%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU097+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 17:42:30 EDT 2023 % Result : Theorem 10.71s 2.19s % Output : Proof 15.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU097+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Aug 23 13:09:38 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.19/1.13 Prover 1: Preprocessing ... % 3.19/1.13 Prover 4: Preprocessing ... % 3.19/1.17 Prover 0: Preprocessing ... % 3.19/1.17 Prover 6: Preprocessing ... % 3.19/1.17 Prover 2: Preprocessing ... % 3.19/1.17 Prover 3: Preprocessing ... % 3.19/1.18 Prover 5: Preprocessing ... % 7.01/1.70 Prover 5: Proving ... % 7.01/1.70 Prover 2: Proving ... % 7.67/1.73 Prover 1: Warning: ignoring some quantifiers % 7.67/1.74 Prover 3: Warning: ignoring some quantifiers % 7.67/1.77 Prover 1: Constructing countermodel ... % 7.67/1.77 Prover 3: Constructing countermodel ... % 7.67/1.78 Prover 6: Proving ... % 8.07/1.78 Prover 4: Warning: ignoring some quantifiers % 8.07/1.83 Prover 4: Constructing countermodel ... % 8.61/1.87 Prover 0: Proving ... % 10.71/2.18 Prover 5: proved (1546ms) % 10.71/2.19 % 10.71/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.71/2.19 % 10.71/2.19 Prover 3: stopped % 10.71/2.19 Prover 0: stopped % 10.71/2.19 Prover 2: stopped % 10.71/2.19 Prover 6: stopped % 10.71/2.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.71/2.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.71/2.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.71/2.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.71/2.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.71/2.30 Prover 7: Preprocessing ... % 10.71/2.31 Prover 8: Preprocessing ... % 11.23/2.32 Prover 10: Preprocessing ... % 11.23/2.34 Prover 13: Preprocessing ... % 11.23/2.35 Prover 11: Preprocessing ... % 12.39/2.40 Prover 7: Warning: ignoring some quantifiers % 12.71/2.44 Prover 7: Constructing countermodel ... % 12.71/2.44 Prover 10: Warning: ignoring some quantifiers % 12.71/2.47 Prover 10: Constructing countermodel ... % 12.71/2.48 Prover 13: Warning: ignoring some quantifiers % 12.71/2.49 Prover 13: Constructing countermodel ... % 13.21/2.50 Prover 8: Warning: ignoring some quantifiers % 13.21/2.52 Prover 8: Constructing countermodel ... % 13.69/2.60 Prover 10: gave up % 13.69/2.62 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.69/2.63 Prover 11: Warning: ignoring some quantifiers % 13.69/2.65 Prover 11: Constructing countermodel ... % 14.43/2.67 Prover 16: Preprocessing ... % 14.70/2.70 Prover 13: gave up % 14.70/2.72 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.04/2.74 Prover 16: Warning: ignoring some quantifiers % 15.04/2.75 Prover 19: Preprocessing ... % 15.04/2.75 Prover 16: Constructing countermodel ... % 15.04/2.79 Prover 7: Found proof (size 14) % 15.04/2.79 Prover 7: proved (590ms) % 15.04/2.79 Prover 16: stopped % 15.04/2.79 Prover 1: stopped % 15.04/2.79 Prover 11: stopped % 15.04/2.79 Prover 8: stopped % 15.04/2.79 Prover 4: stopped % 15.04/2.86 Prover 19: Warning: ignoring some quantifiers % 15.04/2.87 Prover 19: Constructing countermodel ... % 15.04/2.88 Prover 19: stopped % 15.04/2.88 % 15.04/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.04/2.88 % 15.04/2.88 % SZS output start Proof for theBenchmark % 15.04/2.89 Assumptions after simplification: % 15.04/2.89 --------------------------------- % 15.04/2.89 % 15.04/2.89 (commutativity_k2_xboole_0) % 15.75/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 15.75/2.92 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 15.75/2.92 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 15.75/2.92 | (set_union2(v1, v0) = v2 & $i(v2))) % 15.75/2.92 % 15.75/2.92 (d6_xboole_0) % 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = v2) | % 15.75/2.93 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (set_difference(v0, v1) = % 15.75/2.93 v4 & symmetric_difference(v0, v1) = v3 & set_union2(v4, v2) = v3 & $i(v4) % 15.75/2.93 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.75/2.93 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 15.75/2.93 [v4: $i] : (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3 % 15.75/2.93 & set_union2(v2, v4) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] % 15.75/2.93 : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ % 15.75/2.93 $i(v0) | ? [v3: $i] : ? [v4: $i] : (set_difference(v1, v0) = v4 & % 15.75/2.93 set_difference(v0, v1) = v3 & set_union2(v3, v4) = v2 & $i(v4) & $i(v3) & % 15.75/2.93 $i(v2))) % 15.75/2.93 % 15.75/2.93 (fc12_finset_1) % 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | % 15.75/2.93 ~ $i(v1) | ~ $i(v0) | ~ finite(v0) | finite(v2)) % 15.75/2.93 % 15.75/2.93 (fc9_finset_1) % 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 15.75/2.93 $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 15.75/2.93 % 15.75/2.93 (l3_finset_1) % 15.75/2.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 15.75/2.94 $i(v1) | ~ $i(v0) | ~ finite(v1) | ~ finite(v0) | finite(v2)) % 15.75/2.94 % 15.75/2.94 (t16_finset_1) % 15.75/2.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) | % 15.75/2.94 ~ $i(v1) | ~ $i(v0) | ~ finite(v0) | finite(v2)) % 15.75/2.94 % 15.75/2.94 (t28_finset_1) % 15.75/2.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (symmetric_difference(v0, v1) = v2 & % 15.75/2.94 $i(v2) & $i(v1) & $i(v0) & finite(v1) & finite(v0) & ~ finite(v2)) % 15.75/2.94 % 15.75/2.94 Further assumptions not needed in the proof: % 15.75/2.94 -------------------------------------------- % 15.75/2.94 antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1, % 15.75/2.94 cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1, % 15.75/2.94 cc4_arytm_3, commutativity_k5_xboole_0, existence_m1_subset_1, fc12_relat_1, % 15.75/2.94 fc1_subset_1, fc1_xboole_0, fc2_ordinal1, fc2_relat_1, fc2_xboole_0, % 15.75/2.94 fc3_relat_1, fc3_xboole_0, fc4_relat_1, fc8_arytm_3, idempotence_k2_xboole_0, % 15.75/2.94 rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, rc1_ordinal1, % 15.75/2.94 rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_arytm_3, % 15.75/2.94 rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1, % 15.75/2.94 rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1, % 15.75/2.94 rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1, % 15.75/2.94 reflexivity_r1_tarski, t1_boole, t1_subset, t2_subset, t3_boole, t3_subset, % 15.75/2.94 t4_boole, t4_subset, t5_boole, t5_subset, t6_boole, t7_boole, t8_boole % 15.75/2.94 % 15.75/2.94 Those formulas are unsatisfiable: % 15.75/2.94 --------------------------------- % 15.75/2.94 % 15.75/2.94 Begin of proof % 15.75/2.94 | % 15.75/2.94 | ALPHA: (commutativity_k2_xboole_0) implies: % 15.75/2.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 15.75/2.94 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 15.75/2.94 | % 15.75/2.94 | ALPHA: (d6_xboole_0) implies: % 15.75/2.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, % 15.75/2.94 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 15.75/2.94 | (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & % 15.75/2.94 | set_union2(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2))) % 15.75/2.94 | % 15.75/2.94 | DELTA: instantiating (t28_finset_1) with fresh symbols all_85_0, all_85_1, % 15.75/2.94 | all_85_2 gives: % 15.75/2.94 | (3) symmetric_difference(all_85_2, all_85_1) = all_85_0 & $i(all_85_0) & % 15.75/2.94 | $i(all_85_1) & $i(all_85_2) & finite(all_85_1) & finite(all_85_2) & ~ % 15.75/2.94 | finite(all_85_0) % 15.75/2.94 | % 15.75/2.94 | ALPHA: (3) implies: % 15.75/2.95 | (4) ~ finite(all_85_0) % 15.75/2.95 | (5) finite(all_85_2) % 15.75/2.95 | (6) finite(all_85_1) % 15.75/2.95 | (7) $i(all_85_2) % 15.75/2.95 | (8) $i(all_85_1) % 15.75/2.95 | (9) symmetric_difference(all_85_2, all_85_1) = all_85_0 % 15.75/2.95 | % 15.75/2.95 | GROUND_INST: instantiating (2) with all_85_2, all_85_1, all_85_0, simplifying % 15.75/2.95 | with (7), (8), (9) gives: % 15.75/2.95 | (10) ? [v0: $i] : ? [v1: $i] : (set_difference(all_85_1, all_85_2) = v1 & % 15.75/2.95 | set_difference(all_85_2, all_85_1) = v0 & set_union2(v0, v1) = % 15.75/2.95 | all_85_0 & $i(v1) & $i(v0) & $i(all_85_0)) % 15.75/2.95 | % 15.75/2.95 | DELTA: instantiating (10) with fresh symbols all_101_0, all_101_1 gives: % 15.75/2.95 | (11) set_difference(all_85_1, all_85_2) = all_101_0 & % 15.75/2.95 | set_difference(all_85_2, all_85_1) = all_101_1 & set_union2(all_101_1, % 15.75/2.95 | all_101_0) = all_85_0 & $i(all_101_0) & $i(all_101_1) & $i(all_85_0) % 15.75/2.95 | % 15.75/2.95 | ALPHA: (11) implies: % 15.75/2.95 | (12) $i(all_101_1) % 15.75/2.95 | (13) $i(all_101_0) % 15.75/2.95 | (14) set_union2(all_101_1, all_101_0) = all_85_0 % 15.75/2.95 | (15) set_difference(all_85_2, all_85_1) = all_101_1 % 15.75/2.95 | (16) set_difference(all_85_1, all_85_2) = all_101_0 % 15.75/2.95 | % 15.75/2.95 | GROUND_INST: instantiating (1) with all_101_0, all_101_1, all_85_0, % 15.75/2.95 | simplifying with (12), (13), (14) gives: % 15.75/2.95 | (17) set_union2(all_101_0, all_101_1) = all_85_0 & $i(all_85_0) % 15.75/2.95 | % 15.75/2.95 | ALPHA: (17) implies: % 15.75/2.95 | (18) set_union2(all_101_0, all_101_1) = all_85_0 % 15.75/2.95 | % 15.75/2.95 | GROUND_INST: instantiating (t16_finset_1) with all_85_2, all_85_1, all_101_1, % 15.75/2.95 | simplifying with (5), (7), (8), (15) gives: % 15.75/2.95 | (19) finite(all_101_1) % 15.75/2.95 | % 15.75/2.95 | GROUND_INST: instantiating (t16_finset_1) with all_85_1, all_85_2, all_101_0, % 15.75/2.95 | simplifying with (6), (7), (8), (16) gives: % 15.75/2.95 | (20) finite(all_101_0) % 15.75/2.95 | % 15.75/2.95 | GROUND_INST: instantiating (l3_finset_1) with all_101_0, all_101_1, all_85_0, % 15.75/2.95 | simplifying with (4), (12), (13), (18), (19), (20) gives: % 15.75/2.95 | (21) $false % 15.75/2.95 | % 15.75/2.95 | CLOSE: (21) is inconsistent. % 15.75/2.95 | % 15.75/2.95 End of proof % 15.75/2.95 % SZS output end Proof for theBenchmark % 15.75/2.95 % 15.75/2.95 2348ms %------------------------------------------------------------------------------