%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET810+4 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 15:26:32 EDT 2023 % Result : Theorem 11.96s 2.36s % Output : Proof 13.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET810+4 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n011.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 11:15:09 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.92/1.10 Prover 4: Preprocessing ... % 2.92/1.10 Prover 1: Preprocessing ... % 3.16/1.14 Prover 3: Preprocessing ... % 3.16/1.14 Prover 0: Preprocessing ... % 3.16/1.14 Prover 5: Preprocessing ... % 3.16/1.14 Prover 2: Preprocessing ... % 3.16/1.14 Prover 6: Preprocessing ... % 6.80/1.68 Prover 5: Proving ... % 6.80/1.68 Prover 6: Proving ... % 7.37/1.70 Prover 2: Proving ... % 7.37/1.72 Prover 3: Constructing countermodel ... % 7.37/1.72 Prover 1: Constructing countermodel ... % 7.98/1.80 Prover 0: Proving ... % 8.30/1.82 Prover 1: gave up % 8.30/1.82 Prover 6: gave up % 8.30/1.83 Prover 3: gave up % 8.30/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.30/1.84 Prover 4: Constructing countermodel ... % 8.30/1.84 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.30/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.30/1.91 Prover 9: Preprocessing ... % 8.97/1.92 Prover 8: Preprocessing ... % 8.97/1.92 Prover 7: Preprocessing ... % 8.97/2.01 Prover 7: Warning: ignoring some quantifiers % 8.97/2.04 Prover 7: Constructing countermodel ... % 9.96/2.13 Prover 8: Warning: ignoring some quantifiers % 9.96/2.14 Prover 8: Constructing countermodel ... % 11.22/2.23 Prover 8: gave up % 11.22/2.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.22/2.28 Prover 10: Preprocessing ... % 11.22/2.31 Prover 9: Constructing countermodel ... % 11.96/2.35 Prover 0: proved (1714ms) % 11.96/2.35 % 11.96/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.96/2.36 % 11.96/2.36 Prover 9: stopped % 11.96/2.36 Prover 2: stopped % 11.96/2.36 Prover 5: stopped % 11.96/2.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.96/2.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.96/2.38 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.96/2.38 Prover 10: Warning: ignoring some quantifiers % 11.96/2.38 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 11.96/2.39 Prover 16: Preprocessing ... % 11.96/2.39 Prover 11: Preprocessing ... % 12.50/2.39 Prover 7: Found proof (size 17) % 12.50/2.39 Prover 7: proved (569ms) % 12.50/2.39 Prover 10: Constructing countermodel ... % 12.50/2.39 Prover 4: stopped % 12.50/2.40 Prover 13: Preprocessing ... % 12.50/2.42 Prover 19: Preprocessing ... % 12.50/2.42 Prover 10: stopped % 12.50/2.42 Prover 16: stopped % 12.50/2.43 Prover 13: stopped % 12.50/2.45 Prover 11: stopped % 13.24/2.53 Prover 19: Warning: ignoring some quantifiers % 13.24/2.55 Prover 19: Constructing countermodel ... % 13.24/2.55 Prover 19: stopped % 13.24/2.55 % 13.24/2.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.24/2.55 % 13.24/2.56 % SZS output start Proof for theBenchmark % 13.24/2.56 Assumptions after simplification: % 13.24/2.56 --------------------------------- % 13.24/2.56 % 13.24/2.56 (ordinal_number) % 13.24/2.57 $i(member_predicate) & $i(on) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 13.24/2.57 $i(v0) | ~ member(v1, v0) | ~ member(v0, on) | subset(v1, v0)) & ! [v0: % 13.24/2.57 $i] : ( ~ $i(v0) | ~ strict_well_order(member_predicate, v0) | ~ set(v0) | % 13.24/2.57 member(v0, on) | ? [v1: $i] : ($i(v1) & member(v1, v0) & ~ subset(v1, % 13.24/2.57 v0))) & ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, on) | % 13.24/2.57 strict_well_order(member_predicate, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 13.24/2.57 member(v0, on) | set(v0)) % 13.24/2.57 % 13.24/2.57 (rel_member) % 13.24/2.57 $i(member_predicate) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.24/2.57 apply(member_predicate, v0, v1) | member(v0, v1)) & ! [v0: $i] : ! [v1: % 13.24/2.57 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ member(v0, v1) | apply(member_predicate, % 13.24/2.57 v0, v1)) % 13.24/2.57 % 13.24/2.57 (strict_order) % 13.24/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 13.24/2.58 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, % 13.24/2.58 v4) | ~ apply(v0, v2, v3) | ~ strict_order(v0, v1) | ~ member(v4, v1) | % 13.24/2.58 ~ member(v3, v1) | ~ member(v2, v1) | apply(v0, v2, v4)) & ! [v0: $i] : % 13.24/2.58 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 13.24/2.58 ~ $i(v0) | ~ apply(v0, v3, v2) | ~ apply(v0, v2, v3) | ~ strict_order(v0, % 13.24/2.58 v1) | ~ member(v3, v1) | ~ member(v2, v1)) & ? [v0: $i] : ? [v1: $i] : % 13.24/2.58 ( ~ $i(v1) | ~ $i(v0) | strict_order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? % 13.24/2.58 [v4: $i] : ($i(v4) & $i(v3) & $i(v2) & ((apply(v0, v3, v4) & apply(v0, v2, % 13.24/2.58 v3) & member(v4, v1) & member(v3, v1) & member(v2, v1) & ~ % 13.24/2.58 apply(v0, v2, v4)) | (apply(v0, v3, v2) & apply(v0, v2, v3) & % 13.24/2.58 member(v3, v1) & member(v2, v1))))) % 13.24/2.58 % 13.24/2.58 (strict_well_order) % 13.24/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 13.24/2.58 | ~ $i(v1) | ~ $i(v0) | ~ strict_well_order(v0, v1) | ~ member(v3, v2) | % 13.24/2.58 ~ subset(v2, v1) | ? [v4: $i] : ($i(v4) & least(v4, v0, v2))) & ! [v0: % 13.24/2.58 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ strict_order(v0, v1) | % 13.24/2.58 strict_well_order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & % 13.24/2.58 member(v3, v2) & subset(v2, v1) & ! [v4: $i] : ( ~ $i(v4) | ~ least(v4, % 13.24/2.58 v0, v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.24/2.58 strict_well_order(v0, v1) | strict_order(v0, v1)) % 13.24/2.58 % 13.24/2.58 (subset) % 13.24/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.24/2.58 ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [v0: $i] : ? % 13.24/2.58 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & % 13.24/2.58 member(v2, v0) & ~ member(v2, v1))) % 13.24/2.58 % 13.24/2.58 (thV3) % 13.24/2.58 $i(on) & ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & member(v1, v0) & % 13.24/2.58 member(v1, on) & member(v0, v1) & member(v0, on)) % 13.24/2.58 % 13.24/2.58 Further assumptions not needed in the proof: % 13.24/2.58 -------------------------------------------- % 13.24/2.58 difference, empty_set, equal_set, initial_segment, intersection, least, % 13.24/2.58 power_set, product, set_member, singleton, successor, sum, union, unordered_pair % 13.24/2.58 % 13.24/2.58 Those formulas are unsatisfiable: % 13.24/2.58 --------------------------------- % 13.24/2.58 % 13.24/2.58 Begin of proof % 13.24/2.58 | % 13.24/2.58 | ALPHA: (subset) implies: % 13.24/2.58 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 13.24/2.58 | $i(v0) | ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) % 13.24/2.58 | % 13.24/2.58 | ALPHA: (ordinal_number) implies: % 13.24/2.58 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, on) | % 13.24/2.58 | strict_well_order(member_predicate, v0)) % 13.24/2.58 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ member(v1, v0) % 13.24/2.58 | | ~ member(v0, on) | subset(v1, v0)) % 13.24/2.58 | % 13.24/2.58 | ALPHA: (strict_well_order) implies: % 13.24/2.59 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.24/2.59 | strict_well_order(v0, v1) | strict_order(v0, v1)) % 13.24/2.59 | % 13.24/2.59 | ALPHA: (rel_member) implies: % 13.24/2.59 | (5) $i(member_predicate) % 13.24/2.59 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ member(v0, v1) % 13.24/2.59 | | apply(member_predicate, v0, v1)) % 13.24/2.59 | % 13.24/2.59 | ALPHA: (strict_order) implies: % 13.24/2.59 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 13.24/2.59 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) | ~ apply(v0, % 13.24/2.59 | v2, v3) | ~ strict_order(v0, v1) | ~ member(v3, v1) | ~ % 13.24/2.59 | member(v2, v1)) % 13.24/2.59 | % 13.24/2.59 | ALPHA: (thV3) implies: % 13.24/2.59 | (8) ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & member(v1, v0) & % 13.24/2.59 | member(v1, on) & member(v0, v1) & member(v0, on)) % 13.24/2.59 | % 13.24/2.59 | DELTA: instantiating (8) with fresh symbols all_23_0, all_23_1 gives: % 13.24/2.59 | (9) $i(all_23_0) & $i(all_23_1) & member(all_23_0, all_23_1) & % 13.24/2.59 | member(all_23_0, on) & member(all_23_1, all_23_0) & member(all_23_1, % 13.24/2.59 | on) % 13.24/2.59 | % 13.24/2.59 | ALPHA: (9) implies: % 13.24/2.59 | (10) member(all_23_1, all_23_0) % 13.24/2.59 | (11) member(all_23_0, on) % 13.24/2.59 | (12) member(all_23_0, all_23_1) % 13.24/2.59 | (13) $i(all_23_1) % 13.24/2.59 | (14) $i(all_23_0) % 13.24/2.59 | % 13.24/2.59 | GROUND_INST: instantiating (6) with all_23_1, all_23_0, simplifying with (10), % 13.24/2.59 | (13), (14) gives: % 13.24/2.59 | (15) apply(member_predicate, all_23_1, all_23_0) % 13.24/2.59 | % 13.24/2.59 | GROUND_INST: instantiating (3) with all_23_0, all_23_1, simplifying with (10), % 13.24/2.59 | (11), (13), (14) gives: % 13.24/2.59 | (16) subset(all_23_1, all_23_0) % 13.24/2.59 | % 13.24/2.59 | GROUND_INST: instantiating (2) with all_23_0, simplifying with (11), (14) % 13.24/2.59 | gives: % 13.24/2.59 | (17) strict_well_order(member_predicate, all_23_0) % 13.24/2.59 | % 13.24/2.59 | GROUND_INST: instantiating (6) with all_23_0, all_23_1, simplifying with (12), % 13.24/2.59 | (13), (14) gives: % 13.24/2.59 | (18) apply(member_predicate, all_23_0, all_23_1) % 13.24/2.59 | % 13.24/2.59 | GROUND_INST: instantiating (1) with all_23_1, all_23_0, all_23_0, simplifying % 13.24/2.59 | with (12), (13), (14), (16) gives: % 13.24/2.59 | (19) member(all_23_0, all_23_0) % 13.24/2.59 | % 13.24/2.59 | GROUND_INST: instantiating (4) with member_predicate, all_23_0, simplifying % 13.24/2.59 | with (5), (14), (17) gives: % 13.24/2.59 | (20) strict_order(member_predicate, all_23_0) % 13.24/2.59 | % 13.24/2.59 | GROUND_INST: instantiating (7) with member_predicate, all_23_0, all_23_1, % 13.24/2.59 | all_23_0, simplifying with (5), (10), (13), (14), (15), (18), % 13.24/2.59 | (19), (20) gives: % 13.24/2.59 | (21) $false % 13.24/2.60 | % 13.24/2.60 | CLOSE: (21) is inconsistent. % 13.24/2.60 | % 13.24/2.60 End of proof % 13.24/2.60 % SZS output end Proof for theBenchmark % 13.24/2.60 % 13.24/2.60 1981ms %------------------------------------------------------------------------------