agen import AgenState class Worker(Freezable): 'local data for a worker process' @@ -115,67 +114,6 @@ def add_branch_str(self, label): if self.priv.branch_tuples_list is not None: self.priv.branch_tuples_list.append(f'{self.priv.ss.branch_str()} ({label})') - def try_seeded_adversarial(self, dims, abstract_ios): - ''' - generate adversarial image from abstract counterexample seeds - - returns concrete_io_tuple or None - ''' - - Timers.tic('try_seeded_adversarial') - - assert dims == Settings.ADVERSARIAL_ORIG_IMAGE.size - - for cinput, _ in abstract_ios: - - seed_image = nn_unflatten(cinput[:dims], Settings.ADVERSARIAL_ORIG_IMAGE.shape) - - concrete_io_tuple = None - - onnx_path = Settings.ADVERSARIAL_ONNX_PATH - assert onnx_path is not None - - if self.priv.agen is None: - # initialize - ep = Settings.ADVERSARIAL_EPSILON - im = Settings.ADVERSARIAL_ORIG_IMAGE - l = Settings.ADVERSARIAL_ORIG_LABEL - - Timers.tic("AgenState init") - self.priv.agen = AgenState(onnx_path, im, l, ep) - Timers.toc("AgenState init") - - a = self.priv.agen.try_seeded(seed_image) - - if a is not None: - aimage, ep = a - - if Settings.PRINT_OUTPUT: - print(f"try_seeded_adversarial found violation image with ep={ep}") - else: - aimage = None - - if aimage is not None: - flat_image = nn_flatten(aimage) - - output = self.shared.network.execute(flat_image) - flat_output = np.ravel(output) - - olabel = np.argmax(output) - confirmed = olabel != Settings.ADVERSARIAL_ORIG_LABEL - - if Settings.PRINT_OUTPUT: - print(f"Original label: {Settings.ADVERSARIAL_ORIG_LABEL}, output argmax: {olabel}") - print(f"counterexample was confirmed: {confirmed}") - - if confirmed: - concrete_io_tuple = (flat_image, flat_output) - break - - Timers.toc('try_seeded_adversarial') - - return concrete_io_tuple - def consider_overapprox(self): '''conditionally run overapprox analysis @@ -269,12 +207,11 @@ def check_cancel_func(): otypes = Settings.OVERAPPROX_TYPES_NEAR_ROOT res = do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func, gen_limit, - try_seeded_adversarial=self.try_seeded_adversarial, overapprox_types=otypes) if res.concrete_io_tuple is not None: if Settings.PRINT_OUTPUT: - print("\nviolation star found adversarial was a confirmed counterexample.") + print("\nviolation star found a confirmed counterexample.") print(f"\nUnsafe Base Branch: {self.priv.ss.branch_str()} (Mode: {Settings.BRANCH_MODE})") self.found_unsafe(res.concrete_io_tuple) From 22724e4073e10917906e1faa8eeaa1e3a6f844bf Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 16:44:59 -0400 Subject: [PATCH 18/55] added examples for image networks --- .gitignore | 1 + README.md | 6 +- examples/cifar2020/README.md | 1 + examples/cifar2020/cifar10_2_255.onnx | Bin 0 -> 8734338 bytes .../cifar10_spec_idx_11_eps_0.00784_n1.vnnlib | 9246 +++++++++++++++++ examples/mnistfc/README.md | 1 + examples/mnistfc/mnist-net_256x2.onnx | Bin 0 -> 1077894 bytes examples/mnistfc/prop_0_0.03.vnnlib | 3165 ++++++ examples/mnistfc/prop_2_0.03.vnnlib | 3165 ++++++ requirements.txt | 8 +- run_tests.sh | 10 + src/nnenum/enumerate.py | 14 +- src/nnenum/nnenum.py | 33 +- src/nnenum/onnx_network.py | 12 - src/nnenum/overapprox.py | 2 +- 15 files changed, 15634 insertions(+), 30 deletions(-) create mode 100644 examples/cifar2020/README.md create mode 100644 examples/cifar2020/cifar10_2_255.onnx create mode 100644 examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib create mode 100644 examples/mnistfc/README.md create mode 100644 examples/mnistfc/mnist-net_256x2.onnx create mode 100644 examples/mnistfc/prop_0_0.03.vnnlib create mode 100644 examples/mnistfc/prop_2_0.03.vnnlib create mode 100755 run_tests.sh diff --git a/.gitignore b/.gitignore index fbe45dd..967ba15 100644 --- a/.gitignore +++ b/.gitignore @@ -15,3 +15,4 @@ __pycache__ .coverage examples/acasxu/out.txt examples/acasxu/results/* +out.txt diff --git a/README.md b/README.md index 533f1be..5cc5ebf 100644 --- a/README.md +++ b/README.md @@ -7,7 +7,11 @@ The tool is written by Stanley Bak ([homepage](http://stanleybak.com), [twitter] The `Dockerfile` shows how to install all the dependencies (mostly python packages) and set up the environment. The tool loads neural networks directly from ONNX files and properties from vnnlib files. For example, try running: -'python3 -m nnenum.nnenum examples/acasxu/data/ACASXU_run2a_3_3_batch_2000.onnx examples/acasxu/data/prop_9.vnnlib' +``` +python3 -m nnenum.nnenum examples/acasxu/data/ACASXU_run2a_3_3_batch_2000.onnx examples/acasxu/data/prop_9.vnnlib +``` + +You can see a few more examples in `run_tests.sh`. ### VNN 2020 Neural Network Verification Competition (VNN-COMP) Version diff --git a/examples/cifar2020/README.md b/examples/cifar2020/README.md new file mode 100644 index 0000000..e0ecd5e --- /dev/null +++ b/examples/cifar2020/README.md @@ -0,0 +1 @@ +from vnncomp 2021 cifar2020 benchmark (using 2020 setttings): https://github.com/stanleybak/vnncomp2021/tree/main/benchmarks/cifar2020 diff --git a/examples/cifar2020/cifar10_2_255.onnx b/examples/cifar2020/cifar10_2_255.onnx new file mode 100644 index 0000000000000000000000000000000000000000..7a8104e03417334a5a577d9db8a9fee0cd592314 GIT binary patch literal 8734338 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zZ9LBC@%(li<&|7{B!2fpgV|`Q1!r>g+H@pe`U)%AmLqoGS8{DXjs3Ig$japk)T7wP#NH-lwl01Z z`+I>L=(8_{+>0t!7}{3c{%E@ zCGdfzjbvT+3TkOYu8bGsjR>$6PW5$Hc|G)Kr-@*S~1ONZN20Tnu#`)|EICy|#t);7?qb#R2QAJ)^PPP`ikj@K^8a^MWs&^E@&6BT$g%kV literal 0 HcmV?d00001 diff --git a/examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib b/examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib new file mode 100644 index 0000000..af6d225 --- /dev/null +++ b/examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib @@ -0,0 +1,9246 @@ +; Spec for sample id 11 and epsilon 0.00784 + +; Definition of input variables +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) +(declare-const X_5 Real) +(declare-const X_6 Real) +(declare-const X_7 Real) +(declare-const X_8 Real) +(declare-const X_9 Real) +(declare-const X_10 Real) +(declare-const X_11 Real) +(declare-const X_12 Real) +(declare-const X_13 Real) +(declare-const X_14 Real) +(declare-const X_15 Real) +(declare-const X_16 Real) +(declare-const X_17 Real) +(declare-const X_18 Real) +(declare-const X_19 Real) +(declare-const X_20 Real) +(declare-const X_21 Real) +(declare-const X_22 Real) +(declare-const X_23 Real) +(declare-const X_24 Real) +(declare-const X_25 Real) +(declare-const X_26 Real) +(declare-const X_27 Real) +(declare-const X_28 Real) +(declare-const X_29 Real) +(declare-const X_30 Real) +(declare-const X_31 Real) +(declare-const X_32 Real) +(declare-const X_33 Real) +(declare-const X_34 Real) +(declare-const X_35 Real) +(declare-const X_36 Real) +(declare-const X_37 Real) +(declare-const X_38 Real) +(declare-const X_39 Real) +(declare-const X_40 Real) +(declare-const X_41 Real) +(declare-const X_42 Real) +(declare-const X_43 Real) +(declare-const X_44 Real) +(declare-const X_45 Real) +(declare-const X_46 Real) +(declare-const X_47 Real) +(declare-const X_48 Real) +(declare-const X_49 Real) +(declare-const X_50 Real) +(declare-const X_51 Real) +(declare-const X_52 Real) +(declare-const X_53 Real) +(declare-const X_54 Real) +(declare-const X_55 Real) +(declare-const X_56 Real) +(declare-const X_57 Real) +(declare-const X_58 Real) +(declare-const X_59 Real) +(declare-const X_60 Real) +(declare-const X_61 Real) +(declare-const X_62 Real) +(declare-const X_63 Real) +(declare-const X_64 Real) +(declare-const X_65 Real) +(declare-const X_66 Real) +(declare-const X_67 Real) +(declare-const X_68 Real) +(declare-const X_69 Real) +(declare-const X_70 Real) +(declare-const X_71 Real) +(declare-const X_72 Real) +(declare-const X_73 Real) +(declare-const X_74 Real) +(declare-const X_75 Real) +(declare-const X_76 Real) +(declare-const X_77 Real) +(declare-const X_78 Real) +(declare-const X_79 Real) +(declare-const X_80 Real) +(declare-const X_81 Real) +(declare-const X_82 Real) +(declare-const X_83 Real) +(declare-const X_84 Real) +(declare-const X_85 Real) +(declare-const X_86 Real) +(declare-const X_87 Real) +(declare-const X_88 Real) +(declare-const X_89 Real) +(declare-const X_90 Real) +(declare-const X_91 Real) +(declare-const X_92 Real) +(declare-const X_93 Real) +(declare-const X_94 Real) +(declare-const X_95 Real) +(declare-const X_96 Real) +(declare-const X_97 Real) +(declare-const X_98 Real) +(declare-const X_99 Real) +(declare-const X_100 Real) +(declare-const X_101 Real) +(declare-const X_102 Real) +(declare-const X_103 Real) +(declare-const X_104 Real) +(declare-const X_105 Real) +(declare-const X_106 Real) +(declare-const X_107 Real) +(declare-const X_108 Real) +(declare-const X_109 Real) +(declare-const X_110 Real) +(declare-const X_111 Real) +(declare-const X_112 Real) +(declare-const X_113 Real) +(declare-const X_114 Real) +(declare-const X_115 Real) +(declare-const X_116 Real) +(declare-const X_117 Real) +(declare-const X_118 Real) +(declare-const X_119 Real) +(declare-const X_120 Real) +(declare-const X_121 Real) +(declare-const X_122 Real) +(declare-const X_123 Real) +(declare-const X_124 Real) +(declare-const X_125 Real) +(declare-const X_126 Real) +(declare-const X_127 Real) +(declare-const X_128 Real) +(declare-const X_129 Real) +(declare-const X_130 Real) +(declare-const X_131 Real) +(declare-const X_132 Real) +(declare-const X_133 Real) +(declare-const X_134 Real) +(declare-const X_135 Real) +(declare-const X_136 Real) +(declare-const X_137 Real) +(declare-const X_138 Real) +(declare-const X_139 Real) +(declare-const X_140 Real) +(declare-const X_141 Real) +(declare-const X_142 Real) +(declare-const X_143 Real) +(declare-const X_144 Real) +(declare-const X_145 Real) +(declare-const X_146 Real) +(declare-const X_147 Real) +(declare-const X_148 Real) +(declare-const X_149 Real) +(declare-const X_150 Real) +(declare-const X_151 Real) +(declare-const X_152 Real) +(declare-const X_153 Real) +(declare-const X_154 Real) +(declare-const X_155 Real) +(declare-const X_156 Real) +(declare-const X_157 Real) +(declare-const X_158 Real) +(declare-const X_159 Real) +(declare-const 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X_799 Real) +(declare-const X_800 Real) +(declare-const X_801 Real) +(declare-const X_802 Real) +(declare-const X_803 Real) +(declare-const X_804 Real) +(declare-const X_805 Real) +(declare-const X_806 Real) +(declare-const X_807 Real) +(declare-const X_808 Real) +(declare-const X_809 Real) +(declare-const X_810 Real) +(declare-const X_811 Real) +(declare-const X_812 Real) +(declare-const X_813 Real) +(declare-const X_814 Real) +(declare-const X_815 Real) +(declare-const X_816 Real) +(declare-const X_817 Real) +(declare-const X_818 Real) +(declare-const X_819 Real) +(declare-const X_820 Real) +(declare-const X_821 Real) +(declare-const X_822 Real) +(declare-const X_823 Real) +(declare-const X_824 Real) +(declare-const X_825 Real) +(declare-const X_826 Real) +(declare-const X_827 Real) +(declare-const X_828 Real) +(declare-const X_829 Real) +(declare-const X_830 Real) +(declare-const X_831 Real) +(declare-const X_832 Real) +(declare-const X_833 Real) +(declare-const X_834 Real) 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X_870 Real) +(declare-const X_871 Real) +(declare-const X_872 Real) +(declare-const X_873 Real) +(declare-const X_874 Real) +(declare-const X_875 Real) +(declare-const X_876 Real) +(declare-const X_877 Real) +(declare-const X_878 Real) +(declare-const X_879 Real) +(declare-const X_880 Real) +(declare-const X_881 Real) +(declare-const X_882 Real) +(declare-const X_883 Real) +(declare-const X_884 Real) +(declare-const X_885 Real) +(declare-const X_886 Real) +(declare-const X_887 Real) +(declare-const X_888 Real) +(declare-const X_889 Real) +(declare-const X_890 Real) +(declare-const X_891 Real) +(declare-const X_892 Real) +(declare-const X_893 Real) +(declare-const X_894 Real) +(declare-const X_895 Real) +(declare-const X_896 Real) +(declare-const X_897 Real) +(declare-const X_898 Real) +(declare-const X_899 Real) +(declare-const X_900 Real) +(declare-const X_901 Real) +(declare-const X_902 Real) +(declare-const X_903 Real) +(declare-const X_904 Real) +(declare-const X_905 Real) +(declare-const X_906 Real) +(declare-const X_907 Real) +(declare-const X_908 Real) +(declare-const X_909 Real) +(declare-const X_910 Real) +(declare-const X_911 Real) +(declare-const X_912 Real) +(declare-const X_913 Real) +(declare-const X_914 Real) +(declare-const X_915 Real) +(declare-const X_916 Real) +(declare-const X_917 Real) +(declare-const X_918 Real) +(declare-const X_919 Real) +(declare-const X_920 Real) +(declare-const X_921 Real) +(declare-const X_922 Real) +(declare-const X_923 Real) +(declare-const X_924 Real) +(declare-const X_925 Real) +(declare-const X_926 Real) +(declare-const X_927 Real) +(declare-const X_928 Real) +(declare-const X_929 Real) +(declare-const X_930 Real) +(declare-const X_931 Real) +(declare-const X_932 Real) +(declare-const X_933 Real) +(declare-const X_934 Real) +(declare-const X_935 Real) +(declare-const X_936 Real) +(declare-const X_937 Real) +(declare-const X_938 Real) +(declare-const X_939 Real) +(declare-const X_940 Real) +(declare-const X_941 Real) +(declare-const X_942 Real) +(declare-const X_943 Real) +(declare-const X_944 Real) +(declare-const X_945 Real) +(declare-const X_946 Real) +(declare-const X_947 Real) +(declare-const X_948 Real) +(declare-const X_949 Real) +(declare-const X_950 Real) +(declare-const X_951 Real) +(declare-const X_952 Real) +(declare-const X_953 Real) +(declare-const X_954 Real) +(declare-const X_955 Real) +(declare-const X_956 Real) +(declare-const X_957 Real) +(declare-const X_958 Real) +(declare-const X_959 Real) +(declare-const X_960 Real) +(declare-const X_961 Real) +(declare-const X_962 Real) +(declare-const X_963 Real) +(declare-const X_964 Real) +(declare-const X_965 Real) +(declare-const X_966 Real) +(declare-const X_967 Real) +(declare-const X_968 Real) +(declare-const X_969 Real) +(declare-const X_970 Real) +(declare-const X_971 Real) +(declare-const X_972 Real) +(declare-const X_973 Real) +(declare-const X_974 Real) +(declare-const X_975 Real) +(declare-const X_976 Real) +(declare-const X_977 Real) +(declare-const X_978 Real) +(declare-const X_979 Real) +(declare-const X_980 Real) +(declare-const X_981 Real) +(declare-const X_982 Real) +(declare-const X_983 Real) +(declare-const X_984 Real) +(declare-const X_985 Real) +(declare-const X_986 Real) +(declare-const X_987 Real) +(declare-const X_988 Real) +(declare-const X_989 Real) +(declare-const X_990 Real) +(declare-const X_991 Real) +(declare-const X_992 Real) +(declare-const X_993 Real) +(declare-const X_994 Real) +(declare-const X_995 Real) +(declare-const X_996 Real) +(declare-const X_997 Real) +(declare-const X_998 Real) +(declare-const X_999 Real) +(declare-const X_1000 Real) +(declare-const X_1001 Real) +(declare-const X_1002 Real) +(declare-const X_1003 Real) +(declare-const X_1004 Real) +(declare-const X_1005 Real) +(declare-const X_1006 Real) +(declare-const X_1007 Real) +(declare-const X_1008 Real) +(declare-const X_1009 Real) +(declare-const X_1010 Real) +(declare-const X_1011 Real) +(declare-const X_1012 Real) +(declare-const X_1013 Real) +(declare-const X_1014 Real) +(declare-const X_1015 Real) +(declare-const X_1016 Real) +(declare-const X_1017 Real) +(declare-const X_1018 Real) +(declare-const X_1019 Real) +(declare-const X_1020 Real) +(declare-const X_1021 Real) +(declare-const X_1022 Real) +(declare-const X_1023 Real) +(declare-const X_1024 Real) +(declare-const X_1025 Real) +(declare-const X_1026 Real) +(declare-const X_1027 Real) +(declare-const X_1028 Real) +(declare-const X_1029 Real) +(declare-const X_1030 Real) +(declare-const X_1031 Real) +(declare-const X_1032 Real) +(declare-const X_1033 Real) +(declare-const X_1034 Real) +(declare-const X_1035 Real) +(declare-const X_1036 Real) +(declare-const X_1037 Real) +(declare-const X_1038 Real) +(declare-const X_1039 Real) +(declare-const X_1040 Real) +(declare-const X_1041 Real) +(declare-const X_1042 Real) +(declare-const X_1043 Real) +(declare-const X_1044 Real) +(declare-const X_1045 Real) 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+(declare-const X_1080 Real) +(declare-const X_1081 Real) +(declare-const X_1082 Real) +(declare-const X_1083 Real) +(declare-const X_1084 Real) +(declare-const X_1085 Real) +(declare-const X_1086 Real) +(declare-const X_1087 Real) +(declare-const X_1088 Real) +(declare-const X_1089 Real) +(declare-const X_1090 Real) +(declare-const X_1091 Real) +(declare-const X_1092 Real) +(declare-const X_1093 Real) +(declare-const X_1094 Real) +(declare-const X_1095 Real) +(declare-const X_1096 Real) +(declare-const X_1097 Real) +(declare-const X_1098 Real) +(declare-const X_1099 Real) +(declare-const X_1100 Real) +(declare-const X_1101 Real) +(declare-const X_1102 Real) +(declare-const X_1103 Real) +(declare-const X_1104 Real) +(declare-const X_1105 Real) +(declare-const X_1106 Real) +(declare-const X_1107 Real) +(declare-const X_1108 Real) +(declare-const X_1109 Real) +(declare-const X_1110 Real) +(declare-const X_1111 Real) +(declare-const X_1112 Real) +(declare-const X_1113 Real) 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+(declare-const X_1454 Real) +(declare-const X_1455 Real) +(declare-const X_1456 Real) +(declare-const X_1457 Real) +(declare-const X_1458 Real) +(declare-const X_1459 Real) +(declare-const X_1460 Real) +(declare-const X_1461 Real) +(declare-const X_1462 Real) +(declare-const X_1463 Real) +(declare-const X_1464 Real) +(declare-const X_1465 Real) +(declare-const X_1466 Real) +(declare-const X_1467 Real) +(declare-const X_1468 Real) +(declare-const X_1469 Real) +(declare-const X_1470 Real) +(declare-const X_1471 Real) +(declare-const X_1472 Real) +(declare-const X_1473 Real) +(declare-const X_1474 Real) +(declare-const X_1475 Real) +(declare-const X_1476 Real) +(declare-const X_1477 Real) +(declare-const X_1478 Real) +(declare-const X_1479 Real) +(declare-const X_1480 Real) +(declare-const X_1481 Real) +(declare-const X_1482 Real) +(declare-const X_1483 Real) +(declare-const X_1484 Real) +(declare-const X_1485 Real) +(declare-const X_1486 Real) +(declare-const X_1487 Real) +(declare-const X_1488 Real) +(declare-const X_1489 Real) +(declare-const X_1490 Real) +(declare-const X_1491 Real) +(declare-const X_1492 Real) +(declare-const X_1493 Real) +(declare-const X_1494 Real) +(declare-const X_1495 Real) +(declare-const X_1496 Real) +(declare-const X_1497 Real) +(declare-const X_1498 Real) +(declare-const X_1499 Real) +(declare-const X_1500 Real) +(declare-const X_1501 Real) +(declare-const X_1502 Real) +(declare-const X_1503 Real) +(declare-const X_1504 Real) +(declare-const X_1505 Real) +(declare-const X_1506 Real) +(declare-const X_1507 Real) +(declare-const X_1508 Real) +(declare-const X_1509 Real) +(declare-const X_1510 Real) +(declare-const X_1511 Real) +(declare-const X_1512 Real) +(declare-const X_1513 Real) +(declare-const X_1514 Real) +(declare-const X_1515 Real) +(declare-const X_1516 Real) +(declare-const X_1517 Real) +(declare-const X_1518 Real) +(declare-const X_1519 Real) +(declare-const X_1520 Real) +(declare-const X_1521 Real) +(declare-const X_1522 Real) +(declare-const X_1523 Real) +(declare-const X_1524 Real) +(declare-const X_1525 Real) +(declare-const X_1526 Real) +(declare-const X_1527 Real) +(declare-const X_1528 Real) +(declare-const X_1529 Real) +(declare-const X_1530 Real) +(declare-const X_1531 Real) +(declare-const X_1532 Real) +(declare-const X_1533 Real) +(declare-const X_1534 Real) +(declare-const X_1535 Real) +(declare-const X_1536 Real) +(declare-const X_1537 Real) +(declare-const X_1538 Real) +(declare-const X_1539 Real) +(declare-const X_1540 Real) +(declare-const X_1541 Real) +(declare-const X_1542 Real) +(declare-const X_1543 Real) +(declare-const X_1544 Real) +(declare-const X_1545 Real) +(declare-const X_1546 Real) +(declare-const X_1547 Real) +(declare-const X_1548 Real) +(declare-const X_1549 Real) +(declare-const X_1550 Real) +(declare-const X_1551 Real) +(declare-const X_1552 Real) +(declare-const X_1553 Real) +(declare-const X_1554 Real) +(declare-const X_1555 Real) +(declare-const X_1556 Real) +(declare-const X_1557 Real) +(declare-const X_1558 Real) +(declare-const X_1559 Real) +(declare-const X_1560 Real) +(declare-const X_1561 Real) +(declare-const X_1562 Real) +(declare-const X_1563 Real) +(declare-const X_1564 Real) +(declare-const X_1565 Real) +(declare-const X_1566 Real) +(declare-const X_1567 Real) +(declare-const X_1568 Real) +(declare-const X_1569 Real) +(declare-const X_1570 Real) +(declare-const X_1571 Real) +(declare-const X_1572 Real) +(declare-const X_1573 Real) +(declare-const X_1574 Real) +(declare-const X_1575 Real) +(declare-const X_1576 Real) +(declare-const X_1577 Real) +(declare-const X_1578 Real) +(declare-const X_1579 Real) +(declare-const X_1580 Real) +(declare-const X_1581 Real) +(declare-const X_1582 Real) +(declare-const X_1583 Real) +(declare-const X_1584 Real) +(declare-const X_1585 Real) +(declare-const X_1586 Real) +(declare-const X_1587 Real) +(declare-const X_1588 Real) +(declare-const X_1589 Real) +(declare-const X_1590 Real) +(declare-const X_1591 Real) +(declare-const X_1592 Real) +(declare-const X_1593 Real) +(declare-const X_1594 Real) +(declare-const X_1595 Real) +(declare-const X_1596 Real) +(declare-const X_1597 Real) +(declare-const X_1598 Real) +(declare-const X_1599 Real) +(declare-const X_1600 Real) +(declare-const X_1601 Real) +(declare-const X_1602 Real) +(declare-const X_1603 Real) +(declare-const X_1604 Real) +(declare-const X_1605 Real) +(declare-const X_1606 Real) +(declare-const X_1607 Real) +(declare-const X_1608 Real) +(declare-const X_1609 Real) +(declare-const X_1610 Real) +(declare-const X_1611 Real) +(declare-const X_1612 Real) +(declare-const X_1613 Real) +(declare-const X_1614 Real) +(declare-const X_1615 Real) +(declare-const X_1616 Real) +(declare-const X_1617 Real) +(declare-const X_1618 Real) +(declare-const X_1619 Real) +(declare-const X_1620 Real) +(declare-const X_1621 Real) +(declare-const X_1622 Real) +(declare-const X_1623 Real) +(declare-const X_1624 Real) +(declare-const X_1625 Real) +(declare-const X_1626 Real) +(declare-const X_1627 Real) +(declare-const X_1628 Real) +(declare-const X_1629 Real) +(declare-const X_1630 Real) +(declare-const X_1631 Real) +(declare-const X_1632 Real) +(declare-const X_1633 Real) +(declare-const X_1634 Real) +(declare-const X_1635 Real) +(declare-const X_1636 Real) +(declare-const X_1637 Real) +(declare-const X_1638 Real) +(declare-const X_1639 Real) +(declare-const X_1640 Real) +(declare-const X_1641 Real) +(declare-const X_1642 Real) +(declare-const X_1643 Real) +(declare-const X_1644 Real) +(declare-const X_1645 Real) +(declare-const X_1646 Real) +(declare-const X_1647 Real) +(declare-const X_1648 Real) +(declare-const X_1649 Real) +(declare-const X_1650 Real) +(declare-const X_1651 Real) +(declare-const X_1652 Real) +(declare-const X_1653 Real) +(declare-const X_1654 Real) +(declare-const X_1655 Real) +(declare-const X_1656 Real) +(declare-const X_1657 Real) +(declare-const X_1658 Real) +(declare-const X_1659 Real) +(declare-const X_1660 Real) +(declare-const X_1661 Real) +(declare-const X_1662 Real) +(declare-const X_1663 Real) +(declare-const X_1664 Real) +(declare-const X_1665 Real) +(declare-const X_1666 Real) +(declare-const X_1667 Real) +(declare-const X_1668 Real) +(declare-const X_1669 Real) +(declare-const X_1670 Real) +(declare-const X_1671 Real) +(declare-const X_1672 Real) +(declare-const X_1673 Real) +(declare-const X_1674 Real) +(declare-const X_1675 Real) +(declare-const X_1676 Real) +(declare-const X_1677 Real) +(declare-const X_1678 Real) +(declare-const X_1679 Real) +(declare-const X_1680 Real) +(declare-const X_1681 Real) +(declare-const X_1682 Real) +(declare-const X_1683 Real) +(declare-const X_1684 Real) +(declare-const X_1685 Real) +(declare-const X_1686 Real) +(declare-const X_1687 Real) +(declare-const X_1688 Real) +(declare-const X_1689 Real) +(declare-const X_1690 Real) +(declare-const X_1691 Real) +(declare-const X_1692 Real) +(declare-const X_1693 Real) +(declare-const X_1694 Real) +(declare-const X_1695 Real) +(declare-const X_1696 Real) +(declare-const X_1697 Real) +(declare-const X_1698 Real) +(declare-const X_1699 Real) +(declare-const X_1700 Real) +(declare-const X_1701 Real) +(declare-const X_1702 Real) +(declare-const X_1703 Real) +(declare-const X_1704 Real) +(declare-const X_1705 Real) +(declare-const X_1706 Real) +(declare-const X_1707 Real) +(declare-const X_1708 Real) +(declare-const X_1709 Real) +(declare-const X_1710 Real) +(declare-const X_1711 Real) +(declare-const X_1712 Real) +(declare-const X_1713 Real) +(declare-const X_1714 Real) +(declare-const X_1715 Real) +(declare-const X_1716 Real) +(declare-const X_1717 Real) +(declare-const X_1718 Real) +(declare-const X_1719 Real) +(declare-const X_1720 Real) +(declare-const X_1721 Real) +(declare-const X_1722 Real) +(declare-const X_1723 Real) +(declare-const X_1724 Real) +(declare-const X_1725 Real) +(declare-const X_1726 Real) +(declare-const X_1727 Real) +(declare-const X_1728 Real) +(declare-const X_1729 Real) +(declare-const X_1730 Real) +(declare-const X_1731 Real) +(declare-const X_1732 Real) +(declare-const X_1733 Real) +(declare-const X_1734 Real) +(declare-const X_1735 Real) +(declare-const X_1736 Real) +(declare-const X_1737 Real) +(declare-const X_1738 Real) +(declare-const X_1739 Real) +(declare-const X_1740 Real) +(declare-const X_1741 Real) +(declare-const X_1742 Real) +(declare-const X_1743 Real) +(declare-const X_1744 Real) +(declare-const X_1745 Real) +(declare-const X_1746 Real) +(declare-const X_1747 Real) +(declare-const X_1748 Real) +(declare-const X_1749 Real) +(declare-const X_1750 Real) +(declare-const X_1751 Real) +(declare-const X_1752 Real) +(declare-const X_1753 Real) +(declare-const X_1754 Real) +(declare-const X_1755 Real) +(declare-const X_1756 Real) +(declare-const X_1757 Real) +(declare-const X_1758 Real) +(declare-const X_1759 Real) +(declare-const X_1760 Real) +(declare-const X_1761 Real) +(declare-const X_1762 Real) +(declare-const X_1763 Real) +(declare-const X_1764 Real) +(declare-const X_1765 Real) +(declare-const X_1766 Real) +(declare-const X_1767 Real) +(declare-const X_1768 Real) +(declare-const X_1769 Real) +(declare-const X_1770 Real) +(declare-const X_1771 Real) +(declare-const X_1772 Real) +(declare-const X_1773 Real) +(declare-const X_1774 Real) +(declare-const X_1775 Real) +(declare-const X_1776 Real) +(declare-const X_1777 Real) +(declare-const X_1778 Real) +(declare-const X_1779 Real) +(declare-const X_1780 Real) +(declare-const X_1781 Real) +(declare-const X_1782 Real) +(declare-const X_1783 Real) +(declare-const X_1784 Real) +(declare-const X_1785 Real) +(declare-const X_1786 Real) +(declare-const X_1787 Real) +(declare-const X_1788 Real) +(declare-const X_1789 Real) +(declare-const X_1790 Real) +(declare-const X_1791 Real) +(declare-const X_1792 Real) +(declare-const X_1793 Real) +(declare-const X_1794 Real) +(declare-const X_1795 Real) +(declare-const X_1796 Real) +(declare-const X_1797 Real) +(declare-const X_1798 Real) +(declare-const X_1799 Real) +(declare-const X_1800 Real) +(declare-const X_1801 Real) +(declare-const X_1802 Real) +(declare-const X_1803 Real) +(declare-const X_1804 Real) +(declare-const X_1805 Real) +(declare-const X_1806 Real) +(declare-const X_1807 Real) +(declare-const X_1808 Real) +(declare-const X_1809 Real) +(declare-const X_1810 Real) +(declare-const X_1811 Real) +(declare-const X_1812 Real) +(declare-const X_1813 Real) +(declare-const X_1814 Real) +(declare-const X_1815 Real) +(declare-const X_1816 Real) +(declare-const X_1817 Real) +(declare-const X_1818 Real) +(declare-const X_1819 Real) +(declare-const X_1820 Real) +(declare-const X_1821 Real) +(declare-const X_1822 Real) +(declare-const X_1823 Real) +(declare-const X_1824 Real) +(declare-const X_1825 Real) +(declare-const X_1826 Real) +(declare-const X_1827 Real) +(declare-const X_1828 Real) +(declare-const X_1829 Real) +(declare-const X_1830 Real) +(declare-const X_1831 Real) +(declare-const X_1832 Real) +(declare-const X_1833 Real) +(declare-const X_1834 Real) +(declare-const X_1835 Real) +(declare-const X_1836 Real) +(declare-const X_1837 Real) +(declare-const X_1838 Real) +(declare-const X_1839 Real) +(declare-const X_1840 Real) +(declare-const X_1841 Real) +(declare-const X_1842 Real) +(declare-const X_1843 Real) +(declare-const X_1844 Real) +(declare-const X_1845 Real) +(declare-const X_1846 Real) +(declare-const X_1847 Real) +(declare-const X_1848 Real) +(declare-const X_1849 Real) +(declare-const X_1850 Real) +(declare-const X_1851 Real) +(declare-const X_1852 Real) +(declare-const X_1853 Real) +(declare-const X_1854 Real) +(declare-const X_1855 Real) +(declare-const X_1856 Real) +(declare-const X_1857 Real) +(declare-const X_1858 Real) +(declare-const X_1859 Real) +(declare-const X_1860 Real) +(declare-const X_1861 Real) +(declare-const X_1862 Real) +(declare-const X_1863 Real) +(declare-const X_1864 Real) +(declare-const X_1865 Real) +(declare-const X_1866 Real) +(declare-const X_1867 Real) +(declare-const X_1868 Real) +(declare-const X_1869 Real) +(declare-const X_1870 Real) +(declare-const X_1871 Real) +(declare-const X_1872 Real) +(declare-const X_1873 Real) +(declare-const X_1874 Real) +(declare-const X_1875 Real) +(declare-const X_1876 Real) +(declare-const X_1877 Real) +(declare-const X_1878 Real) +(declare-const X_1879 Real) +(declare-const X_1880 Real) +(declare-const X_1881 Real) +(declare-const X_1882 Real) +(declare-const X_1883 Real) +(declare-const X_1884 Real) +(declare-const X_1885 Real) +(declare-const X_1886 Real) +(declare-const X_1887 Real) +(declare-const X_1888 Real) +(declare-const X_1889 Real) +(declare-const X_1890 Real) +(declare-const X_1891 Real) +(declare-const X_1892 Real) +(declare-const X_1893 Real) +(declare-const X_1894 Real) +(declare-const X_1895 Real) +(declare-const X_1896 Real) +(declare-const X_1897 Real) +(declare-const X_1898 Real) +(declare-const X_1899 Real) +(declare-const X_1900 Real) +(declare-const X_1901 Real) +(declare-const X_1902 Real) +(declare-const X_1903 Real) +(declare-const X_1904 Real) +(declare-const X_1905 Real) +(declare-const X_1906 Real) +(declare-const X_1907 Real) +(declare-const X_1908 Real) +(declare-const X_1909 Real) +(declare-const X_1910 Real) +(declare-const X_1911 Real) +(declare-const X_1912 Real) +(declare-const X_1913 Real) +(declare-const X_1914 Real) +(declare-const X_1915 Real) +(declare-const X_1916 Real) +(declare-const X_1917 Real) +(declare-const X_1918 Real) +(declare-const X_1919 Real) +(declare-const X_1920 Real) +(declare-const X_1921 Real) +(declare-const X_1922 Real) +(declare-const X_1923 Real) +(declare-const X_1924 Real) +(declare-const X_1925 Real) +(declare-const X_1926 Real) +(declare-const X_1927 Real) +(declare-const X_1928 Real) +(declare-const X_1929 Real) +(declare-const X_1930 Real) +(declare-const X_1931 Real) +(declare-const X_1932 Real) +(declare-const X_1933 Real) +(declare-const X_1934 Real) +(declare-const X_1935 Real) +(declare-const X_1936 Real) +(declare-const X_1937 Real) +(declare-const X_1938 Real) +(declare-const X_1939 Real) +(declare-const X_1940 Real) +(declare-const X_1941 Real) +(declare-const X_1942 Real) +(declare-const X_1943 Real) +(declare-const X_1944 Real) +(declare-const X_1945 Real) +(declare-const X_1946 Real) +(declare-const X_1947 Real) +(declare-const X_1948 Real) +(declare-const X_1949 Real) +(declare-const X_1950 Real) +(declare-const X_1951 Real) +(declare-const X_1952 Real) +(declare-const X_1953 Real) +(declare-const X_1954 Real) +(declare-const X_1955 Real) +(declare-const X_1956 Real) +(declare-const X_1957 Real) +(declare-const X_1958 Real) +(declare-const X_1959 Real) +(declare-const X_1960 Real) +(declare-const X_1961 Real) +(declare-const X_1962 Real) +(declare-const X_1963 Real) +(declare-const X_1964 Real) +(declare-const X_1965 Real) +(declare-const X_1966 Real) +(declare-const X_1967 Real) +(declare-const X_1968 Real) +(declare-const X_1969 Real) +(declare-const X_1970 Real) +(declare-const X_1971 Real) +(declare-const X_1972 Real) +(declare-const X_1973 Real) +(declare-const X_1974 Real) +(declare-const X_1975 Real) +(declare-const X_1976 Real) +(declare-const X_1977 Real) +(declare-const X_1978 Real) +(declare-const X_1979 Real) +(declare-const X_1980 Real) +(declare-const X_1981 Real) +(declare-const X_1982 Real) +(declare-const X_1983 Real) +(declare-const X_1984 Real) +(declare-const X_1985 Real) +(declare-const X_1986 Real) +(declare-const X_1987 Real) +(declare-const X_1988 Real) +(declare-const X_1989 Real) +(declare-const X_1990 Real) +(declare-const X_1991 Real) +(declare-const X_1992 Real) +(declare-const X_1993 Real) +(declare-const X_1994 Real) +(declare-const X_1995 Real) +(declare-const X_1996 Real) +(declare-const X_1997 Real) +(declare-const X_1998 Real) +(declare-const X_1999 Real) +(declare-const X_2000 Real) +(declare-const X_2001 Real) +(declare-const X_2002 Real) +(declare-const X_2003 Real) +(declare-const X_2004 Real) +(declare-const X_2005 Real) +(declare-const X_2006 Real) +(declare-const X_2007 Real) +(declare-const X_2008 Real) +(declare-const X_2009 Real) +(declare-const X_2010 Real) +(declare-const X_2011 Real) +(declare-const X_2012 Real) +(declare-const X_2013 Real) +(declare-const X_2014 Real) +(declare-const X_2015 Real) +(declare-const X_2016 Real) +(declare-const X_2017 Real) +(declare-const X_2018 Real) +(declare-const X_2019 Real) +(declare-const X_2020 Real) +(declare-const X_2021 Real) +(declare-const X_2022 Real) +(declare-const X_2023 Real) +(declare-const X_2024 Real) +(declare-const X_2025 Real) +(declare-const X_2026 Real) +(declare-const X_2027 Real) +(declare-const X_2028 Real) +(declare-const X_2029 Real) +(declare-const X_2030 Real) +(declare-const X_2031 Real) +(declare-const X_2032 Real) +(declare-const X_2033 Real) +(declare-const X_2034 Real) +(declare-const X_2035 Real) +(declare-const X_2036 Real) +(declare-const X_2037 Real) +(declare-const X_2038 Real) +(declare-const X_2039 Real) +(declare-const X_2040 Real) +(declare-const X_2041 Real) +(declare-const X_2042 Real) +(declare-const X_2043 Real) +(declare-const X_2044 Real) +(declare-const X_2045 Real) +(declare-const X_2046 Real) +(declare-const X_2047 Real) +(declare-const X_2048 Real) +(declare-const X_2049 Real) +(declare-const X_2050 Real) +(declare-const X_2051 Real) +(declare-const X_2052 Real) +(declare-const X_2053 Real) +(declare-const X_2054 Real) +(declare-const X_2055 Real) +(declare-const X_2056 Real) +(declare-const X_2057 Real) +(declare-const X_2058 Real) +(declare-const X_2059 Real) +(declare-const X_2060 Real) +(declare-const X_2061 Real) +(declare-const X_2062 Real) +(declare-const X_2063 Real) +(declare-const X_2064 Real) +(declare-const X_2065 Real) +(declare-const X_2066 Real) +(declare-const X_2067 Real) +(declare-const X_2068 Real) +(declare-const X_2069 Real) +(declare-const X_2070 Real) +(declare-const X_2071 Real) +(declare-const X_2072 Real) +(declare-const X_2073 Real) +(declare-const X_2074 Real) +(declare-const X_2075 Real) +(declare-const X_2076 Real) +(declare-const X_2077 Real) +(declare-const X_2078 Real) +(declare-const X_2079 Real) +(declare-const X_2080 Real) +(declare-const X_2081 Real) +(declare-const X_2082 Real) +(declare-const X_2083 Real) +(declare-const X_2084 Real) +(declare-const X_2085 Real) +(declare-const X_2086 Real) +(declare-const X_2087 Real) +(declare-const X_2088 Real) +(declare-const X_2089 Real) +(declare-const X_2090 Real) +(declare-const X_2091 Real) +(declare-const X_2092 Real) +(declare-const X_2093 Real) +(declare-const X_2094 Real) +(declare-const X_2095 Real) +(declare-const X_2096 Real) +(declare-const X_2097 Real) +(declare-const X_2098 Real) +(declare-const X_2099 Real) +(declare-const X_2100 Real) +(declare-const X_2101 Real) +(declare-const X_2102 Real) +(declare-const X_2103 Real) +(declare-const X_2104 Real) +(declare-const X_2105 Real) +(declare-const X_2106 Real) +(declare-const X_2107 Real) +(declare-const X_2108 Real) +(declare-const X_2109 Real) +(declare-const X_2110 Real) +(declare-const X_2111 Real) +(declare-const X_2112 Real) +(declare-const X_2113 Real) +(declare-const X_2114 Real) +(declare-const X_2115 Real) +(declare-const X_2116 Real) +(declare-const X_2117 Real) +(declare-const X_2118 Real) +(declare-const X_2119 Real) +(declare-const X_2120 Real) +(declare-const X_2121 Real) +(declare-const X_2122 Real) +(declare-const X_2123 Real) +(declare-const X_2124 Real) +(declare-const X_2125 Real) +(declare-const X_2126 Real) +(declare-const X_2127 Real) +(declare-const X_2128 Real) +(declare-const X_2129 Real) +(declare-const X_2130 Real) +(declare-const X_2131 Real) +(declare-const X_2132 Real) +(declare-const X_2133 Real) +(declare-const X_2134 Real) +(declare-const X_2135 Real) +(declare-const X_2136 Real) +(declare-const X_2137 Real) +(declare-const X_2138 Real) +(declare-const X_2139 Real) +(declare-const X_2140 Real) +(declare-const X_2141 Real) +(declare-const X_2142 Real) +(declare-const X_2143 Real) +(declare-const X_2144 Real) +(declare-const X_2145 Real) +(declare-const X_2146 Real) +(declare-const X_2147 Real) +(declare-const X_2148 Real) +(declare-const X_2149 Real) +(declare-const X_2150 Real) +(declare-const X_2151 Real) +(declare-const X_2152 Real) +(declare-const X_2153 Real) +(declare-const X_2154 Real) +(declare-const X_2155 Real) +(declare-const X_2156 Real) +(declare-const X_2157 Real) +(declare-const X_2158 Real) +(declare-const X_2159 Real) +(declare-const X_2160 Real) +(declare-const X_2161 Real) +(declare-const X_2162 Real) +(declare-const X_2163 Real) +(declare-const X_2164 Real) +(declare-const X_2165 Real) +(declare-const X_2166 Real) +(declare-const X_2167 Real) +(declare-const X_2168 Real) +(declare-const X_2169 Real) +(declare-const X_2170 Real) +(declare-const X_2171 Real) +(declare-const X_2172 Real) +(declare-const X_2173 Real) +(declare-const X_2174 Real) +(declare-const X_2175 Real) +(declare-const X_2176 Real) +(declare-const X_2177 Real) +(declare-const X_2178 Real) +(declare-const X_2179 Real) +(declare-const X_2180 Real) +(declare-const X_2181 Real) +(declare-const X_2182 Real) +(declare-const X_2183 Real) +(declare-const X_2184 Real) +(declare-const X_2185 Real) +(declare-const X_2186 Real) +(declare-const X_2187 Real) +(declare-const X_2188 Real) +(declare-const X_2189 Real) +(declare-const X_2190 Real) +(declare-const X_2191 Real) +(declare-const X_2192 Real) +(declare-const X_2193 Real) +(declare-const X_2194 Real) +(declare-const X_2195 Real) +(declare-const X_2196 Real) +(declare-const X_2197 Real) +(declare-const X_2198 Real) +(declare-const X_2199 Real) +(declare-const X_2200 Real) +(declare-const X_2201 Real) 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+(declare-const X_2780 Real) +(declare-const X_2781 Real) +(declare-const X_2782 Real) +(declare-const X_2783 Real) +(declare-const X_2784 Real) +(declare-const X_2785 Real) +(declare-const X_2786 Real) +(declare-const X_2787 Real) +(declare-const X_2788 Real) +(declare-const X_2789 Real) +(declare-const X_2790 Real) +(declare-const X_2791 Real) +(declare-const X_2792 Real) +(declare-const X_2793 Real) +(declare-const X_2794 Real) +(declare-const X_2795 Real) +(declare-const X_2796 Real) +(declare-const X_2797 Real) +(declare-const X_2798 Real) +(declare-const X_2799 Real) +(declare-const X_2800 Real) +(declare-const X_2801 Real) +(declare-const X_2802 Real) +(declare-const X_2803 Real) +(declare-const X_2804 Real) +(declare-const X_2805 Real) +(declare-const X_2806 Real) +(declare-const X_2807 Real) +(declare-const X_2808 Real) +(declare-const X_2809 Real) +(declare-const X_2810 Real) +(declare-const X_2811 Real) +(declare-const X_2812 Real) +(declare-const X_2813 Real) +(declare-const X_2814 Real) +(declare-const X_2815 Real) +(declare-const X_2816 Real) +(declare-const X_2817 Real) +(declare-const X_2818 Real) +(declare-const X_2819 Real) +(declare-const X_2820 Real) +(declare-const X_2821 Real) +(declare-const X_2822 Real) +(declare-const X_2823 Real) +(declare-const X_2824 Real) +(declare-const X_2825 Real) +(declare-const X_2826 Real) +(declare-const X_2827 Real) +(declare-const X_2828 Real) +(declare-const X_2829 Real) +(declare-const X_2830 Real) +(declare-const X_2831 Real) +(declare-const X_2832 Real) +(declare-const X_2833 Real) +(declare-const X_2834 Real) +(declare-const X_2835 Real) +(declare-const X_2836 Real) +(declare-const X_2837 Real) +(declare-const X_2838 Real) +(declare-const X_2839 Real) +(declare-const X_2840 Real) +(declare-const X_2841 Real) +(declare-const X_2842 Real) +(declare-const X_2843 Real) +(declare-const X_2844 Real) +(declare-const X_2845 Real) +(declare-const X_2846 Real) +(declare-const X_2847 Real) +(declare-const X_2848 Real) +(declare-const X_2849 Real) +(declare-const X_2850 Real) +(declare-const X_2851 Real) +(declare-const X_2852 Real) +(declare-const X_2853 Real) +(declare-const X_2854 Real) +(declare-const X_2855 Real) +(declare-const X_2856 Real) +(declare-const X_2857 Real) +(declare-const X_2858 Real) +(declare-const X_2859 Real) +(declare-const X_2860 Real) +(declare-const X_2861 Real) +(declare-const X_2862 Real) +(declare-const X_2863 Real) +(declare-const X_2864 Real) +(declare-const X_2865 Real) +(declare-const X_2866 Real) +(declare-const X_2867 Real) +(declare-const X_2868 Real) +(declare-const X_2869 Real) +(declare-const X_2870 Real) +(declare-const X_2871 Real) +(declare-const X_2872 Real) +(declare-const X_2873 Real) +(declare-const X_2874 Real) +(declare-const X_2875 Real) +(declare-const X_2876 Real) +(declare-const X_2877 Real) +(declare-const X_2878 Real) +(declare-const X_2879 Real) +(declare-const X_2880 Real) +(declare-const X_2881 Real) +(declare-const X_2882 Real) +(declare-const X_2883 Real) +(declare-const X_2884 Real) +(declare-const X_2885 Real) +(declare-const X_2886 Real) +(declare-const X_2887 Real) +(declare-const X_2888 Real) +(declare-const X_2889 Real) +(declare-const X_2890 Real) +(declare-const X_2891 Real) +(declare-const X_2892 Real) +(declare-const X_2893 Real) +(declare-const X_2894 Real) +(declare-const X_2895 Real) +(declare-const X_2896 Real) +(declare-const X_2897 Real) +(declare-const X_2898 Real) +(declare-const X_2899 Real) +(declare-const X_2900 Real) +(declare-const X_2901 Real) +(declare-const X_2902 Real) +(declare-const X_2903 Real) +(declare-const X_2904 Real) +(declare-const X_2905 Real) +(declare-const X_2906 Real) +(declare-const X_2907 Real) +(declare-const X_2908 Real) +(declare-const X_2909 Real) +(declare-const X_2910 Real) +(declare-const X_2911 Real) +(declare-const X_2912 Real) +(declare-const X_2913 Real) +(declare-const X_2914 Real) +(declare-const X_2915 Real) +(declare-const X_2916 Real) +(declare-const X_2917 Real) +(declare-const X_2918 Real) +(declare-const X_2919 Real) +(declare-const X_2920 Real) +(declare-const X_2921 Real) +(declare-const X_2922 Real) +(declare-const X_2923 Real) +(declare-const X_2924 Real) +(declare-const X_2925 Real) +(declare-const X_2926 Real) +(declare-const X_2927 Real) +(declare-const X_2928 Real) +(declare-const X_2929 Real) +(declare-const X_2930 Real) +(declare-const X_2931 Real) +(declare-const X_2932 Real) +(declare-const X_2933 Real) +(declare-const X_2934 Real) +(declare-const X_2935 Real) +(declare-const X_2936 Real) +(declare-const X_2937 Real) +(declare-const X_2938 Real) +(declare-const X_2939 Real) +(declare-const X_2940 Real) +(declare-const X_2941 Real) +(declare-const X_2942 Real) +(declare-const X_2943 Real) +(declare-const X_2944 Real) +(declare-const X_2945 Real) +(declare-const X_2946 Real) +(declare-const X_2947 Real) +(declare-const X_2948 Real) +(declare-const X_2949 Real) +(declare-const X_2950 Real) +(declare-const X_2951 Real) +(declare-const X_2952 Real) +(declare-const X_2953 Real) +(declare-const X_2954 Real) +(declare-const X_2955 Real) +(declare-const X_2956 Real) +(declare-const X_2957 Real) +(declare-const X_2958 Real) +(declare-const X_2959 Real) +(declare-const X_2960 Real) +(declare-const X_2961 Real) +(declare-const X_2962 Real) +(declare-const X_2963 Real) +(declare-const X_2964 Real) +(declare-const X_2965 Real) +(declare-const X_2966 Real) +(declare-const X_2967 Real) +(declare-const X_2968 Real) +(declare-const X_2969 Real) +(declare-const X_2970 Real) +(declare-const X_2971 Real) +(declare-const X_2972 Real) +(declare-const X_2973 Real) +(declare-const X_2974 Real) +(declare-const X_2975 Real) +(declare-const X_2976 Real) +(declare-const X_2977 Real) +(declare-const X_2978 Real) +(declare-const X_2979 Real) +(declare-const X_2980 Real) +(declare-const X_2981 Real) +(declare-const X_2982 Real) +(declare-const X_2983 Real) +(declare-const X_2984 Real) +(declare-const X_2985 Real) +(declare-const X_2986 Real) +(declare-const X_2987 Real) +(declare-const X_2988 Real) +(declare-const X_2989 Real) +(declare-const X_2990 Real) +(declare-const X_2991 Real) +(declare-const X_2992 Real) +(declare-const X_2993 Real) +(declare-const X_2994 Real) +(declare-const X_2995 Real) +(declare-const X_2996 Real) +(declare-const X_2997 Real) +(declare-const X_2998 Real) +(declare-const X_2999 Real) +(declare-const X_3000 Real) +(declare-const X_3001 Real) +(declare-const X_3002 Real) +(declare-const X_3003 Real) +(declare-const X_3004 Real) +(declare-const X_3005 Real) +(declare-const X_3006 Real) +(declare-const X_3007 Real) +(declare-const X_3008 Real) +(declare-const X_3009 Real) +(declare-const X_3010 Real) +(declare-const X_3011 Real) +(declare-const X_3012 Real) +(declare-const X_3013 Real) +(declare-const X_3014 Real) +(declare-const X_3015 Real) +(declare-const X_3016 Real) +(declare-const X_3017 Real) +(declare-const X_3018 Real) +(declare-const X_3019 Real) +(declare-const X_3020 Real) +(declare-const X_3021 Real) +(declare-const X_3022 Real) +(declare-const X_3023 Real) +(declare-const X_3024 Real) +(declare-const X_3025 Real) +(declare-const X_3026 Real) +(declare-const X_3027 Real) +(declare-const X_3028 Real) +(declare-const X_3029 Real) +(declare-const X_3030 Real) +(declare-const X_3031 Real) +(declare-const X_3032 Real) +(declare-const X_3033 Real) +(declare-const X_3034 Real) +(declare-const X_3035 Real) +(declare-const X_3036 Real) +(declare-const X_3037 Real) +(declare-const X_3038 Real) +(declare-const X_3039 Real) +(declare-const X_3040 Real) +(declare-const X_3041 Real) +(declare-const X_3042 Real) +(declare-const X_3043 Real) +(declare-const X_3044 Real) +(declare-const X_3045 Real) +(declare-const X_3046 Real) +(declare-const X_3047 Real) +(declare-const X_3048 Real) +(declare-const X_3049 Real) +(declare-const X_3050 Real) +(declare-const X_3051 Real) +(declare-const X_3052 Real) +(declare-const X_3053 Real) +(declare-const X_3054 Real) +(declare-const X_3055 Real) +(declare-const X_3056 Real) +(declare-const X_3057 Real) +(declare-const X_3058 Real) +(declare-const X_3059 Real) +(declare-const X_3060 Real) +(declare-const X_3061 Real) +(declare-const X_3062 Real) +(declare-const X_3063 Real) +(declare-const X_3064 Real) +(declare-const X_3065 Real) +(declare-const X_3066 Real) +(declare-const X_3067 Real) +(declare-const X_3068 Real) +(declare-const X_3069 Real) +(declare-const X_3070 Real) +(declare-const X_3071 Real) + +; Definition of output variables +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) +(declare-const Y_5 Real) +(declare-const Y_6 Real) +(declare-const Y_7 Real) +(declare-const Y_8 Real) +(declare-const Y_9 Real) + +; Definition of input constraints +(assert (<= X_0 2.51408792)) +(assert (>= X_0 2.47531819)) +(assert (<= X_1 2.49470305)) +(assert (>= X_1 2.41716337)) +(assert (<= X_2 2.47531819)) +(assert (>= X_2 2.39777851)) +(assert (<= X_3 2.43654823)) +(assert (>= X_3 2.35900879)) +(assert (<= X_4 2.43654823)) +(assert (>= X_4 2.35900879)) +(assert (<= X_5 2.47531819)) +(assert (>= X_5 2.39777851)) +(assert (<= X_6 2.49470305)) +(assert (>= X_6 2.41716337)) +(assert (<= X_7 2.47531819)) +(assert (>= X_7 2.39777851)) +(assert (<= X_8 2.45593333)) +(assert (>= X_8 2.37839365)) +(assert (<= X_9 2.45593333)) +(assert (>= X_9 2.37839365)) +(assert (<= X_10 2.49470305)) +(assert (>= X_10 2.41716337)) +(assert (<= X_11 2.47531819)) +(assert (>= X_11 2.39777851)) +(assert (<= X_12 2.49470305)) +(assert (>= X_12 2.41716337)) +(assert (<= X_13 2.51408792)) +(assert (>= X_13 2.43654823)) +(assert (<= X_14 2.51408792)) +(assert (>= X_14 2.43654823)) +(assert (<= X_15 2.51408792)) +(assert (>= X_15 2.43654823)) +(assert (<= X_16 2.51408792)) +(assert (>= X_16 2.43654823)) +(assert (<= X_17 2.51408792)) +(assert (>= X_17 2.43654823)) +(assert (<= X_18 2.49470305)) +(assert (>= X_18 2.41716337)) +(assert (<= X_19 2.49470305)) +(assert (>= X_19 2.41716337)) +(assert (<= X_20 2.51408792)) +(assert (>= X_20 2.43654823)) +(assert (<= X_21 2.51408792)) +(assert (>= X_21 2.43654823)) +(assert (<= X_22 2.51408792)) +(assert (>= X_22 2.43654823)) +(assert (<= X_23 2.51408792)) +(assert (>= X_23 2.43654823)) +(assert (<= X_24 2.49470305)) +(assert (>= X_24 2.41716337)) +(assert (<= X_25 2.49470305)) +(assert (>= X_25 2.41716337)) +(assert (<= X_26 1.69992149)) +(assert (>= X_26 1.62238193)) +(assert (<= X_27 1.33160818)) +(assert (>= X_27 1.25406849)) +(assert (<= X_28 2.41716337)) +(assert (>= X_28 2.33962369)) +(assert (<= X_29 2.51408792)) +(assert (>= X_29 2.45593333)) +(assert (<= X_30 2.51408792)) +(assert (>= X_30 2.43654823)) +(assert (<= X_31 2.51408792)) +(assert (>= X_31 2.45593333)) +(assert (<= X_32 2.47531819)) +(assert (>= X_32 2.39777851)) +(assert (<= X_33 2.41716337)) +(assert (>= X_33 2.33962369)) +(assert (<= X_34 1.68053663)) +(assert (>= X_34 1.60299695)) +(assert (<= X_35 2.06823492)) +(assert (>= X_35 1.99069524)) +(assert (<= X_36 2.45593333)) +(assert (>= X_36 2.37839365)) +(assert (<= X_37 2.37839365)) +(assert (>= X_37 2.30085397)) +(assert (<= X_38 1.44791770)) +(assert (>= X_38 1.37037802)) +(assert (<= X_39 1.29283834)) +(assert (>= X_39 1.21529865)) +(assert (<= X_40 2.37839365)) +(assert (>= X_40 2.30085397)) +(assert (<= X_41 2.45593333)) +(assert (>= X_41 2.37839365)) +(assert (<= X_42 2.39777851)) +(assert (>= X_42 2.32023883)) +(assert (<= X_43 2.47531819)) +(assert (>= X_43 2.39777851)) +(assert (<= X_44 2.45593333)) +(assert (>= X_44 2.37839365)) +(assert (<= X_45 2.41716337)) +(assert (>= X_45 2.33962369)) +(assert (<= X_46 2.45593333)) +(assert (>= X_46 2.37839365)) +(assert (<= X_47 2.47531819)) +(assert (>= X_47 2.39777851)) +(assert (<= X_48 2.43654823)) +(assert (>= X_48 2.35900879)) +(assert (<= X_49 2.43654823)) +(assert (>= X_49 2.35900879)) +(assert (<= X_50 2.45593333)) +(assert (>= X_50 2.37839365)) +(assert (<= X_51 2.45593333)) +(assert (>= X_51 2.37839365)) +(assert (<= X_52 2.43654823)) +(assert (>= X_52 2.35900879)) +(assert (<= X_53 2.43654823)) +(assert (>= X_53 2.35900879)) +(assert (<= X_54 2.43654823)) +(assert (>= X_54 2.35900879)) +(assert (<= X_55 2.45593333)) +(assert (>= X_55 2.37839365)) +(assert (<= X_56 2.45593333)) +(assert (>= X_56 2.37839365)) +(assert (<= X_57 2.47531819)) +(assert (>= X_57 2.39777851)) +(assert (<= X_58 1.09898913)) +(assert (>= X_58 1.02144945)) +(assert (<= X_59 0.42051712)) +(assert (>= X_59 0.34297743)) +(assert (<= X_60 2.30085397)) +(assert (>= X_60 2.22331429)) +(assert (<= X_61 2.47531819)) +(assert (>= X_61 2.39777851)) +(assert (<= X_62 2.47531819)) +(assert (>= X_62 2.39777851)) +(assert (<= X_63 2.49470305)) +(assert (>= X_63 2.41716337)) +(assert (<= X_64 2.45593333)) +(assert (>= X_64 2.37839365)) +(assert (<= X_65 2.41716337)) +(assert (>= X_65 2.33962369)) +(assert (<= X_66 1.29283834)) +(assert (>= X_66 1.21529865)) +(assert (<= X_67 1.81623101)) +(assert (>= X_67 1.73869133)) +(assert (<= X_68 2.49470305)) +(assert (>= X_68 2.41716337)) +(assert (<= X_69 1.81623101)) +(assert (>= X_69 1.73869133)) +(assert (<= X_70 0.69190592)) +(assert (>= X_70 0.61436629)) +(assert (<= X_71 0.75006068)) +(assert (>= X_71 0.67252100)) +(assert (<= X_72 2.08761978)) +(assert (>= X_72 2.01008010)) +(assert (<= X_73 2.32023883)) +(assert (>= X_73 2.24269915)) +(assert (<= X_74 2.37839365)) +(assert (>= X_74 2.30085397)) +(assert (<= X_75 2.20392942)) +(assert (>= X_75 2.12638974)) +(assert (<= X_76 2.32023883)) +(assert (>= X_76 2.24269915)) +(assert (<= X_77 2.39777851)) +(assert (>= X_77 2.32023883)) +(assert (<= X_78 2.41716337)) +(assert (>= X_78 2.33962369)) +(assert (<= X_79 2.47531819)) +(assert (>= X_79 2.39777851)) +(assert (<= X_80 2.43654823)) +(assert (>= X_80 2.35900879)) +(assert (<= X_81 2.45593333)) +(assert (>= X_81 2.37839365)) +(assert (<= X_82 2.33962369)) +(assert (>= X_82 2.26208401)) +(assert (<= X_83 2.33962369)) +(assert (>= X_83 2.26208401)) +(assert (<= X_84 2.43654823)) +(assert (>= X_84 2.35900879)) +(assert (<= X_85 2.39777851)) +(assert (>= X_85 2.32023883)) +(assert (<= X_86 2.41716337)) +(assert (>= X_86 2.33962369)) +(assert (<= X_87 2.39777851)) +(assert (>= X_87 2.32023883)) +(assert (<= X_88 2.39777851)) +(assert (>= X_88 2.32023883)) +(assert (<= X_89 2.47531819)) +(assert (>= X_89 2.39777851)) +(assert (<= X_90 1.44791770)) +(assert (>= X_90 1.37037802)) +(assert (<= X_91 0.67252100)) +(assert (>= X_91 0.59498137)) +(assert (<= X_92 2.06823492)) +(assert (>= X_92 1.99069524)) +(assert (<= X_93 2.49470305)) +(assert (>= X_93 2.41716337)) +(assert (<= X_94 2.47531819)) +(assert (>= X_94 2.39777851)) +(assert (<= X_95 2.49470305)) +(assert (>= X_95 2.41716337)) +(assert (<= X_96 2.41716337)) +(assert (>= X_96 2.33962369)) +(assert (<= X_97 2.43654823)) +(assert (>= X_97 2.35900879)) +(assert (<= X_98 1.35099304)) +(assert (>= X_98 1.27345335)) +(assert (<= X_99 1.48668742)) +(assert (>= X_99 1.40914786)) +(assert (<= X_100 1.93254054)) +(assert (>= X_100 1.85500085)) +(assert (<= X_101 0.61436629)) +(assert (>= X_101 0.53682661)) +(assert (<= X_102 0.32359254)) +(assert (>= X_102 0.24605286)) +(assert (<= X_103 0.71129084)) +(assert (>= X_103 0.63375115)) +(assert (<= X_104 1.11837411)) +(assert (>= X_104 1.04083443)) +(assert (<= X_105 1.31222320)) +(assert (>= X_105 1.23468351)) +(assert (<= X_106 2.33962369)) +(assert (>= X_106 2.26208401)) +(assert (<= X_107 1.07960427)) +(assert (>= X_107 1.00206459)) +(assert (<= X_108 1.77746117)) +(assert (>= X_108 1.69992149)) +(assert (<= X_109 2.51408792)) +(assert (>= X_109 2.45593333)) +(assert (<= X_110 2.43654823)) +(assert (>= X_110 2.35900879)) +(assert (<= X_111 2.47531819)) +(assert (>= X_111 2.39777851)) +(assert (<= X_112 2.28146911)) +(assert (>= X_112 2.20392942)) +(assert (<= X_113 2.39777851)) +(assert (>= X_113 2.32023883)) +(assert (<= X_114 1.66115177)) +(assert (>= X_114 1.58361208)) +(assert (<= X_115 1.52545726)) +(assert (>= X_115 1.44791770)) +(assert (<= X_116 2.51408792)) +(assert (>= X_116 2.47531819)) +(assert (<= X_117 2.41716337)) +(assert (>= X_117 2.33962369)) +(assert (<= X_118 2.51408792)) +(assert (>= X_118 2.45593333)) +(assert (<= X_119 2.02946520)) +(assert (>= X_119 1.95192540)) +(assert (<= X_120 1.64176679)) +(assert (>= X_120 1.56422710)) +(assert (<= X_121 2.30085397)) +(assert (>= X_121 2.22331429)) +(assert (<= X_122 1.00206459)) +(assert (>= X_122 0.92452490)) +(assert (<= X_123 0.26543778)) +(assert (>= X_123 0.18789811)) +(assert (<= X_124 1.07960427)) +(assert (>= X_124 1.00206459)) +(assert (<= X_125 2.35900879)) +(assert (>= X_125 2.28146911)) +(assert (<= X_126 2.37839365)) +(assert (>= X_126 2.30085397)) +(assert (<= X_127 2.43654823)) +(assert (>= X_127 2.35900879)) +(assert (<= X_128 2.43654823)) +(assert (>= X_128 2.35900879)) +(assert 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+(assert (>= X_3060 -0.46546674)) +(assert (<= X_3061 -0.36791530)) +(assert (>= X_3061 -0.44595647)) +(assert (<= X_3062 -0.32889470)) +(assert (>= X_3062 -0.40693587)) +(assert (<= X_3063 -0.28987414)) +(assert (>= X_3063 -0.36791530)) +(assert (<= X_3064 -0.17281239)) +(assert (>= X_3064 -0.25085357)) +(assert (<= X_3065 -0.07526094)) +(assert (>= X_3065 -0.15330210)) +(assert (<= X_3066 0.06131108)) +(assert (>= X_3066 -0.01673007)) +(assert (<= X_3067 0.19788311)) +(assert (>= X_3067 0.11984196)) +(assert (<= X_3068 0.41249645)) +(assert (>= X_3068 0.33445528)) +(assert (<= X_3069 0.62710965)) +(assert (>= X_3069 0.54906851)) +(assert (<= X_3070 0.76368165)) +(assert (>= X_3070 0.68564051)) +(assert (<= X_3071 0.88074344)) +(assert (>= X_3071 0.80270225)) + +; Definition of output constraints +(assert (or + (and (>= Y_0 Y_9)) + (and (>= Y_1 Y_9)) + (and (>= Y_2 Y_9)) + (and (>= Y_3 Y_9)) + (and (>= Y_4 Y_9)) + (and (>= Y_5 Y_9)) + (and (>= Y_6 Y_9)) + (and (>= Y_7 Y_9)) + (and (>= Y_8 Y_9)) +)) diff --git a/examples/mnistfc/README.md b/examples/mnistfc/README.md new file mode 100644 index 0000000..7a8be47 --- /dev/null +++ b/examples/mnistfc/README.md @@ -0,0 +1 @@ +from vnncomp 2021 mnistfc benchmark: https://github.com/stanleybak/vnncomp2021/tree/main/benchmarks/mnistfc diff --git a/examples/mnistfc/mnist-net_256x2.onnx b/examples/mnistfc/mnist-net_256x2.onnx new file mode 100644 index 0000000000000000000000000000000000000000..462b098c3a37faa518a9a3bcfaad8403ba60ccad GIT binary patch literal 1077894 zcmbTdc{EpV^fqiJlqrQ&h@_Ay;dAdp5-CmcZBiME6iKDfWS(aVMF>eVh05pN_eUx; zp;C!LB@L7Yl}dW8=Y8MbyWZ!|=g)K2I%ltSpMCbe_H|ubN=#8QAS7_du1!8_qQ-`% zR-bz2Nvlf>8z~CU)snRL^9T&|@}DUqE#?utb+?Lep|FVbdTHUg(sF(tAzr(78yXn~ zd2QX|6DU3Qe{Ohg_1LW_Y@sFQ;I)1GOgU+B55E8(4`m^tFzZ5L;hE#4#XP+N|G(?8 z(h`BYJp6at{@-txl@_*86t>h7bN2GvBfUXd*z$j3nf&juObq{5ED>X)|HEM8q(`4s z6frjbf5L4Xy*B=zcxL~5JhT5dp2`1NJVp8cbri7iF_iIT8&mp!}Gatfl3tK+kGvtdt76ke~I%Bd;K3Yz6^ 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zkCBakydke$4Ps1U@$CW)h&G-|tK!Wucda|;cBGbg-Lr;jy|Z|zFpID7Y=p|IGpIy~ zCRK-He0FJwxU0#E&QwyCRg@N08Z9d(Eh;N6eM;*8E;gyiip`p>q#!HL-;)0STVm3( JR$^mi{s#%O7rFod literal 0 HcmV?d00001 diff --git a/examples/mnistfc/prop_0_0.03.vnnlib b/examples/mnistfc/prop_0_0.03.vnnlib new file mode 100644 index 0000000..cb8fe6f --- /dev/null +++ b/examples/mnistfc/prop_0_0.03.vnnlib @@ -0,0 +1,3165 @@ +; Mnist property with label: 5. + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) +(declare-const X_5 Real) +(declare-const X_6 Real) +(declare-const X_7 Real) +(declare-const X_8 Real) +(declare-const X_9 Real) +(declare-const X_10 Real) +(declare-const X_11 Real) +(declare-const X_12 Real) +(declare-const X_13 Real) +(declare-const X_14 Real) +(declare-const X_15 Real) +(declare-const X_16 Real) +(declare-const X_17 Real) +(declare-const X_18 Real) +(declare-const X_19 Real) +(declare-const X_20 Real) +(declare-const X_21 Real) +(declare-const X_22 Real) +(declare-const X_23 Real) +(declare-const X_24 Real) +(declare-const X_25 Real) +(declare-const X_26 Real) +(declare-const X_27 Real) +(declare-const X_28 Real) +(declare-const X_29 Real) +(declare-const X_30 Real) +(declare-const X_31 Real) +(declare-const X_32 Real) +(declare-const X_33 Real) +(declare-const X_34 Real) +(declare-const X_35 Real) +(declare-const X_36 Real) +(declare-const X_37 Real) +(declare-const X_38 Real) +(declare-const X_39 Real) +(declare-const X_40 Real) +(declare-const X_41 Real) +(declare-const X_42 Real) +(declare-const X_43 Real) +(declare-const X_44 Real) +(declare-const X_45 Real) +(declare-const X_46 Real) +(declare-const X_47 Real) +(declare-const X_48 Real) +(declare-const X_49 Real) +(declare-const X_50 Real) +(declare-const X_51 Real) +(declare-const X_52 Real) +(declare-const X_53 Real) +(declare-const X_54 Real) +(declare-const X_55 Real) +(declare-const X_56 Real) +(declare-const X_57 Real) +(declare-const X_58 Real) +(declare-const X_59 Real) +(declare-const X_60 Real) +(declare-const X_61 Real) +(declare-const X_62 Real) +(declare-const X_63 Real) +(declare-const X_64 Real) +(declare-const X_65 Real) +(declare-const X_66 Real) +(declare-const X_67 Real) +(declare-const X_68 Real) +(declare-const X_69 Real) +(declare-const X_70 Real) +(declare-const X_71 Real) +(declare-const X_72 Real) +(declare-const X_73 Real) +(declare-const X_74 Real) +(declare-const X_75 Real) +(declare-const X_76 Real) +(declare-const X_77 Real) +(declare-const X_78 Real) +(declare-const X_79 Real) +(declare-const X_80 Real) +(declare-const X_81 Real) +(declare-const X_82 Real) +(declare-const X_83 Real) +(declare-const X_84 Real) +(declare-const X_85 Real) +(declare-const X_86 Real) +(declare-const X_87 Real) +(declare-const X_88 Real) +(declare-const X_89 Real) +(declare-const X_90 Real) +(declare-const X_91 Real) +(declare-const X_92 Real) +(declare-const X_93 Real) +(declare-const X_94 Real) +(declare-const X_95 Real) +(declare-const X_96 Real) +(declare-const X_97 Real) +(declare-const X_98 Real) +(declare-const X_99 Real) +(declare-const X_100 Real) +(declare-const X_101 Real) +(declare-const X_102 Real) +(declare-const X_103 Real) +(declare-const X_104 Real) +(declare-const X_105 Real) +(declare-const X_106 Real) +(declare-const X_107 Real) +(declare-const X_108 Real) +(declare-const X_109 Real) +(declare-const X_110 Real) +(declare-const X_111 Real) +(declare-const X_112 Real) +(declare-const X_113 Real) +(declare-const X_114 Real) +(declare-const X_115 Real) +(declare-const X_116 Real) +(declare-const X_117 Real) +(declare-const X_118 Real) +(declare-const X_119 Real) +(declare-const X_120 Real) +(declare-const X_121 Real) +(declare-const X_122 Real) +(declare-const X_123 Real) +(declare-const X_124 Real) +(declare-const X_125 Real) +(declare-const X_126 Real) +(declare-const X_127 Real) +(declare-const X_128 Real) +(declare-const X_129 Real) +(declare-const X_130 Real) +(declare-const X_131 Real) +(declare-const X_132 Real) +(declare-const X_133 Real) +(declare-const X_134 Real) +(declare-const X_135 Real) +(declare-const X_136 Real) +(declare-const X_137 Real) +(declare-const X_138 Real) +(declare-const X_139 Real) +(declare-const X_140 Real) +(declare-const X_141 Real) +(declare-const X_142 Real) +(declare-const X_143 Real) +(declare-const X_144 Real) +(declare-const X_145 Real) +(declare-const X_146 Real) +(declare-const X_147 Real) +(declare-const X_148 Real) +(declare-const X_149 Real) +(declare-const X_150 Real) +(declare-const X_151 Real) +(declare-const X_152 Real) +(declare-const X_153 Real) +(declare-const X_154 Real) +(declare-const X_155 Real) +(declare-const X_156 Real) +(declare-const X_157 Real) +(declare-const X_158 Real) +(declare-const X_159 Real) +(declare-const X_160 Real) +(declare-const X_161 Real) +(declare-const X_162 Real) +(declare-const X_163 Real) +(declare-const X_164 Real) +(declare-const X_165 Real) +(declare-const X_166 Real) +(declare-const X_167 Real) +(declare-const X_168 Real) +(declare-const X_169 Real) +(declare-const X_170 Real) +(declare-const X_171 Real) +(declare-const X_172 Real) +(declare-const X_173 Real) +(declare-const X_174 Real) +(declare-const X_175 Real) +(declare-const X_176 Real) +(declare-const X_177 Real) +(declare-const X_178 Real) +(declare-const X_179 Real) +(declare-const X_180 Real) +(declare-const X_181 Real) +(declare-const X_182 Real) +(declare-const X_183 Real) +(declare-const X_184 Real) +(declare-const X_185 Real) +(declare-const X_186 Real) +(declare-const X_187 Real) +(declare-const X_188 Real) +(declare-const X_189 Real) +(declare-const X_190 Real) +(declare-const X_191 Real) +(declare-const X_192 Real) +(declare-const X_193 Real) +(declare-const X_194 Real) +(declare-const X_195 Real) +(declare-const X_196 Real) +(declare-const X_197 Real) +(declare-const X_198 Real) +(declare-const X_199 Real) +(declare-const X_200 Real) +(declare-const X_201 Real) +(declare-const X_202 Real) +(declare-const X_203 Real) +(declare-const X_204 Real) +(declare-const X_205 Real) +(declare-const X_206 Real) +(declare-const X_207 Real) +(declare-const X_208 Real) +(declare-const X_209 Real) +(declare-const X_210 Real) +(declare-const X_211 Real) +(declare-const X_212 Real) +(declare-const X_213 Real) +(declare-const X_214 Real) +(declare-const X_215 Real) +(declare-const X_216 Real) +(declare-const X_217 Real) +(declare-const X_218 Real) +(declare-const X_219 Real) +(declare-const X_220 Real) +(declare-const X_221 Real) +(declare-const X_222 Real) +(declare-const X_223 Real) +(declare-const X_224 Real) +(declare-const X_225 Real) +(declare-const X_226 Real) +(declare-const X_227 Real) +(declare-const X_228 Real) +(declare-const X_229 Real) +(declare-const X_230 Real) +(declare-const X_231 Real) +(declare-const X_232 Real) +(declare-const X_233 Real) +(declare-const X_234 Real) +(declare-const X_235 Real) +(declare-const X_236 Real) +(declare-const X_237 Real) +(declare-const X_238 Real) +(declare-const X_239 Real) +(declare-const X_240 Real) +(declare-const X_241 Real) +(declare-const X_242 Real) +(declare-const X_243 Real) +(declare-const X_244 Real) +(declare-const X_245 Real) +(declare-const X_246 Real) +(declare-const X_247 Real) +(declare-const X_248 Real) +(declare-const X_249 Real) +(declare-const X_250 Real) +(declare-const X_251 Real) +(declare-const X_252 Real) +(declare-const X_253 Real) +(declare-const X_254 Real) +(declare-const X_255 Real) +(declare-const X_256 Real) +(declare-const X_257 Real) +(declare-const X_258 Real) +(declare-const X_259 Real) +(declare-const X_260 Real) +(declare-const X_261 Real) +(declare-const X_262 Real) +(declare-const X_263 Real) +(declare-const X_264 Real) +(declare-const X_265 Real) +(declare-const X_266 Real) +(declare-const X_267 Real) +(declare-const X_268 Real) +(declare-const X_269 Real) +(declare-const X_270 Real) +(declare-const X_271 Real) +(declare-const X_272 Real) +(declare-const X_273 Real) +(declare-const X_274 Real) +(declare-const X_275 Real) +(declare-const X_276 Real) +(declare-const X_277 Real) +(declare-const X_278 Real) +(declare-const X_279 Real) +(declare-const X_280 Real) +(declare-const X_281 Real) +(declare-const X_282 Real) +(declare-const X_283 Real) +(declare-const X_284 Real) +(declare-const X_285 Real) +(declare-const X_286 Real) +(declare-const X_287 Real) +(declare-const X_288 Real) +(declare-const X_289 Real) +(declare-const X_290 Real) +(declare-const X_291 Real) +(declare-const X_292 Real) +(declare-const X_293 Real) +(declare-const X_294 Real) +(declare-const X_295 Real) +(declare-const X_296 Real) +(declare-const X_297 Real) +(declare-const X_298 Real) +(declare-const X_299 Real) +(declare-const X_300 Real) +(declare-const X_301 Real) +(declare-const X_302 Real) +(declare-const X_303 Real) +(declare-const X_304 Real) +(declare-const X_305 Real) +(declare-const X_306 Real) +(declare-const X_307 Real) +(declare-const X_308 Real) +(declare-const X_309 Real) +(declare-const X_310 Real) +(declare-const X_311 Real) +(declare-const X_312 Real) +(declare-const X_313 Real) +(declare-const X_314 Real) +(declare-const X_315 Real) +(declare-const X_316 Real) +(declare-const X_317 Real) +(declare-const X_318 Real) +(declare-const X_319 Real) +(declare-const X_320 Real) +(declare-const X_321 Real) +(declare-const X_322 Real) +(declare-const X_323 Real) +(declare-const X_324 Real) +(declare-const X_325 Real) +(declare-const X_326 Real) +(declare-const X_327 Real) +(declare-const X_328 Real) +(declare-const X_329 Real) +(declare-const X_330 Real) +(declare-const X_331 Real) +(declare-const X_332 Real) +(declare-const X_333 Real) +(declare-const X_334 Real) +(declare-const X_335 Real) +(declare-const X_336 Real) +(declare-const X_337 Real) +(declare-const X_338 Real) +(declare-const X_339 Real) +(declare-const X_340 Real) +(declare-const X_341 Real) +(declare-const X_342 Real) +(declare-const X_343 Real) +(declare-const X_344 Real) +(declare-const X_345 Real) +(declare-const X_346 Real) +(declare-const X_347 Real) +(declare-const X_348 Real) +(declare-const X_349 Real) +(declare-const X_350 Real) +(declare-const X_351 Real) +(declare-const X_352 Real) +(declare-const X_353 Real) +(declare-const X_354 Real) +(declare-const X_355 Real) +(declare-const X_356 Real) +(declare-const X_357 Real) +(declare-const X_358 Real) +(declare-const X_359 Real) +(declare-const X_360 Real) +(declare-const X_361 Real) +(declare-const X_362 Real) +(declare-const X_363 Real) +(declare-const X_364 Real) +(declare-const X_365 Real) +(declare-const X_366 Real) +(declare-const X_367 Real) +(declare-const X_368 Real) +(declare-const X_369 Real) +(declare-const X_370 Real) +(declare-const X_371 Real) +(declare-const X_372 Real) +(declare-const X_373 Real) +(declare-const X_374 Real) +(declare-const X_375 Real) +(declare-const X_376 Real) +(declare-const X_377 Real) +(declare-const X_378 Real) +(declare-const X_379 Real) +(declare-const X_380 Real) +(declare-const X_381 Real) +(declare-const X_382 Real) +(declare-const X_383 Real) +(declare-const X_384 Real) +(declare-const X_385 Real) +(declare-const X_386 Real) +(declare-const X_387 Real) +(declare-const X_388 Real) +(declare-const X_389 Real) +(declare-const X_390 Real) +(declare-const X_391 Real) +(declare-const X_392 Real) +(declare-const X_393 Real) +(declare-const X_394 Real) +(declare-const X_395 Real) +(declare-const X_396 Real) +(declare-const X_397 Real) +(declare-const X_398 Real) +(declare-const X_399 Real) +(declare-const X_400 Real) +(declare-const X_401 Real) +(declare-const X_402 Real) +(declare-const X_403 Real) +(declare-const X_404 Real) +(declare-const X_405 Real) +(declare-const X_406 Real) +(declare-const X_407 Real) +(declare-const X_408 Real) +(declare-const X_409 Real) +(declare-const X_410 Real) +(declare-const X_411 Real) +(declare-const X_412 Real) +(declare-const X_413 Real) +(declare-const X_414 Real) +(declare-const X_415 Real) +(declare-const X_416 Real) +(declare-const X_417 Real) +(declare-const X_418 Real) +(declare-const X_419 Real) +(declare-const X_420 Real) +(declare-const X_421 Real) +(declare-const X_422 Real) +(declare-const X_423 Real) +(declare-const X_424 Real) +(declare-const X_425 Real) +(declare-const X_426 Real) +(declare-const X_427 Real) +(declare-const X_428 Real) +(declare-const X_429 Real) +(declare-const X_430 Real) +(declare-const X_431 Real) +(declare-const X_432 Real) +(declare-const X_433 Real) +(declare-const X_434 Real) +(declare-const X_435 Real) +(declare-const X_436 Real) +(declare-const X_437 Real) +(declare-const X_438 Real) +(declare-const X_439 Real) +(declare-const X_440 Real) +(declare-const X_441 Real) +(declare-const X_442 Real) +(declare-const X_443 Real) +(declare-const X_444 Real) +(declare-const X_445 Real) +(declare-const X_446 Real) +(declare-const X_447 Real) +(declare-const X_448 Real) +(declare-const X_449 Real) +(declare-const X_450 Real) +(declare-const X_451 Real) +(declare-const X_452 Real) +(declare-const X_453 Real) +(declare-const X_454 Real) +(declare-const X_455 Real) +(declare-const X_456 Real) +(declare-const X_457 Real) +(declare-const X_458 Real) +(declare-const X_459 Real) +(declare-const X_460 Real) +(declare-const X_461 Real) +(declare-const X_462 Real) +(declare-const X_463 Real) +(declare-const X_464 Real) +(declare-const X_465 Real) +(declare-const X_466 Real) +(declare-const X_467 Real) +(declare-const X_468 Real) +(declare-const X_469 Real) +(declare-const X_470 Real) +(declare-const X_471 Real) +(declare-const X_472 Real) +(declare-const X_473 Real) +(declare-const X_474 Real) +(declare-const X_475 Real) +(declare-const X_476 Real) +(declare-const X_477 Real) +(declare-const X_478 Real) +(declare-const X_479 Real) +(declare-const X_480 Real) +(declare-const X_481 Real) +(declare-const X_482 Real) +(declare-const X_483 Real) +(declare-const X_484 Real) +(declare-const X_485 Real) +(declare-const X_486 Real) +(declare-const X_487 Real) +(declare-const X_488 Real) +(declare-const X_489 Real) +(declare-const X_490 Real) +(declare-const X_491 Real) +(declare-const X_492 Real) +(declare-const X_493 Real) +(declare-const X_494 Real) +(declare-const X_495 Real) +(declare-const X_496 Real) +(declare-const X_497 Real) +(declare-const X_498 Real) +(declare-const X_499 Real) +(declare-const X_500 Real) +(declare-const X_501 Real) +(declare-const X_502 Real) +(declare-const X_503 Real) +(declare-const X_504 Real) +(declare-const X_505 Real) +(declare-const X_506 Real) +(declare-const X_507 Real) +(declare-const X_508 Real) +(declare-const X_509 Real) +(declare-const X_510 Real) +(declare-const X_511 Real) +(declare-const X_512 Real) +(declare-const X_513 Real) +(declare-const X_514 Real) +(declare-const X_515 Real) +(declare-const X_516 Real) +(declare-const X_517 Real) +(declare-const X_518 Real) +(declare-const X_519 Real) +(declare-const X_520 Real) +(declare-const X_521 Real) +(declare-const X_522 Real) +(declare-const X_523 Real) +(declare-const X_524 Real) +(declare-const X_525 Real) +(declare-const X_526 Real) +(declare-const X_527 Real) +(declare-const X_528 Real) +(declare-const X_529 Real) +(declare-const X_530 Real) +(declare-const X_531 Real) +(declare-const X_532 Real) +(declare-const X_533 Real) +(declare-const X_534 Real) +(declare-const X_535 Real) +(declare-const X_536 Real) +(declare-const X_537 Real) +(declare-const X_538 Real) +(declare-const X_539 Real) +(declare-const X_540 Real) +(declare-const X_541 Real) +(declare-const X_542 Real) +(declare-const X_543 Real) +(declare-const X_544 Real) +(declare-const X_545 Real) +(declare-const X_546 Real) +(declare-const X_547 Real) +(declare-const X_548 Real) +(declare-const X_549 Real) +(declare-const X_550 Real) +(declare-const X_551 Real) +(declare-const X_552 Real) +(declare-const X_553 Real) +(declare-const X_554 Real) +(declare-const X_555 Real) +(declare-const X_556 Real) +(declare-const X_557 Real) +(declare-const X_558 Real) +(declare-const X_559 Real) +(declare-const X_560 Real) +(declare-const X_561 Real) +(declare-const X_562 Real) +(declare-const X_563 Real) +(declare-const X_564 Real) +(declare-const X_565 Real) +(declare-const X_566 Real) +(declare-const X_567 Real) +(declare-const X_568 Real) +(declare-const X_569 Real) +(declare-const X_570 Real) +(declare-const X_571 Real) +(declare-const X_572 Real) +(declare-const X_573 Real) +(declare-const X_574 Real) +(declare-const X_575 Real) +(declare-const X_576 Real) +(declare-const X_577 Real) +(declare-const X_578 Real) +(declare-const X_579 Real) +(declare-const X_580 Real) +(declare-const X_581 Real) +(declare-const X_582 Real) +(declare-const X_583 Real) +(declare-const X_584 Real) +(declare-const X_585 Real) +(declare-const X_586 Real) +(declare-const X_587 Real) +(declare-const X_588 Real) +(declare-const X_589 Real) +(declare-const X_590 Real) +(declare-const X_591 Real) +(declare-const X_592 Real) +(declare-const X_593 Real) +(declare-const X_594 Real) +(declare-const X_595 Real) +(declare-const X_596 Real) +(declare-const X_597 Real) +(declare-const X_598 Real) +(declare-const X_599 Real) +(declare-const X_600 Real) +(declare-const X_601 Real) +(declare-const X_602 Real) +(declare-const X_603 Real) +(declare-const X_604 Real) +(declare-const X_605 Real) +(declare-const X_606 Real) +(declare-const X_607 Real) +(declare-const X_608 Real) +(declare-const X_609 Real) +(declare-const X_610 Real) +(declare-const X_611 Real) +(declare-const X_612 Real) +(declare-const X_613 Real) +(declare-const X_614 Real) +(declare-const X_615 Real) +(declare-const X_616 Real) +(declare-const X_617 Real) +(declare-const X_618 Real) +(declare-const X_619 Real) +(declare-const X_620 Real) +(declare-const X_621 Real) +(declare-const X_622 Real) +(declare-const X_623 Real) +(declare-const X_624 Real) +(declare-const X_625 Real) +(declare-const X_626 Real) +(declare-const X_627 Real) +(declare-const X_628 Real) +(declare-const X_629 Real) +(declare-const X_630 Real) +(declare-const X_631 Real) +(declare-const X_632 Real) +(declare-const X_633 Real) +(declare-const X_634 Real) +(declare-const X_635 Real) +(declare-const X_636 Real) +(declare-const X_637 Real) +(declare-const X_638 Real) +(declare-const X_639 Real) +(declare-const X_640 Real) +(declare-const X_641 Real) +(declare-const X_642 Real) +(declare-const X_643 Real) +(declare-const X_644 Real) +(declare-const X_645 Real) +(declare-const X_646 Real) +(declare-const X_647 Real) +(declare-const X_648 Real) +(declare-const X_649 Real) +(declare-const X_650 Real) +(declare-const X_651 Real) +(declare-const X_652 Real) +(declare-const X_653 Real) +(declare-const X_654 Real) +(declare-const X_655 Real) +(declare-const X_656 Real) +(declare-const X_657 Real) +(declare-const X_658 Real) +(declare-const X_659 Real) +(declare-const X_660 Real) +(declare-const X_661 Real) +(declare-const X_662 Real) +(declare-const X_663 Real) +(declare-const X_664 Real) +(declare-const X_665 Real) +(declare-const X_666 Real) +(declare-const X_667 Real) +(declare-const X_668 Real) +(declare-const X_669 Real) +(declare-const X_670 Real) +(declare-const X_671 Real) +(declare-const X_672 Real) +(declare-const X_673 Real) +(declare-const X_674 Real) +(declare-const X_675 Real) +(declare-const X_676 Real) +(declare-const X_677 Real) +(declare-const X_678 Real) +(declare-const X_679 Real) +(declare-const X_680 Real) +(declare-const X_681 Real) +(declare-const X_682 Real) +(declare-const X_683 Real) +(declare-const X_684 Real) +(declare-const X_685 Real) +(declare-const X_686 Real) +(declare-const X_687 Real) +(declare-const X_688 Real) +(declare-const X_689 Real) +(declare-const X_690 Real) +(declare-const X_691 Real) +(declare-const X_692 Real) +(declare-const X_693 Real) +(declare-const X_694 Real) +(declare-const X_695 Real) +(declare-const X_696 Real) +(declare-const X_697 Real) +(declare-const X_698 Real) +(declare-const X_699 Real) +(declare-const X_700 Real) +(declare-const X_701 Real) +(declare-const X_702 Real) +(declare-const X_703 Real) +(declare-const X_704 Real) +(declare-const X_705 Real) +(declare-const X_706 Real) +(declare-const X_707 Real) +(declare-const X_708 Real) +(declare-const X_709 Real) +(declare-const X_710 Real) +(declare-const X_711 Real) +(declare-const X_712 Real) +(declare-const X_713 Real) +(declare-const X_714 Real) +(declare-const X_715 Real) +(declare-const X_716 Real) +(declare-const X_717 Real) +(declare-const X_718 Real) +(declare-const X_719 Real) +(declare-const X_720 Real) +(declare-const X_721 Real) +(declare-const X_722 Real) +(declare-const X_723 Real) +(declare-const X_724 Real) +(declare-const X_725 Real) +(declare-const X_726 Real) +(declare-const X_727 Real) +(declare-const X_728 Real) +(declare-const X_729 Real) +(declare-const X_730 Real) +(declare-const X_731 Real) +(declare-const X_732 Real) +(declare-const X_733 Real) +(declare-const X_734 Real) +(declare-const X_735 Real) +(declare-const X_736 Real) +(declare-const X_737 Real) +(declare-const X_738 Real) +(declare-const X_739 Real) +(declare-const X_740 Real) +(declare-const X_741 Real) +(declare-const X_742 Real) +(declare-const X_743 Real) +(declare-const X_744 Real) +(declare-const X_745 Real) +(declare-const X_746 Real) +(declare-const X_747 Real) +(declare-const X_748 Real) +(declare-const X_749 Real) +(declare-const X_750 Real) +(declare-const X_751 Real) +(declare-const X_752 Real) +(declare-const X_753 Real) +(declare-const X_754 Real) +(declare-const X_755 Real) +(declare-const X_756 Real) +(declare-const X_757 Real) +(declare-const X_758 Real) +(declare-const X_759 Real) +(declare-const X_760 Real) +(declare-const X_761 Real) +(declare-const X_762 Real) +(declare-const X_763 Real) +(declare-const X_764 Real) +(declare-const X_765 Real) +(declare-const X_766 Real) +(declare-const X_767 Real) +(declare-const X_768 Real) +(declare-const X_769 Real) +(declare-const X_770 Real) +(declare-const X_771 Real) +(declare-const X_772 Real) +(declare-const X_773 Real) +(declare-const X_774 Real) +(declare-const X_775 Real) +(declare-const X_776 Real) +(declare-const X_777 Real) +(declare-const X_778 Real) +(declare-const X_779 Real) +(declare-const X_780 Real) +(declare-const X_781 Real) +(declare-const X_782 Real) +(declare-const X_783 Real) + + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) +(declare-const Y_5 Real) +(declare-const Y_6 Real) +(declare-const Y_7 Real) +(declare-const Y_8 Real) +(declare-const Y_9 Real) + +; Input constraints: +(assert (<= X_0 0.029999999329447746)) +(assert (>= X_0 0.0)) + +(assert (<= X_1 0.029999999329447746)) +(assert (>= X_1 0.0)) + +(assert (<= X_2 0.029999999329447746)) +(assert (>= X_2 0.0)) + +(assert (<= X_3 0.029999999329447746)) +(assert (>= X_3 0.0)) + +(assert (<= X_4 0.029999999329447746)) +(assert (>= X_4 0.0)) + +(assert (<= X_5 0.029999999329447746)) +(assert (>= X_5 0.0)) + +(assert (<= X_6 0.029999999329447746)) +(assert (>= X_6 0.0)) + +(assert (<= X_7 0.029999999329447746)) +(assert (>= X_7 0.0)) + +(assert (<= X_8 0.029999999329447746)) +(assert (>= X_8 0.0)) + +(assert (<= X_9 0.029999999329447746)) +(assert (>= X_9 0.0)) + +(assert (<= X_10 0.029999999329447746)) +(assert (>= X_10 0.0)) + +(assert (<= X_11 0.029999999329447746)) +(assert (>= X_11 0.0)) + +(assert (<= X_12 0.029999999329447746)) +(assert (>= X_12 0.0)) + +(assert (<= X_13 0.029999999329447746)) +(assert (>= X_13 0.0)) + +(assert (<= X_14 0.029999999329447746)) +(assert (>= X_14 0.0)) + +(assert (<= X_15 0.029999999329447746)) +(assert (>= X_15 0.0)) + +(assert (<= X_16 0.029999999329447746)) +(assert (>= X_16 0.0)) + +(assert (<= X_17 0.029999999329447746)) +(assert (>= X_17 0.0)) + +(assert (<= X_18 0.029999999329447746)) +(assert (>= X_18 0.0)) + +(assert (<= X_19 0.029999999329447746)) +(assert (>= X_19 0.0)) + +(assert (<= X_20 0.029999999329447746)) +(assert (>= X_20 0.0)) + +(assert (<= X_21 0.029999999329447746)) +(assert (>= X_21 0.0)) + +(assert (<= X_22 0.029999999329447746)) +(assert (>= X_22 0.0)) + +(assert (<= X_23 0.029999999329447746)) +(assert (>= X_23 0.0)) + +(assert (<= X_24 0.029999999329447746)) +(assert (>= X_24 0.0)) + +(assert (<= X_25 0.029999999329447746)) +(assert (>= X_25 0.0)) + +(assert (<= X_26 0.029999999329447746)) +(assert (>= X_26 0.0)) + +(assert (<= X_27 0.029999999329447746)) +(assert (>= X_27 0.0)) + +(assert (<= X_28 0.029999999329447746)) +(assert (>= X_28 0.0)) + +(assert (<= X_29 0.029999999329447746)) +(assert (>= X_29 0.0)) + +(assert (<= X_30 0.029999999329447746)) +(assert (>= X_30 0.0)) + +(assert (<= X_31 0.029999999329447746)) +(assert (>= X_31 0.0)) + +(assert (<= X_32 0.029999999329447746)) +(assert (>= X_32 0.0)) + +(assert (<= X_33 0.029999999329447746)) +(assert (>= X_33 0.0)) + +(assert (<= X_34 0.029999999329447746)) +(assert (>= X_34 0.0)) + +(assert (<= X_35 0.029999999329447746)) +(assert (>= X_35 0.0)) + +(assert (<= X_36 0.029999999329447746)) +(assert (>= X_36 0.0)) + +(assert (<= X_37 0.029999999329447746)) +(assert (>= X_37 0.0)) + +(assert (<= X_38 0.029999999329447746)) +(assert (>= X_38 0.0)) + +(assert (<= X_39 0.029999999329447746)) +(assert (>= X_39 0.0)) + +(assert (<= X_40 0.029999999329447746)) +(assert (>= X_40 0.0)) + +(assert (<= X_41 0.029999999329447746)) +(assert (>= X_41 0.0)) + +(assert (<= X_42 0.029999999329447746)) +(assert (>= X_42 0.0)) + +(assert (<= X_43 0.029999999329447746)) +(assert (>= X_43 0.0)) + +(assert (<= X_44 0.029999999329447746)) +(assert (>= X_44 0.0)) + +(assert (<= X_45 0.029999999329447746)) +(assert (>= X_45 0.0)) + +(assert (<= X_46 0.029999999329447746)) +(assert (>= X_46 0.0)) + +(assert (<= X_47 0.029999999329447746)) +(assert (>= X_47 0.0)) + +(assert (<= X_48 0.029999999329447746)) +(assert (>= X_48 0.0)) + +(assert (<= X_49 0.029999999329447746)) +(assert (>= X_49 0.0)) + +(assert (<= X_50 0.029999999329447746)) +(assert (>= X_50 0.0)) + +(assert (<= X_51 0.029999999329447746)) +(assert (>= X_51 0.0)) + +(assert (<= X_52 0.029999999329447746)) +(assert (>= X_52 0.0)) + +(assert (<= X_53 0.029999999329447746)) +(assert (>= X_53 0.0)) + +(assert (<= X_54 0.029999999329447746)) +(assert (>= X_54 0.0)) + +(assert (<= X_55 0.029999999329447746)) +(assert (>= X_55 0.0)) + +(assert (<= X_56 0.029999999329447746)) +(assert (>= X_56 0.0)) + +(assert (<= X_57 0.029999999329447746)) +(assert (>= X_57 0.0)) + +(assert (<= X_58 0.029999999329447746)) +(assert (>= X_58 0.0)) + +(assert (<= X_59 0.029999999329447746)) +(assert (>= X_59 0.0)) + +(assert (<= X_60 0.029999999329447746)) +(assert (>= X_60 0.0)) + +(assert (<= X_61 0.029999999329447746)) +(assert (>= X_61 0.0)) + +(assert (<= X_62 0.029999999329447746)) +(assert (>= X_62 0.0)) + +(assert (<= X_63 0.029999999329447746)) +(assert (>= X_63 0.0)) + +(assert (<= X_64 0.029999999329447746)) +(assert (>= X_64 0.0)) + +(assert (<= X_65 0.029999999329447746)) +(assert (>= X_65 0.0)) + +(assert (<= X_66 0.029999999329447746)) +(assert (>= X_66 0.0)) + +(assert (<= X_67 0.029999999329447746)) +(assert (>= X_67 0.0)) + +(assert (<= X_68 0.029999999329447746)) +(assert (>= X_68 0.0)) + +(assert (<= X_69 0.029999999329447746)) +(assert (>= X_69 0.0)) + +(assert (<= X_70 0.029999999329447746)) +(assert (>= X_70 0.0)) + +(assert (<= X_71 0.029999999329447746)) +(assert (>= X_71 0.0)) + +(assert (<= X_72 0.029999999329447746)) +(assert (>= X_72 0.0)) + +(assert (<= X_73 0.029999999329447746)) +(assert (>= X_73 0.0)) + +(assert (<= X_74 0.029999999329447746)) +(assert (>= X_74 0.0)) + +(assert (<= X_75 0.029999999329447746)) +(assert (>= X_75 0.0)) + +(assert (<= X_76 0.029999999329447746)) +(assert (>= X_76 0.0)) + +(assert (<= X_77 0.029999999329447746)) +(assert (>= X_77 0.0)) + +(assert (<= X_78 0.029999999329447746)) +(assert (>= X_78 0.0)) + +(assert (<= X_79 0.029999999329447746)) +(assert (>= X_79 0.0)) + +(assert (<= X_80 0.029999999329447746)) +(assert (>= X_80 0.0)) + +(assert (<= X_81 0.029999999329447746)) +(assert (>= X_81 0.0)) + +(assert (<= X_82 0.029999999329447746)) +(assert (>= X_82 0.0)) + +(assert (<= X_83 0.029999999329447746)) +(assert (>= X_83 0.0)) + +(assert (<= X_84 0.029999999329447746)) +(assert (>= X_84 0.0)) + +(assert (<= X_85 0.029999999329447746)) +(assert (>= X_85 0.0)) + +(assert (<= X_86 0.029999999329447746)) +(assert (>= X_86 0.0)) + +(assert (<= X_87 0.029999999329447746)) +(assert (>= X_87 0.0)) + +(assert (<= X_88 0.029999999329447746)) +(assert (>= X_88 0.0)) + +(assert (<= X_89 0.029999999329447746)) +(assert (>= X_89 0.0)) + +(assert (<= X_90 0.029999999329447746)) +(assert (>= X_90 0.0)) + +(assert (<= X_91 0.029999999329447746)) +(assert (>= X_91 0.0)) + +(assert (<= X_92 0.029999999329447746)) +(assert (>= X_92 0.0)) + +(assert (<= X_93 0.029999999329447746)) +(assert (>= X_93 0.0)) + +(assert (<= X_94 0.029999999329447746)) +(assert 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(>= X_573 0.0)) + +(assert (<= X_574 0.029999999329447746)) +(assert (>= X_574 0.0)) + +(assert (<= X_575 0.2182352989912033)) +(assert (>= X_575 0.15823529660701752)) + +(assert (<= X_576 1.0)) +(assert (>= X_576 0.9660784602165222)) + +(assert (<= X_577 1.0)) +(assert (>= X_577 0.9621568918228149)) + +(assert (<= X_578 1.0)) +(assert (>= X_578 0.9621568918228149)) + +(assert (<= X_579 0.22215686738491058)) +(assert (>= X_579 0.1621568650007248)) + +(assert (<= X_580 0.029999999329447746)) +(assert (>= X_580 0.0)) + +(assert (<= X_581 0.029999999329447746)) +(assert (>= X_581 0.0)) + +(assert (<= X_582 0.029999999329447746)) +(assert (>= X_582 0.0)) + +(assert (<= X_583 0.029999999329447746)) +(assert (>= X_583 0.0)) + +(assert (<= X_584 0.029999999329447746)) +(assert (>= X_584 0.0)) + +(assert (<= X_585 0.029999999329447746)) +(assert (>= X_585 0.0)) + +(assert (<= X_586 0.029999999329447746)) +(assert (>= X_586 0.0)) + +(assert (<= X_587 0.029999999329447746)) +(assert (>= X_587 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+(assert (>= X_658 0.9621568918228149)) + +(assert (<= X_659 1.0)) +(assert (>= X_659 0.9621568918228149)) + +(assert (<= X_660 1.0)) +(assert (>= X_660 0.9660784602165222)) + +(assert (<= X_661 1.0)) +(assert (>= X_661 0.9621568918228149)) + +(assert (<= X_662 0.9045097827911377)) +(assert (>= X_662 0.8445098400115967)) + +(assert (<= X_663 0.05745097994804382)) +(assert (>= X_663 0.0)) + +(assert (<= X_664 0.029999999329447746)) +(assert (>= X_664 0.0)) + +(assert (<= X_665 0.029999999329447746)) +(assert (>= X_665 0.0)) + +(assert (<= X_666 0.029999999329447746)) +(assert (>= X_666 0.0)) + +(assert (<= X_667 0.029999999329447746)) +(assert (>= X_667 0.0)) + +(assert (<= X_668 0.029999999329447746)) +(assert (>= X_668 0.0)) + +(assert (<= X_669 0.029999999329447746)) +(assert (>= X_669 0.0)) + +(assert (<= X_670 0.029999999329447746)) +(assert (>= X_670 0.0)) + +(assert (<= X_671 0.029999999329447746)) +(assert (>= X_671 0.0)) + +(assert (<= X_672 0.029999999329447746)) +(assert (>= X_672 0.0)) + +(assert (<= X_673 0.029999999329447746)) +(assert (>= X_673 0.0)) + +(assert (<= X_674 0.029999999329447746)) +(assert (>= X_674 0.0)) + +(assert (<= X_675 0.029999999329447746)) +(assert (>= X_675 0.0)) + +(assert (<= X_676 0.029999999329447746)) +(assert (>= X_676 0.0)) + +(assert (<= X_677 0.029999999329447746)) +(assert (>= X_677 0.0)) + +(assert (<= X_678 0.029999999329447746)) +(assert (>= X_678 0.0)) + +(assert (<= X_679 0.029999999329447746)) +(assert (>= X_679 0.0)) + +(assert (<= X_680 0.029999999329447746)) +(assert (>= X_680 0.0)) + +(assert (<= X_681 0.029999999329447746)) +(assert (>= X_681 0.0)) + +(assert (<= X_682 0.1554902046918869)) +(assert (>= X_682 0.09549020230770111)) + +(assert (<= X_683 0.5907843112945557)) +(assert (>= X_683 0.5307843685150146)) + +(assert (<= X_684 0.6064705848693848)) +(assert (>= X_684 0.5464706420898438)) + +(assert (<= X_685 1.0)) +(assert (>= X_685 0.9621568918228149)) + +(assert (<= X_686 1.0)) +(assert (>= X_686 0.9621568918228149)) + +(assert (<= X_687 1.0)) +(assert (>= X_687 0.9621568918228149)) + +(assert (<= X_688 1.0)) +(assert (>= X_688 0.9660784602165222)) + +(assert (<= X_689 0.908431351184845)) +(assert (>= X_689 0.848431408405304)) + +(assert (<= X_690 0.37117648124694824)) +(assert (>= X_690 0.31117647886276245)) + +(assert (<= X_691 0.029999999329447746)) +(assert (>= X_691 0.0)) + +(assert (<= X_692 0.029999999329447746)) +(assert (>= X_692 0.0)) + +(assert (<= X_693 0.029999999329447746)) +(assert (>= X_693 0.0)) + +(assert (<= X_694 0.029999999329447746)) +(assert (>= X_694 0.0)) + +(assert (<= X_695 0.029999999329447746)) +(assert (>= X_695 0.0)) + +(assert (<= X_696 0.029999999329447746)) +(assert (>= X_696 0.0)) + +(assert (<= X_697 0.029999999329447746)) +(assert (>= X_697 0.0)) + +(assert (<= X_698 0.029999999329447746)) +(assert (>= X_698 0.0)) + +(assert (<= X_699 0.029999999329447746)) +(assert (>= X_699 0.0)) + +(assert (<= X_700 0.029999999329447746)) +(assert (>= X_700 0.0)) + +(assert (<= X_701 0.029999999329447746)) +(assert (>= X_701 0.0)) + +(assert (<= X_702 0.029999999329447746)) +(assert (>= X_702 0.0)) + +(assert (<= X_703 0.029999999329447746)) +(assert (>= X_703 0.0)) + +(assert (<= X_704 0.029999999329447746)) +(assert (>= X_704 0.0)) + +(assert (<= X_705 0.029999999329447746)) +(assert (>= X_705 0.0)) + +(assert (<= X_706 0.029999999329447746)) +(assert (>= X_706 0.0)) + +(assert (<= X_707 0.029999999329447746)) +(assert (>= X_707 0.0)) + +(assert (<= X_708 0.029999999329447746)) +(assert (>= X_708 0.0)) + +(assert (<= X_709 0.029999999329447746)) +(assert (>= X_709 0.0)) + +(assert (<= X_710 0.029999999329447746)) +(assert (>= X_710 0.0)) + +(assert (<= X_711 0.029999999329447746)) +(assert (>= X_711 0.0)) + +(assert (<= X_712 0.029999999329447746)) +(assert (>= X_712 0.0)) + +(assert (<= X_713 0.029999999329447746)) +(assert (>= X_713 0.0)) + +(assert (<= X_714 0.029999999329447746)) +(assert (>= X_714 0.0)) + +(assert (<= X_715 0.029999999329447746)) +(assert (>= X_715 0.0)) + +(assert (<= X_716 0.029999999329447746)) +(assert (>= X_716 0.0)) + +(assert (<= X_717 0.029999999329447746)) +(assert (>= X_717 0.0)) + +(assert (<= X_718 0.029999999329447746)) +(assert (>= X_718 0.0)) + +(assert (<= X_719 0.029999999329447746)) +(assert (>= X_719 0.0)) + +(assert (<= X_720 0.029999999329447746)) +(assert (>= X_720 0.0)) + +(assert (<= X_721 0.029999999329447746)) +(assert (>= X_721 0.0)) + +(assert (<= X_722 0.029999999329447746)) +(assert (>= X_722 0.0)) + +(assert (<= X_723 0.029999999329447746)) +(assert (>= X_723 0.0)) + +(assert (<= X_724 0.029999999329447746)) +(assert (>= X_724 0.0)) + +(assert (<= X_725 0.029999999329447746)) +(assert (>= X_725 0.0)) + +(assert (<= X_726 0.029999999329447746)) +(assert (>= X_726 0.0)) + +(assert (<= X_727 0.029999999329447746)) +(assert (>= X_727 0.0)) + +(assert (<= X_728 0.029999999329447746)) +(assert (>= X_728 0.0)) + +(assert (<= X_729 0.029999999329447746)) +(assert (>= X_729 0.0)) + +(assert (<= X_730 0.029999999329447746)) +(assert (>= X_730 0.0)) + +(assert (<= X_731 0.029999999329447746)) +(assert (>= X_731 0.0)) + +(assert (<= X_732 0.029999999329447746)) +(assert (>= X_732 0.0)) + +(assert (<= X_733 0.029999999329447746)) +(assert (>= X_733 0.0)) + +(assert (<= X_734 0.029999999329447746)) +(assert (>= X_734 0.0)) + +(assert (<= X_735 0.029999999329447746)) +(assert (>= X_735 0.0)) + +(assert (<= X_736 0.029999999329447746)) +(assert (>= X_736 0.0)) + +(assert (<= X_737 0.029999999329447746)) +(assert (>= X_737 0.0)) + +(assert (<= X_738 0.029999999329447746)) +(assert (>= X_738 0.0)) + +(assert (<= X_739 0.029999999329447746)) +(assert (>= X_739 0.0)) + +(assert (<= X_740 0.029999999329447746)) +(assert (>= X_740 0.0)) + +(assert (<= X_741 0.029999999329447746)) +(assert (>= X_741 0.0)) + +(assert (<= X_742 0.029999999329447746)) +(assert (>= X_742 0.0)) + +(assert (<= X_743 0.029999999329447746)) +(assert (>= X_743 0.0)) + +(assert (<= X_744 0.029999999329447746)) +(assert (>= X_744 0.0)) + +(assert (<= X_745 0.029999999329447746)) +(assert (>= X_745 0.0)) + +(assert (<= X_746 0.029999999329447746)) +(assert (>= X_746 0.0)) + +(assert (<= X_747 0.029999999329447746)) +(assert (>= X_747 0.0)) + +(assert (<= X_748 0.029999999329447746)) +(assert (>= X_748 0.0)) + +(assert (<= X_749 0.029999999329447746)) +(assert (>= X_749 0.0)) + +(assert (<= X_750 0.029999999329447746)) +(assert (>= X_750 0.0)) + +(assert (<= X_751 0.029999999329447746)) +(assert (>= X_751 0.0)) + +(assert (<= X_752 0.029999999329447746)) +(assert (>= X_752 0.0)) + +(assert (<= X_753 0.029999999329447746)) +(assert (>= X_753 0.0)) + +(assert (<= X_754 0.029999999329447746)) +(assert (>= X_754 0.0)) + +(assert (<= X_755 0.029999999329447746)) +(assert (>= X_755 0.0)) + +(assert (<= X_756 0.029999999329447746)) +(assert (>= X_756 0.0)) + +(assert (<= X_757 0.029999999329447746)) +(assert (>= X_757 0.0)) + +(assert (<= X_758 0.029999999329447746)) +(assert (>= X_758 0.0)) + +(assert (<= X_759 0.029999999329447746)) +(assert (>= X_759 0.0)) + +(assert (<= X_760 0.029999999329447746)) +(assert (>= X_760 0.0)) + +(assert (<= X_761 0.029999999329447746)) +(assert (>= X_761 0.0)) + +(assert (<= X_762 0.029999999329447746)) +(assert (>= X_762 0.0)) + +(assert (<= X_763 0.029999999329447746)) +(assert (>= X_763 0.0)) + +(assert (<= X_764 0.029999999329447746)) +(assert (>= X_764 0.0)) + +(assert (<= X_765 0.029999999329447746)) +(assert (>= X_765 0.0)) + +(assert (<= X_766 0.029999999329447746)) +(assert (>= X_766 0.0)) + +(assert (<= X_767 0.029999999329447746)) +(assert (>= X_767 0.0)) + +(assert (<= X_768 0.029999999329447746)) +(assert (>= X_768 0.0)) + +(assert (<= X_769 0.029999999329447746)) +(assert (>= X_769 0.0)) + +(assert (<= X_770 0.029999999329447746)) +(assert (>= X_770 0.0)) + +(assert (<= X_771 0.029999999329447746)) +(assert (>= X_771 0.0)) + +(assert (<= X_772 0.029999999329447746)) +(assert (>= X_772 0.0)) + +(assert (<= X_773 0.029999999329447746)) +(assert (>= X_773 0.0)) + +(assert (<= X_774 0.029999999329447746)) +(assert (>= X_774 0.0)) + +(assert (<= X_775 0.029999999329447746)) +(assert (>= X_775 0.0)) + +(assert (<= X_776 0.029999999329447746)) +(assert (>= X_776 0.0)) + +(assert (<= X_777 0.029999999329447746)) +(assert (>= X_777 0.0)) + +(assert (<= X_778 0.029999999329447746)) +(assert (>= X_778 0.0)) + +(assert (<= X_779 0.029999999329447746)) +(assert (>= X_779 0.0)) + +(assert (<= X_780 0.029999999329447746)) +(assert (>= X_780 0.0)) + +(assert (<= X_781 0.029999999329447746)) +(assert (>= X_781 0.0)) + +(assert (<= X_782 0.029999999329447746)) +(assert (>= X_782 0.0)) + +(assert (<= X_783 0.029999999329447746)) +(assert (>= X_783 0.0)) + + +; Output constraints: +(assert (or + (and (>= Y_0 Y_5)) + (and (>= Y_1 Y_5)) + (and (>= Y_2 Y_5)) + (and (>= Y_3 Y_5)) + (and (>= Y_4 Y_5)) + (and (>= Y_6 Y_5)) + (and (>= Y_7 Y_5)) + (and (>= Y_8 Y_5)) + (and (>= Y_9 Y_5)) +)) \ No newline at end of file diff --git a/examples/mnistfc/prop_2_0.03.vnnlib b/examples/mnistfc/prop_2_0.03.vnnlib new file mode 100644 index 0000000..2a53446 --- /dev/null +++ b/examples/mnistfc/prop_2_0.03.vnnlib @@ -0,0 +1,3165 @@ +; Mnist property with label: 7. + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) +(declare-const X_5 Real) +(declare-const X_6 Real) +(declare-const X_7 Real) +(declare-const X_8 Real) +(declare-const X_9 Real) +(declare-const X_10 Real) +(declare-const X_11 Real) +(declare-const X_12 Real) +(declare-const X_13 Real) +(declare-const X_14 Real) +(declare-const X_15 Real) +(declare-const X_16 Real) +(declare-const X_17 Real) +(declare-const X_18 Real) +(declare-const X_19 Real) +(declare-const X_20 Real) +(declare-const X_21 Real) +(declare-const X_22 Real) +(declare-const X_23 Real) +(declare-const X_24 Real) +(declare-const X_25 Real) +(declare-const X_26 Real) +(declare-const X_27 Real) +(declare-const X_28 Real) +(declare-const X_29 Real) +(declare-const X_30 Real) +(declare-const X_31 Real) +(declare-const X_32 Real) +(declare-const X_33 Real) +(declare-const X_34 Real) +(declare-const X_35 Real) +(declare-const X_36 Real) +(declare-const X_37 Real) +(declare-const X_38 Real) +(declare-const X_39 Real) +(declare-const X_40 Real) +(declare-const X_41 Real) +(declare-const X_42 Real) +(declare-const X_43 Real) +(declare-const X_44 Real) +(declare-const X_45 Real) +(declare-const X_46 Real) +(declare-const X_47 Real) +(declare-const X_48 Real) +(declare-const X_49 Real) +(declare-const X_50 Real) +(declare-const X_51 Real) +(declare-const X_52 Real) +(declare-const X_53 Real) +(declare-const X_54 Real) +(declare-const X_55 Real) +(declare-const X_56 Real) +(declare-const X_57 Real) +(declare-const X_58 Real) +(declare-const X_59 Real) +(declare-const X_60 Real) +(declare-const X_61 Real) +(declare-const X_62 Real) +(declare-const X_63 Real) +(declare-const X_64 Real) +(declare-const X_65 Real) +(declare-const X_66 Real) +(declare-const X_67 Real) +(declare-const X_68 Real) +(declare-const X_69 Real) +(declare-const X_70 Real) +(declare-const X_71 Real) +(declare-const X_72 Real) +(declare-const X_73 Real) +(declare-const X_74 Real) +(declare-const X_75 Real) +(declare-const X_76 Real) +(declare-const X_77 Real) +(declare-const X_78 Real) +(declare-const X_79 Real) +(declare-const X_80 Real) +(declare-const X_81 Real) +(declare-const X_82 Real) +(declare-const X_83 Real) +(declare-const X_84 Real) +(declare-const X_85 Real) +(declare-const X_86 Real) +(declare-const X_87 Real) +(declare-const X_88 Real) +(declare-const X_89 Real) +(declare-const X_90 Real) +(declare-const X_91 Real) +(declare-const X_92 Real) +(declare-const X_93 Real) +(declare-const X_94 Real) +(declare-const X_95 Real) +(declare-const X_96 Real) +(declare-const X_97 Real) +(declare-const X_98 Real) +(declare-const X_99 Real) +(declare-const X_100 Real) +(declare-const X_101 Real) +(declare-const X_102 Real) +(declare-const X_103 Real) +(declare-const X_104 Real) +(declare-const X_105 Real) +(declare-const X_106 Real) +(declare-const X_107 Real) +(declare-const X_108 Real) +(declare-const X_109 Real) +(declare-const X_110 Real) +(declare-const X_111 Real) +(declare-const X_112 Real) +(declare-const X_113 Real) +(declare-const X_114 Real) +(declare-const X_115 Real) +(declare-const X_116 Real) +(declare-const X_117 Real) +(declare-const X_118 Real) +(declare-const X_119 Real) +(declare-const X_120 Real) +(declare-const X_121 Real) +(declare-const X_122 Real) +(declare-const X_123 Real) +(declare-const X_124 Real) +(declare-const X_125 Real) +(declare-const X_126 Real) +(declare-const X_127 Real) +(declare-const X_128 Real) +(declare-const X_129 Real) +(declare-const X_130 Real) +(declare-const X_131 Real) +(declare-const X_132 Real) +(declare-const X_133 Real) +(declare-const X_134 Real) +(declare-const X_135 Real) +(declare-const X_136 Real) +(declare-const X_137 Real) +(declare-const X_138 Real) +(declare-const X_139 Real) +(declare-const X_140 Real) +(declare-const X_141 Real) +(declare-const X_142 Real) +(declare-const X_143 Real) +(declare-const X_144 Real) +(declare-const X_145 Real) +(declare-const X_146 Real) +(declare-const X_147 Real) +(declare-const X_148 Real) +(declare-const X_149 Real) +(declare-const X_150 Real) +(declare-const X_151 Real) +(declare-const X_152 Real) +(declare-const X_153 Real) +(declare-const X_154 Real) +(declare-const X_155 Real) +(declare-const X_156 Real) +(declare-const X_157 Real) +(declare-const X_158 Real) +(declare-const X_159 Real) +(declare-const X_160 Real) +(declare-const X_161 Real) +(declare-const X_162 Real) +(declare-const X_163 Real) +(declare-const X_164 Real) +(declare-const X_165 Real) +(declare-const X_166 Real) +(declare-const X_167 Real) +(declare-const X_168 Real) +(declare-const X_169 Real) +(declare-const X_170 Real) +(declare-const X_171 Real) +(declare-const X_172 Real) +(declare-const X_173 Real) +(declare-const X_174 Real) +(declare-const X_175 Real) +(declare-const X_176 Real) +(declare-const X_177 Real) +(declare-const X_178 Real) +(declare-const X_179 Real) +(declare-const X_180 Real) +(declare-const X_181 Real) +(declare-const X_182 Real) +(declare-const X_183 Real) +(declare-const X_184 Real) +(declare-const X_185 Real) +(declare-const X_186 Real) +(declare-const X_187 Real) +(declare-const X_188 Real) +(declare-const X_189 Real) +(declare-const X_190 Real) +(declare-const X_191 Real) +(declare-const X_192 Real) +(declare-const X_193 Real) +(declare-const X_194 Real) +(declare-const X_195 Real) +(declare-const X_196 Real) +(declare-const X_197 Real) +(declare-const X_198 Real) +(declare-const X_199 Real) +(declare-const X_200 Real) +(declare-const X_201 Real) +(declare-const X_202 Real) +(declare-const X_203 Real) +(declare-const X_204 Real) +(declare-const X_205 Real) +(declare-const X_206 Real) +(declare-const X_207 Real) +(declare-const X_208 Real) +(declare-const X_209 Real) +(declare-const X_210 Real) +(declare-const X_211 Real) +(declare-const X_212 Real) +(declare-const X_213 Real) +(declare-const X_214 Real) +(declare-const X_215 Real) +(declare-const X_216 Real) +(declare-const X_217 Real) +(declare-const X_218 Real) +(declare-const X_219 Real) +(declare-const X_220 Real) +(declare-const X_221 Real) +(declare-const X_222 Real) +(declare-const X_223 Real) +(declare-const X_224 Real) +(declare-const X_225 Real) +(declare-const X_226 Real) +(declare-const X_227 Real) +(declare-const X_228 Real) +(declare-const X_229 Real) +(declare-const X_230 Real) +(declare-const X_231 Real) +(declare-const X_232 Real) +(declare-const X_233 Real) +(declare-const X_234 Real) +(declare-const X_235 Real) +(declare-const X_236 Real) +(declare-const X_237 Real) +(declare-const X_238 Real) +(declare-const X_239 Real) +(declare-const X_240 Real) +(declare-const X_241 Real) +(declare-const X_242 Real) +(declare-const X_243 Real) +(declare-const X_244 Real) +(declare-const X_245 Real) +(declare-const X_246 Real) +(declare-const X_247 Real) +(declare-const X_248 Real) +(declare-const X_249 Real) +(declare-const X_250 Real) +(declare-const X_251 Real) +(declare-const X_252 Real) +(declare-const X_253 Real) +(declare-const X_254 Real) +(declare-const X_255 Real) +(declare-const X_256 Real) +(declare-const X_257 Real) +(declare-const X_258 Real) +(declare-const X_259 Real) +(declare-const X_260 Real) +(declare-const X_261 Real) +(declare-const X_262 Real) +(declare-const X_263 Real) +(declare-const X_264 Real) +(declare-const X_265 Real) +(declare-const X_266 Real) +(declare-const X_267 Real) +(declare-const X_268 Real) +(declare-const X_269 Real) +(declare-const X_270 Real) +(declare-const X_271 Real) +(declare-const X_272 Real) +(declare-const X_273 Real) +(declare-const X_274 Real) +(declare-const X_275 Real) +(declare-const X_276 Real) +(declare-const X_277 Real) +(declare-const X_278 Real) +(declare-const X_279 Real) +(declare-const X_280 Real) +(declare-const X_281 Real) +(declare-const X_282 Real) +(declare-const X_283 Real) +(declare-const X_284 Real) +(declare-const X_285 Real) +(declare-const X_286 Real) +(declare-const X_287 Real) +(declare-const X_288 Real) +(declare-const X_289 Real) +(declare-const X_290 Real) +(declare-const X_291 Real) +(declare-const X_292 Real) +(declare-const X_293 Real) +(declare-const X_294 Real) +(declare-const X_295 Real) +(declare-const X_296 Real) +(declare-const X_297 Real) +(declare-const X_298 Real) +(declare-const X_299 Real) +(declare-const X_300 Real) +(declare-const X_301 Real) +(declare-const X_302 Real) +(declare-const X_303 Real) +(declare-const X_304 Real) +(declare-const X_305 Real) +(declare-const X_306 Real) +(declare-const X_307 Real) +(declare-const X_308 Real) +(declare-const X_309 Real) +(declare-const X_310 Real) +(declare-const X_311 Real) +(declare-const X_312 Real) +(declare-const X_313 Real) +(declare-const X_314 Real) +(declare-const X_315 Real) +(declare-const X_316 Real) +(declare-const X_317 Real) +(declare-const X_318 Real) +(declare-const X_319 Real) +(declare-const X_320 Real) +(declare-const X_321 Real) +(declare-const X_322 Real) +(declare-const X_323 Real) +(declare-const X_324 Real) +(declare-const X_325 Real) +(declare-const X_326 Real) +(declare-const X_327 Real) +(declare-const X_328 Real) +(declare-const X_329 Real) +(declare-const X_330 Real) +(declare-const X_331 Real) +(declare-const X_332 Real) +(declare-const X_333 Real) +(declare-const X_334 Real) +(declare-const X_335 Real) +(declare-const X_336 Real) +(declare-const X_337 Real) +(declare-const X_338 Real) +(declare-const X_339 Real) +(declare-const X_340 Real) +(declare-const X_341 Real) +(declare-const X_342 Real) +(declare-const X_343 Real) +(declare-const X_344 Real) +(declare-const X_345 Real) +(declare-const X_346 Real) +(declare-const X_347 Real) +(declare-const X_348 Real) +(declare-const X_349 Real) +(declare-const X_350 Real) +(declare-const X_351 Real) +(declare-const X_352 Real) +(declare-const X_353 Real) +(declare-const X_354 Real) +(declare-const X_355 Real) +(declare-const X_356 Real) +(declare-const X_357 Real) +(declare-const X_358 Real) +(declare-const X_359 Real) +(declare-const X_360 Real) +(declare-const X_361 Real) +(declare-const X_362 Real) +(declare-const X_363 Real) +(declare-const X_364 Real) +(declare-const X_365 Real) +(declare-const X_366 Real) +(declare-const X_367 Real) +(declare-const X_368 Real) +(declare-const X_369 Real) +(declare-const X_370 Real) +(declare-const X_371 Real) +(declare-const X_372 Real) +(declare-const X_373 Real) +(declare-const X_374 Real) +(declare-const X_375 Real) +(declare-const X_376 Real) +(declare-const X_377 Real) +(declare-const X_378 Real) +(declare-const X_379 Real) +(declare-const X_380 Real) +(declare-const X_381 Real) +(declare-const X_382 Real) +(declare-const X_383 Real) +(declare-const X_384 Real) +(declare-const X_385 Real) +(declare-const X_386 Real) +(declare-const X_387 Real) +(declare-const X_388 Real) +(declare-const X_389 Real) +(declare-const X_390 Real) +(declare-const X_391 Real) +(declare-const X_392 Real) +(declare-const X_393 Real) +(declare-const X_394 Real) +(declare-const X_395 Real) +(declare-const X_396 Real) +(declare-const X_397 Real) +(declare-const X_398 Real) +(declare-const X_399 Real) +(declare-const X_400 Real) +(declare-const X_401 Real) +(declare-const X_402 Real) +(declare-const X_403 Real) +(declare-const X_404 Real) +(declare-const X_405 Real) +(declare-const X_406 Real) +(declare-const X_407 Real) +(declare-const X_408 Real) +(declare-const X_409 Real) +(declare-const X_410 Real) +(declare-const X_411 Real) +(declare-const X_412 Real) +(declare-const X_413 Real) +(declare-const X_414 Real) +(declare-const X_415 Real) +(declare-const X_416 Real) +(declare-const X_417 Real) +(declare-const X_418 Real) +(declare-const X_419 Real) +(declare-const X_420 Real) +(declare-const X_421 Real) +(declare-const X_422 Real) +(declare-const X_423 Real) +(declare-const X_424 Real) +(declare-const X_425 Real) +(declare-const X_426 Real) +(declare-const X_427 Real) +(declare-const X_428 Real) +(declare-const X_429 Real) +(declare-const X_430 Real) +(declare-const X_431 Real) +(declare-const X_432 Real) +(declare-const X_433 Real) +(declare-const X_434 Real) +(declare-const X_435 Real) +(declare-const X_436 Real) +(declare-const X_437 Real) +(declare-const X_438 Real) +(declare-const X_439 Real) +(declare-const X_440 Real) +(declare-const X_441 Real) +(declare-const X_442 Real) +(declare-const X_443 Real) +(declare-const X_444 Real) +(declare-const X_445 Real) +(declare-const X_446 Real) +(declare-const X_447 Real) +(declare-const X_448 Real) +(declare-const X_449 Real) +(declare-const X_450 Real) +(declare-const X_451 Real) +(declare-const X_452 Real) +(declare-const X_453 Real) +(declare-const X_454 Real) +(declare-const X_455 Real) +(declare-const X_456 Real) +(declare-const X_457 Real) +(declare-const X_458 Real) +(declare-const X_459 Real) +(declare-const X_460 Real) +(declare-const X_461 Real) +(declare-const X_462 Real) +(declare-const X_463 Real) +(declare-const X_464 Real) +(declare-const X_465 Real) +(declare-const X_466 Real) +(declare-const X_467 Real) +(declare-const X_468 Real) +(declare-const X_469 Real) +(declare-const X_470 Real) +(declare-const X_471 Real) +(declare-const X_472 Real) +(declare-const X_473 Real) +(declare-const X_474 Real) +(declare-const X_475 Real) +(declare-const X_476 Real) +(declare-const X_477 Real) +(declare-const X_478 Real) +(declare-const X_479 Real) +(declare-const X_480 Real) +(declare-const X_481 Real) +(declare-const X_482 Real) +(declare-const X_483 Real) +(declare-const X_484 Real) +(declare-const X_485 Real) +(declare-const X_486 Real) +(declare-const X_487 Real) +(declare-const X_488 Real) +(declare-const X_489 Real) +(declare-const X_490 Real) +(declare-const X_491 Real) +(declare-const X_492 Real) +(declare-const X_493 Real) +(declare-const X_494 Real) +(declare-const X_495 Real) +(declare-const X_496 Real) +(declare-const X_497 Real) +(declare-const X_498 Real) +(declare-const X_499 Real) +(declare-const X_500 Real) +(declare-const X_501 Real) +(declare-const X_502 Real) +(declare-const X_503 Real) +(declare-const X_504 Real) +(declare-const X_505 Real) +(declare-const X_506 Real) +(declare-const X_507 Real) +(declare-const X_508 Real) +(declare-const X_509 Real) +(declare-const X_510 Real) +(declare-const X_511 Real) +(declare-const X_512 Real) +(declare-const X_513 Real) +(declare-const X_514 Real) +(declare-const X_515 Real) +(declare-const X_516 Real) +(declare-const X_517 Real) +(declare-const X_518 Real) +(declare-const X_519 Real) +(declare-const X_520 Real) +(declare-const X_521 Real) +(declare-const X_522 Real) +(declare-const X_523 Real) +(declare-const X_524 Real) +(declare-const X_525 Real) +(declare-const X_526 Real) +(declare-const X_527 Real) +(declare-const X_528 Real) +(declare-const X_529 Real) +(declare-const X_530 Real) +(declare-const X_531 Real) +(declare-const X_532 Real) +(declare-const X_533 Real) +(declare-const X_534 Real) +(declare-const X_535 Real) +(declare-const X_536 Real) +(declare-const X_537 Real) +(declare-const X_538 Real) +(declare-const X_539 Real) +(declare-const X_540 Real) +(declare-const X_541 Real) +(declare-const X_542 Real) +(declare-const X_543 Real) +(declare-const X_544 Real) +(declare-const X_545 Real) +(declare-const X_546 Real) +(declare-const X_547 Real) +(declare-const X_548 Real) +(declare-const X_549 Real) +(declare-const X_550 Real) +(declare-const X_551 Real) +(declare-const X_552 Real) +(declare-const X_553 Real) +(declare-const X_554 Real) +(declare-const X_555 Real) +(declare-const X_556 Real) +(declare-const X_557 Real) +(declare-const X_558 Real) +(declare-const X_559 Real) +(declare-const X_560 Real) +(declare-const X_561 Real) +(declare-const X_562 Real) +(declare-const X_563 Real) +(declare-const X_564 Real) +(declare-const X_565 Real) +(declare-const X_566 Real) +(declare-const X_567 Real) +(declare-const X_568 Real) +(declare-const X_569 Real) +(declare-const X_570 Real) +(declare-const X_571 Real) +(declare-const X_572 Real) +(declare-const X_573 Real) +(declare-const X_574 Real) +(declare-const X_575 Real) +(declare-const X_576 Real) +(declare-const X_577 Real) +(declare-const X_578 Real) +(declare-const X_579 Real) +(declare-const X_580 Real) +(declare-const X_581 Real) +(declare-const X_582 Real) +(declare-const X_583 Real) +(declare-const X_584 Real) +(declare-const X_585 Real) +(declare-const X_586 Real) +(declare-const X_587 Real) +(declare-const X_588 Real) +(declare-const X_589 Real) +(declare-const X_590 Real) +(declare-const X_591 Real) +(declare-const X_592 Real) +(declare-const X_593 Real) +(declare-const X_594 Real) +(declare-const X_595 Real) +(declare-const X_596 Real) +(declare-const X_597 Real) +(declare-const X_598 Real) +(declare-const X_599 Real) +(declare-const X_600 Real) +(declare-const X_601 Real) +(declare-const X_602 Real) +(declare-const X_603 Real) +(declare-const X_604 Real) +(declare-const X_605 Real) +(declare-const X_606 Real) +(declare-const X_607 Real) +(declare-const X_608 Real) +(declare-const X_609 Real) +(declare-const X_610 Real) +(declare-const X_611 Real) +(declare-const X_612 Real) +(declare-const X_613 Real) +(declare-const X_614 Real) +(declare-const X_615 Real) +(declare-const X_616 Real) +(declare-const X_617 Real) +(declare-const X_618 Real) +(declare-const X_619 Real) +(declare-const X_620 Real) +(declare-const X_621 Real) +(declare-const X_622 Real) +(declare-const X_623 Real) +(declare-const X_624 Real) +(declare-const X_625 Real) +(declare-const X_626 Real) +(declare-const X_627 Real) +(declare-const X_628 Real) +(declare-const X_629 Real) +(declare-const X_630 Real) +(declare-const X_631 Real) +(declare-const X_632 Real) +(declare-const X_633 Real) +(declare-const X_634 Real) +(declare-const X_635 Real) +(declare-const X_636 Real) +(declare-const X_637 Real) +(declare-const X_638 Real) +(declare-const X_639 Real) +(declare-const X_640 Real) +(declare-const X_641 Real) +(declare-const X_642 Real) +(declare-const X_643 Real) +(declare-const X_644 Real) +(declare-const X_645 Real) +(declare-const X_646 Real) +(declare-const X_647 Real) +(declare-const X_648 Real) +(declare-const X_649 Real) +(declare-const X_650 Real) +(declare-const X_651 Real) +(declare-const X_652 Real) +(declare-const X_653 Real) +(declare-const X_654 Real) +(declare-const X_655 Real) +(declare-const X_656 Real) +(declare-const X_657 Real) +(declare-const X_658 Real) +(declare-const X_659 Real) +(declare-const X_660 Real) +(declare-const X_661 Real) +(declare-const X_662 Real) +(declare-const X_663 Real) +(declare-const X_664 Real) +(declare-const X_665 Real) +(declare-const X_666 Real) +(declare-const X_667 Real) +(declare-const X_668 Real) +(declare-const X_669 Real) +(declare-const X_670 Real) +(declare-const X_671 Real) +(declare-const X_672 Real) +(declare-const X_673 Real) +(declare-const X_674 Real) +(declare-const X_675 Real) +(declare-const X_676 Real) +(declare-const X_677 Real) +(declare-const X_678 Real) +(declare-const X_679 Real) +(declare-const X_680 Real) +(declare-const X_681 Real) +(declare-const X_682 Real) +(declare-const X_683 Real) +(declare-const X_684 Real) +(declare-const X_685 Real) +(declare-const X_686 Real) +(declare-const X_687 Real) +(declare-const X_688 Real) +(declare-const X_689 Real) +(declare-const X_690 Real) +(declare-const X_691 Real) +(declare-const X_692 Real) +(declare-const X_693 Real) +(declare-const X_694 Real) +(declare-const X_695 Real) +(declare-const X_696 Real) +(declare-const X_697 Real) +(declare-const X_698 Real) +(declare-const X_699 Real) +(declare-const X_700 Real) +(declare-const X_701 Real) +(declare-const X_702 Real) +(declare-const X_703 Real) +(declare-const X_704 Real) +(declare-const X_705 Real) +(declare-const X_706 Real) +(declare-const X_707 Real) +(declare-const X_708 Real) +(declare-const X_709 Real) +(declare-const X_710 Real) +(declare-const X_711 Real) +(declare-const X_712 Real) +(declare-const X_713 Real) +(declare-const X_714 Real) +(declare-const X_715 Real) +(declare-const X_716 Real) +(declare-const X_717 Real) +(declare-const X_718 Real) +(declare-const X_719 Real) +(declare-const X_720 Real) +(declare-const X_721 Real) +(declare-const X_722 Real) +(declare-const X_723 Real) +(declare-const X_724 Real) +(declare-const X_725 Real) +(declare-const X_726 Real) +(declare-const X_727 Real) +(declare-const X_728 Real) +(declare-const X_729 Real) +(declare-const X_730 Real) +(declare-const X_731 Real) +(declare-const X_732 Real) +(declare-const X_733 Real) +(declare-const X_734 Real) +(declare-const X_735 Real) +(declare-const X_736 Real) +(declare-const X_737 Real) +(declare-const X_738 Real) +(declare-const X_739 Real) +(declare-const X_740 Real) +(declare-const X_741 Real) +(declare-const X_742 Real) +(declare-const X_743 Real) +(declare-const X_744 Real) +(declare-const X_745 Real) +(declare-const X_746 Real) +(declare-const X_747 Real) +(declare-const X_748 Real) +(declare-const X_749 Real) +(declare-const X_750 Real) +(declare-const X_751 Real) +(declare-const X_752 Real) +(declare-const X_753 Real) +(declare-const X_754 Real) +(declare-const X_755 Real) +(declare-const X_756 Real) +(declare-const X_757 Real) +(declare-const X_758 Real) +(declare-const X_759 Real) +(declare-const X_760 Real) +(declare-const X_761 Real) +(declare-const X_762 Real) +(declare-const X_763 Real) +(declare-const X_764 Real) +(declare-const X_765 Real) +(declare-const X_766 Real) +(declare-const X_767 Real) +(declare-const X_768 Real) +(declare-const X_769 Real) +(declare-const X_770 Real) +(declare-const X_771 Real) +(declare-const X_772 Real) +(declare-const X_773 Real) +(declare-const X_774 Real) +(declare-const X_775 Real) +(declare-const X_776 Real) +(declare-const X_777 Real) +(declare-const X_778 Real) +(declare-const X_779 Real) +(declare-const X_780 Real) +(declare-const X_781 Real) +(declare-const X_782 Real) +(declare-const X_783 Real) + + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) +(declare-const Y_5 Real) +(declare-const Y_6 Real) +(declare-const Y_7 Real) +(declare-const Y_8 Real) +(declare-const Y_9 Real) + +; Input constraints: +(assert (<= X_0 0.029999999329447746)) +(assert (>= X_0 0.0)) + +(assert (<= X_1 0.029999999329447746)) +(assert (>= X_1 0.0)) + +(assert (<= X_2 0.029999999329447746)) +(assert (>= X_2 0.0)) + +(assert (<= X_3 0.029999999329447746)) +(assert (>= X_3 0.0)) + +(assert (<= X_4 0.029999999329447746)) +(assert (>= X_4 0.0)) + +(assert (<= X_5 0.029999999329447746)) +(assert (>= X_5 0.0)) + +(assert (<= X_6 0.029999999329447746)) +(assert (>= X_6 0.0)) + +(assert (<= X_7 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0.029999999329447746)) +(assert (>= X_761 0.0)) + +(assert (<= X_762 0.029999999329447746)) +(assert (>= X_762 0.0)) + +(assert (<= X_763 0.029999999329447746)) +(assert (>= X_763 0.0)) + +(assert (<= X_764 0.029999999329447746)) +(assert (>= X_764 0.0)) + +(assert (<= X_765 0.029999999329447746)) +(assert (>= X_765 0.0)) + +(assert (<= X_766 0.029999999329447746)) +(assert (>= X_766 0.0)) + +(assert (<= X_767 0.029999999329447746)) +(assert (>= X_767 0.0)) + +(assert (<= X_768 0.029999999329447746)) +(assert (>= X_768 0.0)) + +(assert (<= X_769 0.029999999329447746)) +(assert (>= X_769 0.0)) + +(assert (<= X_770 0.029999999329447746)) +(assert (>= X_770 0.0)) + +(assert (<= X_771 0.029999999329447746)) +(assert (>= X_771 0.0)) + +(assert (<= X_772 0.029999999329447746)) +(assert (>= X_772 0.0)) + +(assert (<= X_773 0.029999999329447746)) +(assert (>= X_773 0.0)) + +(assert (<= X_774 0.029999999329447746)) +(assert (>= X_774 0.0)) + +(assert (<= X_775 0.029999999329447746)) +(assert (>= X_775 0.0)) + +(assert (<= X_776 0.029999999329447746)) +(assert (>= X_776 0.0)) + +(assert (<= X_777 0.029999999329447746)) +(assert (>= X_777 0.0)) + +(assert (<= X_778 0.029999999329447746)) +(assert (>= X_778 0.0)) + +(assert (<= X_779 0.029999999329447746)) +(assert (>= X_779 0.0)) + +(assert (<= X_780 0.029999999329447746)) +(assert (>= X_780 0.0)) + +(assert (<= X_781 0.029999999329447746)) +(assert (>= X_781 0.0)) + +(assert (<= X_782 0.029999999329447746)) +(assert (>= X_782 0.0)) + +(assert (<= X_783 0.029999999329447746)) +(assert (>= X_783 0.0)) + + +; Output constraints: +(assert (or + (and (>= Y_0 Y_7)) + (and (>= Y_1 Y_7)) + (and (>= Y_2 Y_7)) + (and (>= Y_3 Y_7)) + (and (>= Y_4 Y_7)) + (and (>= Y_5 Y_7)) + (and (>= Y_6 Y_7)) + (and (>= Y_8 Y_7)) + (and (>= Y_9 Y_7)) +)) \ No newline at end of file diff --git a/requirements.txt b/requirements.txt index d447b10..d77a924 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,10 +1,8 @@ -tensorflow==2.2.1 -numpy==1.17.4 +numpy==1.19.5 scipy==1.4.1 -foolbox==2.4.0 threadpoolctl==2.1.0 -onnx==1.7.0 -onnxruntime==1.3.0 +onnx==1.9.0 +onnxruntime==1.8.0 skl2onnx==1.7.0 swiglpk termcolor diff --git a/run_tests.sh b/run_tests.sh new file mode 100755 index 0000000..1b453ac --- /dev/null +++ b/run_tests.sh @@ -0,0 +1,10 @@ +#!/bin/bash -e + +python3 -m nnenum.nnenum examples/acasxu/data/ACASXU_run2a_1_1_batch_2000.onnx examples/acasxu/data/prop_1.vnnlib + + +python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/prop_0_0.03.vnnlib + +python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/prop_2_0.03.vnnlib + +python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255.onnx examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib diff --git a/src/nnenum/enumerate.py b/src/nnenum/enumerate.py index 9f95dcc..12d731f 100644 --- a/src/nnenum/enumerate.py +++ b/src/nnenum/enumerate.py @@ -22,7 +22,6 @@ from nnenum.network import NeuralNetwork, nn_flatten from nnenum.worker import Worker from nnenum.overapprox import try_quick_overapprox -from nnenum.onnx_network import reinit_onnx_sessions from nnenum.prefilter import LpCanceledException @@ -49,8 +48,9 @@ def make_init_ss(init, network, spec, start_time): assert isinstance(init, LpStarState), f"unsupported init type: {type(init)}" ss = init - assert len(ss.star.init_bias) == network_inputs, f"init_bias len: {len(ss.star.init_bias)}" + \ - f", network inputs: {network_inputs}" + if ss.star.init_bias is not None: + assert len(ss.star.init_bias) == network_inputs, f"init_bias len: {len(ss.star.init_bias)}" + \ + f", network inputs: {network_inputs}" ss.should_try_overapprox = False @@ -104,6 +104,7 @@ def enumerate_network(init, network, spec=None): "RESULT_SAVE_TIMERS cannot be used if TIMING_STATS is False" init_ss = None + concrete_io_tuple = None if time.perf_counter() - start < Settings.TIMEOUT: init_ss = make_init_ss(init, network, spec, start) # returns None if timeout @@ -173,11 +174,14 @@ def enumerate_network(init, network, spec=None): Timers.toc('run workers') + assert shared.more_work_queue.qsize() == 0 rv = shared.result rv.total_secs = time.perf_counter() - start process_result(shared) + + if rv.total_secs is None: rv.total_secs = time.perf_counter() - start @@ -465,7 +469,6 @@ def worker_func(worker_index, shared): np.seterr(all='raise', under=Settings.UNDERFLOW_BEHAVIOR) # raise exceptions on floating-point errors if shared.multithreaded: - reinit_onnx_sessions(shared.network) Timers.stack.clear() # reset inherited Timers tag = f" (Process {worker_index})" else: @@ -474,7 +477,7 @@ def worker_func(worker_index, shared): timer_name = f'worker_func{tag}' Timers.tic(timer_name) - + priv = PrivateState(worker_index) priv.start_time = shared.start_time w = Worker(shared, priv) @@ -594,4 +597,3 @@ def worker_func(worker_index, shared): Timers.toc(timer_name) - diff --git a/src/nnenum/nnenum.py b/src/nnenum/nnenum.py index 1c01edb..b8a7436 100644 --- a/src/nnenum/nnenum.py +++ b/src/nnenum/nnenum.py @@ -14,7 +14,7 @@ from nnenum.enumerate import enumerate_network from nnenum.settings import Settings from nnenum.result import Result -from nnenum.onnx_network import load_onnx_network_optimized +from nnenum.onnx_network import load_onnx_network_optimized, load_onnx_network from nnenum.specification import Specification, DisjunctiveSpec from nnenum.vnnlib import get_num_inputs_outputs, read_vnnlib_simple @@ -44,7 +44,6 @@ def make_spec(vnnlib_filename, onnx_filename): def set_control_settings(): 'set settings for smaller control benchmarks' - Settings.reset() Settings.TIMING_STATS = False Settings.PARALLEL_ROOT_LP = False Settings.SPLIT_IF_IDLE = False @@ -65,13 +64,24 @@ def set_control_settings(): def set_image_settings(): 'set settings for larger image benchmarks' - pass + Settings.COMPRESS_INIT_BOX = False + Settings.BRANCH_MODE = Settings.BRANCH_OVERAPPROX + + Settings.OVERAPPROX_MIN_GEN_LIMIT = np.inf + Settings.SPLIT_IF_IDLE = False + Settings.OVERAPPROX_LP_TIMEOUT = np.inf + Settings.TIMING_STATS = False + + # contraction doesn't help in high dimensions + #Settings.OVERAPPROX_CONTRACT_ZONO_LP = False + Settings.CONTRACT_ZONOTOPE = False + Settings.CONTRACT_ZONOTOPE_LP = False def main(): 'main entry point' if len(sys.argv) < 3: - print('usage: "python3 nnenum.py [timeout=None] [outfile=None]"') + print('usage: "python3 nnenum.py [timeout=None] [outfile=None] [processes=]"') sys.exit(1) onnx_filename = sys.argv[1] @@ -85,10 +95,19 @@ def main(): if len(sys.argv) >= 5: outfile = sys.argv[4] + if len(sys.argv) >= 6: + processes = int(sys.argv[5]) + Settings.NUM_PROCESSES = processes + # spec_list, input_dtype = make_spec(vnnlib_filename, onnx_filename) - network = load_onnx_network_optimized(onnx_filename) + try: + network = load_onnx_network_optimized(onnx_filename) + except AssertionError: + # cannot do optimized load due to unsupported layers + network = load_onnx_network(onnx_filename) + result_str = 'none' # gets overridden num_inputs = len(spec_list[0][0]) @@ -98,6 +117,10 @@ def main(): else: set_image_settings() + print("using debug settings (nnenum.py)...") + #Settings.NUM_PROCESSES = 1 + Settings.TRY_QUICK_OVERAPPROX = False + for init_box, spec in spec_list: init_box = np.array(init_box, dtype=input_dtype) diff --git a/src/nnenum/onnx_network.py b/src/nnenum/onnx_network.py index 39300c1..54b03be 100644 --- a/src/nnenum/onnx_network.py +++ b/src/nnenum/onnx_network.py @@ -79,11 +79,6 @@ def get_output_shape(self): return self.output_shape - def reinit_onnx_session(self): - 'reinitailzie the onnx session' - - self.sess = ort.InferenceSession(self.model_str) - def transform_star(self, star): 'transform the star' @@ -805,10 +800,3 @@ def load_onnx_network(filename): layers.append(l) return NeuralNetwork(layers) - -def reinit_onnx_sessions(network): - 'reinit onnx sessions in the network' - - for l in network.layers: - if isinstance(l, LinearOnnxSubnetworkLayer): - l.reinit_onnx_session() diff --git a/src/nnenum/overapprox.py b/src/nnenum/overapprox.py index ffeb057..041c815 100644 --- a/src/nnenum/overapprox.py +++ b/src/nnenum/overapprox.py @@ -318,7 +318,7 @@ def do_overapprox_rounds(ss, network, spec, prerelu_sims, check_cancel_func=None if vstars: dims = ss.star.lpi.get_num_cols() - abstract_ios, rv.concrete_io_tuple = test_abstract_violation(dims, vstars, vindices, network, spec) + _abstract_ios, rv.concrete_io_tuple = test_abstract_violation(dims, vstars, vindices, network, spec) if first_round: first_round = False From e57fbc54795bfb23e8705e94ed6e2ca29fe1eb0e Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 17:00:44 -0400 Subject: [PATCH 19/55] changed to 'c' order flattening --- ...255.onnx => cifar10_2_255_simplified.onnx} | Bin 8734338 -> 8536048 bytes run_tests.sh | 2 +- src/nnenum/network.py | 5 ++--- 3 files changed, 3 insertions(+), 4 deletions(-) rename examples/cifar2020/{cifar10_2_255.onnx => cifar10_2_255_simplified.onnx} (97%) diff --git a/examples/cifar2020/cifar10_2_255.onnx b/examples/cifar2020/cifar10_2_255_simplified.onnx similarity index 97% rename from examples/cifar2020/cifar10_2_255.onnx rename to examples/cifar2020/cifar10_2_255_simplified.onnx index 7a8104e03417334a5a577d9db8a9fee0cd592314..b36113fbe91e7c27dc103acc91a43003ece04669 100644 GIT binary patch delta 1148 zcmZY9OHUI~7=YnSJJ`d}LTR-iAXY@VD7Bs5m?DT(@ybO6FDPii3e^foi+~rbC_w@) zNTb~$dzUN-G5iTP{tZoBxxu%wG)+zOB%L{VzcZPf%)-Y{^3UB5@);pp43l&5iK&sX z3cbtW4*cM*vLY$ctWpvU&4s684yR)#92p&pE2iv?;YcWE(Yah}gAt#LKWdHK8;(vZ ztCGS+wp8;=)sZRPYlB*{Q*t)BsXe*1CtG{+YtLF=Fdg-KiF}!;njL*y`)dpx(NH`d z9&apCSja1iYY%(Q_BI}a@m)JOkx+ZkaH4s$=jk! zd0X_x(v&O`QqD%6t<`V(LS6Yr!py>drDth-M-LeV*q7SgF&ImC4dPGk6#tgBP5jc^ z))T+=tcXN=&hGxD`k+7|6coV-6N*s+GfH8B75i}jHk6?p2T_4aRN)Y+aTs*U*VBbfX8?(Tf}CLqBff7H;DX25=YmFo+@C#{+~gj1fFU7>_WDF+}hfPY}gZ zjAH_mc!nv&5XUs0V+OOB!wbB`E4;=$-XMXuSin2HPt^w(O(m^D$vJCU^1H=p{n{mz sf2U{fL~EP1){44Moi)R_za0#~(0_y7O^ delta 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@@ -7,4 +7,4 @@ python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/ python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/prop_2_0.03.vnnlib -python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255.onnx examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib +python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib diff --git a/src/nnenum/network.py b/src/nnenum/network.py index fd7ad1e..9db0273 100644 --- a/src/nnenum/network.py +++ b/src/nnenum/network.py @@ -837,8 +837,7 @@ def images_to_init_box(min_image, max_image): def nn_flatten(image): 'flatten a multichannel image to a 1-d array' - # note: fortran-style flattening makes Tran's example network classify correctly, so I guess it's the standard - return image.flatten('F') + return image.flatten('C') def nn_unflatten(image, shape): '''unflatten to a multichannel image from a 1-d array @@ -848,7 +847,7 @@ def nn_unflatten(image, shape): assert len(image.shape) == 1 - rv = image.reshape(shape, order='F') + rv = image.reshape(shape, order='C') return rv From e0971d66678e33f7b11abc3481c3cf6e6d988c4a Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 17:01:57 -0400 Subject: [PATCH 20/55] removed debug settings --- src/nnenum/nnenum.py | 4 ---- 1 file changed, 4 deletions(-) diff --git a/src/nnenum/nnenum.py b/src/nnenum/nnenum.py index b8a7436..cdc6cb4 100644 --- a/src/nnenum/nnenum.py +++ b/src/nnenum/nnenum.py @@ -117,10 +117,6 @@ def main(): else: set_image_settings() - print("using debug settings (nnenum.py)...") - #Settings.NUM_PROCESSES = 1 - Settings.TRY_QUICK_OVERAPPROX = False - for init_box, spec in spec_list: init_box = np.array(init_box, dtype=input_dtype) From a19dfb798d9963d59176d046077c5f1f23c26835 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 19:28:40 -0400 Subject: [PATCH 21/55] added cifar spec --- run_tests.sh | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/run_tests.sh b/run_tests.sh index 36d9f1e..4da2e69 100755 --- a/run_tests.sh +++ b/run_tests.sh @@ -8,3 +8,7 @@ python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/ python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/prop_2_0.03.vnnlib python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib + +python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib 45 /dev/null + +echo "Passed all tests" From c6c3de36aa375ebf342b0467f9726849e833dc4a Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 19:57:30 -0400 Subject: [PATCH 22/55] added run in docker command --- .travis.yml | 5 +- Dockerfile | 3 +- .../cifar10_spec_idx_3_eps_0.00784_n1.vnnlib | 9246 +++++++++++++++++ run_in_docker.sh | 34 + run_tests.sh | 3 +- 5 files changed, 9284 insertions(+), 7 deletions(-) create mode 100644 examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib create mode 100755 run_in_docker.sh diff --git a/.travis.yml b/.travis.yml index 9e2b4c4..6aec55e 100644 --- a/.travis.yml +++ b/.travis.yml @@ -12,8 +12,5 @@ services: - docker script: -# build Docker container -- docker build -t nnenum . +- ./run_tests.sh -# run tests -- docker run nnenum diff --git a/Dockerfile b/Dockerfile index 17dfe1a..2a57d65 100644 --- a/Dockerfile +++ b/Dockerfile @@ -14,10 +14,11 @@ COPY ./requirements.txt /work/requirements.txt WORKDIR /work # install python package dependencies +RUN pip install --upgrade pip RUN pip3 install -r requirements.txt # set environment variables -ENV PYTHONPATH=$PYTHONPATH:/work/nnenum +ENV PYTHONPATH=$PYTHONPATH:/work/src ENV OPENBLAS_NUM_THREADS=1 ENV OMP_NUM_THREADS=1 diff --git a/examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib b/examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib new file mode 100644 index 0000000..0b325b5 --- /dev/null +++ b/examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib @@ -0,0 +1,9246 @@ +; Spec for sample id 3 and epsilon 0.00784 + +; Definition of input variables +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) +(declare-const X_5 Real) +(declare-const X_6 Real) +(declare-const X_7 Real) +(declare-const X_8 Real) +(declare-const X_9 Real) +(declare-const X_10 Real) +(declare-const X_11 Real) +(declare-const X_12 Real) +(declare-const X_13 Real) +(declare-const X_14 Real) +(declare-const X_15 Real) +(declare-const X_16 Real) +(declare-const X_17 Real) +(declare-const X_18 Real) +(declare-const X_19 Real) +(declare-const X_20 Real) +(declare-const X_21 Real) +(declare-const X_22 Real) +(declare-const X_23 Real) +(declare-const X_24 Real) +(declare-const X_25 Real) +(declare-const X_26 Real) +(declare-const X_27 Real) +(declare-const X_28 Real) +(declare-const X_29 Real) +(declare-const X_30 Real) +(declare-const X_31 Real) +(declare-const X_32 Real) +(declare-const X_33 Real) +(declare-const X_34 Real) +(declare-const X_35 Real) +(declare-const X_36 Real) +(declare-const X_37 Real) +(declare-const X_38 Real) +(declare-const X_39 Real) +(declare-const X_40 Real) +(declare-const X_41 Real) +(declare-const X_42 Real) +(declare-const X_43 Real) +(declare-const X_44 Real) +(declare-const X_45 Real) +(declare-const X_46 Real) +(declare-const X_47 Real) +(declare-const X_48 Real) +(declare-const X_49 Real) +(declare-const X_50 Real) +(declare-const X_51 Real) +(declare-const X_52 Real) +(declare-const X_53 Real) +(declare-const X_54 Real) +(declare-const X_55 Real) +(declare-const X_56 Real) +(declare-const X_57 Real) +(declare-const X_58 Real) +(declare-const X_59 Real) +(declare-const X_60 Real) +(declare-const X_61 Real) +(declare-const X_62 Real) +(declare-const X_63 Real) +(declare-const X_64 Real) +(declare-const X_65 Real) +(declare-const 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+(declare-const X_955 Real) +(declare-const X_956 Real) +(declare-const X_957 Real) +(declare-const X_958 Real) +(declare-const X_959 Real) +(declare-const X_960 Real) +(declare-const X_961 Real) +(declare-const X_962 Real) +(declare-const X_963 Real) +(declare-const X_964 Real) +(declare-const X_965 Real) +(declare-const X_966 Real) +(declare-const X_967 Real) +(declare-const X_968 Real) +(declare-const X_969 Real) +(declare-const X_970 Real) +(declare-const X_971 Real) +(declare-const X_972 Real) +(declare-const X_973 Real) +(declare-const X_974 Real) +(declare-const X_975 Real) +(declare-const X_976 Real) +(declare-const X_977 Real) +(declare-const X_978 Real) +(declare-const X_979 Real) +(declare-const X_980 Real) +(declare-const X_981 Real) +(declare-const X_982 Real) +(declare-const X_983 Real) +(declare-const X_984 Real) +(declare-const X_985 Real) +(declare-const X_986 Real) +(declare-const X_987 Real) +(declare-const X_988 Real) +(declare-const X_989 Real) +(declare-const X_990 Real) +(declare-const X_991 Real) +(declare-const X_992 Real) +(declare-const X_993 Real) +(declare-const X_994 Real) +(declare-const X_995 Real) +(declare-const X_996 Real) +(declare-const X_997 Real) +(declare-const X_998 Real) +(declare-const X_999 Real) +(declare-const X_1000 Real) +(declare-const X_1001 Real) +(declare-const X_1002 Real) +(declare-const X_1003 Real) +(declare-const X_1004 Real) +(declare-const X_1005 Real) +(declare-const X_1006 Real) +(declare-const X_1007 Real) +(declare-const X_1008 Real) +(declare-const X_1009 Real) +(declare-const X_1010 Real) +(declare-const X_1011 Real) +(declare-const X_1012 Real) +(declare-const X_1013 Real) +(declare-const X_1014 Real) +(declare-const X_1015 Real) +(declare-const X_1016 Real) +(declare-const X_1017 Real) +(declare-const X_1018 Real) +(declare-const X_1019 Real) +(declare-const X_1020 Real) +(declare-const X_1021 Real) +(declare-const X_1022 Real) +(declare-const X_1023 Real) +(declare-const X_1024 Real) +(declare-const X_1025 Real) +(declare-const X_1026 Real) +(declare-const X_1027 Real) +(declare-const X_1028 Real) +(declare-const X_1029 Real) +(declare-const X_1030 Real) +(declare-const X_1031 Real) +(declare-const X_1032 Real) +(declare-const X_1033 Real) +(declare-const X_1034 Real) +(declare-const X_1035 Real) +(declare-const X_1036 Real) +(declare-const X_1037 Real) +(declare-const X_1038 Real) +(declare-const X_1039 Real) +(declare-const X_1040 Real) +(declare-const X_1041 Real) +(declare-const X_1042 Real) +(declare-const X_1043 Real) +(declare-const X_1044 Real) +(declare-const X_1045 Real) +(declare-const X_1046 Real) +(declare-const X_1047 Real) +(declare-const X_1048 Real) +(declare-const X_1049 Real) +(declare-const X_1050 Real) +(declare-const X_1051 Real) +(declare-const X_1052 Real) +(declare-const X_1053 Real) +(declare-const X_1054 Real) +(declare-const X_1055 Real) +(declare-const X_1056 Real) +(declare-const X_1057 Real) +(declare-const X_1058 Real) +(declare-const X_1059 Real) +(declare-const X_1060 Real) +(declare-const X_1061 Real) +(declare-const X_1062 Real) +(declare-const X_1063 Real) +(declare-const X_1064 Real) +(declare-const X_1065 Real) +(declare-const X_1066 Real) +(declare-const X_1067 Real) +(declare-const X_1068 Real) +(declare-const X_1069 Real) +(declare-const X_1070 Real) +(declare-const X_1071 Real) +(declare-const X_1072 Real) +(declare-const X_1073 Real) +(declare-const X_1074 Real) +(declare-const X_1075 Real) +(declare-const X_1076 Real) +(declare-const X_1077 Real) +(declare-const X_1078 Real) +(declare-const X_1079 Real) +(declare-const X_1080 Real) +(declare-const X_1081 Real) +(declare-const X_1082 Real) +(declare-const X_1083 Real) +(declare-const X_1084 Real) +(declare-const X_1085 Real) +(declare-const X_1086 Real) +(declare-const X_1087 Real) +(declare-const X_1088 Real) +(declare-const X_1089 Real) +(declare-const X_1090 Real) +(declare-const X_1091 Real) +(declare-const X_1092 Real) +(declare-const X_1093 Real) +(declare-const X_1094 Real) +(declare-const X_1095 Real) +(declare-const X_1096 Real) +(declare-const X_1097 Real) +(declare-const X_1098 Real) +(declare-const X_1099 Real) +(declare-const X_1100 Real) +(declare-const X_1101 Real) +(declare-const X_1102 Real) +(declare-const X_1103 Real) +(declare-const X_1104 Real) +(declare-const X_1105 Real) +(declare-const X_1106 Real) +(declare-const X_1107 Real) +(declare-const X_1108 Real) +(declare-const X_1109 Real) +(declare-const X_1110 Real) +(declare-const X_1111 Real) +(declare-const X_1112 Real) +(declare-const X_1113 Real) +(declare-const X_1114 Real) +(declare-const X_1115 Real) +(declare-const X_1116 Real) +(declare-const X_1117 Real) +(declare-const X_1118 Real) +(declare-const X_1119 Real) +(declare-const X_1120 Real) +(declare-const X_1121 Real) +(declare-const X_1122 Real) +(declare-const X_1123 Real) +(declare-const X_1124 Real) +(declare-const X_1125 Real) +(declare-const X_1126 Real) +(declare-const X_1127 Real) +(declare-const X_1128 Real) +(declare-const X_1129 Real) +(declare-const X_1130 Real) +(declare-const X_1131 Real) +(declare-const X_1132 Real) +(declare-const X_1133 Real) +(declare-const X_1134 Real) +(declare-const X_1135 Real) +(declare-const X_1136 Real) +(declare-const X_1137 Real) +(declare-const X_1138 Real) +(declare-const X_1139 Real) +(declare-const X_1140 Real) +(declare-const X_1141 Real) +(declare-const X_1142 Real) +(declare-const X_1143 Real) +(declare-const X_1144 Real) +(declare-const X_1145 Real) +(declare-const X_1146 Real) +(declare-const X_1147 Real) +(declare-const X_1148 Real) +(declare-const X_1149 Real) +(declare-const X_1150 Real) +(declare-const X_1151 Real) +(declare-const X_1152 Real) +(declare-const X_1153 Real) +(declare-const X_1154 Real) +(declare-const X_1155 Real) +(declare-const X_1156 Real) +(declare-const X_1157 Real) +(declare-const X_1158 Real) +(declare-const X_1159 Real) +(declare-const X_1160 Real) +(declare-const X_1161 Real) +(declare-const X_1162 Real) +(declare-const X_1163 Real) +(declare-const X_1164 Real) +(declare-const X_1165 Real) +(declare-const X_1166 Real) +(declare-const X_1167 Real) +(declare-const X_1168 Real) +(declare-const X_1169 Real) +(declare-const X_1170 Real) +(declare-const X_1171 Real) +(declare-const X_1172 Real) +(declare-const X_1173 Real) +(declare-const X_1174 Real) +(declare-const X_1175 Real) +(declare-const X_1176 Real) +(declare-const X_1177 Real) +(declare-const X_1178 Real) +(declare-const X_1179 Real) +(declare-const X_1180 Real) +(declare-const X_1181 Real) +(declare-const X_1182 Real) +(declare-const X_1183 Real) +(declare-const X_1184 Real) +(declare-const X_1185 Real) +(declare-const X_1186 Real) +(declare-const X_1187 Real) +(declare-const X_1188 Real) +(declare-const X_1189 Real) +(declare-const X_1190 Real) +(declare-const X_1191 Real) +(declare-const X_1192 Real) +(declare-const X_1193 Real) +(declare-const X_1194 Real) +(declare-const X_1195 Real) +(declare-const X_1196 Real) +(declare-const X_1197 Real) +(declare-const X_1198 Real) +(declare-const X_1199 Real) +(declare-const X_1200 Real) +(declare-const X_1201 Real) +(declare-const X_1202 Real) +(declare-const X_1203 Real) +(declare-const X_1204 Real) +(declare-const X_1205 Real) +(declare-const X_1206 Real) +(declare-const X_1207 Real) +(declare-const X_1208 Real) +(declare-const X_1209 Real) +(declare-const X_1210 Real) +(declare-const X_1211 Real) +(declare-const X_1212 Real) +(declare-const X_1213 Real) +(declare-const X_1214 Real) +(declare-const X_1215 Real) +(declare-const X_1216 Real) +(declare-const X_1217 Real) +(declare-const X_1218 Real) +(declare-const X_1219 Real) +(declare-const X_1220 Real) +(declare-const X_1221 Real) +(declare-const X_1222 Real) +(declare-const X_1223 Real) +(declare-const X_1224 Real) +(declare-const X_1225 Real) +(declare-const X_1226 Real) +(declare-const X_1227 Real) +(declare-const X_1228 Real) +(declare-const X_1229 Real) +(declare-const X_1230 Real) +(declare-const X_1231 Real) +(declare-const X_1232 Real) +(declare-const X_1233 Real) +(declare-const X_1234 Real) +(declare-const X_1235 Real) +(declare-const X_1236 Real) +(declare-const X_1237 Real) +(declare-const X_1238 Real) +(declare-const X_1239 Real) +(declare-const X_1240 Real) +(declare-const X_1241 Real) +(declare-const X_1242 Real) +(declare-const X_1243 Real) +(declare-const X_1244 Real) +(declare-const X_1245 Real) +(declare-const X_1246 Real) +(declare-const X_1247 Real) +(declare-const X_1248 Real) +(declare-const X_1249 Real) +(declare-const X_1250 Real) +(declare-const X_1251 Real) +(declare-const X_1252 Real) +(declare-const X_1253 Real) +(declare-const X_1254 Real) +(declare-const X_1255 Real) +(declare-const X_1256 Real) +(declare-const X_1257 Real) +(declare-const X_1258 Real) +(declare-const X_1259 Real) +(declare-const X_1260 Real) +(declare-const X_1261 Real) +(declare-const X_1262 Real) +(declare-const X_1263 Real) +(declare-const X_1264 Real) +(declare-const X_1265 Real) +(declare-const X_1266 Real) +(declare-const X_1267 Real) +(declare-const X_1268 Real) +(declare-const X_1269 Real) +(declare-const X_1270 Real) +(declare-const X_1271 Real) +(declare-const X_1272 Real) +(declare-const X_1273 Real) +(declare-const X_1274 Real) +(declare-const X_1275 Real) +(declare-const X_1276 Real) +(declare-const X_1277 Real) +(declare-const X_1278 Real) +(declare-const X_1279 Real) +(declare-const X_1280 Real) +(declare-const X_1281 Real) +(declare-const X_1282 Real) +(declare-const X_1283 Real) +(declare-const X_1284 Real) +(declare-const X_1285 Real) +(declare-const X_1286 Real) +(declare-const X_1287 Real) +(declare-const X_1288 Real) +(declare-const X_1289 Real) +(declare-const X_1290 Real) +(declare-const X_1291 Real) +(declare-const X_1292 Real) +(declare-const X_1293 Real) +(declare-const X_1294 Real) +(declare-const X_1295 Real) +(declare-const X_1296 Real) +(declare-const X_1297 Real) +(declare-const X_1298 Real) +(declare-const X_1299 Real) +(declare-const X_1300 Real) +(declare-const X_1301 Real) +(declare-const X_1302 Real) +(declare-const X_1303 Real) +(declare-const X_1304 Real) +(declare-const X_1305 Real) +(declare-const X_1306 Real) +(declare-const X_1307 Real) +(declare-const X_1308 Real) +(declare-const X_1309 Real) +(declare-const X_1310 Real) +(declare-const X_1311 Real) +(declare-const X_1312 Real) +(declare-const X_1313 Real) +(declare-const X_1314 Real) +(declare-const X_1315 Real) +(declare-const X_1316 Real) +(declare-const X_1317 Real) +(declare-const X_1318 Real) +(declare-const X_1319 Real) +(declare-const X_1320 Real) +(declare-const X_1321 Real) +(declare-const X_1322 Real) +(declare-const X_1323 Real) +(declare-const X_1324 Real) +(declare-const X_1325 Real) +(declare-const X_1326 Real) +(declare-const X_1327 Real) +(declare-const X_1328 Real) +(declare-const X_1329 Real) +(declare-const X_1330 Real) +(declare-const X_1331 Real) +(declare-const X_1332 Real) +(declare-const X_1333 Real) +(declare-const X_1334 Real) +(declare-const X_1335 Real) +(declare-const X_1336 Real) +(declare-const X_1337 Real) +(declare-const X_1338 Real) +(declare-const X_1339 Real) +(declare-const X_1340 Real) +(declare-const X_1341 Real) +(declare-const X_1342 Real) +(declare-const X_1343 Real) +(declare-const X_1344 Real) +(declare-const X_1345 Real) +(declare-const X_1346 Real) +(declare-const X_1347 Real) +(declare-const X_1348 Real) +(declare-const X_1349 Real) +(declare-const X_1350 Real) +(declare-const X_1351 Real) +(declare-const X_1352 Real) +(declare-const X_1353 Real) +(declare-const X_1354 Real) +(declare-const X_1355 Real) +(declare-const X_1356 Real) +(declare-const X_1357 Real) +(declare-const X_1358 Real) +(declare-const X_1359 Real) +(declare-const X_1360 Real) +(declare-const X_1361 Real) +(declare-const X_1362 Real) +(declare-const X_1363 Real) +(declare-const X_1364 Real) +(declare-const X_1365 Real) +(declare-const X_1366 Real) +(declare-const X_1367 Real) +(declare-const X_1368 Real) +(declare-const X_1369 Real) +(declare-const X_1370 Real) +(declare-const X_1371 Real) +(declare-const X_1372 Real) +(declare-const X_1373 Real) +(declare-const X_1374 Real) +(declare-const X_1375 Real) +(declare-const X_1376 Real) +(declare-const X_1377 Real) +(declare-const X_1378 Real) +(declare-const X_1379 Real) +(declare-const X_1380 Real) +(declare-const X_1381 Real) +(declare-const X_1382 Real) +(declare-const X_1383 Real) +(declare-const X_1384 Real) +(declare-const X_1385 Real) +(declare-const X_1386 Real) +(declare-const X_1387 Real) +(declare-const X_1388 Real) +(declare-const X_1389 Real) +(declare-const X_1390 Real) +(declare-const X_1391 Real) +(declare-const X_1392 Real) +(declare-const X_1393 Real) +(declare-const X_1394 Real) +(declare-const X_1395 Real) +(declare-const X_1396 Real) +(declare-const X_1397 Real) +(declare-const X_1398 Real) +(declare-const X_1399 Real) +(declare-const X_1400 Real) +(declare-const X_1401 Real) +(declare-const X_1402 Real) +(declare-const X_1403 Real) +(declare-const X_1404 Real) +(declare-const X_1405 Real) +(declare-const X_1406 Real) +(declare-const X_1407 Real) +(declare-const X_1408 Real) +(declare-const X_1409 Real) +(declare-const X_1410 Real) +(declare-const X_1411 Real) +(declare-const X_1412 Real) +(declare-const X_1413 Real) +(declare-const X_1414 Real) +(declare-const X_1415 Real) +(declare-const X_1416 Real) +(declare-const X_1417 Real) +(declare-const X_1418 Real) +(declare-const X_1419 Real) +(declare-const X_1420 Real) +(declare-const X_1421 Real) +(declare-const X_1422 Real) +(declare-const X_1423 Real) +(declare-const X_1424 Real) +(declare-const X_1425 Real) +(declare-const X_1426 Real) +(declare-const X_1427 Real) +(declare-const X_1428 Real) +(declare-const X_1429 Real) +(declare-const X_1430 Real) +(declare-const X_1431 Real) +(declare-const X_1432 Real) +(declare-const X_1433 Real) +(declare-const X_1434 Real) +(declare-const X_1435 Real) +(declare-const X_1436 Real) +(declare-const X_1437 Real) +(declare-const X_1438 Real) +(declare-const X_1439 Real) +(declare-const X_1440 Real) +(declare-const X_1441 Real) +(declare-const X_1442 Real) +(declare-const X_1443 Real) +(declare-const X_1444 Real) +(declare-const X_1445 Real) +(declare-const X_1446 Real) +(declare-const X_1447 Real) +(declare-const X_1448 Real) +(declare-const X_1449 Real) +(declare-const X_1450 Real) +(declare-const X_1451 Real) +(declare-const X_1452 Real) +(declare-const X_1453 Real) +(declare-const X_1454 Real) +(declare-const X_1455 Real) +(declare-const X_1456 Real) +(declare-const X_1457 Real) +(declare-const X_1458 Real) +(declare-const X_1459 Real) +(declare-const X_1460 Real) +(declare-const X_1461 Real) +(declare-const X_1462 Real) +(declare-const X_1463 Real) +(declare-const X_1464 Real) +(declare-const X_1465 Real) +(declare-const X_1466 Real) +(declare-const X_1467 Real) +(declare-const X_1468 Real) +(declare-const X_1469 Real) +(declare-const X_1470 Real) +(declare-const X_1471 Real) +(declare-const X_1472 Real) +(declare-const X_1473 Real) +(declare-const X_1474 Real) +(declare-const X_1475 Real) +(declare-const X_1476 Real) +(declare-const X_1477 Real) +(declare-const X_1478 Real) +(declare-const X_1479 Real) +(declare-const X_1480 Real) +(declare-const X_1481 Real) +(declare-const X_1482 Real) +(declare-const X_1483 Real) +(declare-const X_1484 Real) +(declare-const X_1485 Real) +(declare-const X_1486 Real) +(declare-const X_1487 Real) +(declare-const X_1488 Real) +(declare-const X_1489 Real) +(declare-const X_1490 Real) +(declare-const X_1491 Real) +(declare-const X_1492 Real) +(declare-const X_1493 Real) +(declare-const X_1494 Real) +(declare-const X_1495 Real) +(declare-const X_1496 Real) +(declare-const X_1497 Real) +(declare-const X_1498 Real) +(declare-const X_1499 Real) +(declare-const X_1500 Real) +(declare-const X_1501 Real) +(declare-const X_1502 Real) +(declare-const X_1503 Real) +(declare-const X_1504 Real) +(declare-const X_1505 Real) +(declare-const X_1506 Real) +(declare-const X_1507 Real) +(declare-const X_1508 Real) +(declare-const X_1509 Real) +(declare-const X_1510 Real) +(declare-const X_1511 Real) +(declare-const X_1512 Real) +(declare-const X_1513 Real) +(declare-const X_1514 Real) +(declare-const X_1515 Real) +(declare-const X_1516 Real) +(declare-const X_1517 Real) +(declare-const X_1518 Real) +(declare-const X_1519 Real) +(declare-const X_1520 Real) +(declare-const X_1521 Real) +(declare-const X_1522 Real) +(declare-const X_1523 Real) +(declare-const X_1524 Real) +(declare-const X_1525 Real) +(declare-const X_1526 Real) +(declare-const X_1527 Real) +(declare-const X_1528 Real) +(declare-const X_1529 Real) +(declare-const X_1530 Real) +(declare-const X_1531 Real) +(declare-const X_1532 Real) +(declare-const X_1533 Real) +(declare-const X_1534 Real) +(declare-const X_1535 Real) +(declare-const X_1536 Real) +(declare-const X_1537 Real) +(declare-const X_1538 Real) +(declare-const X_1539 Real) +(declare-const X_1540 Real) +(declare-const X_1541 Real) +(declare-const X_1542 Real) +(declare-const X_1543 Real) +(declare-const X_1544 Real) +(declare-const X_1545 Real) +(declare-const X_1546 Real) +(declare-const X_1547 Real) +(declare-const X_1548 Real) +(declare-const X_1549 Real) +(declare-const X_1550 Real) +(declare-const X_1551 Real) +(declare-const X_1552 Real) +(declare-const X_1553 Real) +(declare-const X_1554 Real) +(declare-const X_1555 Real) +(declare-const X_1556 Real) +(declare-const X_1557 Real) +(declare-const X_1558 Real) +(declare-const X_1559 Real) +(declare-const X_1560 Real) +(declare-const X_1561 Real) +(declare-const X_1562 Real) +(declare-const X_1563 Real) +(declare-const X_1564 Real) +(declare-const X_1565 Real) +(declare-const X_1566 Real) +(declare-const X_1567 Real) +(declare-const X_1568 Real) +(declare-const X_1569 Real) +(declare-const X_1570 Real) +(declare-const X_1571 Real) +(declare-const X_1572 Real) +(declare-const X_1573 Real) +(declare-const X_1574 Real) +(declare-const X_1575 Real) +(declare-const X_1576 Real) +(declare-const X_1577 Real) +(declare-const X_1578 Real) +(declare-const X_1579 Real) +(declare-const X_1580 Real) +(declare-const X_1581 Real) +(declare-const X_1582 Real) +(declare-const X_1583 Real) +(declare-const X_1584 Real) +(declare-const X_1585 Real) +(declare-const X_1586 Real) +(declare-const X_1587 Real) +(declare-const X_1588 Real) +(declare-const X_1589 Real) +(declare-const X_1590 Real) +(declare-const X_1591 Real) +(declare-const X_1592 Real) +(declare-const X_1593 Real) +(declare-const X_1594 Real) +(declare-const X_1595 Real) +(declare-const X_1596 Real) +(declare-const X_1597 Real) +(declare-const X_1598 Real) +(declare-const X_1599 Real) +(declare-const X_1600 Real) +(declare-const X_1601 Real) +(declare-const X_1602 Real) +(declare-const X_1603 Real) +(declare-const X_1604 Real) +(declare-const X_1605 Real) +(declare-const X_1606 Real) +(declare-const X_1607 Real) +(declare-const X_1608 Real) +(declare-const X_1609 Real) +(declare-const X_1610 Real) +(declare-const X_1611 Real) +(declare-const X_1612 Real) +(declare-const X_1613 Real) +(declare-const X_1614 Real) +(declare-const X_1615 Real) +(declare-const X_1616 Real) +(declare-const X_1617 Real) +(declare-const X_1618 Real) +(declare-const X_1619 Real) +(declare-const X_1620 Real) +(declare-const X_1621 Real) +(declare-const X_1622 Real) +(declare-const X_1623 Real) +(declare-const X_1624 Real) +(declare-const X_1625 Real) +(declare-const X_1626 Real) +(declare-const X_1627 Real) +(declare-const X_1628 Real) +(declare-const X_1629 Real) +(declare-const X_1630 Real) +(declare-const X_1631 Real) +(declare-const X_1632 Real) +(declare-const X_1633 Real) +(declare-const X_1634 Real) +(declare-const X_1635 Real) +(declare-const X_1636 Real) +(declare-const X_1637 Real) +(declare-const X_1638 Real) +(declare-const X_1639 Real) +(declare-const X_1640 Real) +(declare-const X_1641 Real) +(declare-const X_1642 Real) +(declare-const X_1643 Real) +(declare-const X_1644 Real) +(declare-const X_1645 Real) +(declare-const X_1646 Real) +(declare-const X_1647 Real) +(declare-const X_1648 Real) +(declare-const X_1649 Real) +(declare-const X_1650 Real) +(declare-const X_1651 Real) +(declare-const X_1652 Real) +(declare-const X_1653 Real) +(declare-const X_1654 Real) +(declare-const X_1655 Real) +(declare-const X_1656 Real) +(declare-const X_1657 Real) +(declare-const X_1658 Real) +(declare-const X_1659 Real) +(declare-const X_1660 Real) +(declare-const X_1661 Real) +(declare-const X_1662 Real) +(declare-const X_1663 Real) +(declare-const X_1664 Real) +(declare-const X_1665 Real) +(declare-const X_1666 Real) +(declare-const X_1667 Real) +(declare-const X_1668 Real) +(declare-const X_1669 Real) +(declare-const X_1670 Real) +(declare-const X_1671 Real) +(declare-const X_1672 Real) +(declare-const X_1673 Real) +(declare-const X_1674 Real) +(declare-const X_1675 Real) +(declare-const X_1676 Real) +(declare-const X_1677 Real) +(declare-const X_1678 Real) +(declare-const X_1679 Real) +(declare-const X_1680 Real) +(declare-const X_1681 Real) +(declare-const X_1682 Real) +(declare-const X_1683 Real) +(declare-const X_1684 Real) +(declare-const X_1685 Real) +(declare-const X_1686 Real) +(declare-const X_1687 Real) +(declare-const X_1688 Real) +(declare-const X_1689 Real) +(declare-const X_1690 Real) +(declare-const X_1691 Real) +(declare-const X_1692 Real) +(declare-const X_1693 Real) +(declare-const X_1694 Real) +(declare-const X_1695 Real) +(declare-const X_1696 Real) +(declare-const X_1697 Real) +(declare-const X_1698 Real) +(declare-const X_1699 Real) +(declare-const X_1700 Real) +(declare-const X_1701 Real) +(declare-const X_1702 Real) +(declare-const X_1703 Real) +(declare-const X_1704 Real) +(declare-const X_1705 Real) +(declare-const X_1706 Real) +(declare-const X_1707 Real) +(declare-const X_1708 Real) +(declare-const X_1709 Real) +(declare-const X_1710 Real) +(declare-const X_1711 Real) +(declare-const X_1712 Real) +(declare-const X_1713 Real) +(declare-const X_1714 Real) +(declare-const X_1715 Real) +(declare-const X_1716 Real) +(declare-const X_1717 Real) +(declare-const X_1718 Real) +(declare-const X_1719 Real) +(declare-const X_1720 Real) +(declare-const X_1721 Real) +(declare-const X_1722 Real) +(declare-const X_1723 Real) +(declare-const X_1724 Real) +(declare-const X_1725 Real) +(declare-const X_1726 Real) +(declare-const X_1727 Real) +(declare-const X_1728 Real) +(declare-const X_1729 Real) +(declare-const X_1730 Real) +(declare-const X_1731 Real) +(declare-const X_1732 Real) +(declare-const X_1733 Real) +(declare-const X_1734 Real) +(declare-const X_1735 Real) +(declare-const X_1736 Real) +(declare-const X_1737 Real) +(declare-const X_1738 Real) +(declare-const X_1739 Real) +(declare-const X_1740 Real) +(declare-const X_1741 Real) +(declare-const X_1742 Real) +(declare-const X_1743 Real) +(declare-const X_1744 Real) +(declare-const X_1745 Real) +(declare-const X_1746 Real) +(declare-const X_1747 Real) +(declare-const X_1748 Real) +(declare-const X_1749 Real) +(declare-const X_1750 Real) +(declare-const X_1751 Real) +(declare-const X_1752 Real) +(declare-const X_1753 Real) +(declare-const X_1754 Real) +(declare-const X_1755 Real) +(declare-const X_1756 Real) +(declare-const X_1757 Real) +(declare-const X_1758 Real) +(declare-const X_1759 Real) +(declare-const X_1760 Real) +(declare-const X_1761 Real) +(declare-const X_1762 Real) +(declare-const X_1763 Real) +(declare-const X_1764 Real) +(declare-const X_1765 Real) +(declare-const X_1766 Real) +(declare-const X_1767 Real) +(declare-const X_1768 Real) +(declare-const X_1769 Real) +(declare-const X_1770 Real) +(declare-const X_1771 Real) +(declare-const X_1772 Real) +(declare-const X_1773 Real) +(declare-const X_1774 Real) +(declare-const X_1775 Real) +(declare-const X_1776 Real) +(declare-const X_1777 Real) +(declare-const X_1778 Real) +(declare-const X_1779 Real) +(declare-const X_1780 Real) +(declare-const X_1781 Real) +(declare-const X_1782 Real) +(declare-const X_1783 Real) +(declare-const X_1784 Real) +(declare-const X_1785 Real) +(declare-const X_1786 Real) +(declare-const X_1787 Real) +(declare-const X_1788 Real) +(declare-const X_1789 Real) +(declare-const X_1790 Real) +(declare-const X_1791 Real) +(declare-const X_1792 Real) +(declare-const X_1793 Real) +(declare-const X_1794 Real) +(declare-const X_1795 Real) +(declare-const X_1796 Real) +(declare-const X_1797 Real) +(declare-const X_1798 Real) +(declare-const X_1799 Real) +(declare-const X_1800 Real) +(declare-const X_1801 Real) +(declare-const X_1802 Real) +(declare-const X_1803 Real) +(declare-const X_1804 Real) +(declare-const X_1805 Real) +(declare-const X_1806 Real) +(declare-const X_1807 Real) +(declare-const X_1808 Real) +(declare-const X_1809 Real) +(declare-const X_1810 Real) +(declare-const X_1811 Real) +(declare-const X_1812 Real) +(declare-const X_1813 Real) +(declare-const X_1814 Real) +(declare-const X_1815 Real) +(declare-const X_1816 Real) +(declare-const X_1817 Real) +(declare-const X_1818 Real) +(declare-const X_1819 Real) +(declare-const X_1820 Real) +(declare-const X_1821 Real) +(declare-const X_1822 Real) +(declare-const X_1823 Real) +(declare-const X_1824 Real) +(declare-const X_1825 Real) +(declare-const X_1826 Real) +(declare-const X_1827 Real) +(declare-const X_1828 Real) +(declare-const X_1829 Real) +(declare-const X_1830 Real) +(declare-const X_1831 Real) +(declare-const X_1832 Real) +(declare-const X_1833 Real) +(declare-const X_1834 Real) +(declare-const X_1835 Real) +(declare-const X_1836 Real) +(declare-const X_1837 Real) +(declare-const X_1838 Real) +(declare-const X_1839 Real) +(declare-const X_1840 Real) +(declare-const X_1841 Real) +(declare-const X_1842 Real) +(declare-const X_1843 Real) +(declare-const X_1844 Real) +(declare-const X_1845 Real) +(declare-const X_1846 Real) +(declare-const X_1847 Real) +(declare-const X_1848 Real) +(declare-const X_1849 Real) +(declare-const X_1850 Real) +(declare-const X_1851 Real) +(declare-const X_1852 Real) +(declare-const X_1853 Real) +(declare-const X_1854 Real) +(declare-const X_1855 Real) +(declare-const X_1856 Real) +(declare-const X_1857 Real) +(declare-const X_1858 Real) +(declare-const X_1859 Real) +(declare-const X_1860 Real) +(declare-const X_1861 Real) +(declare-const X_1862 Real) +(declare-const X_1863 Real) +(declare-const X_1864 Real) +(declare-const X_1865 Real) +(declare-const X_1866 Real) +(declare-const X_1867 Real) +(declare-const X_1868 Real) +(declare-const X_1869 Real) +(declare-const X_1870 Real) +(declare-const X_1871 Real) +(declare-const X_1872 Real) +(declare-const X_1873 Real) +(declare-const X_1874 Real) +(declare-const X_1875 Real) +(declare-const X_1876 Real) +(declare-const X_1877 Real) +(declare-const X_1878 Real) +(declare-const X_1879 Real) +(declare-const X_1880 Real) +(declare-const X_1881 Real) +(declare-const X_1882 Real) +(declare-const X_1883 Real) +(declare-const X_1884 Real) +(declare-const X_1885 Real) +(declare-const X_1886 Real) +(declare-const X_1887 Real) +(declare-const X_1888 Real) +(declare-const X_1889 Real) +(declare-const X_1890 Real) +(declare-const X_1891 Real) +(declare-const X_1892 Real) +(declare-const X_1893 Real) +(declare-const X_1894 Real) +(declare-const X_1895 Real) +(declare-const X_1896 Real) +(declare-const X_1897 Real) +(declare-const X_1898 Real) +(declare-const X_1899 Real) +(declare-const X_1900 Real) +(declare-const X_1901 Real) +(declare-const X_1902 Real) +(declare-const X_1903 Real) +(declare-const X_1904 Real) +(declare-const X_1905 Real) +(declare-const X_1906 Real) +(declare-const X_1907 Real) +(declare-const X_1908 Real) +(declare-const X_1909 Real) +(declare-const X_1910 Real) +(declare-const X_1911 Real) +(declare-const X_1912 Real) +(declare-const X_1913 Real) +(declare-const X_1914 Real) +(declare-const X_1915 Real) +(declare-const X_1916 Real) +(declare-const X_1917 Real) +(declare-const X_1918 Real) +(declare-const X_1919 Real) +(declare-const X_1920 Real) +(declare-const X_1921 Real) +(declare-const X_1922 Real) +(declare-const X_1923 Real) +(declare-const X_1924 Real) +(declare-const X_1925 Real) +(declare-const X_1926 Real) +(declare-const X_1927 Real) +(declare-const X_1928 Real) +(declare-const X_1929 Real) +(declare-const X_1930 Real) +(declare-const X_1931 Real) +(declare-const X_1932 Real) +(declare-const X_1933 Real) +(declare-const X_1934 Real) +(declare-const X_1935 Real) +(declare-const X_1936 Real) +(declare-const X_1937 Real) +(declare-const X_1938 Real) +(declare-const X_1939 Real) +(declare-const X_1940 Real) +(declare-const X_1941 Real) +(declare-const X_1942 Real) +(declare-const X_1943 Real) +(declare-const X_1944 Real) +(declare-const X_1945 Real) +(declare-const X_1946 Real) +(declare-const X_1947 Real) +(declare-const X_1948 Real) +(declare-const X_1949 Real) +(declare-const X_1950 Real) +(declare-const X_1951 Real) +(declare-const X_1952 Real) +(declare-const X_1953 Real) +(declare-const X_1954 Real) +(declare-const X_1955 Real) +(declare-const X_1956 Real) +(declare-const X_1957 Real) +(declare-const X_1958 Real) +(declare-const X_1959 Real) +(declare-const X_1960 Real) +(declare-const X_1961 Real) +(declare-const X_1962 Real) +(declare-const X_1963 Real) +(declare-const X_1964 Real) +(declare-const X_1965 Real) +(declare-const X_1966 Real) +(declare-const X_1967 Real) +(declare-const X_1968 Real) +(declare-const X_1969 Real) +(declare-const X_1970 Real) +(declare-const X_1971 Real) +(declare-const X_1972 Real) +(declare-const X_1973 Real) +(declare-const X_1974 Real) +(declare-const X_1975 Real) +(declare-const X_1976 Real) +(declare-const X_1977 Real) +(declare-const X_1978 Real) +(declare-const X_1979 Real) +(declare-const X_1980 Real) +(declare-const X_1981 Real) +(declare-const X_1982 Real) +(declare-const X_1983 Real) +(declare-const X_1984 Real) +(declare-const X_1985 Real) +(declare-const X_1986 Real) +(declare-const X_1987 Real) +(declare-const X_1988 Real) +(declare-const X_1989 Real) +(declare-const X_1990 Real) +(declare-const X_1991 Real) +(declare-const X_1992 Real) +(declare-const X_1993 Real) +(declare-const X_1994 Real) +(declare-const X_1995 Real) +(declare-const X_1996 Real) +(declare-const X_1997 Real) +(declare-const X_1998 Real) +(declare-const X_1999 Real) +(declare-const X_2000 Real) +(declare-const X_2001 Real) +(declare-const X_2002 Real) +(declare-const X_2003 Real) +(declare-const X_2004 Real) +(declare-const X_2005 Real) +(declare-const X_2006 Real) +(declare-const X_2007 Real) +(declare-const X_2008 Real) +(declare-const X_2009 Real) +(declare-const X_2010 Real) +(declare-const X_2011 Real) +(declare-const X_2012 Real) +(declare-const X_2013 Real) +(declare-const X_2014 Real) +(declare-const X_2015 Real) +(declare-const X_2016 Real) +(declare-const X_2017 Real) +(declare-const X_2018 Real) +(declare-const X_2019 Real) +(declare-const X_2020 Real) +(declare-const X_2021 Real) +(declare-const X_2022 Real) +(declare-const X_2023 Real) +(declare-const X_2024 Real) +(declare-const X_2025 Real) +(declare-const X_2026 Real) +(declare-const X_2027 Real) +(declare-const X_2028 Real) +(declare-const X_2029 Real) +(declare-const X_2030 Real) +(declare-const X_2031 Real) +(declare-const X_2032 Real) +(declare-const X_2033 Real) +(declare-const X_2034 Real) +(declare-const X_2035 Real) +(declare-const X_2036 Real) +(declare-const X_2037 Real) +(declare-const X_2038 Real) +(declare-const X_2039 Real) +(declare-const X_2040 Real) +(declare-const X_2041 Real) +(declare-const X_2042 Real) +(declare-const X_2043 Real) +(declare-const X_2044 Real) +(declare-const X_2045 Real) +(declare-const X_2046 Real) +(declare-const X_2047 Real) +(declare-const X_2048 Real) +(declare-const X_2049 Real) +(declare-const X_2050 Real) +(declare-const X_2051 Real) +(declare-const X_2052 Real) +(declare-const X_2053 Real) +(declare-const X_2054 Real) +(declare-const X_2055 Real) +(declare-const X_2056 Real) +(declare-const X_2057 Real) +(declare-const X_2058 Real) +(declare-const X_2059 Real) +(declare-const X_2060 Real) +(declare-const X_2061 Real) +(declare-const X_2062 Real) +(declare-const X_2063 Real) +(declare-const X_2064 Real) +(declare-const X_2065 Real) +(declare-const X_2066 Real) +(declare-const X_2067 Real) +(declare-const X_2068 Real) +(declare-const X_2069 Real) +(declare-const X_2070 Real) +(declare-const X_2071 Real) +(declare-const X_2072 Real) +(declare-const X_2073 Real) +(declare-const X_2074 Real) +(declare-const X_2075 Real) +(declare-const X_2076 Real) +(declare-const X_2077 Real) +(declare-const X_2078 Real) +(declare-const X_2079 Real) +(declare-const X_2080 Real) +(declare-const X_2081 Real) +(declare-const X_2082 Real) +(declare-const X_2083 Real) +(declare-const X_2084 Real) +(declare-const X_2085 Real) +(declare-const X_2086 Real) +(declare-const X_2087 Real) +(declare-const X_2088 Real) +(declare-const X_2089 Real) +(declare-const X_2090 Real) +(declare-const X_2091 Real) +(declare-const X_2092 Real) +(declare-const X_2093 Real) +(declare-const X_2094 Real) +(declare-const X_2095 Real) +(declare-const X_2096 Real) +(declare-const X_2097 Real) +(declare-const X_2098 Real) +(declare-const X_2099 Real) +(declare-const X_2100 Real) +(declare-const X_2101 Real) +(declare-const X_2102 Real) +(declare-const X_2103 Real) +(declare-const X_2104 Real) +(declare-const X_2105 Real) +(declare-const X_2106 Real) +(declare-const X_2107 Real) +(declare-const X_2108 Real) +(declare-const X_2109 Real) +(declare-const X_2110 Real) +(declare-const X_2111 Real) +(declare-const X_2112 Real) +(declare-const X_2113 Real) +(declare-const X_2114 Real) +(declare-const X_2115 Real) +(declare-const X_2116 Real) +(declare-const X_2117 Real) +(declare-const X_2118 Real) +(declare-const X_2119 Real) +(declare-const X_2120 Real) +(declare-const X_2121 Real) +(declare-const X_2122 Real) +(declare-const X_2123 Real) +(declare-const X_2124 Real) +(declare-const X_2125 Real) +(declare-const X_2126 Real) +(declare-const X_2127 Real) +(declare-const X_2128 Real) +(declare-const X_2129 Real) +(declare-const X_2130 Real) +(declare-const X_2131 Real) +(declare-const X_2132 Real) +(declare-const X_2133 Real) +(declare-const X_2134 Real) +(declare-const X_2135 Real) +(declare-const X_2136 Real) +(declare-const X_2137 Real) +(declare-const X_2138 Real) +(declare-const X_2139 Real) +(declare-const X_2140 Real) +(declare-const X_2141 Real) +(declare-const X_2142 Real) +(declare-const X_2143 Real) +(declare-const X_2144 Real) +(declare-const X_2145 Real) +(declare-const X_2146 Real) +(declare-const X_2147 Real) +(declare-const X_2148 Real) +(declare-const X_2149 Real) +(declare-const X_2150 Real) +(declare-const X_2151 Real) +(declare-const X_2152 Real) +(declare-const X_2153 Real) +(declare-const X_2154 Real) +(declare-const X_2155 Real) +(declare-const X_2156 Real) +(declare-const X_2157 Real) +(declare-const X_2158 Real) +(declare-const X_2159 Real) +(declare-const X_2160 Real) +(declare-const X_2161 Real) +(declare-const X_2162 Real) +(declare-const X_2163 Real) +(declare-const X_2164 Real) +(declare-const X_2165 Real) +(declare-const X_2166 Real) +(declare-const X_2167 Real) +(declare-const X_2168 Real) +(declare-const X_2169 Real) +(declare-const X_2170 Real) +(declare-const X_2171 Real) +(declare-const X_2172 Real) +(declare-const X_2173 Real) +(declare-const X_2174 Real) +(declare-const X_2175 Real) +(declare-const X_2176 Real) +(declare-const X_2177 Real) +(declare-const X_2178 Real) +(declare-const X_2179 Real) +(declare-const X_2180 Real) +(declare-const X_2181 Real) +(declare-const X_2182 Real) +(declare-const X_2183 Real) +(declare-const X_2184 Real) +(declare-const X_2185 Real) +(declare-const X_2186 Real) +(declare-const X_2187 Real) +(declare-const X_2188 Real) +(declare-const X_2189 Real) +(declare-const X_2190 Real) +(declare-const X_2191 Real) +(declare-const X_2192 Real) +(declare-const X_2193 Real) +(declare-const X_2194 Real) +(declare-const X_2195 Real) +(declare-const X_2196 Real) +(declare-const X_2197 Real) +(declare-const X_2198 Real) +(declare-const X_2199 Real) +(declare-const X_2200 Real) +(declare-const X_2201 Real) +(declare-const X_2202 Real) +(declare-const X_2203 Real) +(declare-const X_2204 Real) +(declare-const X_2205 Real) +(declare-const X_2206 Real) +(declare-const X_2207 Real) +(declare-const X_2208 Real) +(declare-const X_2209 Real) +(declare-const X_2210 Real) +(declare-const X_2211 Real) +(declare-const X_2212 Real) +(declare-const X_2213 Real) +(declare-const X_2214 Real) +(declare-const X_2215 Real) +(declare-const X_2216 Real) +(declare-const X_2217 Real) +(declare-const X_2218 Real) +(declare-const X_2219 Real) +(declare-const X_2220 Real) +(declare-const X_2221 Real) +(declare-const X_2222 Real) +(declare-const X_2223 Real) +(declare-const X_2224 Real) +(declare-const X_2225 Real) +(declare-const X_2226 Real) +(declare-const X_2227 Real) +(declare-const X_2228 Real) +(declare-const X_2229 Real) +(declare-const X_2230 Real) +(declare-const X_2231 Real) +(declare-const X_2232 Real) +(declare-const X_2233 Real) +(declare-const X_2234 Real) +(declare-const X_2235 Real) +(declare-const X_2236 Real) +(declare-const X_2237 Real) +(declare-const X_2238 Real) +(declare-const X_2239 Real) +(declare-const X_2240 Real) +(declare-const X_2241 Real) +(declare-const X_2242 Real) +(declare-const X_2243 Real) +(declare-const X_2244 Real) +(declare-const X_2245 Real) +(declare-const X_2246 Real) +(declare-const X_2247 Real) +(declare-const X_2248 Real) +(declare-const X_2249 Real) +(declare-const X_2250 Real) +(declare-const X_2251 Real) +(declare-const X_2252 Real) +(declare-const X_2253 Real) +(declare-const X_2254 Real) +(declare-const X_2255 Real) +(declare-const X_2256 Real) +(declare-const X_2257 Real) +(declare-const X_2258 Real) +(declare-const X_2259 Real) +(declare-const X_2260 Real) +(declare-const X_2261 Real) +(declare-const X_2262 Real) +(declare-const X_2263 Real) +(declare-const X_2264 Real) +(declare-const X_2265 Real) +(declare-const X_2266 Real) +(declare-const X_2267 Real) +(declare-const X_2268 Real) +(declare-const X_2269 Real) +(declare-const X_2270 Real) +(declare-const X_2271 Real) +(declare-const X_2272 Real) +(declare-const X_2273 Real) +(declare-const X_2274 Real) +(declare-const X_2275 Real) +(declare-const X_2276 Real) +(declare-const X_2277 Real) +(declare-const X_2278 Real) +(declare-const X_2279 Real) +(declare-const X_2280 Real) +(declare-const X_2281 Real) +(declare-const X_2282 Real) +(declare-const X_2283 Real) +(declare-const X_2284 Real) +(declare-const X_2285 Real) +(declare-const X_2286 Real) +(declare-const X_2287 Real) +(declare-const X_2288 Real) +(declare-const X_2289 Real) +(declare-const X_2290 Real) +(declare-const X_2291 Real) +(declare-const X_2292 Real) +(declare-const X_2293 Real) +(declare-const X_2294 Real) +(declare-const X_2295 Real) +(declare-const X_2296 Real) +(declare-const X_2297 Real) +(declare-const X_2298 Real) +(declare-const X_2299 Real) +(declare-const X_2300 Real) +(declare-const X_2301 Real) +(declare-const X_2302 Real) +(declare-const X_2303 Real) +(declare-const X_2304 Real) +(declare-const X_2305 Real) +(declare-const X_2306 Real) +(declare-const X_2307 Real) +(declare-const X_2308 Real) +(declare-const X_2309 Real) +(declare-const X_2310 Real) +(declare-const X_2311 Real) +(declare-const X_2312 Real) +(declare-const X_2313 Real) +(declare-const X_2314 Real) +(declare-const X_2315 Real) +(declare-const X_2316 Real) +(declare-const X_2317 Real) +(declare-const X_2318 Real) +(declare-const X_2319 Real) +(declare-const X_2320 Real) +(declare-const X_2321 Real) +(declare-const X_2322 Real) +(declare-const X_2323 Real) +(declare-const X_2324 Real) +(declare-const X_2325 Real) +(declare-const X_2326 Real) +(declare-const X_2327 Real) +(declare-const X_2328 Real) +(declare-const X_2329 Real) +(declare-const X_2330 Real) +(declare-const X_2331 Real) +(declare-const X_2332 Real) +(declare-const X_2333 Real) +(declare-const X_2334 Real) +(declare-const X_2335 Real) +(declare-const X_2336 Real) +(declare-const X_2337 Real) +(declare-const X_2338 Real) +(declare-const X_2339 Real) +(declare-const X_2340 Real) +(declare-const X_2341 Real) +(declare-const X_2342 Real) +(declare-const X_2343 Real) +(declare-const X_2344 Real) +(declare-const X_2345 Real) +(declare-const X_2346 Real) +(declare-const X_2347 Real) +(declare-const X_2348 Real) +(declare-const X_2349 Real) +(declare-const X_2350 Real) +(declare-const X_2351 Real) +(declare-const X_2352 Real) +(declare-const X_2353 Real) +(declare-const X_2354 Real) +(declare-const X_2355 Real) +(declare-const X_2356 Real) +(declare-const X_2357 Real) +(declare-const X_2358 Real) +(declare-const X_2359 Real) +(declare-const X_2360 Real) +(declare-const X_2361 Real) +(declare-const X_2362 Real) +(declare-const X_2363 Real) +(declare-const X_2364 Real) +(declare-const X_2365 Real) +(declare-const X_2366 Real) +(declare-const X_2367 Real) +(declare-const X_2368 Real) +(declare-const X_2369 Real) +(declare-const X_2370 Real) +(declare-const X_2371 Real) +(declare-const X_2372 Real) +(declare-const X_2373 Real) +(declare-const X_2374 Real) +(declare-const X_2375 Real) +(declare-const X_2376 Real) +(declare-const X_2377 Real) +(declare-const X_2378 Real) +(declare-const X_2379 Real) +(declare-const X_2380 Real) +(declare-const X_2381 Real) +(declare-const X_2382 Real) +(declare-const X_2383 Real) +(declare-const X_2384 Real) +(declare-const X_2385 Real) +(declare-const X_2386 Real) +(declare-const X_2387 Real) +(declare-const X_2388 Real) +(declare-const X_2389 Real) +(declare-const X_2390 Real) +(declare-const X_2391 Real) +(declare-const X_2392 Real) +(declare-const X_2393 Real) +(declare-const X_2394 Real) +(declare-const X_2395 Real) +(declare-const X_2396 Real) +(declare-const X_2397 Real) +(declare-const X_2398 Real) +(declare-const X_2399 Real) +(declare-const X_2400 Real) +(declare-const X_2401 Real) +(declare-const X_2402 Real) +(declare-const X_2403 Real) +(declare-const X_2404 Real) +(declare-const X_2405 Real) +(declare-const X_2406 Real) +(declare-const X_2407 Real) +(declare-const X_2408 Real) +(declare-const X_2409 Real) +(declare-const X_2410 Real) +(declare-const X_2411 Real) +(declare-const X_2412 Real) +(declare-const X_2413 Real) +(declare-const X_2414 Real) +(declare-const X_2415 Real) +(declare-const X_2416 Real) +(declare-const X_2417 Real) +(declare-const X_2418 Real) +(declare-const X_2419 Real) +(declare-const X_2420 Real) +(declare-const X_2421 Real) +(declare-const X_2422 Real) +(declare-const X_2423 Real) +(declare-const X_2424 Real) +(declare-const X_2425 Real) +(declare-const X_2426 Real) +(declare-const X_2427 Real) +(declare-const X_2428 Real) +(declare-const X_2429 Real) +(declare-const X_2430 Real) +(declare-const X_2431 Real) +(declare-const X_2432 Real) +(declare-const X_2433 Real) +(declare-const X_2434 Real) +(declare-const X_2435 Real) +(declare-const X_2436 Real) +(declare-const X_2437 Real) +(declare-const X_2438 Real) +(declare-const X_2439 Real) +(declare-const X_2440 Real) +(declare-const X_2441 Real) +(declare-const X_2442 Real) +(declare-const X_2443 Real) +(declare-const X_2444 Real) +(declare-const X_2445 Real) +(declare-const X_2446 Real) +(declare-const X_2447 Real) +(declare-const X_2448 Real) +(declare-const X_2449 Real) +(declare-const X_2450 Real) +(declare-const X_2451 Real) +(declare-const X_2452 Real) 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+(declare-const X_2929 Real) +(declare-const X_2930 Real) +(declare-const X_2931 Real) +(declare-const X_2932 Real) +(declare-const X_2933 Real) +(declare-const X_2934 Real) +(declare-const X_2935 Real) +(declare-const X_2936 Real) +(declare-const X_2937 Real) +(declare-const X_2938 Real) +(declare-const X_2939 Real) +(declare-const X_2940 Real) +(declare-const X_2941 Real) +(declare-const X_2942 Real) +(declare-const X_2943 Real) +(declare-const X_2944 Real) +(declare-const X_2945 Real) +(declare-const X_2946 Real) +(declare-const X_2947 Real) +(declare-const X_2948 Real) +(declare-const X_2949 Real) +(declare-const X_2950 Real) +(declare-const X_2951 Real) +(declare-const X_2952 Real) +(declare-const X_2953 Real) +(declare-const X_2954 Real) +(declare-const X_2955 Real) +(declare-const X_2956 Real) +(declare-const X_2957 Real) +(declare-const X_2958 Real) +(declare-const X_2959 Real) +(declare-const X_2960 Real) +(declare-const X_2961 Real) +(declare-const X_2962 Real) +(declare-const X_2963 Real) +(declare-const X_2964 Real) +(declare-const X_2965 Real) +(declare-const X_2966 Real) +(declare-const X_2967 Real) +(declare-const X_2968 Real) +(declare-const X_2969 Real) +(declare-const X_2970 Real) +(declare-const X_2971 Real) +(declare-const X_2972 Real) +(declare-const X_2973 Real) +(declare-const X_2974 Real) +(declare-const X_2975 Real) +(declare-const X_2976 Real) +(declare-const X_2977 Real) +(declare-const X_2978 Real) +(declare-const X_2979 Real) +(declare-const X_2980 Real) +(declare-const X_2981 Real) +(declare-const X_2982 Real) +(declare-const X_2983 Real) +(declare-const X_2984 Real) +(declare-const X_2985 Real) +(declare-const X_2986 Real) +(declare-const X_2987 Real) +(declare-const X_2988 Real) +(declare-const X_2989 Real) +(declare-const X_2990 Real) +(declare-const X_2991 Real) +(declare-const X_2992 Real) +(declare-const X_2993 Real) +(declare-const X_2994 Real) +(declare-const X_2995 Real) +(declare-const X_2996 Real) +(declare-const X_2997 Real) +(declare-const X_2998 Real) +(declare-const X_2999 Real) +(declare-const X_3000 Real) +(declare-const X_3001 Real) +(declare-const X_3002 Real) +(declare-const X_3003 Real) +(declare-const X_3004 Real) +(declare-const X_3005 Real) +(declare-const X_3006 Real) +(declare-const X_3007 Real) +(declare-const X_3008 Real) +(declare-const X_3009 Real) +(declare-const X_3010 Real) +(declare-const X_3011 Real) +(declare-const X_3012 Real) +(declare-const X_3013 Real) +(declare-const X_3014 Real) +(declare-const X_3015 Real) +(declare-const X_3016 Real) +(declare-const X_3017 Real) +(declare-const X_3018 Real) +(declare-const X_3019 Real) +(declare-const X_3020 Real) +(declare-const X_3021 Real) +(declare-const X_3022 Real) +(declare-const X_3023 Real) +(declare-const X_3024 Real) +(declare-const X_3025 Real) +(declare-const X_3026 Real) +(declare-const X_3027 Real) +(declare-const X_3028 Real) +(declare-const X_3029 Real) +(declare-const X_3030 Real) +(declare-const X_3031 Real) +(declare-const X_3032 Real) +(declare-const X_3033 Real) +(declare-const X_3034 Real) +(declare-const X_3035 Real) +(declare-const X_3036 Real) +(declare-const X_3037 Real) +(declare-const X_3038 Real) +(declare-const X_3039 Real) +(declare-const X_3040 Real) +(declare-const X_3041 Real) +(declare-const X_3042 Real) +(declare-const X_3043 Real) +(declare-const X_3044 Real) +(declare-const X_3045 Real) +(declare-const X_3046 Real) +(declare-const X_3047 Real) +(declare-const X_3048 Real) +(declare-const X_3049 Real) +(declare-const X_3050 Real) +(declare-const X_3051 Real) +(declare-const X_3052 Real) +(declare-const X_3053 Real) +(declare-const X_3054 Real) +(declare-const X_3055 Real) +(declare-const X_3056 Real) +(declare-const X_3057 Real) +(declare-const X_3058 Real) +(declare-const X_3059 Real) +(declare-const X_3060 Real) +(declare-const X_3061 Real) +(declare-const X_3062 Real) +(declare-const X_3063 Real) +(declare-const X_3064 Real) +(declare-const X_3065 Real) +(declare-const X_3066 Real) +(declare-const X_3067 Real) +(declare-const X_3068 Real) +(declare-const X_3069 Real) +(declare-const X_3070 Real) +(declare-const X_3071 Real) + +; Definition of output variables +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) +(declare-const Y_5 Real) +(declare-const Y_6 Real) +(declare-const Y_7 Real) +(declare-const Y_8 Real) +(declare-const Y_9 Real) + +; Definition of input constraints +(assert (<= X_0 0.61436629)) +(assert (>= X_0 0.53682661)) +(assert (<= X_1 0.84698528)) +(assert (>= X_1 0.76944560)) +(assert (<= X_2 1.02144945)) +(assert (>= X_2 0.94390982)) +(assert (<= X_3 1.29283834)) +(assert (>= X_3 1.21529865)) +(assert (<= X_4 1.04083443)) +(assert (>= X_4 0.96329474)) +(assert (<= X_5 0.82760036)) +(assert (>= X_5 0.75006068)) +(assert (<= X_6 0.86637014)) +(assert (>= X_6 0.78883052)) +(assert (<= X_7 0.82760036)) +(assert (>= X_7 0.75006068)) +(assert (<= X_8 0.90513998)) +(assert (>= X_8 0.82760036)) +(assert (<= X_9 1.07960427)) +(assert (>= X_9 1.00206459)) +(assert (<= X_10 1.23468351)) +(assert (>= X_10 1.15714395)) +(assert (<= X_11 1.23468351)) +(assert (>= X_11 1.15714395)) +(assert (<= X_12 1.23468351)) +(assert (>= X_12 1.15714395)) +(assert (<= X_13 1.23468351)) +(assert (>= X_13 1.15714395)) +(assert (<= X_14 1.17652881)) +(assert (>= X_14 1.09898913)) +(assert (<= X_15 1.17652881)) +(assert (>= X_15 1.09898913)) +(assert (<= X_16 1.13775897)) +(assert (>= X_16 1.06021929)) +(assert (<= X_17 1.09898913)) +(assert (>= X_17 1.02144945)) +(assert (<= X_18 1.17652881)) +(assert (>= X_18 1.09898913)) +(assert (<= X_19 1.21529865)) +(assert (>= X_19 1.13775897)) +(assert (<= X_20 1.23468351)) +(assert (>= X_20 1.15714395)) +(assert (<= X_21 1.23468351)) +(assert (>= X_21 1.15714395)) +(assert (<= X_22 1.25406849)) +(assert (>= X_22 1.17652881)) +(assert (<= X_23 1.27345335)) +(assert (>= X_23 1.19591379)) +(assert (<= X_24 1.23468351)) +(assert (>= X_24 1.15714395)) +(assert (<= X_25 1.23468351)) +(assert (>= X_25 1.15714395)) +(assert (<= X_26 1.25406849)) +(assert (>= X_26 1.17652881)) +(assert (<= X_27 1.38976288)) +(assert (>= X_27 1.31222320)) +(assert (<= X_28 1.50607240)) +(assert (>= X_28 1.42853272)) +(assert (<= X_29 1.50607240)) +(assert (>= X_29 1.42853272)) +(assert (<= X_30 1.52545726)) +(assert (>= X_30 1.44791770)) +(assert (<= X_31 1.33160818)) +(assert (>= X_31 1.25406849)) +(assert (<= X_32 0.57559645)) +(assert (>= X_32 0.49805677)) +(assert (<= X_33 0.76944560)) +(assert (>= X_33 0.69190592)) +(assert (<= X_34 0.92452490)) +(assert (>= X_34 0.84698528)) +(assert (<= X_35 1.23468351)) +(assert (>= X_35 1.15714395)) +(assert (<= X_36 1.07960427)) +(assert (>= X_36 1.00206459)) +(assert (<= X_37 0.61436629)) +(assert (>= X_37 0.53682661)) +(assert (<= X_38 0.59498137)) +(assert (>= X_38 0.51744169)) +(assert (<= X_39 0.69190592)) +(assert (>= X_39 0.61436629)) +(assert (<= X_40 0.69190592)) +(assert (>= X_40 0.61436629)) +(assert (<= X_41 0.80821544)) +(assert (>= X_41 0.73067576)) +(assert (<= X_42 0.92452490)) +(assert (>= X_42 0.84698528)) +(assert (<= X_43 1.00206459)) +(assert (>= X_43 0.92452490)) +(assert (<= X_44 0.88575506)) +(assert (>= X_44 0.80821544)) +(assert (<= X_45 0.92452490)) +(assert (>= X_45 0.84698528)) +(assert (<= X_46 0.75006068)) +(assert (>= X_46 0.67252100)) +(assert (<= X_47 0.80821544)) +(assert (>= X_47 0.73067576)) +(assert (<= X_48 0.90513998)) +(assert (>= X_48 0.82760036)) +(assert (<= X_49 0.78883052)) +(assert (>= X_49 0.71129084)) +(assert (<= X_50 0.82760036)) +(assert (>= X_50 0.75006068)) +(assert (<= X_51 0.80821544)) +(assert (>= X_51 0.73067576)) +(assert (<= X_52 0.84698528)) +(assert (>= X_52 0.76944560)) +(assert (<= X_53 0.96329474)) +(assert (>= X_53 0.88575506)) +(assert (<= X_54 0.88575506)) +(assert (>= X_54 0.80821544)) +(assert (<= X_55 0.86637014)) +(assert (>= X_55 0.78883052)) +(assert (<= X_56 0.88575506)) +(assert (>= X_56 0.80821544)) +(assert (<= X_57 0.96329474)) +(assert (>= X_57 0.88575506)) +(assert (<= X_58 1.29283834)) +(assert (>= X_58 1.21529865)) +(assert (<= X_59 1.52545726)) +(assert (>= X_59 1.44791770)) +(assert (<= X_60 1.56422710)) +(assert (>= X_60 1.48668742)) +(assert (<= X_61 1.52545726)) +(assert (>= X_61 1.44791770)) +(assert (<= X_62 1.54484224)) +(assert (>= X_62 1.46730256)) +(assert (<= X_63 1.27345335)) +(assert (>= X_63 1.19591379)) +(assert (<= X_64 0.61436629)) +(assert (>= X_64 0.53682661)) +(assert (<= X_65 0.71129084)) +(assert (>= X_65 0.63375115)) +(assert (<= X_66 0.86637014)) +(assert (>= X_66 0.78883052)) +(assert (<= X_67 1.17652881)) +(assert (>= X_67 1.09898913)) +(assert (<= X_68 1.23468351)) +(assert (>= X_68 1.15714395)) +(assert (<= X_69 0.98267967)) +(assert (>= X_69 0.90513998)) +(assert (<= X_70 1.02144945)) +(assert (>= X_70 0.94390982)) +(assert (<= X_71 1.25406849)) +(assert (>= X_71 1.17652881)) +(assert (<= X_72 1.13775897)) +(assert (>= X_72 1.06021929)) +(assert (<= X_73 1.07960427)) +(assert (>= X_73 1.00206459)) +(assert (<= X_74 1.04083443)) +(assert (>= X_74 0.96329474)) +(assert (<= X_75 1.29283834)) +(assert (>= X_75 1.21529865)) +(assert (<= X_76 1.33160818)) +(assert (>= X_76 1.25406849)) +(assert (<= X_77 1.37037802)) +(assert (>= X_77 1.29283834)) +(assert (<= X_78 1.25406849)) +(assert (>= X_78 1.17652881)) +(assert (<= X_79 1.19591379)) +(assert (>= X_79 1.11837411)) +(assert (<= X_80 1.35099304)) +(assert (>= X_80 1.27345335)) +(assert (<= X_81 1.37037802)) +(assert (>= X_81 1.29283834)) +(assert (<= X_82 1.35099304)) +(assert (>= X_82 1.27345335)) +(assert (<= X_83 1.37037802)) +(assert (>= X_83 1.29283834)) +(assert (<= X_84 1.38976288)) +(assert (>= X_84 1.31222320)) +(assert (<= X_85 1.42853272)) +(assert (>= X_85 1.35099304)) +(assert (<= X_86 1.35099304)) +(assert (>= X_86 1.27345335)) +(assert (<= X_87 1.31222320)) +(assert (>= X_87 1.23468351)) +(assert (<= X_88 1.31222320)) +(assert (>= X_88 1.23468351)) +(assert (<= X_89 1.42853272)) +(assert (>= X_89 1.35099304)) +(assert (<= X_90 1.60299695)) +(assert (>= X_90 1.52545726)) +(assert (<= X_91 1.62238193)) +(assert (>= X_91 1.54484224)) +(assert (<= X_92 1.64176679)) +(assert (>= X_92 1.56422710)) +(assert (<= X_93 1.60299695)) +(assert (>= X_93 1.52545726)) +(assert (<= X_94 1.56422710)) +(assert (>= X_94 1.48668742)) +(assert (<= X_95 1.27345335)) +(assert (>= X_95 1.19591379)) +(assert (<= X_96 0.53682661)) +(assert (>= X_96 0.45928693)) +(assert (<= X_97 0.65313607)) +(assert (>= X_97 0.57559645)) +(assert (<= X_98 0.82760036)) +(assert (>= X_98 0.75006068)) +(assert (<= X_99 1.04083443)) +(assert (>= X_99 0.96329474)) +(assert (<= X_100 1.09898913)) +(assert (>= X_100 1.02144945)) +(assert (<= X_101 1.19591379)) +(assert (>= X_101 1.11837411)) +(assert (<= X_102 1.46730256)) +(assert (>= X_102 1.38976288)) +(assert (<= X_103 1.42853272)) +(assert (>= X_103 1.35099304)) +(assert (<= X_104 1.13775897)) +(assert (>= X_104 1.06021929)) +(assert (<= X_105 1.56422710)) +(assert (>= X_105 1.48668742)) +(assert (<= X_106 1.58361208)) +(assert (>= X_106 1.50607240)) +(assert (<= X_107 1.44791770)) +(assert (>= X_107 1.37037802)) +(assert (<= X_108 1.68053663)) +(assert (>= X_108 1.60299695)) +(assert (<= X_109 1.42853272)) +(assert (>= X_109 1.35099304)) +(assert (<= X_110 1.40914786)) +(assert (>= X_110 1.33160818)) +(assert (<= X_111 1.54484224)) +(assert (>= X_111 1.46730256)) +(assert (<= X_112 1.58361208)) +(assert (>= X_112 1.50607240)) +(assert (<= X_113 1.62238193)) +(assert (>= X_113 1.54484224)) +(assert (<= X_114 1.68053663)) +(assert (>= X_114 1.60299695)) +(assert (<= X_115 1.54484224)) +(assert (>= X_115 1.46730256)) +(assert (<= X_116 1.62238193)) +(assert (>= X_116 1.54484224)) +(assert (<= X_117 1.68053663)) +(assert (>= X_117 1.60299695)) +(assert (<= X_118 1.42853272)) +(assert (>= X_118 1.35099304)) +(assert (<= X_119 1.56422710)) +(assert (>= X_119 1.48668742)) +(assert (<= X_120 1.64176679)) +(assert (>= X_120 1.56422710)) +(assert (<= X_121 1.44791770)) +(assert (>= X_121 1.37037802)) +(assert (<= X_122 1.56422710)) +(assert (>= X_122 1.48668742)) +(assert (<= X_123 1.50607240)) +(assert (>= X_123 1.42853272)) +(assert (<= X_124 1.66115177)) +(assert (>= X_124 1.58361208)) +(assert (<= X_125 1.62238193)) +(assert (>= X_125 1.54484224)) +(assert (<= X_126 1.60299695)) +(assert (>= X_126 1.52545726)) +(assert (<= X_127 1.33160818)) +(assert (>= X_127 1.25406849)) +(assert (<= X_128 0.53682661)) +(assert (>= X_128 0.45928693)) +(assert (<= X_129 0.67252100)) +(assert (>= X_129 0.59498137)) +(assert (<= X_130 0.86637014)) +(assert (>= X_130 0.78883052)) +(assert (<= X_131 0.98267967)) +(assert (>= X_131 0.90513998)) +(assert (<= X_132 1.04083443)) +(assert (>= X_132 0.96329474)) +(assert (<= X_133 1.11837411)) +(assert (>= X_133 1.04083443)) +(assert (<= X_134 1.31222320)) +(assert (>= X_134 1.23468351)) +(assert (<= X_135 1.40914786)) +(assert (>= X_135 1.33160818)) +(assert (<= X_136 1.15714395)) +(assert (>= X_136 1.07960427)) +(assert (<= X_137 1.37037802)) +(assert (>= X_137 1.29283834)) +(assert (<= X_138 1.27345335)) +(assert (>= X_138 1.19591379)) +(assert (<= X_139 1.19591379)) +(assert (>= X_139 1.11837411)) +(assert (<= X_140 1.40914786)) +(assert (>= X_140 1.33160818)) +(assert (<= X_141 1.19591379)) +(assert (>= X_141 1.11837411)) +(assert (<= X_142 1.19591379)) +(assert (>= X_142 1.11837411)) +(assert (<= X_143 1.52545726)) +(assert (>= X_143 1.44791770)) +(assert (<= X_144 1.46730256)) +(assert (>= X_144 1.38976288)) +(assert (<= X_145 1.46730256)) +(assert (>= X_145 1.38976288)) +(assert (<= X_146 1.48668742)) +(assert (>= X_146 1.40914786)) +(assert (<= X_147 1.33160818)) +(assert (>= X_147 1.25406849)) +(assert (<= X_148 1.38976288)) +(assert (>= X_148 1.31222320)) +(assert (<= X_149 1.46730256)) +(assert (>= X_149 1.38976288)) +(assert (<= X_150 1.29283834)) +(assert (>= X_150 1.21529865)) +(assert (<= X_151 1.25406849)) +(assert (>= X_151 1.17652881)) +(assert (<= X_152 1.50607240)) +(assert (>= X_152 1.42853272)) +(assert (<= X_153 1.46730256)) +(assert (>= X_153 1.38976288)) +(assert (<= X_154 1.50607240)) +(assert (>= X_154 1.42853272)) +(assert (<= X_155 1.40914786)) +(assert (>= X_155 1.33160818)) +(assert (<= X_156 1.60299695)) +(assert (>= X_156 1.52545726)) +(assert (<= X_157 1.56422710)) +(assert (>= X_157 1.48668742)) +(assert (<= X_158 1.62238193)) +(assert (>= X_158 1.54484224)) +(assert (<= X_159 1.40914786)) +(assert (>= X_159 1.33160818)) +(assert (<= X_160 0.47867185)) +(assert (>= X_160 0.40113220)) +(assert (<= X_161 0.63375115)) +(assert (>= X_161 0.55621153)) +(assert (<= X_162 0.84698528)) +(assert (>= X_162 0.76944560)) +(assert (<= X_163 0.98267967)) +(assert (>= X_163 0.90513998)) +(assert (<= X_164 0.92452490)) +(assert (>= X_164 0.84698528)) +(assert (<= X_165 0.98267967)) +(assert (>= X_165 0.90513998)) +(assert (<= X_166 1.40914786)) +(assert (>= X_166 1.33160818)) +(assert (<= X_167 1.38976288)) +(assert (>= X_167 1.31222320)) +(assert (<= X_168 1.33160818)) +(assert (>= X_168 1.25406849)) +(assert (<= X_169 1.29283834)) +(assert (>= X_169 1.21529865)) +(assert (<= X_170 1.27345335)) +(assert (>= X_170 1.19591379)) +(assert (<= X_171 1.17652881)) +(assert (>= X_171 1.09898913)) +(assert (<= X_172 1.23468351)) +(assert (>= X_172 1.15714395)) +(assert (<= X_173 1.27345335)) +(assert (>= X_173 1.19591379)) +(assert (<= X_174 1.27345335)) +(assert (>= X_174 1.19591379)) +(assert (<= X_175 1.31222320)) +(assert (>= X_175 1.23468351)) +(assert (<= X_176 1.29283834)) +(assert (>= X_176 1.21529865)) +(assert (<= X_177 1.38976288)) +(assert (>= X_177 1.31222320)) +(assert (<= X_178 1.23468351)) +(assert (>= X_178 1.15714395)) +(assert (<= X_179 1.44791770)) +(assert (>= X_179 1.37037802)) +(assert (<= X_180 1.33160818)) +(assert (>= X_180 1.25406849)) +(assert (<= X_181 1.25406849)) +(assert (>= X_181 1.17652881)) +(assert (<= X_182 1.33160818)) +(assert (>= X_182 1.25406849)) +(assert (<= X_183 1.35099304)) +(assert (>= X_183 1.27345335)) +(assert (<= X_184 1.58361208)) +(assert (>= X_184 1.50607240)) +(assert (<= X_185 1.60299695)) +(assert (>= X_185 1.52545726)) +(assert (<= X_186 1.54484224)) +(assert (>= X_186 1.46730256)) +(assert (<= X_187 1.66115177)) +(assert (>= X_187 1.58361208)) +(assert (<= X_188 1.71930647)) +(assert (>= X_188 1.64176679)) +(assert (<= X_189 1.64176679)) +(assert (>= X_189 1.56422710)) +(assert (<= X_190 1.66115177)) +(assert (>= X_190 1.58361208)) +(assert (<= X_191 1.40914786)) +(assert (>= X_191 1.33160818)) +(assert (<= X_192 0.47867185)) +(assert (>= X_192 0.40113220)) +(assert (<= X_193 0.57559645)) +(assert (>= X_193 0.49805677)) +(assert (<= X_194 0.80821544)) +(assert (>= X_194 0.73067576)) +(assert (<= X_195 0.98267967)) +(assert (>= X_195 0.90513998)) +(assert (<= X_196 0.86637014)) +(assert (>= X_196 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+(assert (>= X_3053 -1.05077553)) +(assert (<= X_3054 -1.01175499)) +(assert (>= X_3054 -1.08979607)) +(assert (<= X_3055 -1.07028580)) +(assert (>= X_3055 -1.14832699)) +(assert (<= X_3056 -1.01175499)) +(assert (>= X_3056 -1.08979607)) +(assert (<= X_3057 -0.97273445)) +(assert (>= X_3057 -1.05077553)) +(assert (<= X_3058 -0.93371373)) +(assert (>= X_3058 -1.01175487)) +(assert (<= X_3059 -0.93371373)) +(assert (>= X_3059 -1.01175487)) +(assert (<= X_3060 -0.93371373)) +(assert (>= X_3060 -1.01175487)) +(assert (<= X_3061 -1.14832699)) +(assert (>= X_3061 -1.22636819)) +(assert (<= X_3062 -1.16783726)) +(assert (>= X_3062 -1.24587846)) +(assert (<= X_3063 -1.10930634)) +(assert (>= X_3063 -1.18734753)) +(assert (<= X_3064 -0.81665194)) +(assert (>= X_3064 -0.89469314)) +(assert (<= X_3065 -0.17281239)) +(assert (>= X_3065 -0.25085357)) +(assert (<= X_3066 -0.13379182)) +(assert (>= X_3066 -0.21183297)) +(assert (<= X_3067 -0.77763140)) +(assert (>= X_3067 -0.85567254)) +(assert (<= X_3068 -1.14832699)) +(assert (>= X_3068 -1.22636819)) +(assert (<= X_3069 -1.20685780)) +(assert (>= X_3069 -1.28489912)) +(assert (<= X_3070 -1.16783726)) +(assert (>= X_3070 -1.24587846)) +(assert (<= X_3071 -1.20685780)) +(assert (>= X_3071 -1.28489912)) + +; Definition of output constraints +(assert (or + (and (>= Y_1 Y_0)) + (and (>= Y_2 Y_0)) + (and (>= Y_3 Y_0)) + (and (>= Y_4 Y_0)) + (and (>= Y_5 Y_0)) + (and (>= Y_6 Y_0)) + (and (>= Y_7 Y_0)) + (and (>= Y_8 Y_0)) + (and (>= Y_9 Y_0)) +)) diff --git a/run_in_docker.sh b/run_in_docker.sh new file mode 100755 index 0000000..6fda4fd --- /dev/null +++ b/run_in_docker.sh @@ -0,0 +1,34 @@ +#!/bin/bash +# run code in docker + +PREFIX=nnenum + +CONTAINER=${PREFIX}_container +IMAGE=${PREFIX}_image + +rm -f ${RESULT_FILE} +echo "Running in Docker using container name $CONTAINER and image name $IMAGE" + +docker kill $CONTAINER +docker stop $CONTAINER +docker rm $CONTAINER + +docker build . -t $IMAGE + +docker run -d --name $CONTAINER $IMAGE tail -f /dev/null + +docker run $IMAGE +RV=$? +# "docker ps" should now list the image as running + +# to get a shell, remove the lines at the end that delete the container and do: "docker exec -it $CONTAINER bash" + +#docker cp $CONTAINER:/${RESULT_FILE} ${RESULT_FILE} + +docker kill $CONTAINER +docker stop $CONTAINER +docker rm $CONTAINER + +echo "Done with exit code $RV." + +exit $RV diff --git a/run_tests.sh b/run_tests.sh index 4da2e69..39a91c5 100755 --- a/run_tests.sh +++ b/run_tests.sh @@ -2,13 +2,12 @@ python3 -m nnenum.nnenum examples/acasxu/data/ACASXU_run2a_1_1_batch_2000.onnx examples/acasxu/data/prop_1.vnnlib - python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/prop_0_0.03.vnnlib python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/prop_2_0.03.vnnlib python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx examples/cifar2020/cifar10_spec_idx_11_eps_0.00784_n1.vnnlib -python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib 45 /dev/null +python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib 60 /dev/null echo "Passed all tests" From ad7e34b97896b599a3780ea5c9d04a902a2a1d47 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 19:59:42 -0400 Subject: [PATCH 23/55] typo --- Dockerfile | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Dockerfile b/Dockerfile index 2a57d65..06671d0 100644 --- a/Dockerfile +++ b/Dockerfile @@ -14,7 +14,7 @@ COPY ./requirements.txt /work/requirements.txt WORKDIR /work # install python package dependencies -RUN pip install --upgrade pip +RUN pip3 install --upgrade pip RUN pip3 install -r requirements.txt # set environment variables From c02de5fa5597868defc39afd3324a4ddc79b5104 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 20:03:14 -0400 Subject: [PATCH 24/55] reverted travis ci yml --- .travis.yml | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/.travis.yml b/.travis.yml index 6aec55e..9e2b4c4 100644 --- a/.travis.yml +++ b/.travis.yml @@ -12,5 +12,8 @@ services: - docker script: -- ./run_tests.sh +# build Docker container +- docker build -t nnenum . +# run tests +- docker run nnenum From 29e8cf86b91887d02b5510d003212594ac618037 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 20:05:58 -0400 Subject: [PATCH 25/55] update config --- .travis.yml | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/.travis.yml b/.travis.yml index 9e2b4c4..7010b06 100644 --- a/.travis.yml +++ b/.travis.yml @@ -1,12 +1,11 @@ # configuration file for continuous integration testing using travis-ci.org -dist: xenial - -language: python - dist: - - trusty + - xenial + +language: + - python services: - docker From d7894004e20e62db70659f2998c6e5e368803601 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 10 Jun 2021 20:12:26 -0400 Subject: [PATCH 26/55] removed upgrade pip in docker file --- Dockerfile | 1 - README.md | 9 +++++---- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/Dockerfile b/Dockerfile index 06671d0..140570c 100644 --- a/Dockerfile +++ b/Dockerfile @@ -14,7 +14,6 @@ COPY ./requirements.txt /work/requirements.txt WORKDIR /work # install python package dependencies -RUN pip3 install --upgrade pip RUN pip3 install -r requirements.txt # set environment variables diff --git a/README.md b/README.md index 5cc5ebf..05fccd4 100644 --- a/README.md +++ b/README.md @@ -1,10 +1,12 @@ +[![Build Status](https://travis-ci.com/stanleybak/nnenum.svg?branch=master)](https://travis-ci.com/stanleybak/nnenum) + # nnenum - The Neural Network Enumeration Tool -**nnenum** (pronounced *en-en-en-um*) is a high-performance neural network verification tool. Multiple levels of abstraction are used to quickly verify ReLU networks without sacrificing completeness. Analysis combines three types of zonotopes with star set (triangle) overapproximations, and uses [efficient parallelized ReLU case splitting](http://stanleybak.com/papers/bak2020cav.pdf). The verification tree search can be augmented with adversarial example generation using multiple attacks from the [foolbox library](https://github.com/bethgelab/foolbox) to quickly find property violations. The tool is written in Python 3, uses GLPK for LP solving and directly accepts [ONNX](https://github.com/onnx/onnx) network files as input. The [ImageStar trick](https://arxiv.org/abs/2004.05511) allows sets to be quickly propagated through all layers supported by the [ONNX runtime](https://github.com/microsoft/onnxruntime), such as convolutional layers with arbitrary parameters. +**nnenum** (pronounced *en-en-en-um*) is a high-performance neural network verification tool. Multiple levels of abstraction are used to quickly verify ReLU networks without sacrificing completeness. Analysis combines three types of zonotopes with star set (triangle) overapproximations, and uses [efficient parallelized ReLU case splitting](http://stanleybak.com/papers/bak2020cav.pdf). The tool is written in Python 3, uses GLPK for LP solving and directly accepts [ONNX](https://github.com/onnx/onnx) network files and `vnnlib` specifications as input. The [ImageStar trick](https://arxiv.org/abs/2004.05511) allows sets to be quickly propagated through all layers supported by the [ONNX runtime](https://github.com/microsoft/onnxruntime), such as convolutional layers with arbitrary parameters. The tool is written by Stanley Bak ([homepage](http://stanleybak.com), [twitter](https://twitter.com/StanleyBak)). ### Getting Started -The `Dockerfile` shows how to install all the dependencies (mostly python packages) and set up the environment. The tool loads neural networks directly from ONNX files and properties from vnnlib files. +The `Dockerfile` shows how to install all the dependencies (mostly python packages) and set up the environment. The tool loads neural networks directly from ONNX files and properties to check from `vnnlib` files. For example, try running: ``` @@ -13,14 +15,13 @@ python3 -m nnenum.nnenum examples/acasxu/data/ACASXU_run2a_3_3_batch_2000.onnx e You can see a few more examples in `run_tests.sh`. - ### VNN 2020 Neural Network Verification Competition (VNN-COMP) Version The nnenum tool performed well in VNN-COMP 2020, being the only tool to verify all the ACAS-Xu benchmarks (each in under 10 seconds). The version used for the competition as well as model files and scripts to run the compeition benchmarks are in the `vnn2020` branch. ### CAV 2020 Paper Version The CAV 2020 paper ["Improved Geometric Path Enumeration for Verifying ReLU Neural Networks"](http://stanleybak.com/papers/bak2020cav.pdf) by S. Bak, H.D Tran, K. Hobbs and T. T. Johnson corresponds to optimizations integrated into the exact analysis mode of nnenum, which also benefits overapproximative analysis. The paper version and repeatability evaluation package instructions are available [here](http://stanleybak.com/papers/bak2020cav_repeatability.zip). -### Citing ### +### Citing nnenum ### The following citations can be used for nnenum: ``` From caec1d13af9d04d738c9d65eb01d93c44097ab37 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 10:28:33 -0400 Subject: [PATCH 27/55] minor --- src/nnenum/nnenum.py | 3 ++- src/nnenum/onnx_network.py | 5 ++-- src/nnenum/overapprox.py | 46 ++++++++++++++++++++++----------- src/nnenum/zonotope.py | 52 +++++++++++++++++++++++--------------- 4 files changed, 67 insertions(+), 39 deletions(-) diff --git a/src/nnenum/nnenum.py b/src/nnenum/nnenum.py index cdc6cb4..0f253d7 100644 --- a/src/nnenum/nnenum.py +++ b/src/nnenum/nnenum.py @@ -66,11 +66,12 @@ def set_image_settings(): Settings.COMPRESS_INIT_BOX = False Settings.BRANCH_MODE = Settings.BRANCH_OVERAPPROX + Settings.TRY_QUICK_OVERAPPROX = False Settings.OVERAPPROX_MIN_GEN_LIMIT = np.inf Settings.SPLIT_IF_IDLE = False Settings.OVERAPPROX_LP_TIMEOUT = np.inf - Settings.TIMING_STATS = False + Settings.TIMING_STATS = True # contraction doesn't help in high dimensions #Settings.OVERAPPROX_CONTRACT_ZONO_LP = False diff --git a/src/nnenum/onnx_network.py b/src/nnenum/onnx_network.py index 54b03be..bd99e30 100644 --- a/src/nnenum/onnx_network.py +++ b/src/nnenum/onnx_network.py @@ -110,16 +110,15 @@ def transform_star(self, star): def transform_zono(self, zono): 'transform the zono' - zono_copy = zono.deep_copy() - cols = [] for col in range(zono.mat_t.shape[1]): #print(f".transforming zono: {col} / {zono.mat_t.shape[1]})") vec = zono.mat_t[:, col] vec = nn_unflatten(vec, self.input_shape) - + res = self.execute(vec) + res = res - self.zero_output res = nn_flatten(res) diff --git a/src/nnenum/overapprox.py b/src/nnenum/overapprox.py index 041c815..f28ba30 100644 --- a/src/nnenum/overapprox.py +++ b/src/nnenum/overapprox.py @@ -11,6 +11,7 @@ from nnenum.prefilter import update_bounds_lp, sort_splits from nnenum.specification import DisjunctiveSpec from nnenum.network import ReluLayer, FullyConnectedLayer, nn_flatten, nn_unflatten +from nnenum.zonotope import zono_box_bounds def try_quick_overapprox(ss, network, spec, start_time): 'try a quick overapproximation, return is_safe, concrete_io_tuple' @@ -387,6 +388,8 @@ def run_overapprox_round(network, ss_init, sets, prerelu_sims, check_cancel_func layer_bounds, split_indices = s.tighten_bounds(layer_bounds, split_indices, sim, check_cancel_func, depth) + assert layer_bounds is not None + #print(f". layer bounds {layer_num}:\n{layer_bounds}") # bounds are now as tight as they will get @@ -535,8 +538,10 @@ def execute_with_bounds(self, _layer_num, layer_bounds, split_indices, zero_indi if self.get_num_gens() + len(split_indices) > self.max_gens: raise OverapproxCanceledException(f'{self.type_string} gens exceeds limit (> {self.max_gens})') - + + Timers.tic('update_zono') update_zono(self.zono, self.relu_update_func, layer_bounds, split_indices, zero_indices) + Timers.toc('update_zono') def transform_linear(self, layer): 'affine transformation' @@ -552,16 +557,13 @@ def tighten_bounds(self, layer_bounds, _split_indices, _sim, _check_cancel_func, returns (layer_bounds, split_indices), split_indices can be None ''' - box_bounds = self.zono.box_bounds() - - if layer_bounds is None: - layer_bounds = box_bounds - else: - layer_bounds[:, 0] = np.maximum(layer_bounds[:, 0], box_bounds[:, 0]) - layer_bounds[:, 1] = np.minimum(layer_bounds[:, 1], box_bounds[:, 1]) + Timers.tic('tighten_bounds_zono') + self.zono.make_gens() # need to manually call befor jit'd box_bounds + layer_bounds = tighten_bounds_zono(layer_bounds, self.zono) + Timers.toc('tighten_bounds_zono') return layer_bounds, None - + def check_spec(self, spec, _check_cancel_func): 'returns is_safe?' @@ -574,6 +576,20 @@ def get_num_gens(self): return self.zono.mat_t.shape[1] +def tighten_bounds_zono(layer_bounds, zono): + 'tighten bounds using zonotope' + + #box_bounds = zono.box_bounds() + box_bounds = zono_box_bounds(zono.mat_t, zono.center, zono.pos1_gens, zono.neg1_gens, zono.dtype) + + if layer_bounds is None: + layer_bounds = box_bounds + else: + layer_bounds[:, 0] = np.maximum(layer_bounds[:, 0], box_bounds[:, 0]) + layer_bounds[:, 1] = np.minimum(layer_bounds[:, 1], box_bounds[:, 1]) + + return layer_bounds + def update_zono(z, relu_update_func, bounds, splits, zeros): 'update a zono with the current bounds' @@ -585,29 +601,29 @@ def update_zono(z, relu_update_func, bounds, splits, zeros): center = z.center # these are the bounds on the input for each neuron in the current layer - Timers.tic('assign_zeros') + #Timers.tic('assign_zeros') center[zeros] = 0 gen_mat_t[zeros, :] = 0 - Timers.toc('assign_zeros') + #Timers.toc('assign_zeros') if splits.size > 0: new_generators = np.zeros((gen_mat_t.shape[0], len(splits)), dtype=z.dtype) - Timers.tic('relu_update') + #Timers.tic('relu_update') for i, split_index in enumerate(splits): lb, ub = bounds[split_index] # need to add a new generator for the overapproximation relu_update_func(lb, ub, split_index, gen_mat_t, center, new_generators[:, i]) - Timers.toc('relu_update') + #Timers.toc('relu_update') - Timers.tic('stack_new_generators') + #Timers.tic('stack_new_generators') # need to update zonotope with new generators z.init_bounds += [(-1, 1) for _ in range(len(splits))] z.mat_t = np.hstack([z.mat_t, new_generators]) - Timers.toc('stack_new_generators') + #Timers.toc('stack_new_generators') def relu_update_interval_zono(_lb, ub, output_dim, gen_mat_t, center, new_gen): '''update one dimension (output) of a zonotope due to a relu split diff --git a/src/nnenum/zonotope.py b/src/nnenum/zonotope.py index bd91eef..5e720f8 100644 --- a/src/nnenum/zonotope.py +++ b/src/nnenum/zonotope.py @@ -225,6 +225,15 @@ def minimize_val(self, vector): return rv + def make_gens(self): + 'pos_1_gens may need to be updated if matrix size changed due to assignment' + + if self.pos1_gens is None or self.pos1_gens.shape[0] != self.mat_t.shape[1]: + self.neg1_gens = np.array([i[0] for i in self.init_bounds], dtype=self.dtype) + self.pos1_gens = np.array([i[1] for i in self.init_bounds], dtype=self.dtype) + + assert self.pos1_gens.shape[0] == self.mat_t.shape[1] + def box_bounds(self): '''compute box bounds for the zonotope @@ -233,27 +242,9 @@ def box_bounds(self): Timers.tic('zono.box_bounds') - mat_t = self.mat_t - size = self.center.size - - # pos_1_gens may need to be updated if matrix size changed due to assignment - if self.pos1_gens is None or self.pos1_gens.shape[0] != self.mat_t.shape[1]: - self.neg1_gens = np.array([i[0] for i in self.init_bounds], dtype=self.dtype) - self.pos1_gens = np.array([i[1] for i in self.init_bounds], dtype=self.dtype) - - assert self.pos1_gens.shape[0] == self.mat_t.shape[1] - - pos_mat = np.clip(mat_t, 0, np.inf) - neg_mat = np.clip(mat_t, -np.inf, 0) - - pos_pos = np.dot(self.pos1_gens, pos_mat.T) - neg_neg = np.dot(self.neg1_gens, neg_mat.T) - pos_neg = np.dot(self.pos1_gens, neg_mat.T) - neg_pos = np.dot(self.neg1_gens, pos_mat.T) + self.make_gens() - rv = np.zeros((size, 2), dtype=self.dtype) - rv[:, 0] = self.center + pos_neg + neg_pos - rv[:, 1] = self.center + pos_pos + neg_neg + rv = zono_box_bounds(self.mat_t, self.center, self.pos1_gens, self.neg1_gens, self.dtype) Timers.toc('zono.box_bounds') @@ -436,3 +427,24 @@ def max_func(vec): return kamenev.get_verts(2, max_func, epsilon=epsilon) +#@njit(cache=True) +def zono_box_bounds(mat_t, center, pos1_gens, neg1_gens, dtype): + 'pure zono box bounds function' + + size = center.size + + #pos_mat = np.clip(mat_t, 0, np.inf) + #neg_mat = np.clip(mat_t, -np.inf, 0) + pos_mat = np.maximum(mat_t, 0) + neg_mat = np.minimum(mat_t, 0) + + pos_pos = np.dot(pos1_gens, pos_mat.T) + neg_neg = np.dot(neg1_gens, neg_mat.T) + pos_neg = np.dot(pos1_gens, neg_mat.T) + neg_pos = np.dot(neg1_gens, pos_mat.T) + + rv = np.zeros((size, 2), dtype=dtype) + rv[:, 0] = center + pos_neg + neg_pos + rv[:, 1] = center + pos_pos + neg_neg + + return rv From 53c1b24f2f3c8a719d5f7d5b39de32e7b424253c Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 10:49:08 -0400 Subject: [PATCH 28/55] added tool scripts --- vnncomp_scripts/README.md | 5 +++++ vnncomp_scripts/install_tool.sh | 20 ++++++++++++++++++++ vnncomp_scripts/prepare_instance.sh | 25 +++++++++++++++++++++++++ vnncomp_scripts/run_instance.sh | 27 +++++++++++++++++++++++++++ 4 files changed, 77 insertions(+) create mode 100644 vnncomp_scripts/README.md create mode 100755 vnncomp_scripts/install_tool.sh create mode 100755 vnncomp_scripts/prepare_instance.sh create mode 100755 vnncomp_scripts/run_instance.sh diff --git a/vnncomp_scripts/README.md b/vnncomp_scripts/README.md new file mode 100644 index 0000000..8c74461 --- /dev/null +++ b/vnncomp_scripts/README.md @@ -0,0 +1,5 @@ +These are the scripts needed to run the tool for use with VNNCOMP. + +*** Manual Setup *** + +There is no manual setup. Everything is done automatically in install_tool.sh diff --git a/vnncomp_scripts/install_tool.sh b/vnncomp_scripts/install_tool.sh new file mode 100755 index 0000000..842a11e --- /dev/null +++ b/vnncomp_scripts/install_tool.sh @@ -0,0 +1,20 @@ +#!/bin/bash +# install_tool.sh script for VNNCOMP for nnenum +# Stanley Bak + +TOOL_NAME=nnenum +VERSION_STRING=v1 + +# check arguments +if [ "$1" != ${VERSION_STRING} ]; then + echo "Expected first argument (version string) '$VERSION_STRING', got '$1'" + exit 1 +fi + +echo "Installing $TOOL_NAME" +DIR=$(dirname $(dirname $(realpath $0))) + +apt-get update && +apt-get install -y python3 python3-pip && +apt-get install -y psmisc && # for killall, used in prepare_instance.sh script +pip3 install -r "$DIR/requirements.txt" diff --git a/vnncomp_scripts/prepare_instance.sh b/vnncomp_scripts/prepare_instance.sh new file mode 100755 index 0000000..f76d390 --- /dev/null +++ b/vnncomp_scripts/prepare_instance.sh @@ -0,0 +1,25 @@ +#!/bin/bash +# example prepare_instance.sh script for VNNCOMP for simple_adversarial_generator (https://github.com/stanleybak/simple_adversarial_generator) +# four arguments, first is "v1", second is a benchmark category identifier string such as "acasxu", third is path to the .onnx file and fourth is path to .vnnlib file +# Stanley Bak, Feb 2021 + +TOOL_NAME=simple_adv_gen +VERSION_STRING=v1 + +# check arguments +if [ "$1" != ${VERSION_STRING} ]; then + echo "Expected first argument (version string) '$VERSION_STRING', got '$1'" + exit 1 +fi + +CATEGORY=$2 +ONNX_FILE=$3 +VNNLIB_FILE=$4 + +echo "Preparing $TOOL_NAME for benchmark instance in category '$CATEGORY' with onnx file '$ONNX_FILE' and vnnlib file '$VNNLIB_FILE'" + +# kill any zombie processes +killall -q python3 + +# script returns a 0 exit code if successful. If you want to skip a benchmark category you can return non-zero. +exit 0 diff --git a/vnncomp_scripts/run_instance.sh b/vnncomp_scripts/run_instance.sh new file mode 100755 index 0000000..b6464dc --- /dev/null +++ b/vnncomp_scripts/run_instance.sh @@ -0,0 +1,27 @@ +#!/bin/bash +# example run_benchmark.sh script for VNNCOMP for simple_adversarial_generator (https://github.com/stanleybak/simple_adversarial_generator) +# six arguments, first is "v1", second is a benchmark category itentifier string such as "acasxu", third is path to the .onnx file, fourth is path to .vnnlib file, fifth is a path to the results file, and sixth is a timeout in seconds. +# Stanley Bak, Feb 2021 + +VERSION_STRING=v1 + +# check arguments +if [ "$1" != ${VERSION_STRING} ]; then + echo "Expected first argument (version string) '$VERSION_STRING', got '$1'" + exit 1 +fi + +CATEGORY=$2 +ONNX_FILE=$3 +VNNLIB_FILE=$4 +RESULTS_FILE=$5 +TIMEOUT=$6 + +echo "Running benchmark instance in category '$CATEGORY' with onnx file '$ONNX_FILE', vnnlib file '$VNNLIB_FILE', results file $RESULTS_FILE, and timeout $TIMEOUT" + +# setup environment variable for tool (doing it earlier won't be persistent with docker)" +DIR=$(dirname $(dirname $(realpath $0))) +export PYTHONPATH="$PYTHONPATH:$DIR/src" + +# run the tool to produce the results file +python3 -m agen.randgen "$ONNX_FILE" "$VNNLIB_FILE" "$RESULTS_FILE" From 01272dc6f6a6aa3f2992da2de44469df78e271ee Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 10:52:42 -0400 Subject: [PATCH 29/55] minor --- README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/README.md b/README.md index 05fccd4..0cfbc32 100644 --- a/README.md +++ b/README.md @@ -44,3 +44,4 @@ The following citations can be used for nnenum: organization={Springer} } ``` + From 1e51c83d482c64728007dff3e722d2c509e6b542 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 11:02:23 -0400 Subject: [PATCH 30/55] updated run_instance --- vnncomp_scripts/run_instance.sh | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/vnncomp_scripts/run_instance.sh b/vnncomp_scripts/run_instance.sh index b6464dc..8e570e5 100755 --- a/vnncomp_scripts/run_instance.sh +++ b/vnncomp_scripts/run_instance.sh @@ -24,4 +24,4 @@ DIR=$(dirname $(dirname $(realpath $0))) export PYTHONPATH="$PYTHONPATH:$DIR/src" # run the tool to produce the results file -python3 -m agen.randgen "$ONNX_FILE" "$VNNLIB_FILE" "$RESULTS_FILE" +python3 -m nnenum.nnenum "$ONNX_FILE" "$VNNLIB_FILE" "$TIMEOUT" "$RESULTS_FILE" From ac99dc507876efcd7daf8f1a413f43497b950b73 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 11:05:44 -0400 Subject: [PATCH 31/55] updated env variables --- vnncomp_scripts/run_instance.sh | 3 +++ 1 file changed, 3 insertions(+) diff --git a/vnncomp_scripts/run_instance.sh b/vnncomp_scripts/run_instance.sh index 8e570e5..2e581f2 100755 --- a/vnncomp_scripts/run_instance.sh +++ b/vnncomp_scripts/run_instance.sh @@ -23,5 +23,8 @@ echo "Running benchmark instance in category '$CATEGORY' with onnx file '$ONNX_F DIR=$(dirname $(dirname $(realpath $0))) export PYTHONPATH="$PYTHONPATH:$DIR/src" +export OPENBLAS_NUM_THREADS=1 +export OMP_NUM_THREADS=1 + # run the tool to produce the results file python3 -m nnenum.nnenum "$ONNX_FILE" "$VNNLIB_FILE" "$TIMEOUT" "$RESULTS_FILE" From 6c0a5dcb2ac4098c8845661002297f7b7b21e945 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 12:14:01 -0400 Subject: [PATCH 32/55] fixed optimized network load bug --- examples/test/README.md | 1 + examples/test/test_prop.vnnlib | 40 ++++++++++++++++++++++++ examples/test/test_sat.onnx | Bin 0 -> 55889 bytes examples/test/test_unsat.onnx | Bin 0 -> 55889 bytes run_tests.sh | 10 +++++- src/nnenum/network.py | 8 ++--- src/nnenum/nnenum.py | 15 +++++++-- src/nnenum/onnx_network.py | 8 ++--- src/nnenum/overapprox.py | 53 +++++++++----------------------- src/nnenum/zonotope.py | 54 +++++++++++++-------------------- 10 files changed, 106 insertions(+), 83 deletions(-) create mode 100644 examples/test/README.md create mode 100644 examples/test/test_prop.vnnlib create mode 100644 examples/test/test_sat.onnx create mode 100644 examples/test/test_unsat.onnx diff --git a/examples/test/README.md b/examples/test/README.md new file mode 100644 index 0000000..a714dac --- /dev/null +++ b/examples/test/README.md @@ -0,0 +1 @@ +these are the test properties from VNNCOMP 2021. diff --git a/examples/test/test_prop.vnnlib b/examples/test/test_prop.vnnlib new file mode 100644 index 0000000..536d62f --- /dev/null +++ b/examples/test/test_prop.vnnlib @@ -0,0 +1,40 @@ +; test property is acas xu property 3 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) + +(declare-const Y_0 Real) +(declare-const Y_1 Real) +(declare-const Y_2 Real) +(declare-const Y_3 Real) +(declare-const Y_4 Real) + +; input constraints +; Unscaled Input 0: (1500, 1800) +(assert (<= X_0 -0.29855281193475053)) +(assert (>= X_0 -0.30353115613746867)) + +; Unscaled Input 1: (-0.06, 0.06) +(assert (<= X_1 0.009549296585513092)) +(assert (>= X_1 -0.009549296585513092)) + +; Unscaled Input 2: (3.1, 3.1415926535) +(assert (<= X_2 0.49999999998567607)) +(assert (>= X_2 0.4933803235848431)) + +; Unscaled Input 3: (980, 1200) +(assert (<= X_3 0.5)) +(assert (>= X_3 0.3)) + +; Unscaled Input 4: (960, 1200) +(assert (<= X_4 0.5)) +(assert (>= X_4 0.3)) + +; output constraints (property 3, sat if CoC is minimal) +(assert (<= Y_0 Y_1)) +(assert (<= Y_0 Y_2)) +(assert (<= Y_0 Y_3)) +(assert (<= Y_0 Y_4)) diff --git a/examples/test/test_sat.onnx b/examples/test/test_sat.onnx new file mode 100644 index 0000000000000000000000000000000000000000..40021f68c0de023168034b31847a7d62c1363977 GIT binary patch literal 55889 zcmZsic_3BY_x~k?NR%N%MUr_|xM#1eluFU0L6cHw&_HNZ#t0!KWe921JgM&4Yip(f zQA8z8(wyeGpWpL+p5M3M=kxH#wcq>P>%Q(iXYF;?dT+(f8iLngpV5Pd^c@-yu(a>! 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If 'Passed all tests.' is printed at then end, then we were successful." + +python3 -m nnenum.nnenum examples/test/test_sat.onnx examples/test/test_prop.vnnlib 60 out.txt +grep "violated" out.txt + +python3 -m nnenum.nnenum examples/test/test_unsat.onnx examples/test/test_prop.vnnlib 60 out.txt +grep "holds" out.txt + python3 -m nnenum.nnenum examples/acasxu/data/ACASXU_run2a_1_1_batch_2000.onnx examples/acasxu/data/prop_1.vnnlib python3 -m nnenum.nnenum examples/mnistfc/mnist-net_256x2.onnx examples/mnistfc/prop_0_0.03.vnnlib @@ -10,4 +18,4 @@ python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx exampl python3 -m nnenum.nnenum examples/cifar2020/cifar10_2_255_simplified.onnx examples/cifar2020/cifar10_spec_idx_3_eps_0.00784_n1.vnnlib 60 /dev/null -echo "Passed all tests" +echo "Passed all tests." diff --git a/src/nnenum/network.py b/src/nnenum/network.py index 9db0273..6e60832 100644 --- a/src/nnenum/network.py +++ b/src/nnenum/network.py @@ -834,12 +834,12 @@ def images_to_init_box(min_image, max_image): return rv -def nn_flatten(image): +def nn_flatten(image, order='C'): 'flatten a multichannel image to a 1-d array' - return image.flatten('C') + return image.flatten(order) -def nn_unflatten(image, shape): +def nn_unflatten(image, shape, order='C'): '''unflatten to a multichannel image from a 1-d array this uses reshape, so may not be a copy @@ -847,7 +847,7 @@ def nn_unflatten(image, shape): assert len(image.shape) == 1 - rv = image.reshape(shape, order='C') + rv = image.reshape(shape, order=order) return rv diff --git a/src/nnenum/nnenum.py b/src/nnenum/nnenum.py index 0f253d7..0d02fa4 100644 --- a/src/nnenum/nnenum.py +++ b/src/nnenum/nnenum.py @@ -1,7 +1,7 @@ ''' nnenum vnnlib front end -usage: "python3 nnenum.py [timeout=None]" +usage: "python3 nnenum.py [timeout=None] [outfile=None]" Stanley Bak June 2021 @@ -108,7 +108,7 @@ def main(): except AssertionError: # cannot do optimized load due to unsupported layers network = load_onnx_network(onnx_filename) - + result_str = 'none' # gets overridden num_inputs = len(spec_list[0][0]) @@ -127,7 +127,7 @@ def main(): break Settings.TIMEOUT = timeout - + res = enumerate_network(init_box, network, spec) result_str = res.result_str @@ -138,9 +138,18 @@ def main(): if result_str != "safe": break + # rename for VNNCOMP21: + + if result_str == "safe": + result_str = "holds" + elif "unsafe" in result_str: + result_str = "violated" + if outfile is not None: with open(outfile, 'w') as f: f.write(result_str) + + #print(result_str) if result_str == 'error': sys.exit(Result.results.index('error')) diff --git a/src/nnenum/onnx_network.py b/src/nnenum/onnx_network.py index bd99e30..a29ceea 100644 --- a/src/nnenum/onnx_network.py +++ b/src/nnenum/onnx_network.py @@ -286,7 +286,7 @@ def load_onnx_network_optimized(filename): b = np.frombuffer(init.raw_data, dtype=' self.max_gens: raise OverapproxCanceledException(f'{self.type_string} gens exceeds limit (> {self.max_gens})') - - Timers.tic('update_zono') + update_zono(self.zono, self.relu_update_func, layer_bounds, split_indices, zero_indices) - Timers.toc('update_zono') def transform_linear(self, layer): 'affine transformation' @@ -557,13 +545,16 @@ def tighten_bounds(self, layer_bounds, _split_indices, _sim, _check_cancel_func, returns (layer_bounds, split_indices), split_indices can be None ''' - Timers.tic('tighten_bounds_zono') - self.zono.make_gens() # need to manually call befor jit'd box_bounds - layer_bounds = tighten_bounds_zono(layer_bounds, self.zono) - Timers.toc('tighten_bounds_zono') + box_bounds = self.zono.box_bounds() + + if layer_bounds is None: + layer_bounds = box_bounds + else: + layer_bounds[:, 0] = np.maximum(layer_bounds[:, 0], box_bounds[:, 0]) + layer_bounds[:, 1] = np.minimum(layer_bounds[:, 1], box_bounds[:, 1]) return layer_bounds, None - + def check_spec(self, spec, _check_cancel_func): 'returns is_safe?' @@ -576,20 +567,6 @@ def get_num_gens(self): return self.zono.mat_t.shape[1] -def tighten_bounds_zono(layer_bounds, zono): - 'tighten bounds using zonotope' - - #box_bounds = zono.box_bounds() - box_bounds = zono_box_bounds(zono.mat_t, zono.center, zono.pos1_gens, zono.neg1_gens, zono.dtype) - - if layer_bounds is None: - layer_bounds = box_bounds - else: - layer_bounds[:, 0] = np.maximum(layer_bounds[:, 0], box_bounds[:, 0]) - layer_bounds[:, 1] = np.minimum(layer_bounds[:, 1], box_bounds[:, 1]) - - return layer_bounds - def update_zono(z, relu_update_func, bounds, splits, zeros): 'update a zono with the current bounds' @@ -601,29 +578,29 @@ def update_zono(z, relu_update_func, bounds, splits, zeros): center = z.center # these are the bounds on the input for each neuron in the current layer - #Timers.tic('assign_zeros') + Timers.tic('assign_zeros') center[zeros] = 0 gen_mat_t[zeros, :] = 0 - #Timers.toc('assign_zeros') + Timers.toc('assign_zeros') if splits.size > 0: new_generators = np.zeros((gen_mat_t.shape[0], len(splits)), dtype=z.dtype) - #Timers.tic('relu_update') + Timers.tic('relu_update') for i, split_index in enumerate(splits): lb, ub = bounds[split_index] # need to add a new generator for the overapproximation relu_update_func(lb, ub, split_index, gen_mat_t, center, new_generators[:, i]) - #Timers.toc('relu_update') + Timers.toc('relu_update') - #Timers.tic('stack_new_generators') + Timers.tic('stack_new_generators') # need to update zonotope with new generators z.init_bounds += [(-1, 1) for _ in range(len(splits))] z.mat_t = np.hstack([z.mat_t, new_generators]) - #Timers.toc('stack_new_generators') + Timers.toc('stack_new_generators') def relu_update_interval_zono(_lb, ub, output_dim, gen_mat_t, center, new_gen): '''update one dimension (output) of a zonotope due to a relu split diff --git a/src/nnenum/zonotope.py b/src/nnenum/zonotope.py index 5e720f8..a50946e 100644 --- a/src/nnenum/zonotope.py +++ b/src/nnenum/zonotope.py @@ -1,5 +1,5 @@ ''' -Zonotope performance tests +Zonotope nnenum implementation Stanley Bak ''' @@ -225,15 +225,6 @@ def minimize_val(self, vector): return rv - def make_gens(self): - 'pos_1_gens may need to be updated if matrix size changed due to assignment' - - if self.pos1_gens is None or self.pos1_gens.shape[0] != self.mat_t.shape[1]: - self.neg1_gens = np.array([i[0] for i in self.init_bounds], dtype=self.dtype) - self.pos1_gens = np.array([i[1] for i in self.init_bounds], dtype=self.dtype) - - assert self.pos1_gens.shape[0] == self.mat_t.shape[1] - def box_bounds(self): '''compute box bounds for the zonotope @@ -242,9 +233,27 @@ def box_bounds(self): Timers.tic('zono.box_bounds') - self.make_gens() + mat_t = self.mat_t + size = self.center.size + + # pos_1_gens may need to be updated if matrix size changed due to assignment + if self.pos1_gens is None or self.pos1_gens.shape[0] != self.mat_t.shape[1]: + self.neg1_gens = np.array([i[0] for i in self.init_bounds], dtype=self.dtype) + self.pos1_gens = np.array([i[1] for i in self.init_bounds], dtype=self.dtype) + + assert self.pos1_gens.shape[0] == self.mat_t.shape[1] + + pos_mat = np.clip(mat_t, 0, np.inf) + neg_mat = np.clip(mat_t, -np.inf, 0) + + pos_pos = np.dot(self.pos1_gens, pos_mat.T) + neg_neg = np.dot(self.neg1_gens, neg_mat.T) + pos_neg = np.dot(self.pos1_gens, neg_mat.T) + neg_pos = np.dot(self.neg1_gens, pos_mat.T) - rv = zono_box_bounds(self.mat_t, self.center, self.pos1_gens, self.neg1_gens, self.dtype) + rv = np.zeros((size, 2), dtype=self.dtype) + rv[:, 0] = self.center + pos_neg + neg_pos + rv[:, 1] = self.center + pos_pos + neg_neg Timers.toc('zono.box_bounds') @@ -427,24 +436,3 @@ def max_func(vec): return kamenev.get_verts(2, max_func, epsilon=epsilon) -#@njit(cache=True) -def zono_box_bounds(mat_t, center, pos1_gens, neg1_gens, dtype): - 'pure zono box bounds function' - - size = center.size - - #pos_mat = np.clip(mat_t, 0, np.inf) - #neg_mat = np.clip(mat_t, -np.inf, 0) - pos_mat = np.maximum(mat_t, 0) - neg_mat = np.minimum(mat_t, 0) - - pos_pos = np.dot(pos1_gens, pos_mat.T) - neg_neg = np.dot(neg1_gens, neg_mat.T) - pos_neg = np.dot(pos1_gens, neg_mat.T) - neg_pos = np.dot(neg1_gens, pos_mat.T) - - rv = np.zeros((size, 2), dtype=dtype) - rv[:, 0] = center + pos_neg + neg_pos - rv[:, 1] = center + pos_pos + neg_neg - - return rv From 75f3fd462e271fbff2c1248ae52de8caf57acc76 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 12:29:48 -0400 Subject: [PATCH 33/55] updated scripts --- vnncomp_scripts/prepare_instance.sh | 2 +- vnncomp_scripts/run_instance.sh | 5 +++-- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/vnncomp_scripts/prepare_instance.sh b/vnncomp_scripts/prepare_instance.sh index f76d390..7da9fa1 100755 --- a/vnncomp_scripts/prepare_instance.sh +++ b/vnncomp_scripts/prepare_instance.sh @@ -3,7 +3,7 @@ # four arguments, first is "v1", second is a benchmark category identifier string such as "acasxu", third is path to the .onnx file and fourth is path to .vnnlib file # Stanley Bak, Feb 2021 -TOOL_NAME=simple_adv_gen +TOOL_NAME=nnenum VERSION_STRING=v1 # check arguments diff --git a/vnncomp_scripts/run_instance.sh b/vnncomp_scripts/run_instance.sh index 2e581f2..6ff04f6 100755 --- a/vnncomp_scripts/run_instance.sh +++ b/vnncomp_scripts/run_instance.sh @@ -1,8 +1,9 @@ #!/bin/bash -# example run_benchmark.sh script for VNNCOMP for simple_adversarial_generator (https://github.com/stanleybak/simple_adversarial_generator) +# example run_benchmark.sh script for VNNCOMP for nnenum # six arguments, first is "v1", second is a benchmark category itentifier string such as "acasxu", third is path to the .onnx file, fourth is path to .vnnlib file, fifth is a path to the results file, and sixth is a timeout in seconds. # Stanley Bak, Feb 2021 +TOOL_NAME=nnenum VERSION_STRING=v1 # check arguments @@ -17,7 +18,7 @@ VNNLIB_FILE=$4 RESULTS_FILE=$5 TIMEOUT=$6 -echo "Running benchmark instance in category '$CATEGORY' with onnx file '$ONNX_FILE', vnnlib file '$VNNLIB_FILE', results file $RESULTS_FILE, and timeout $TIMEOUT" +echo "Running $TOOL_NAME on benchmark instance in category '$CATEGORY' with onnx file '$ONNX_FILE', vnnlib file '$VNNLIB_FILE', results file $RESULTS_FILE, and timeout $TIMEOUT" # setup environment variable for tool (doing it earlier won't be persistent with docker)" DIR=$(dirname $(dirname $(realpath $0))) From c93a39cb568f58a26015bd151acafab34d2d4929 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sun, 13 Jun 2021 13:28:09 -0400 Subject: [PATCH 34/55] updated readme --- vnncomp_scripts/README.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/vnncomp_scripts/README.md b/vnncomp_scripts/README.md index 8c74461..cf9f86d 100644 --- a/vnncomp_scripts/README.md +++ b/vnncomp_scripts/README.md @@ -1,5 +1,5 @@ -These are the scripts needed to run the tool for use with VNNCOMP. +1. Tool Name: nnenum -*** Manual Setup *** +2. Manual Setup or Licenses: None. Everything is done automatically in install_tool.sh -There is no manual setup. Everything is done automatically in install_tool.sh +3. Use CPU/GPU AWS Instance? CPU From 6854a6b0bb766806bb42570230adcbd0ecfab809 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Tue, 15 Jun 2021 17:15:14 -0400 Subject: [PATCH 35/55] fixed kamenev plotting bug --- src/nnenum/kamenev.py | 18 +++++++----------- 1 file changed, 7 insertions(+), 11 deletions(-) diff --git a/src/nnenum/kamenev.py b/src/nnenum/kamenev.py index 0c40595..432d236 100644 --- a/src/nnenum/kamenev.py +++ b/src/nnenum/kamenev.py @@ -46,21 +46,17 @@ def _find_two_points(dims, supp_point_func): vec = np.array([-1 if i == d else 0 for i in range(dims)], dtype=float) # try min - p = supp_point_func(vec) - assert len(p) == dims, f"support fuction returned {len(p)}-dimensional point, expected {dims}-d" + p1 = supp_point_func(vec) + assert len(p1) == dims, f"support fuction returned {len(p1)}-dimensional point, expected {dims}-d" + + pts = [p1] - if not pts: - pts.append(p) - elif not np.allclose(p, pts[0]): - pts.append(p) - break - # try max vec = np.array([1 if i == d else 0 for i in range(dims)], dtype=float) - p = supp_point_func(vec) + p2 = supp_point_func(vec) - if not np.allclose(p, pts[0]): - pts.append(p) + if not np.allclose(p1, p2): + pts = [p1, p2] break return pts From 997f257915c4ae466807d09711d621d70d1dee05 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Sat, 2 Oct 2021 21:48:46 -0400 Subject: [PATCH 36/55] updated to enable settings selection --- examples/test/test_nano.onnx | Bin 0 -> 219 bytes examples/test/test_nano.vnnlib | 7 +++++++ src/nnenum/nnenum.py | 35 +++++++++++++++++++++++++++++---- src/nnenum/onnx_network.py | 4 +++- 4 files changed, 41 insertions(+), 5 deletions(-) create mode 100644 examples/test/test_nano.onnx create mode 100644 examples/test/test_nano.vnnlib diff --git a/examples/test/test_nano.onnx b/examples/test/test_nano.onnx new file mode 100644 index 0000000000000000000000000000000000000000..b04356a8a04110d1e8333d9640315ff3bb42e587 GIT binary patch literal 219 zcmd;J7vd<+&N0f*%d3!LHPkcLGf-kr%+v$%H5jb6Fmjo4apdNwq~^qD=5g`(CdT_F zmiU(DBo~(mv1MeYq@?Caal%EF*dVf23|uN)P-!7fi1z%_5-Ike)cBy(oKhtg5NX9A z#NiLL2gKHr;$Y-p6kt?hVPIgecS5l!N(|uyAucWs4n`psE+!7fBylc;*~k)3EL;o% Fd;s?zH#-0T literal 0 HcmV?d00001 diff --git a/examples/test/test_nano.vnnlib b/examples/test/test_nano.vnnlib new file mode 100644 index 0000000..207d28c --- /dev/null +++ b/examples/test/test_nano.vnnlib @@ -0,0 +1,7 @@ +(declare-const X_0 Real) +(declare-const Y_0 Real) + +(assert (>= X_0 -1)) +(assert (<= X_0 1)) + +(assert (<= Y_0 -1)) diff --git a/src/nnenum/nnenum.py b/src/nnenum/nnenum.py index 0d02fa4..6d0d0f7 100644 --- a/src/nnenum/nnenum.py +++ b/src/nnenum/nnenum.py @@ -61,6 +61,20 @@ def set_control_settings(): Settings.OVERAPPROX_LP_TIMEOUT = 0.02 Settings.OVERAPPROX_MIN_GEN_LIMIT = 70 +def set_exact_settings(): + 'set settings for smaller control benchmarks' + + Settings.TIMING_STATS = True + Settings.TRY_QUICK_OVERAPPROX = False + + Settings.CONTRACT_ZONOTOPE_LP = True + Settings.CONTRACT_LP_OPTIMIZED = True + Settings.CONTRACT_LP_TRACK_WITNESSES = True + + Settings.OVERAPPROX_BOTH_BOUNDS = False + + Settings.BRANCH_MODE = Settings.BRANCH_EXACT + def set_image_settings(): 'set settings for larger image benchmarks' @@ -100,23 +114,36 @@ def main(): processes = int(sys.argv[5]) Settings.NUM_PROCESSES = processes + if len(sys.argv) >= 7: + settings_str = sys.argv[6] + else: + settings_str = "auto" + # spec_list, input_dtype = make_spec(vnnlib_filename, onnx_filename) try: network = load_onnx_network_optimized(onnx_filename) - except AssertionError: + except: # cannot do optimized load due to unsupported layers network = load_onnx_network(onnx_filename) result_str = 'none' # gets overridden num_inputs = len(spec_list[0][0]) - - if num_inputs < 700: + + if settings_str == "auto": + if num_inputs < 700: + set_control_settings() + else: + set_image_settings() + elif settings_str == "control": set_control_settings() - else: + elif settings_str == "image": set_image_settings() + else: + assert settings_str == "exact" + set_exact_settings() for init_box, spec in spec_list: init_box = np.array(init_box, dtype=input_dtype) diff --git a/src/nnenum/onnx_network.py b/src/nnenum/onnx_network.py index a29ceea..94f7063 100644 --- a/src/nnenum/onnx_network.py +++ b/src/nnenum/onnx_network.py @@ -273,7 +273,8 @@ def load_onnx_network_optimized(filename): while cur_node is not None: assert cur_node.input[0] == cur_input_name, \ - f'input[0] should be previous output {cur_input_name} in node {cur_node.name}' + f"cur_node.input[0] ({cur_node.input[0]}) should be previous output ({cur_input_name}) in " + \ + f"node:\n{cur_node.name}" op = cur_node.op_type layer = None @@ -305,6 +306,7 @@ def load_onnx_network_optimized(filename): elif op == 'MatMul': assert len(cur_node.input) == 2 init = init_map[cur_node.input[1]] + assert init.data_type == onnx_type_float b = np.frombuffer(init.raw_data, dtype=' Date: Sun, 14 Nov 2021 10:15:56 -0500 Subject: [PATCH 37/55] updated loading with non-standard first layers --- src/nnenum/onnx_network.py | 19 ++++++++++--------- 1 file changed, 10 insertions(+), 9 deletions(-) diff --git a/src/nnenum/onnx_network.py b/src/nnenum/onnx_network.py index 94f7063..76e5371 100644 --- a/src/nnenum/onnx_network.py +++ b/src/nnenum/onnx_network.py @@ -278,7 +278,13 @@ def load_onnx_network_optimized(filename): op = cur_node.op_type layer = None - + + if layers: + prev_shape = layers[-1].get_output_shape() + else: + s_node = graph.input[0].type.tensor_type.shape + prev_shape = tuple(d.dim_value if d.dim_value != 0 else 1 for d in s_node.dim) + if op in ['Add', 'Sub']: assert len(cur_node.input) == 2 init = init_map[cur_node.input[1]] @@ -295,11 +301,6 @@ def load_onnx_network_optimized(filename): layer = AddLayer(len(layers), b) elif op == 'Flatten': assert cur_node.attribute[0].i == 1 # flatten along columns - if layers: - prev_shape = layers[-1].get_output_shape() - else: - s_node = graph.input[0].type.tensor_type.shape - prev_shape = tuple(d.dim_value for d in s_node.dim) layer = FlattenLayer(len(layers), prev_shape) @@ -314,12 +315,12 @@ def load_onnx_network_optimized(filename): b = nn_unflatten(b, shape, order='F') - layer = MatMulLayer(len(layers), b, layers[-1].get_output_shape()) + layer = MatMulLayer(len(layers), b, prev_shape) elif op == 'Relu': assert layers, "expected previous layer before relu layer" - layer = ReluLayer(len(layers), layers[-1].get_output_shape()) + layer = ReluLayer(len(layers), prev_shape) elif op == 'Gemm': assert len(cur_node.input) == 3 @@ -349,7 +350,7 @@ def load_onnx_network_optimized(filename): assert a.i == 1 weight_mat = weight_mat.transpose().copy() - layer = FullyConnectedLayer(len(layers), weight_mat, bias_vec, layers[-1].get_output_shape()) + layer = FullyConnectedLayer(len(layers), weight_mat, bias_vec, prev_shape) else: assert False, f"unsupported onnx op_type {op} in node {cur_node.name}" From 2ad47c186f8113e75f16d45db9e314b1a0b72827 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Thu, 9 Dec 2021 11:58:54 -0500 Subject: [PATCH 38/55] minor note https://github.com/joblib/threadpoolctl --- src/nnenum/settings.py | 1 + 1 file changed, 1 insertion(+) diff --git a/src/nnenum/settings.py b/src/nnenum/settings.py index 7396c1d..3b7a168 100644 --- a/src/nnenum/settings.py +++ b/src/nnenum/settings.py @@ -49,6 +49,7 @@ def reset(cls): cls.TIMING_STATS = False # compute and print detailed timing stats cls.CHECK_SINGLE_THREAD_BLAS = True + # idea... replace this with threadpoolctl: https://github.com/joblib/threadpoolctl cls.UPDATE_SHARED_VARS_INTERVAL = 0.05 # interval for each thread to update shared state From fd07f2b6c55ca46387954559f40992ae0c9b06b7 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Fri, 21 Jan 2022 16:48:57 -0500 Subject: [PATCH 39/55] fixed shriver bug --- src/nnenum/prefilter.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/nnenum/prefilter.py b/src/nnenum/prefilter.py index dd15fee..df88a0d 100644 --- a/src/nnenum/prefilter.py +++ b/src/nnenum/prefilter.py @@ -260,7 +260,7 @@ def init_relu_layer(self, star, layer, start_time, depth): if Settings.TEST_FUNC_BEFORE_ASSIGNMENT is not None: Settings.TEST_FUNC_BEFORE_ASSIGNMENT() - zero_indices = np.nonzero(self.output_bounds.layer_bounds[:, 1] < -Settings.SPLIT_TOLERANCE)[0] + zero_indices = np.nonzero(self.output_bounds.layer_bounds[:, 1] <= Settings.SPLIT_TOLERANCE)[0] self.assign_zeros(star, zero_indices) def split_relu(self, neuron_index, pos_star, neg_star, self_gets_positive, start_time, depth): From fa1463b6f345ca143662c4143dfb4774e6615672 Mon Sep 17 00:00:00 2001 From: Stanley Bak Date: Mon, 6 Jun 2022 12:13:46 -0400 Subject: [PATCH 40/55] updated settings --- examples/mnistcnn/README.md | 1 + examples/mnistcnn/generate_spec.py | 171 ++ examples/mnistcnn/image0.vnnlib | 3164 ++++++++++++++++++++++ examples/mnistcnn/mnist_0.1.onnx | Bin 0 -> 1432985 bytes examples/mnistcnn/mnist_0.1_noscale.onnx | Bin 0 -> 1401281 bytes examples/mnistcnn/mnist_test.csv | 100 + src/nnenum/nnenum.py | 2 +- src/nnenum/onnx_network.py | 4 + src/nnenum/overapprox.py | 7 +- src/nnenum/settings.py | 3 +- 10 files changed, 3449 insertions(+), 3 deletions(-) create mode 100644 examples/mnistcnn/README.md create mode 100644 examples/mnistcnn/generate_spec.py create mode 100644 examples/mnistcnn/image0.vnnlib create mode 100644 examples/mnistcnn/mnist_0.1.onnx create mode 100644 examples/mnistcnn/mnist_0.1_noscale.onnx create mode 100644 examples/mnistcnn/mnist_test.csv diff --git a/examples/mnistcnn/README.md b/examples/mnistcnn/README.md new file mode 100644 index 0000000..9cc89b9 --- /dev/null +++ b/examples/mnistcnn/README.md @@ -0,0 +1 @@ +This network / code is based on the "GGN" vnncomp 2020 benchmark, which is in the vcnn/eth folder of the vnn2020 branch of nnenum. \ No newline at end of file diff --git a/examples/mnistcnn/generate_spec.py b/examples/mnistcnn/generate_spec.py new file mode 100644 index 0000000..2c7bb16 --- /dev/null +++ b/examples/mnistcnn/generate_spec.py @@ -0,0 +1,171 @@ +''' +eth vnn benchmark 2020 +''' + +import sys +import time +from pathlib import Path + +import onnx +import onnxruntime as ort + +import numpy as np + +from nnenum.onnx_network import load_onnx_network +from nnenum.network import nn_flatten + +def load_unscaled_images(filename, specific_image=None, epsilon=0.0): + '''read images from csv file + + if epsilon is set, it gets added to the loaded image to get min/max images + ''' + + image_list = [] + labels = [] + + line_num = 0 + + mnist = 'mnist' in filename + + with open(filename, 'r') as f: + line = f.readline() + + while line is not None and len(line) > 0: + line_num += 1 + + if specific_image is not None and line_num - 1 != specific_image: + line = f.readline() + continue + + parts = line.split(',') + labels.append(int(parts[0])) + + if mnist: + line_list = [int(x.strip())/255.0 for x in parts[1:]] + + # add epsilon + for i, val in enumerate(line_list): + line_list[i] = max(0.0, min(1.0, val + epsilon)) + + image = np.array(line_list, dtype=np.float32) + + image.shape = (1, 1, 28, 28) + else: + #cifar load + + rgb_lists = [[], [], []] + rgb_index = 0 + + for x in parts[1:]: + val = int(x.strip())/255.0 + val = max(0.0, min(1.0, val + epsilon)) + + rgb_lists[rgb_index].append(val) + rgb_index = (rgb_index + 1) % 3 + + image = np.array(rgb_lists, dtype=np.float32) + + image.shape = (1, 3, 32, 32) + + image_list.append(image) + + line = f.readline() + + return image_list, labels + +def make_init_box(min_image, max_image): + 'make init box' + + flat_min_image = nn_flatten(min_image) + flat_max_image = nn_flatten(max_image) + + assert flat_min_image.size == flat_max_image.size + + box = list(zip(flat_min_image, flat_max_image)) + + return box + +def make_init(nn, image_filename, epsilon, specific_image=None): + 'returns list of (image_id, image_data, classification_label, init_star_state, spec)' + + rv = [] + + images, labels = load_unscaled_images(image_filename, specific_image=specific_image) + min_images, _ = load_unscaled_images(image_filename, specific_image=specific_image, epsilon=-epsilon) + max_images, _ = load_unscaled_images(image_filename, specific_image=specific_image, epsilon=epsilon) + + print("making init states") + + with open("image0.vnnlib", 'w') as f: + + for image_id, (image, classification) in enumerate(zip(images, labels)): + output = nn.execute(image) + flat_output = nn_flatten(output) + + num_outputs = flat_output.shape[0] + label = np.argmax(flat_output) + + if label == labels[image_id]: + # correctly classified + + min_image = min_images[image_id] + max_image = max_images[image_id] + + init_box = make_init_box(min_image, max_image) + + f.write(f"; GNN benchmark image {image_id + 1} with epsilon = {epsilon}\n\n") + + for i in range(len(init_box)): + f.write(f"(declare-const X_{i} Real)\n") + + f.write("\n") + + for i in range(10): + f.write(f"(declare-const Y_{i} Real)\n") + + f.write("\n; Input constraints:\n") + + for i, (lb, ub) in enumerate(init_box): + f.write(f"(assert (<= X_{i} {ub:.18f}))\n") + f.write(f"(assert (>= X_{i} {lb:.18f}))\n\n") + + f.write("\n; Output constraints:\n") + f.write("(assert (or\n") + + for i in range(num_outputs): + if i == classification: + continue + + f.write(f" (and (>= Y_{i} Y_{classification}))\n") + + f.write("))") + + break + + return rv + +def main(): + 'main entry point' + + netname = 'mnist_0.1' + onnx_filename = f'{netname}_noscale.onnx' + epsilon = 0.1 + + image_filename = 'mnist_test.csv' + + onnx_filename = f'{onnx_filename}' + + #nn = load_onnx_network(onnx_filename) + #print(f"loading onnx network from {onnx_filename}") + nn = load_onnx_network(onnx_filename) + print(f"loaded network with {nn.num_relu_layers()} ReLU layers and {nn.num_relu_neurons()} ReLU neurons") + + specific_image = None + print("Loading images...") + tup_list = make_init(nn, image_filename, epsilon, specific_image=specific_image) + print(f"made {len(tup_list)} init states") + + +if __name__ == '__main__': + main() + diff --git a/examples/mnistcnn/image0.vnnlib b/examples/mnistcnn/image0.vnnlib new file mode 100644 index 0000000..ccd929e --- /dev/null +++ b/examples/mnistcnn/image0.vnnlib @@ -0,0 +1,3164 @@ +; GNN benchmark image 1 with epsilon = 0.1 + +(declare-const X_0 Real) +(declare-const X_1 Real) +(declare-const X_2 Real) +(declare-const X_3 Real) +(declare-const X_4 Real) +(declare-const X_5 Real) +(declare-const X_6 Real) +(declare-const X_7 Real) +(declare-const X_8 Real) +(declare-const X_9 Real) +(declare-const X_10 Real) +(declare-const X_11 Real) +(declare-const X_12 Real) +(declare-const X_13 Real) +(declare-const X_14 Real) +(declare-const X_15 Real) +(declare-const X_16 Real) +(declare-const X_17 Real) +(declare-const X_18 Real) +(declare-const X_19 Real) +(declare-const X_20 Real) +(declare-const X_21 Real) +(declare-const X_22 Real) +(declare-const X_23 Real) +(declare-const X_24 Real) +(declare-const X_25 Real) +(declare-const X_26 Real) +(declare-const X_27 Real) +(declare-const X_28 Real) +(declare-const X_29 Real) +(declare-const X_30 Real) +(declare-const X_31 Real) +(declare-const X_32 Real) +(declare-const X_33 Real) +(declare-const X_34 Real) +(declare-const X_35 Real) +(declare-const X_36 Real) +(declare-const X_37 Real) +(declare-const X_38 Real) +(declare-const X_39 Real) +(declare-const X_40 Real) +(declare-const X_41 Real) +(declare-const X_42 Real) +(declare-const X_43 Real) +(declare-const X_44 Real) +(declare-const X_45 Real) +(declare-const X_46 Real) +(declare-const X_47 Real) +(declare-const X_48 Real) +(declare-const X_49 Real) +(declare-const X_50 Real) +(declare-const X_51 Real) +(declare-const X_52 Real) +(declare-const X_53 Real) +(declare-const X_54 Real) +(declare-const X_55 Real) +(declare-const X_56 Real) +(declare-const X_57 Real) +(declare-const X_58 Real) +(declare-const X_59 Real) +(declare-const X_60 Real) +(declare-const X_61 Real) +(declare-const X_62 Real) +(declare-const X_63 Real) +(declare-const X_64 Real) +(declare-const X_65 Real) +(declare-const X_66 Real) +(declare-const X_67 Real) +(declare-const X_68 Real) +(declare-const X_69 Real) +(declare-const X_70 Real) +(declare-const X_71 Real) +(declare-const X_72 Real) +(declare-const X_73 Real) +(declare-const X_74 Real) +(declare-const X_75 Real) +(declare-const X_76 Real) +(declare-const X_77 Real) +(declare-const X_78 Real) +(declare-const X_79 Real) +(declare-const X_80 Real) +(declare-const X_81 Real) +(declare-const X_82 Real) +(declare-const X_83 Real) +(declare-const X_84 Real) +(declare-const X_85 Real) +(declare-const X_86 Real) +(declare-const X_87 Real) +(declare-const X_88 Real) +(declare-const X_89 Real) +(declare-const X_90 Real) +(declare-const X_91 Real) +(declare-const X_92 Real) +(declare-const X_93 Real) +(declare-const X_94 Real) +(declare-const X_95 Real) +(declare-const X_96 Real) +(declare-const X_97 Real) +(declare-const X_98 Real) +(declare-const X_99 Real) +(declare-const X_100 Real) +(declare-const X_101 Real) +(declare-const X_102 Real) +(declare-const X_103 Real) +(declare-const X_104 Real) +(declare-const X_105 Real) +(declare-const X_106 Real) +(declare-const X_107 Real) +(declare-const X_108 Real) +(declare-const X_109 Real) +(declare-const X_110 Real) +(declare-const X_111 Real) +(declare-const X_112 Real) +(declare-const X_113 Real) +(declare-const X_114 Real) +(declare-const X_115 Real) +(declare-const X_116 Real) +(declare-const X_117 Real) +(declare-const X_118 Real) +(declare-const X_119 Real) +(declare-const X_120 Real) +(declare-const X_121 Real) +(declare-const X_122 Real) +(declare-const X_123 Real) +(declare-const X_124 Real) +(declare-const X_125 Real) +(declare-const X_126 Real) +(declare-const X_127 Real) +(declare-const X_128 Real) +(declare-const X_129 Real) +(declare-const X_130 Real) +(declare-const X_131 Real) +(declare-const X_132 Real) +(declare-const X_133 Real) +(declare-const X_134 Real) +(declare-const X_135 Real) +(declare-const X_136 Real) +(declare-const X_137 Real) +(declare-const X_138 Real) +(declare-const X_139 Real) +(declare-const X_140 Real) +(declare-const X_141 Real) +(declare-const X_142 Real) +(declare-const X_143 Real) +(declare-const X_144 Real) +(declare-const X_145 Real) +(declare-const X_146 Real) +(declare-const X_147 Real) +(declare-const X_148 Real) +(declare-const X_149 Real) +(declare-const X_150 Real) +(declare-const X_151 Real) +(declare-const X_152 Real) +(declare-const X_153 Real) +(declare-const X_154 Real) +(declare-const X_155 Real) +(declare-const X_156 Real) +(declare-const X_157 Real) +(declare-const X_158 Real) +(declare-const X_159 Real) +(declare-const X_160 Real) +(declare-const X_161 Real) +(declare-const X_162 Real) +(declare-const X_163 Real) +(declare-const X_164 Real) +(declare-const X_165 Real) +(declare-const X_166 Real) +(declare-const X_167 Real) +(declare-const X_168 Real) +(declare-const X_169 Real) +(declare-const X_170 Real) +(declare-const X_171 Real) +(declare-const X_172 Real) +(declare-const X_173 Real) +(declare-const X_174 Real) +(declare-const X_175 Real) +(declare-const X_176 Real) +(declare-const X_177 Real) +(declare-const X_178 Real) +(declare-const X_179 Real) +(declare-const X_180 Real) +(declare-const X_181 Real) +(declare-const X_182 Real) +(declare-const X_183 Real) +(declare-const X_184 Real) +(declare-const X_185 Real) +(declare-const X_186 Real) +(declare-const X_187 Real) +(declare-const X_188 Real) +(declare-const X_189 Real) +(declare-const X_190 Real) +(declare-const X_191 Real) +(declare-const X_192 Real) +(declare-const X_193 Real) +(declare-const X_194 Real) +(declare-const X_195 Real) +(declare-const X_196 Real) +(declare-const X_197 Real) +(declare-const X_198 Real) +(declare-const X_199 Real) +(declare-const X_200 Real) +(declare-const X_201 Real) +(declare-const X_202 Real) +(declare-const X_203 Real) +(declare-const X_204 Real) +(declare-const X_205 Real) +(declare-const X_206 Real) +(declare-const X_207 Real) +(declare-const X_208 Real) +(declare-const X_209 Real) +(declare-const X_210 Real) +(declare-const X_211 Real) +(declare-const X_212 Real) +(declare-const X_213 Real) +(declare-const X_214 Real) +(declare-const X_215 Real) +(declare-const X_216 Real) +(declare-const X_217 Real) +(declare-const X_218 Real) +(declare-const X_219 Real) +(declare-const X_220 Real) +(declare-const X_221 Real) +(declare-const X_222 Real) +(declare-const X_223 Real) +(declare-const X_224 Real) +(declare-const X_225 Real) +(declare-const X_226 Real) +(declare-const X_227 Real) +(declare-const X_228 Real) +(declare-const X_229 Real) +(declare-const X_230 Real) +(declare-const X_231 Real) +(declare-const X_232 Real) +(declare-const X_233 Real) +(declare-const X_234 Real) +(declare-const X_235 Real) +(declare-const X_236 Real) +(declare-const X_237 Real) +(declare-const X_238 Real) +(declare-const X_239 Real) +(declare-const X_240 Real) +(declare-const X_241 Real) +(declare-const X_242 Real) +(declare-const X_243 Real) +(declare-const X_244 Real) +(declare-const X_245 Real) +(declare-const X_246 Real) +(declare-const X_247 Real) +(declare-const X_248 Real) +(declare-const X_249 Real) +(declare-const X_250 Real) +(declare-const X_251 Real) +(declare-const X_252 Real) +(declare-const X_253 Real) +(declare-const X_254 Real) +(declare-const X_255 Real) +(declare-const X_256 Real) +(declare-const X_257 Real) +(declare-const X_258 Real) +(declare-const X_259 Real) +(declare-const X_260 Real) +(declare-const X_261 Real) +(declare-const X_262 Real) +(declare-const X_263 Real) +(declare-const X_264 Real) +(declare-const X_265 Real) +(declare-const X_266 Real) +(declare-const X_267 Real) +(declare-const X_268 Real) +(declare-const X_269 Real) +(declare-const X_270 Real) +(declare-const X_271 Real) +(declare-const X_272 Real) +(declare-const X_273 Real) +(declare-const X_274 Real) +(declare-const X_275 Real) +(declare-const X_276 Real) +(declare-const X_277 Real) +(declare-const X_278 Real) +(declare-const X_279 Real) +(declare-const X_280 Real) +(declare-const X_281 Real) +(declare-const X_282 Real) +(declare-const X_283 Real) +(declare-const X_284 Real) +(declare-const X_285 Real) +(declare-const X_286 Real) +(declare-const X_287 Real) +(declare-const X_288 Real) +(declare-const X_289 Real) +(declare-const X_290 Real) +(declare-const X_291 Real) +(declare-const X_292 Real) +(declare-const X_293 Real) +(declare-const X_294 Real) +(declare-const X_295 Real) +(declare-const X_296 Real) +(declare-const X_297 Real) +(declare-const X_298 Real) +(declare-const X_299 Real) +(declare-const X_300 Real) +(declare-const X_301 Real) +(declare-const X_302 Real) +(declare-const X_303 Real) +(declare-const X_304 Real) +(declare-const X_305 Real) +(declare-const X_306 Real) +(declare-const X_307 Real) +(declare-const X_308 Real) +(declare-const X_309 Real) +(declare-const X_310 Real) +(declare-const X_311 Real) +(declare-const X_312 Real) +(declare-const X_313 Real) +(declare-const X_314 Real) +(declare-const X_315 Real) +(declare-const X_316 Real) +(declare-const X_317 Real) +(declare-const X_318 Real) +(declare-const X_319 Real) +(declare-const X_320 Real) +(declare-const X_321 Real) +(declare-const X_322 Real) +(declare-const X_323 Real) +(declare-const X_324 Real) +(declare-const X_325 Real) +(declare-const X_326 Real) +(declare-const X_327 Real) +(declare-const X_328 Real) +(declare-const X_329 Real) +(declare-const X_330 Real) +(declare-const X_331 Real) +(declare-const X_332 Real) +(declare-const X_333 Real) +(declare-const X_334 Real) +(declare-const X_335 Real) +(declare-const X_336 Real) +(declare-const X_337 Real) +(declare-const X_338 Real) +(declare-const X_339 Real) +(declare-const X_340 Real) +(declare-const X_341 Real) +(declare-const X_342 Real) +(declare-const X_343 Real) +(declare-const X_344 Real) +(declare-const X_345 Real) +(declare-const X_346 Real) +(declare-const X_347 Real) +(declare-const X_348 Real) +(declare-const X_349 Real) +(declare-const X_350 Real) +(declare-const X_351 Real) +(declare-const X_352 Real) +(declare-const X_353 Real) +(declare-const X_354 Real) +(declare-const X_355 Real) +(declare-const X_356 Real) +(declare-const X_357 Real) +(declare-const X_358 Real) +(declare-const X_359 Real) +(declare-const X_360 Real) +(declare-const X_361 Real) +(declare-const X_362 Real) +(declare-const X_363 Real) +(declare-const X_364 Real) +(declare-const X_365 Real) +(declare-const X_366 Real) +(declare-const X_367 Real) +(declare-const X_368 Real) +(declare-const X_369 Real) +(declare-const X_370 Real) +(declare-const X_371 Real) +(declare-const X_372 Real) +(declare-const X_373 Real) +(declare-const X_374 Real) +(declare-const X_375 Real) +(declare-const X_376 Real) +(declare-const X_377 Real) +(declare-const X_378 Real) +(declare-const X_379 Real) +(declare-const X_380 Real) +(declare-const X_381 Real) +(declare-const X_382 Real) +(declare-const X_383 Real) +(declare-const X_384 Real) +(declare-const X_385 Real) +(declare-const X_386 Real) +(declare-const X_387 Real) +(declare-const X_388 Real) +(declare-const X_389 Real) +(declare-const X_390 Real) +(declare-const X_391 Real) +(declare-const X_392 Real) +(declare-const X_393 Real) +(declare-const X_394 Real) +(declare-const X_395 Real) +(declare-const X_396 Real) +(declare-const X_397 Real) +(declare-const X_398 Real) +(declare-const X_399 Real) +(declare-const X_400 Real) +(declare-const X_401 Real) +(declare-const X_402 Real) +(declare-const X_403 Real) +(declare-const X_404 Real) +(declare-const X_405 Real) +(declare-const X_406 Real) +(declare-const X_407 Real) +(declare-const X_408 Real) +(declare-const X_409 Real) +(declare-const X_410 Real) +(declare-const X_411 Real) +(declare-const X_412 Real) +(declare-const X_413 Real) +(declare-const X_414 Real) +(declare-const X_415 Real) +(declare-const X_416 Real) +(declare-const X_417 Real) +(declare-const X_418 Real) +(declare-const X_419 Real) +(declare-const X_420 Real) +(declare-const X_421 Real) +(declare-const X_422 Real) +(declare-const X_423 Real) +(declare-const X_424 Real) +(declare-const X_425 Real) +(declare-const X_426 Real) +(declare-const X_427 Real) +(declare-const X_428 Real) +(declare-const X_429 Real) +(declare-const X_430 Real) +(declare-const X_431 Real) +(declare-const X_432 Real) +(declare-const X_433 Real) +(declare-const X_434 Real) +(declare-const X_435 Real) +(declare-const X_436 Real) +(declare-const X_437 Real) +(declare-const X_438 Real) +(declare-const X_439 Real) +(declare-const X_440 Real) +(declare-const X_441 Real) +(declare-const X_442 Real) +(declare-const X_443 Real) +(declare-const X_444 Real) +(declare-const X_445 Real) +(declare-const X_446 Real) +(declare-const X_447 Real) +(declare-const X_448 Real) +(declare-const X_449 Real) +(declare-const X_450 Real) +(declare-const X_451 Real) +(declare-const X_452 Real) +(declare-const X_453 Real) +(declare-const X_454 Real) +(declare-const X_455 Real) +(declare-const X_456 Real) +(declare-const X_457 Real) +(declare-const X_458 Real) +(declare-const X_459 Real) +(declare-const X_460 Real) +(declare-const X_461 Real) +(declare-const X_462 Real) +(declare-const X_463 Real) +(declare-const X_464 Real) +(declare-const X_465 Real) +(declare-const X_466 Real) +(declare-const X_467 Real) +(declare-const X_468 Real) +(declare-const X_469 Real) +(declare-const X_470 Real) +(declare-const X_471 Real) +(declare-const X_472 Real) +(declare-const X_473 Real) +(declare-const X_474 Real) +(declare-const X_475 Real) +(declare-const X_476 Real) +(declare-const X_477 Real) +(declare-const X_478 Real) +(declare-const X_479 Real) +(declare-const X_480 Real) +(declare-const X_481 Real) +(declare-const X_482 Real) +(declare-const X_483 Real) +(declare-const X_484 Real) +(declare-const X_485 Real) +(declare-const X_486 Real) +(declare-const X_487 Real) +(declare-const X_488 Real) +(declare-const X_489 Real) +(declare-const X_490 Real) +(declare-const X_491 Real) +(declare-const X_492 Real) +(declare-const X_493 Real) +(declare-const X_494 Real) +(declare-const X_495 Real) +(declare-const X_496 Real) +(declare-const X_497 Real) +(declare-const X_498 Real) +(declare-const X_499 Real) +(declare-const X_500 Real) +(declare-const X_501 Real) +(declare-const X_502 Real) +(declare-const X_503 Real) +(declare-const X_504 Real) +(declare-const X_505 Real) +(declare-const X_506 Real) +(declare-const X_507 Real) +(declare-const X_508 Real) +(declare-const X_509 Real) +(declare-const X_510 Real) +(declare-const X_511 Real) +(declare-const X_512 Real) +(declare-const X_513 Real) +(declare-const X_514 Real) +(declare-const X_515 Real) +(declare-const X_516 Real) +(declare-const X_517 Real) +(declare-const X_518 Real) +(declare-const X_519 Real) +(declare-const X_520 Real) +(declare-const X_521 Real) +(declare-const X_522 Real) +(declare-const X_523 Real) +(declare-const X_524 Real) +(declare-const X_525 Real) +(declare-const X_526 Real) +(declare-const X_527 Real) +(declare-const X_528 Real) +(declare-const X_529 Real) +(declare-const X_530 Real) +(declare-const X_531 Real) +(declare-const X_532 Real) +(declare-const X_533 Real) +(declare-const X_534 Real) +(declare-const X_535 Real) +(declare-const X_536 Real) +(declare-const X_537 Real) +(declare-const X_538 Real) +(declare-const X_539 Real) +(declare-const X_540 Real) +(declare-const X_541 Real) +(declare-const X_542 Real) +(declare-const X_543 Real) +(declare-const X_544 Real) +(declare-const X_545 Real) +(declare-const X_546 Real) +(declare-const X_547 Real) +(declare-const X_548 Real) +(declare-const X_549 Real) +(declare-const X_550 Real) +(declare-const X_551 Real) +(declare-const X_552 Real) +(declare-const X_553 Real) +(declare-const X_554 Real) +(declare-const X_555 Real) +(declare-const X_556 Real) +(declare-const X_557 Real) +(declare-const X_558 Real) +(declare-const X_559 Real) +(declare-const X_560 Real) +(declare-const X_561 Real) +(declare-const X_562 Real) +(declare-const X_563 Real) +(declare-const X_564 Real) +(declare-const X_565 Real) +(declare-const X_566 Real) +(declare-const X_567 Real) +(declare-const X_568 Real) +(declare-const X_569 Real) +(declare-const X_570 Real) +(declare-const X_571 Real) +(declare-const X_572 Real) +(declare-const X_573 Real) +(declare-const X_574 Real) +(declare-const X_575 Real) +(declare-const X_576 Real) +(declare-const X_577 Real) +(declare-const X_578 Real) +(declare-const X_579 Real) +(declare-const X_580 Real) +(declare-const X_581 Real) +(declare-const X_582 Real) +(declare-const X_583 Real) +(declare-const X_584 Real) +(declare-const X_585 Real) +(declare-const X_586 Real) +(declare-const X_587 Real) +(declare-const X_588 Real) +(declare-const X_589 Real) +(declare-const X_590 Real) +(declare-const X_591 Real) +(declare-const X_592 Real) +(declare-const X_593 Real) +(declare-const X_594 Real) +(declare-const X_595 Real) +(declare-const X_596 Real) +(declare-const X_597 Real) +(declare-const X_598 Real) +(declare-const X_599 Real) +(declare-const X_600 Real) +(declare-const X_601 Real) +(declare-const X_602 Real) +(declare-const X_603 Real) +(declare-const X_604 Real) +(declare-const X_605 Real) +(declare-const X_606 Real) +(declare-const X_607 Real) +(declare-const X_608 Real) +(declare-const X_609 Real) +(declare-const X_610 Real) +(declare-const X_611 Real) +(declare-const X_612 Real) +(declare-const X_613 Real) +(declare-const X_614 Real) +(declare-const X_615 Real) +(declare-const X_616 Real) +(declare-const X_617 Real) +(declare-const X_618 Real) +(declare-const X_619 Real) +(declare-const X_620 Real) +(declare-const X_621 Real) +(declare-const X_622 Real) +(declare-const X_623 Real) +(declare-const X_624 Real) +(declare-const X_625 Real) +(declare-const X_626 Real) +(declare-const X_627 Real) +(declare-const X_628 Real) +(declare-const X_629 Real) +(declare-const X_630 Real) +(declare-const X_631 Real) +(declare-const X_632 Real) +(declare-const X_633 Real) +(declare-const X_634 Real) +(declare-const X_635 Real) +(declare-const X_636 Real) +(declare-const X_637 Real) +(declare-const X_638 Real) +(declare-const X_639 Real) +(declare-const X_640 Real) +(declare-const X_641 Real) +(declare-const X_642 Real) +(declare-const X_643 Real) +(declare-const X_644 Real) +(declare-const X_645 Real) +(declare-const X_646 Real) +(declare-const X_647 Real) +(declare-const X_648 Real) +(declare-const X_649 Real) +(declare-const X_650 Real) +(declare-const X_651 Real) +(declare-const X_652 Real) +(declare-const X_653 Real) +(declare-const X_654 Real) +(declare-const X_655 Real) +(declare-const X_656 Real) +(declare-const X_657 Real) +(declare-const X_658 Real) +(declare-const X_659 Real) +(declare-const X_660 Real) +(declare-const X_661 Real) +(declare-const X_662 Real) +(declare-const X_663 Real) +(declare-const X_664 Real) +(declare-const X_665 Real) +(declare-const X_666 Real) +(declare-const X_667 Real) +(declare-const X_668 Real) +(declare-const X_669 Real) +(declare-const X_670 Real) +(declare-const X_671 Real) +(declare-const X_672 Real) +(declare-const X_673 Real) +(declare-const X_674 Real) +(declare-const X_675 Real) +(declare-const X_676 Real) +(declare-const X_677 Real) +(declare-const X_678 Real) +(declare-const X_679 Real) +(declare-const X_680 Real) +(declare-const X_681 Real) +(declare-const X_682 Real) +(declare-const X_683 Real) +(declare-const X_684 Real) +(declare-const X_685 Real) +(declare-const X_686 Real) +(declare-const X_687 Real) +(declare-const X_688 Real) +(declare-const X_689 Real) +(declare-const X_690 Real) +(declare-const X_691 Real) +(declare-const X_692 Real) +(declare-const X_693 Real) +(declare-const X_694 Real) +(declare-const X_695 Real) +(declare-const X_696 Real) +(declare-const X_697 Real) +(declare-const X_698 Real) +(declare-const X_699 Real) +(declare-const X_700 Real) +(declare-const X_701 Real) +(declare-const X_702 Real) +(declare-const X_703 Real) +(declare-const X_704 Real) +(declare-const X_705 Real) +(declare-const X_706 Real) +(declare-const X_707 Real) +(declare-const X_708 Real) +(declare-const X_709 Real) +(declare-const X_710 Real) +(declare-const X_711 Real) +(declare-const X_712 Real) +(declare-const X_713 Real) +(declare-const X_714 Real) +(declare-const X_715 Real) +(declare-const X_716 Real) +(declare-const X_717 Real) +(declare-const X_718 Real) +(declare-const X_719 Real) +(declare-const X_720 Real) +(declare-const X_721 Real) +(declare-const X_722 Real) +(declare-const X_723 Real) +(declare-const X_724 Real) +(declare-const X_725 Real) +(declare-const X_726 Real) +(declare-const X_727 Real) +(declare-const X_728 Real) +(declare-const X_729 Real) +(declare-const X_730 Real) +(declare-const X_731 Real) +(declare-const X_732 Real) +(declare-const X_733 Real) +(declare-const X_734 Real) +(declare-const X_735 Real) +(declare-const X_736 Real) +(declare-const X_737 Real) +(declare-const X_738 Real) +(declare-const X_739 Real) +(declare-const X_740 Real) +(declare-const X_741 Real) +(declare-const X_742 Real) +(declare-const X_743 Real) +(declare-const X_744 Real) +(declare-const X_745 Real) +(declare-const X_746 Real) +(declare-const X_747 Real) +(declare-const X_748 Real) +(declare-const X_749 Real) +(declare-const X_750 Real) +(declare-const X_751 Real) +(declare-const X_752 Real) +(declare-const X_753 Real) +(declare-const X_754 Real) +(declare-const X_755 Real) +(declare-const X_756 Real) +(declare-const X_757 Real) +(declare-const X_758 Real) +(declare-const X_759 Real) +(declare-const X_760 Real) +(declare-const X_761 Real) +(declare-const X_762 Real) +(declare-const X_763 Real) +(declare-const X_764 Real) +(declare-const X_765 Real) +(declare-const X_766 Real) +(declare-const X_767 Real) +(declare-const X_768 Real) +(declare-const X_769 Real) +(declare-const X_770 Real) +(declare-const X_771 Real) +(declare-const X_772 Real) +(declare-const 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0.100000001490116119)) +(assert (>= X_767 0.000000000000000000)) + +(assert (<= X_768 0.100000001490116119)) +(assert (>= X_768 0.000000000000000000)) + +(assert (<= X_769 0.100000001490116119)) +(assert (>= X_769 0.000000000000000000)) + +(assert (<= X_770 0.100000001490116119)) +(assert (>= X_770 0.000000000000000000)) + +(assert (<= X_771 0.100000001490116119)) +(assert (>= X_771 0.000000000000000000)) + +(assert (<= X_772 0.100000001490116119)) +(assert (>= X_772 0.000000000000000000)) + +(assert (<= X_773 0.100000001490116119)) +(assert (>= X_773 0.000000000000000000)) + +(assert (<= X_774 0.100000001490116119)) +(assert (>= X_774 0.000000000000000000)) + +(assert (<= X_775 0.100000001490116119)) +(assert (>= X_775 0.000000000000000000)) + +(assert (<= X_776 0.100000001490116119)) +(assert (>= X_776 0.000000000000000000)) + +(assert (<= X_777 0.100000001490116119)) +(assert (>= X_777 0.000000000000000000)) + +(assert (<= X_778 0.100000001490116119)) +(assert (>= X_778 0.000000000000000000)) + +(assert (<= X_779 0.100000001490116119)) +(assert (>= X_779 0.000000000000000000)) + +(assert (<= X_780 0.100000001490116119)) +(assert (>= X_780 0.000000000000000000)) + +(assert (<= X_781 0.100000001490116119)) +(assert (>= X_781 0.000000000000000000)) + +(assert (<= X_782 0.100000001490116119)) +(assert (>= X_782 0.000000000000000000)) + +(assert (<= X_783 0.100000001490116119)) +(assert (>= X_783 0.000000000000000000)) + + +; Output constraints: +(assert (or + (and (>= Y_0 Y_7)) + (and (>= Y_1 Y_7)) + (and (>= Y_2 Y_7)) + (and (>= Y_3 Y_7)) + (and (>= Y_4 Y_7)) + (and (>= Y_5 Y_7)) + (and (>= Y_6 Y_7)) + (and (>= Y_8 Y_7)) + (and (>= Y_9 Y_7)) +)) \ No newline at end of file diff --git a/examples/mnistcnn/mnist_0.1.onnx b/examples/mnistcnn/mnist_0.1.onnx new file mode 100644 index 0000000000000000000000000000000000000000..ea3eb2b24bcd30354d7281b3a1dea5464e64b1ed GIT binary patch literal 1432985 zcmeF)d0b4<|2Y2kU7Jc#Y13kPQ!^zLQPH9-p$#dC6pB_YqD@gr3K1eLbI+NX 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