%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n017.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 12:54:24 PM UTC 2026 % Result : Theorem 7.92s 1.94s % Output : Proof 13.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL636+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.03 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.09/0.34 % Computer : n017.cluster.edu % 0.09/0.34 % Model : x86_64 x86_64 % 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.34 % Memory : 8046.5625MB % 0.09/0.34 % OS : Linux 6.8.0-71-generic % 0.09/0.34 % CPULimit : 300 % 0.09/0.34 % WCLimit : 300 % 0.09/0.34 % DateTime : Sat Sep 5 13:17:06 UTC 2026 % 0.09/0.34 % CPUTime : % 0.11/0.36 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. % 0.53/0.70 ________ _____ % 0.53/0.70 ___ __ \_________(_)________________________________ % 0.53/0.70 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.53/0.70 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.70 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.70 % 0.67/0.70 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.70 (2023-06-19) % 0.67/0.70 % 0.67/0.70 (c) Philipp Rümmer, 2009-2023 % 0.67/0.70 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.70 Amanda Stjerna. % 0.67/0.70 Free software under BSD-3-Clause. % 0.67/0.70 % 0.67/0.70 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.70 % 0.67/0.70 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.72 Running up to 7 provers in parallel. % 0.67/0.73 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.73 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.73 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.73 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.73 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.73 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.73 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.26/1.37 Prover 4: Preprocessing ... % 3.26/1.37 Prover 1: Preprocessing ... % 4.03/1.44 Prover 6: Preprocessing ... % 4.03/1.44 Prover 0: Preprocessing ... % 4.03/1.44 Prover 2: Preprocessing ... % 4.03/1.45 Prover 5: Preprocessing ... % 4.03/1.45 Prover 3: Preprocessing ... % 6.36/1.80 Prover 5: Constructing countermodel ... % 7.15/1.81 Prover 2: Constructing countermodel ... % 7.92/1.90 Prover 1: Constructing countermodel ... % 7.92/1.93 Prover 5: proved (1204ms) % 7.92/1.93 % 7.92/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.92/1.94 % 7.92/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.92/1.94 Prover 2: stopped % 7.92/1.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.92/1.94 Prover 3: Constructing countermodel ... % 7.92/1.96 Prover 3: stopped % 7.92/1.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.92/1.99 Prover 7: Preprocessing ... % 7.92/2.04 Prover 8: Preprocessing ... % 9.07/2.05 Prover 6: Proving ... % 9.07/2.05 Prover 10: Preprocessing ... % 9.07/2.05 Prover 7: Constructing countermodel ... % 9.07/2.07 Prover 6: stopped % 9.07/2.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.86/2.17 Prover 7: Found proof (size 4) % 9.86/2.17 Prover 7: proved (234ms) % 9.86/2.17 Prover 1: stopped % 9.86/2.19 Prover 11: Preprocessing ... % 10.22/2.23 Prover 10: Constructing countermodel ... % 10.22/2.23 Prover 10: stopped % 10.22/2.28 Prover 8: Warning: ignoring some quantifiers % 10.22/2.29 Prover 8: Constructing countermodel ... % 10.22/2.30 Prover 8: stopped % 11.00/2.30 Prover 11: stopped % 12.81/2.69 Prover 4: Constructing countermodel ... % 12.81/2.69 Prover 4: stopped % 13.39/2.70 Prover 0: Proving ... % 13.39/2.71 Prover 0: stopped % 13.39/2.71 % 13.39/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.39/2.71 % 13.39/2.72 % SZS output start Proof for theBenchmark % 13.39/2.72 Assumptions after simplification: % 13.39/2.72 --------------------------------- % 13.39/2.72 % 13.39/2.72 (main) % 13.39/2.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) & p100(v0) % 13.39/2.75 & p101(v2) & p101(v1) & p2(v1) & r1(v0, v2) & r1(v0, v1) & ~ p101(v0) & ~ % 13.39/2.75 p102(v2) & ~ p102(v1) & ~ p102(v0) & ~ p2(v2) & ! [v3: $i] : ! [v4: $i] % 13.39/2.75 : ( ~ $i(v4) | ~ $i(v3) | ~ p1(v4) | ~ p100(v4) | ~ p100(v3) | ~ r1(v3, % 13.39/2.75 v4) | ~ r1(v0, v3) | p1(v3)) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | % 13.39/2.75 ~ $i(v3) | ~ p1(v3) | ~ p100(v4) | ~ p100(v3) | ~ r1(v3, v4) | ~ % 13.39/2.75 r1(v0, v3) | p1(v4)) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) % 13.39/2.75 | ~ p101(v4) | ~ p101(v3) | ~ p2(v4) | ~ r1(v3, v4) | ~ r1(v0, v3) | % 13.39/2.75 p2(v3)) & ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ p101(v4) % 13.39/2.75 | ~ p101(v3) | ~ p2(v3) | ~ r1(v3, v4) | ~ r1(v0, v3) | p2(v4)) & ! % 13.39/2.75 [v3: $i] : ( ~ $i(v3) | ~ p100(v3) | ~ r1(v0, v3) | p101(v3) | ? [v4: $i] % 13.39/2.75 : ($i(v4) & p101(v4) & p2(v4) & r1(v3, v4) & ~ p102(v4))) & ! [v3: $i] : % 13.39/2.75 ( ~ $i(v3) | ~ p100(v3) | ~ r1(v0, v3) | p101(v3) | ? [v4: $i] : ($i(v4) % 13.39/2.75 & p101(v4) & r1(v3, v4) & ~ p102(v4) & ~ p2(v4))) & ! [v3: $i] : ( ~ % 13.39/2.75 $i(v3) | ~ p101(v3) | ~ r1(v0, v3) | p100(v3)) & ! [v3: $i] : ( ~ % 13.39/2.75 $i(v3) | ~ p102(v3) | ~ r1(v0, v3) | p101(v3)) & ! [v3: $i] : ( ~ % 13.39/2.75 $i(v3) | ~ r1(v0, v3) | p2(v3)) & ( ~ p1(v0) | ! [v3: $i] : ( ~ $i(v3) | % 13.39/2.75 ~ p100(v3) | ~ r1(v0, v3) | p1(v3))) & (p1(v0) | ! [v3: $i] : ( ~ % 13.39/2.75 $i(v3) | ~ p1(v3) | ~ p100(v3) | ~ r1(v0, v3)))) % 13.39/2.75 % 13.39/2.75 Those formulas are unsatisfiable: % 13.39/2.75 --------------------------------- % 13.39/2.75 % 13.39/2.75 Begin of proof % 13.39/2.75 | % 13.39/2.75 | DELTA: instantiating (main) with fresh symbols all_2_0, all_2_1, all_2_2 % 13.39/2.75 | gives: % 13.39/2.76 | (1) $i(all_2_0) & $i(all_2_1) & $i(all_2_2) & p100(all_2_2) & p101(all_2_0) % 13.39/2.76 | & p101(all_2_1) & p2(all_2_1) & r1(all_2_2, all_2_0) & r1(all_2_2, % 13.39/2.76 | all_2_1) & ~ p101(all_2_2) & ~ p102(all_2_0) & ~ p102(all_2_1) & % 13.39/2.76 | ~ p102(all_2_2) & ~ p2(all_2_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 13.39/2.76 | $i(v1) | ~ $i(v0) | ~ p1(v1) | ~ p100(v1) | ~ p100(v0) | ~ % 13.39/2.76 | r1(v0, v1) | ~ r1(all_2_2, v0) | p1(v0)) & ! [v0: $i] : ! [v1: $i] % 13.39/2.76 | : ( ~ $i(v1) | ~ $i(v0) | ~ p1(v0) | ~ p100(v1) | ~ p100(v0) | ~ % 13.39/2.76 | r1(v0, v1) | ~ r1(all_2_2, v0) | p1(v1)) & ! [v0: $i] : ! [v1: $i] % 13.39/2.76 | : ( ~ $i(v1) | ~ $i(v0) | ~ p101(v1) | ~ p101(v0) | ~ p2(v1) | ~ % 13.39/2.76 | r1(v0, v1) | ~ r1(all_2_2, v0) | p2(v0)) & ! [v0: $i] : ! [v1: $i] % 13.39/2.76 | : ( ~ $i(v1) | ~ $i(v0) | ~ p101(v1) | ~ p101(v0) | ~ p2(v0) | ~ % 13.39/2.76 | r1(v0, v1) | ~ r1(all_2_2, v0) | p2(v1)) & ! [v0: $i] : ( ~ $i(v0) % 13.39/2.76 | | ~ p100(v0) | ~ r1(all_2_2, v0) | p101(v0) | ? [v1: $i] : ($i(v1) % 13.39/2.76 | & p101(v1) & p2(v1) & r1(v0, v1) & ~ p102(v1))) & ! [v0: $i] : ( % 13.39/2.76 | ~ $i(v0) | ~ p100(v0) | ~ r1(all_2_2, v0) | p101(v0) | ? [v1: $i] % 13.39/2.77 | : ($i(v1) & p101(v1) & r1(v0, v1) & ~ p102(v1) & ~ p2(v1))) & ! % 13.39/2.77 | [v0: $i] : ( ~ $i(v0) | ~ p101(v0) | ~ r1(all_2_2, v0) | p100(v0)) & % 13.39/2.77 | ! [v0: $i] : ( ~ $i(v0) | ~ p102(v0) | ~ r1(all_2_2, v0) | p101(v0)) % 13.39/2.77 | & ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_2, v0) | p2(v0)) & ( ~ % 13.39/2.77 | p1(all_2_2) | ! [v0: $i] : ( ~ $i(v0) | ~ p100(v0) | ~ r1(all_2_2, % 13.39/2.77 | v0) | p1(v0))) & (p1(all_2_2) | ! [v0: $i] : ( ~ $i(v0) | ~ % 13.39/2.77 | p1(v0) | ~ p100(v0) | ~ r1(all_2_2, v0))) % 13.39/2.77 | % 13.39/2.77 | ALPHA: (1) implies: % 13.39/2.77 | (2) ~ p2(all_2_0) % 13.39/2.77 | (3) r1(all_2_2, all_2_0) % 13.39/2.77 | (4) $i(all_2_0) % 13.39/2.77 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ r1(all_2_2, v0) | p2(v0)) % 13.39/2.77 | % 13.39/2.77 | GROUND_INST: instantiating (5) with all_2_0, simplifying with (2), (3), (4) % 13.39/2.77 | gives: % 13.39/2.77 | (6) $false % 13.39/2.77 | % 13.39/2.77 | CLOSE: (6) is inconsistent. % 13.39/2.77 | % 13.39/2.77 End of proof % 13.39/2.77 % SZS output end Proof for theBenchmark % 13.39/2.77 % 13.39/2.77 2072ms %------------------------------------------------------------------------------