%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET809+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 : n013.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 15.11s 2.92s % Output : Proof 15.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET809+4 : 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 : n013.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 14:08:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.53/1.20 Prover 4: Preprocessing ... % 3.53/1.20 Prover 1: Preprocessing ... % 3.53/1.26 Prover 3: Preprocessing ... % 3.53/1.26 Prover 0: Preprocessing ... % 3.53/1.27 Prover 6: Preprocessing ... % 3.53/1.27 Prover 2: Preprocessing ... % 3.53/1.27 Prover 5: Preprocessing ... % 8.65/2.06 Prover 5: Proving ... % 8.65/2.06 Prover 2: Proving ... % 8.65/2.06 Prover 6: Proving ... % 8.65/2.09 Prover 1: Constructing countermodel ... % 8.65/2.10 Prover 3: Constructing countermodel ... % 10.64/2.24 Prover 1: gave up % 10.64/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.64/2.25 Prover 3: gave up % 10.64/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.15/2.31 Prover 6: gave up % 11.15/2.32 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 11.15/2.34 Prover 4: Constructing countermodel ... % 11.15/2.34 Prover 8: Preprocessing ... % 11.15/2.34 Prover 7: Preprocessing ... % 12.06/2.45 Prover 0: Proving ... % 12.06/2.45 Prover 9: Preprocessing ... % 12.06/2.50 Prover 7: Warning: ignoring some quantifiers % 12.85/2.55 Prover 7: Constructing countermodel ... % 13.91/2.69 Prover 8: Warning: ignoring some quantifiers % 13.91/2.74 Prover 8: Constructing countermodel ... % 13.91/2.77 Prover 7: Found proof (size 12) % 13.91/2.77 Prover 7: proved (526ms) % 13.91/2.78 Prover 2: stopped % 13.91/2.78 Prover 5: stopped % 13.91/2.78 Prover 0: proved (2146ms) % 13.91/2.78 Prover 4: stopped % 13.91/2.79 Prover 8: stopped % 15.11/2.90 Prover 9: Constructing countermodel ... % 15.11/2.92 Prover 9: stopped % 15.11/2.92 % 15.11/2.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 15.11/2.92 % 15.11/2.92 % SZS output start Proof for theBenchmark % 15.11/2.93 Assumptions after simplification: % 15.11/2.93 --------------------------------- % 15.11/2.93 % 15.11/2.93 (ordinal_number) % 15.11/2.94 $i(member_predicate) & $i(on) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 15.11/2.94 $i(v0) | ~ member(v1, v0) | ~ member(v0, on) | subset(v1, v0)) & ! [v0: % 15.11/2.94 $i] : ( ~ $i(v0) | ~ strict_well_order(member_predicate, v0) | ~ set(v0) | % 15.11/2.94 member(v0, on) | ? [v1: $i] : ($i(v1) & member(v1, v0) & ~ subset(v1, % 15.11/2.94 v0))) & ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, on) | % 15.11/2.94 strict_well_order(member_predicate, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 15.11/2.94 member(v0, on) | set(v0)) % 15.11/2.94 % 15.11/2.94 (rel_member) % 15.11/2.94 $i(member_predicate) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 15.11/2.94 apply(member_predicate, v0, v1) | member(v0, v1)) & ! [v0: $i] : ! [v1: % 15.11/2.94 $i] : ( ~ $i(v1) | ~ $i(v0) | ~ member(v0, v1) | apply(member_predicate, % 15.11/2.94 v0, v1)) % 15.11/2.94 % 15.11/2.94 (strict_order) % 15.11/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 15.11/2.95 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, % 15.11/2.95 v4) | ~ apply(v0, v2, v3) | ~ strict_order(v0, v1) | ~ member(v4, v1) | % 15.11/2.95 ~ member(v3, v1) | ~ member(v2, v1) | apply(v0, v2, v4)) & ! [v0: $i] : % 15.11/2.95 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 15.11/2.95 ~ $i(v0) | ~ apply(v0, v3, v2) | ~ apply(v0, v2, v3) | ~ strict_order(v0, % 15.11/2.95 v1) | ~ member(v3, v1) | ~ member(v2, v1)) & ? [v0: $i] : ? [v1: $i] : % 15.11/2.95 ( ~ $i(v1) | ~ $i(v0) | strict_order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ? % 15.11/2.95 [v4: $i] : ($i(v4) & $i(v3) & $i(v2) & ((apply(v0, v3, v4) & apply(v0, v2, % 15.11/2.95 v3) & member(v4, v1) & member(v3, v1) & member(v2, v1) & ~ % 15.11/2.95 apply(v0, v2, v4)) | (apply(v0, v3, v2) & apply(v0, v2, v3) & % 15.11/2.95 member(v3, v1) & member(v2, v1))))) % 15.11/2.95 % 15.11/2.95 (strict_well_order) % 15.11/2.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) % 15.11/2.95 | ~ $i(v1) | ~ $i(v0) | ~ strict_well_order(v0, v1) | ~ member(v3, v2) | % 15.11/2.95 ~ subset(v2, v1) | ? [v4: $i] : ($i(v4) & least(v4, v0, v2))) & ! [v0: % 15.11/2.95 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ strict_order(v0, v1) | % 15.11/2.95 strict_well_order(v0, v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & $i(v2) & % 15.11/2.95 member(v3, v2) & subset(v2, v1) & ! [v4: $i] : ( ~ $i(v4) | ~ least(v4, % 15.11/2.95 v0, v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 15.11/2.95 strict_well_order(v0, v1) | strict_order(v0, v1)) % 15.11/2.95 % 15.11/2.96 (thV2) % 15.11/2.96 $i(on) & ? [v0: $i] : ($i(v0) & member(v0, v0) & member(v0, on)) % 15.11/2.96 % 15.11/2.96 Further assumptions not needed in the proof: % 15.11/2.96 -------------------------------------------- % 15.11/2.96 difference, empty_set, equal_set, initial_segment, intersection, least, % 15.11/2.96 power_set, product, set_member, singleton, subset, successor, sum, union, % 15.11/2.96 unordered_pair % 15.11/2.96 % 15.11/2.96 Those formulas are unsatisfiable: % 15.11/2.96 --------------------------------- % 15.11/2.96 % 15.11/2.96 Begin of proof % 15.11/2.96 | % 15.11/2.96 | ALPHA: (ordinal_number) implies: % 15.11/2.96 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, on) | % 15.11/2.96 | strict_well_order(member_predicate, v0)) % 15.11/2.96 | % 15.11/2.96 | ALPHA: (strict_well_order) implies: % 15.11/2.96 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 15.11/2.96 | strict_well_order(v0, v1) | strict_order(v0, v1)) % 15.11/2.96 | % 15.11/2.96 | ALPHA: (rel_member) implies: % 15.61/2.96 | (3) $i(member_predicate) % 15.61/2.96 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ member(v0, v1) % 15.61/2.96 | | apply(member_predicate, v0, v1)) % 15.61/2.96 | % 15.61/2.96 | ALPHA: (strict_order) implies: % 15.61/2.97 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ % 15.61/2.97 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ apply(v0, v3, v2) | ~ apply(v0, % 15.61/2.97 | v2, v3) | ~ strict_order(v0, v1) | ~ member(v3, v1) | ~ % 15.61/2.97 | member(v2, v1)) % 15.61/2.97 | % 15.61/2.97 | ALPHA: (thV2) implies: % 15.61/2.97 | (6) ? [v0: $i] : ($i(v0) & member(v0, v0) & member(v0, on)) % 15.61/2.97 | % 15.61/2.97 | DELTA: instantiating (6) with fresh symbol all_23_0 gives: % 15.61/2.97 | (7) $i(all_23_0) & member(all_23_0, all_23_0) & member(all_23_0, on) % 15.61/2.97 | % 15.61/2.97 | ALPHA: (7) implies: % 15.61/2.97 | (8) member(all_23_0, on) % 15.61/2.97 | (9) member(all_23_0, all_23_0) % 15.61/2.97 | (10) $i(all_23_0) % 15.61/2.97 | % 15.61/2.97 | GROUND_INST: instantiating (1) with all_23_0, simplifying with (8), (10) % 15.61/2.97 | gives: % 15.61/2.97 | (11) strict_well_order(member_predicate, all_23_0) % 15.61/2.97 | % 15.61/2.97 | GROUND_INST: instantiating (4) with all_23_0, all_23_0, simplifying with (9), % 15.61/2.97 | (10) gives: % 15.61/2.97 | (12) apply(member_predicate, all_23_0, all_23_0) % 15.61/2.97 | % 15.61/2.97 | GROUND_INST: instantiating (2) with member_predicate, all_23_0, simplifying % 15.61/2.97 | with (3), (10), (11) gives: % 15.61/2.97 | (13) strict_order(member_predicate, all_23_0) % 15.61/2.97 | % 15.61/2.97 | GROUND_INST: instantiating (5) with member_predicate, all_23_0, all_23_0, % 15.61/2.97 | all_23_0, simplifying with (3), (9), (10), (12), (13) gives: % 15.61/2.97 | (14) $false % 15.61/2.98 | % 15.61/2.98 | CLOSE: (14) is inconsistent. % 15.61/2.98 | % 15.61/2.98 End of proof % 15.61/2.98 % SZS output end Proof for theBenchmark % 15.61/2.98 % 15.61/2.98 2359ms %------------------------------------------------------------------------------