%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 15:26:23 EDT 2023 % Result : Theorem 12.16s 2.42s % Output : Proof 13.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SET776+4 : TPTP v8.1.2. Released v2.2.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.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 : Sat Aug 26 16:27:18 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.82/1.10 Prover 1: Preprocessing ... % 3.04/1.11 Prover 4: Preprocessing ... % 3.27/1.14 Prover 6: Preprocessing ... % 3.27/1.14 Prover 5: Preprocessing ... % 3.27/1.14 Prover 0: Preprocessing ... % 3.27/1.14 Prover 2: Preprocessing ... % 3.27/1.14 Prover 3: Preprocessing ... % 6.83/1.68 Prover 5: Proving ... % 6.83/1.70 Prover 2: Proving ... % 6.83/1.71 Prover 3: Constructing countermodel ... % 6.83/1.72 Prover 6: Proving ... % 7.54/1.78 Prover 1: Constructing countermodel ... % 8.85/1.92 Prover 3: gave up % 8.85/1.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.02/1.95 Prover 4: Constructing countermodel ... % 9.02/1.95 Prover 7: Preprocessing ... % 9.77/2.04 Prover 7: Warning: ignoring some quantifiers % 9.77/2.05 Prover 0: Proving ... % 9.77/2.09 Prover 7: Constructing countermodel ... % 10.70/2.21 Prover 1: gave up % 10.70/2.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.35/2.25 Prover 8: Preprocessing ... % 12.16/2.42 Prover 0: proved (1782ms) % 12.16/2.42 % 12.16/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.16/2.42 % 12.16/2.42 Prover 8: Warning: ignoring some quantifiers % 12.16/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.16/2.42 Prover 6: stopped % 12.16/2.42 Prover 5: stopped % 12.16/2.42 Prover 2: stopped % 12.16/2.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.16/2.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.16/2.43 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 12.16/2.43 Prover 8: Constructing countermodel ... % 12.16/2.43 Prover 7: Found proof (size 8) % 12.16/2.43 Prover 7: proved (510ms) % 12.16/2.44 Prover 4: stopped % 12.16/2.44 Prover 8: stopped % 12.89/2.46 Prover 10: Preprocessing ... % 12.89/2.46 Prover 11: Preprocessing ... % 12.89/2.46 Prover 13: Preprocessing ... % 12.89/2.46 Prover 16: Preprocessing ... % 12.89/2.47 Prover 10: stopped % 12.89/2.49 Prover 16: stopped % 12.89/2.49 Prover 13: stopped % 13.21/2.51 Prover 11: stopped % 13.21/2.51 % 13.21/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.21/2.51 % 13.21/2.51 % SZS output start Proof for theBenchmark % 13.21/2.52 Assumptions after simplification: % 13.21/2.52 --------------------------------- % 13.21/2.52 % 13.21/2.52 (pre_order) % 13.21/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.21/2.53 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ pre_order(v0, % 13.21/2.53 v1) | ~ apply(v0, v3, v4) | ~ apply(v0, v2, v3) | ~ member(v4, v1) | ~ % 13.21/2.53 member(v3, v1) | ~ member(v2, v1) | apply(v0, v2, v4)) & ! [v0: $i] : ! % 13.21/2.53 [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ pre_order(v0, % 13.21/2.53 v1) | ~ member(v2, v1) | apply(v0, v2, v2)) & ? [v0: $i] : ? [v1: $i] : % 13.21/2.53 ( ~ $i(v1) | ~ $i(v0) | pre_order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? % 13.21/2.53 [v4: $i] : ($i(v4) & $i(v3) & $i(v2) & ((apply(v0, v3, v4) & apply(v0, v2, % 13.21/2.53 v3) & member(v4, v1) & member(v3, v1) & member(v2, v1) & ~ % 13.21/2.53 apply(v0, v2, v4)) | (member(v2, v1) & ~ apply(v0, v2, v2))))) % 13.21/2.53 % 13.21/2.53 (thIII12) % 13.21/2.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 13.21/2.53 $i] : ? [v6: $i] : ($i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 13.21/2.53 $i(v0) & pre_order(v1, v0) & apply(v2, v4, v6) & apply(v2, v3, v5) & % 13.21/2.53 apply(v1, v3, v4) & member(v6, v0) & member(v5, v0) & member(v4, v0) & % 13.21/2.53 member(v3, v0) & ~ apply(v1, v5, v6) & ! [v7: $i] : ! [v8: $i] : ( ~ % 13.21/2.53 $i(v8) | ~ $i(v7) | ~ apply(v2, v7, v8) | ~ member(v8, v0) | ~ % 13.21/2.53 member(v7, v0) | apply(v1, v8, v7)) & ! [v7: $i] : ! [v8: $i] : ( ~ % 13.21/2.53 $i(v8) | ~ $i(v7) | ~ apply(v2, v7, v8) | ~ member(v8, v0) | ~ % 13.21/2.53 member(v7, v0) | apply(v1, v7, v8)) & ! [v7: $i] : ! [v8: $i] : ( ~ % 13.21/2.53 $i(v8) | ~ $i(v7) | ~ apply(v1, v8, v7) | ~ apply(v1, v7, v8) | ~ % 13.21/2.53 member(v8, v0) | ~ member(v7, v0) | apply(v2, v7, v8))) % 13.21/2.53 % 13.21/2.53 Further assumptions not needed in the proof: % 13.21/2.53 -------------------------------------------- % 13.21/2.53 difference, disjoint, empty_set, equal_set, equivalence, equivalence_class, % 13.21/2.53 intersection, partition, power_set, product, singleton, subset, sum, union, % 13.21/2.53 unordered_pair % 13.21/2.53 % 13.21/2.53 Those formulas are unsatisfiable: % 13.21/2.53 --------------------------------- % 13.21/2.53 % 13.21/2.53 Begin of proof % 13.21/2.53 | % 13.21/2.53 | ALPHA: (pre_order) implies: % 13.21/2.53 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 13.21/2.53 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 13.21/2.53 | pre_order(v0, v1) | ~ apply(v0, v3, v4) | ~ apply(v0, v2, v3) | ~ % 13.21/2.53 | member(v4, v1) | ~ member(v3, v1) | ~ member(v2, v1) | apply(v0, % 13.21/2.54 | v2, v4)) % 13.21/2.54 | % 13.21/2.54 | DELTA: instantiating (thIII12) with fresh symbols all_27_0, all_27_1, % 13.21/2.54 | all_27_2, all_27_3, all_27_4, all_27_5, all_27_6 gives: % 13.44/2.54 | (2) $i(all_27_0) & $i(all_27_1) & $i(all_27_2) & $i(all_27_3) & % 13.44/2.54 | $i(all_27_4) & $i(all_27_5) & $i(all_27_6) & pre_order(all_27_5, % 13.44/2.54 | all_27_6) & apply(all_27_4, all_27_2, all_27_0) & apply(all_27_4, % 13.44/2.54 | all_27_3, all_27_1) & apply(all_27_5, all_27_3, all_27_2) & % 13.44/2.54 | member(all_27_0, all_27_6) & member(all_27_1, all_27_6) & % 13.44/2.54 | member(all_27_2, all_27_6) & member(all_27_3, all_27_6) & ~ % 13.44/2.54 | apply(all_27_5, all_27_1, all_27_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.44/2.54 | $i(v1) | ~ $i(v0) | ~ apply(all_27_4, v0, v1) | ~ member(v1, % 13.44/2.54 | all_27_6) | ~ member(v0, all_27_6) | apply(all_27_5, v1, v0)) & ! % 13.44/2.54 | [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ apply(all_27_4, % 13.44/2.54 | v0, v1) | ~ member(v1, all_27_6) | ~ member(v0, all_27_6) | % 13.44/2.54 | apply(all_27_5, v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 13.44/2.54 | ~ $i(v0) | ~ apply(all_27_5, v1, v0) | ~ apply(all_27_5, v0, v1) | % 13.44/2.54 | ~ member(v1, all_27_6) | ~ member(v0, all_27_6) | apply(all_27_4, % 13.44/2.54 | v0, v1)) % 13.44/2.54 | % 13.44/2.54 | ALPHA: (2) implies: % 13.44/2.54 | (3) ~ apply(all_27_5, all_27_1, all_27_0) % 13.44/2.54 | (4) member(all_27_3, all_27_6) % 13.44/2.54 | (5) member(all_27_2, all_27_6) % 13.46/2.54 | (6) member(all_27_1, all_27_6) % 13.46/2.54 | (7) member(all_27_0, all_27_6) % 13.46/2.54 | (8) apply(all_27_5, all_27_3, all_27_2) % 13.46/2.54 | (9) apply(all_27_4, all_27_3, all_27_1) % 13.46/2.54 | (10) apply(all_27_4, all_27_2, all_27_0) % 13.46/2.54 | (11) pre_order(all_27_5, all_27_6) % 13.46/2.54 | (12) $i(all_27_6) % 13.46/2.54 | (13) $i(all_27_5) % 13.46/2.54 | (14) $i(all_27_3) % 13.46/2.54 | (15) $i(all_27_2) % 13.46/2.54 | (16) $i(all_27_1) % 13.46/2.54 | (17) $i(all_27_0) % 13.46/2.54 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.46/2.54 | apply(all_27_4, v0, v1) | ~ member(v1, all_27_6) | ~ member(v0, % 13.46/2.54 | all_27_6) | apply(all_27_5, v0, v1)) % 13.46/2.54 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.46/2.54 | apply(all_27_4, v0, v1) | ~ member(v1, all_27_6) | ~ member(v0, % 13.46/2.55 | all_27_6) | apply(all_27_5, v1, v0)) % 13.46/2.55 | % 13.46/2.55 | GROUND_INST: instantiating (19) with all_27_3, all_27_1, simplifying with (4), % 13.46/2.55 | (6), (9), (14), (16) gives: % 13.46/2.55 | (20) apply(all_27_5, all_27_1, all_27_3) % 13.46/2.55 | % 13.46/2.55 | GROUND_INST: instantiating (18) with all_27_2, all_27_0, simplifying with (5), % 13.46/2.55 | (7), (10), (15), (17) gives: % 13.46/2.55 | (21) apply(all_27_5, all_27_2, all_27_0) % 13.46/2.55 | % 13.46/2.55 | GROUND_INST: instantiating (1) with all_27_5, all_27_6, all_27_1, all_27_3, % 13.46/2.55 | all_27_2, simplifying with (4), (5), (6), (8), (11), (12), (13), % 13.46/2.55 | (14), (15), (16), (20) gives: % 13.46/2.55 | (22) apply(all_27_5, all_27_1, all_27_2) % 13.46/2.55 | % 13.46/2.55 | GROUND_INST: instantiating (1) with all_27_5, all_27_6, all_27_1, all_27_2, % 13.46/2.55 | all_27_0, simplifying with (3), (5), (6), (7), (11), (12), (13), % 13.46/2.55 | (15), (16), (17), (21), (22) gives: % 13.46/2.55 | (23) $false % 13.46/2.55 | % 13.46/2.55 | CLOSE: (23) is inconsistent. % 13.46/2.55 | % 13.46/2.55 End of proof % 13.46/2.55 % SZS output end Proof for theBenchmark % 13.46/2.55 % 13.46/2.55 1939ms %------------------------------------------------------------------------------