%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL954_19 : TPTP v9.3.1. Released v8.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 12:55:09 PM UTC 2026 % Result : Theorem 73.67s 10.45s % Output : Proof 124.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL954_19 : TPTP v9.3.1. Released v8.2.0. % 0.00/0.04 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.37 % Computer : n009.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Sat Sep 5 14:50:21 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.39 OpenJDK 64-Bit Server VM warning: Options -Xverify:none and -noverify were deprecated in JDK 13 and will likely be removed in a future release. % 0.71/0.70 ________ _____ % 0.71/0.70 ___ __ \_________(_)________________________________ % 0.71/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.71/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.71/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.71/0.71 % 0.71/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.71/0.71 (2023-06-19) % 0.71/0.71 % 0.71/0.71 (c) Philipp Rümmer, 2009-2023 % 0.71/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.71/0.71 Amanda Stjerna. % 0.71/0.71 Free software under BSD-3-Clause. % 0.71/0.71 % 0.71/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.71/0.71 % 0.71/0.71 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.71/0.73 Running up to 7 provers in parallel. % 0.71/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.71/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.71/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.71/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.71/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.71/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.71/0.74 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 18.43/3.35 Prover 4: Preprocessing ... % 18.43/3.39 Prover 3: Preprocessing ... % 20.01/3.52 Prover 6: Preprocessing ... % 20.01/3.53 Prover 1: Preprocessing ... % 20.79/3.66 Prover 2: Preprocessing ... % 20.79/3.66 Prover 5: Preprocessing ... % 21.63/3.73 Prover 0: Preprocessing ... % 62.80/9.00 Prover 5: Proving ... % 70.70/10.02 Prover 2: Proving ... % 70.70/10.06 Prover 6: Proving ... % 73.67/10.45 Prover 2: proved (9701ms) % 73.67/10.45 % 73.67/10.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 73.67/10.45 % 73.67/10.45 Prover 5: stopped % 73.67/10.46 Prover 6: stopped % 73.67/10.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.67/10.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 73.67/10.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 74.44/10.52 Prover 1: Warning: ignoring some quantifiers % 74.44/10.53 Prover 3: Warning: ignoring some quantifiers % 74.44/10.57 Prover 1: Constructing countermodel ... % 75.22/10.69 Prover 3: Constructing countermodel ... % 76.00/10.71 Prover 3: stopped % 76.00/10.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 79.59/11.22 Prover 0: stopped % 79.59/11.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 85.30/11.94 Prover 7: Preprocessing ... % 86.07/12.08 Prover 10: Preprocessing ... % 88.02/12.29 Prover 8: Preprocessing ... % 89.12/12.48 Prover 11: Preprocessing ... % 92.27/12.83 Prover 13: Preprocessing ... % 93.74/13.00 Prover 10: Warning: ignoring some quantifiers % 94.98/13.23 Prover 10: Constructing countermodel ... % 96.80/13.43 Prover 7: Warning: ignoring some quantifiers % 97.60/13.58 Prover 7: Constructing countermodel ... % 100.00/13.89 Prover 10: Found proof (size 5) % 100.00/13.89 Prover 10: proved (3429ms) % 100.00/13.89 Prover 1: stopped % 100.00/13.89 Prover 7: stopped % 100.00/13.89 Prover 11: stopped % 102.19/14.15 Prover 13: Warning: ignoring some quantifiers % 102.81/14.26 Prover 13: Constructing countermodel ... % 103.17/14.32 Prover 13: stopped % 108.86/15.41 Prover 8: Warning: ignoring some quantifiers % 108.86/15.49 Prover 8: Constructing countermodel ... % 109.36/15.51 Prover 8: stopped % 122.45/19.40 Prover 4: Warning: ignoring some quantifiers % 124.06/19.85 Prover 4: Constructing countermodel ... % 124.06/19.88 Prover 4: stopped % 124.06/19.88 % 124.06/19.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 124.06/19.88 % 124.06/19.89 % SZS output start Proof for theBenchmark % 124.47/19.90 Assumptions after simplification: % 124.47/19.90 --------------------------------- % 124.47/19.90 % 124.47/19.90 (verify) % 124.47/19.91 $ki_world($ki_local_world) & ? [v0: $ki_world] : ? [v1: $ki_world] : % 124.47/19.91 ($ki_world(v1) & $ki_world(v0) & $ki_accessible(v0, v1) & % 124.47/19.91 $ki_accessible($ki_local_world, v0) & ~ true(v1) & ! [v2: $ki_world] : ( ~ % 124.47/19.91 $ki_world(v2) | ~ $ki_accessible(v0, v2) | true(v2))) % 124.47/19.91 % 124.47/19.91 Further assumptions not needed in the proof: % 124.47/19.91 -------------------------------------------- % 124.47/19.91 $ki_exists_in_world_$i_nonempty, a_select2_substitution_1, % 124.47/19.91 a_select2_substitution_2, a_select3_substitution_1, a_select3_substitution_2, % 124.47/19.91 a_select3_substitution_3, const_array1_select, const_array2_select, defuse, % 124.47/19.91 dim_substitution_1, dim_substitution_2, finite_domain_0, finite_domain_1, % 124.47/19.91 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5, % 124.47/19.91 geq_substitution_1, geq_substitution_2, gt_0_tptp_minus_1, gt_1_0, % 124.47/19.91 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, % 124.47/19.91 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, % 124.47/19.91 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_substitution_1, % 124.47/19.91 gt_substitution_2, gt_succ, inv_substitution_1, irreflexivity_gt, leq_geq, % 124.47/19.91 leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_substitution_1, % 124.47/19.91 leq_substitution_2, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, % 124.47/19.91 lt_gt, lt_substitution_1, lt_substitution_2, matrix_symm_aba1, matrix_symm_aba2, % 124.47/19.91 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, % 124.47/19.91 matrix_symm_trans, matrix_symm_update_diagonal, minus_substitution_1, % 124.47/19.91 minus_substitution_2, mrel_reflexive, mrel_transitive, plus_substitution_1, % 124.47/19.91 plus_substitution_2, pred_minus_1, pred_substitution_1, pred_succ, reflexivity, % 124.47/19.91 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, % 124.47/19.91 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, % 124.47/19.91 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, % 124.47/19.91 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_substitution_1, succ_tptp_minus_1, % 124.47/19.91 successor_1, successor_2, successor_3, successor_4, successor_5, sum_plus_base, % 124.47/19.91 sum_plus_base_float, sum_substitution_1, sum_substitution_2, sum_substitution_3, % 124.47/19.91 symmetry, totality, tptp_const_array1_substitution_1, % 124.47/19.91 tptp_const_array1_substitution_2, tptp_const_array2_substitution_1, % 124.47/19.91 tptp_const_array2_substitution_2, tptp_const_array2_substitution_3, % 124.47/19.91 tptp_madd_substitution_1, tptp_madd_substitution_2, tptp_mmul_substitution_1, % 124.47/19.91 tptp_mmul_substitution_2, tptp_msub_substitution_1, tptp_msub_substitution_2, % 124.47/19.91 tptp_update2_substitution_1, tptp_update2_substitution_2, % 124.47/19.91 tptp_update2_substitution_3, tptp_update3_substitution_1, % 124.47/19.91 tptp_update3_substitution_2, tptp_update3_substitution_3, % 124.47/19.91 tptp_update3_substitution_4, trans_substitution_1, transitivity, % 124.47/19.91 transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi, % 124.47/19.91 uniform_int_rand_ranges_lo, uniform_int_rnd_substitution_1, % 124.47/19.91 uniform_int_rnd_substitution_2 % 124.47/19.91 % 124.47/19.91 Those formulas are unsatisfiable: % 124.47/19.91 --------------------------------- % 124.47/19.91 % 124.47/19.91 Begin of proof % 124.47/19.92 | % 124.47/19.92 | ALPHA: (verify) implies: % 124.47/19.92 | (1) ? [v0: $ki_world] : ? [v1: $ki_world] : ($ki_world(v1) & % 124.47/19.92 | $ki_world(v0) & $ki_accessible(v0, v1) & % 124.47/19.92 | $ki_accessible($ki_local_world, v0) & ~ true(v1) & ! [v2: % 124.47/19.92 | $ki_world] : ( ~ $ki_world(v2) | ~ $ki_accessible(v0, v2) | % 124.47/19.92 | true(v2))) % 124.47/19.92 | % 124.47/19.92 | DELTA: instantiating (1) with fresh symbols all_145_0, all_145_1 gives: % 124.47/19.93 | (2) $ki_world(all_145_0) & $ki_world(all_145_1) & $ki_accessible(all_145_1, % 124.47/19.93 | all_145_0) & $ki_accessible($ki_local_world, all_145_1) & ~ % 124.47/19.93 | true(all_145_0) & ! [v0: $ki_world] : ( ~ $ki_world(v0) | ~ % 124.47/19.93 | $ki_accessible(all_145_1, v0) | true(v0)) % 124.47/19.93 | % 124.47/19.93 | ALPHA: (2) implies: % 124.47/19.93 | (3) ~ true(all_145_0) % 124.47/19.93 | (4) $ki_accessible(all_145_1, all_145_0) % 124.47/19.93 | (5) $ki_world(all_145_0) % 124.47/19.93 | (6) ! [v0: $ki_world] : ( ~ $ki_world(v0) | ~ $ki_accessible(all_145_1, % 124.47/19.93 | v0) | true(v0)) % 124.47/19.93 | % 124.47/19.93 | GROUND_INST: instantiating (6) with all_145_0, simplifying with (3), (4), (5) % 124.47/19.93 | gives: % 124.47/19.93 | (7) $false % 124.47/19.94 | % 124.47/19.94 | CLOSE: (7) is inconsistent. % 124.47/19.94 | % 124.47/19.94 End of proof % 124.47/19.94 % SZS output end Proof for theBenchmark % 124.47/19.94 % 124.47/19.94 19228ms %------------------------------------------------------------------------------