%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : LCL666+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 : n027.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 12:54:36 PM UTC 2026 % Result : Theorem 4.47s 1.40s % Output : Proof 5.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL666+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 % 0.11/0.37 % Computer : n027.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sat Sep 5 21:21:28 UTC 2026 % 0.11/0.37 % CPUTime : % 0.11/0.39 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. % 0.67/0.73 ________ _____ % 0.67/0.73 ___ __ \_________(_)________________________________ % 0.67/0.73 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.67/0.73 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.67/0.73 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.67/0.73 % 0.67/0.73 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.67/0.73 (2023-06-19) % 0.67/0.73 % 0.67/0.73 (c) Philipp Rümmer, 2009-2023 % 0.67/0.73 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.67/0.73 Amanda Stjerna. % 0.67/0.73 Free software under BSD-3-Clause. % 0.67/0.73 % 0.67/0.73 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.67/0.73 % 0.67/0.74 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.67/0.76 Running up to 7 provers in parallel. % 0.67/0.77 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.67/0.77 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.67/0.77 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.67/0.77 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.67/0.77 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.67/0.77 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.67/0.77 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.91/1.09 Prover 1: Preprocessing ... % 1.91/1.09 Prover 4: Preprocessing ... % 2.60/1.18 Prover 5: Preprocessing ... % 2.60/1.18 Prover 0: Preprocessing ... % 2.60/1.18 Prover 2: Preprocessing ... % 2.60/1.18 Prover 6: Preprocessing ... % 2.60/1.19 Prover 3: Preprocessing ... % 3.03/1.27 Prover 2: Proving ... % 3.03/1.27 Prover 5: Proving ... % 3.03/1.27 Prover 4: Constructing countermodel ... % 3.03/1.28 Prover 3: Constructing countermodel ... % 3.03/1.28 Prover 1: Constructing countermodel ... % 3.03/1.28 Prover 6: Proving ... % 3.72/1.30 Prover 0: Proving ... % 3.72/1.37 Prover 3: gave up % 3.72/1.37 Prover 1: gave up % 3.72/1.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.72/1.38 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.47/1.40 Prover 2: proved (630ms) % 4.47/1.40 % 4.47/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.47/1.40 % 4.47/1.40 Prover 5: proved (629ms) % 4.47/1.40 % 4.47/1.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.47/1.40 % 4.47/1.41 Prover 7: Preprocessing ... % 4.47/1.41 Prover 0: stopped % 4.47/1.41 Prover 6: stopped % 4.47/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.47/1.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.47/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.47/1.41 Prover 8: Preprocessing ... % 4.47/1.41 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.47/1.42 Prover 7: Warning: ignoring some quantifiers % 4.47/1.42 Prover 7: Constructing countermodel ... % 4.47/1.43 Prover 16: Preprocessing ... % 4.47/1.43 Prover 10: Preprocessing ... % 4.47/1.44 Prover 16: Warning: ignoring some quantifiers % 4.47/1.44 Prover 16: Constructing countermodel ... % 4.47/1.44 Prover 10: Warning: ignoring some quantifiers % 4.47/1.44 Prover 13: Preprocessing ... % 4.47/1.44 Prover 10: Constructing countermodel ... % 4.47/1.45 Prover 11: Preprocessing ... % 4.47/1.47 Prover 10: gave up % 4.47/1.47 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 4.47/1.47 Prover 16: gave up % 4.47/1.47 Prover 13: Warning: ignoring some quantifiers % 4.47/1.47 Prover 7: gave up % 4.47/1.48 Prover 13: Constructing countermodel ... % 4.47/1.48 Prover 19: Preprocessing ... % 5.26/1.50 Prover 8: Warning: ignoring some quantifiers % 5.26/1.51 Prover 8: Constructing countermodel ... % 5.26/1.51 Prover 13: gave up % 5.26/1.52 Prover 19: Warning: ignoring some quantifiers % 5.26/1.52 Prover 19: Constructing countermodel ... % 5.26/1.54 Prover 4: Found proof (size 19) % 5.26/1.54 Prover 4: proved (774ms) % 5.26/1.54 Prover 8: stopped % 5.26/1.55 Prover 19: stopped % 5.26/1.55 Prover 11: Constructing countermodel ... % 5.26/1.55 Prover 11: stopped % 5.26/1.55 % 5.26/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.26/1.56 % 5.26/1.57 % SZS output start Proof for theBenchmark % 5.26/1.58 Assumptions after simplification: % 5.26/1.58 --------------------------------- % 5.26/1.58 % 5.26/1.58 (main) % 5.83/1.62 ? [v0: $i] : (p201(v0) = 0 & p101(v0) = 0 & $i(v0) & ! [v1: $i] : ( ~ % 5.83/1.62 (p201(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (p101(v1) = v3 % 5.83/1.62 & r1(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~ % 5.83/1.62 (p101(v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (p201(v1) = v3 % 5.83/1.62 & r1(v0, v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~ % 5.83/1.62 (r1(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (p201(v1) = % 5.83/1.62 v2 & p101(v1) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0))))) % 5.83/1.62 % 5.83/1.62 (reflexivity) % 5.83/1.62 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (r1(v0, v0) = v1) | ~ $i(v0)) % 5.83/1.62 % 5.83/1.62 (function-axioms) % 5.83/1.63 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.83/1.63 [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) & ! [v0: % 5.83/1.63 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 5.83/1.63 ~ (p201(v2) = v1) | ~ (p201(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 5.83/1.63 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (p101(v2) = v1) | ~ % 5.83/1.63 (p101(v2) = v0)) % 5.83/1.63 % 5.83/1.63 Those formulas are unsatisfiable: % 5.83/1.63 --------------------------------- % 5.83/1.63 % 5.83/1.63 Begin of proof % 5.83/1.63 | % 5.83/1.63 | ALPHA: (function-axioms) implies: % 5.83/1.63 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.83/1.63 | (v1 = v0 | ~ (p201(v2) = v1) | ~ (p201(v2) = v0)) % 5.83/1.63 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.83/1.63 | ! [v3: $i] : (v1 = v0 | ~ (r1(v3, v2) = v1) | ~ (r1(v3, v2) = v0)) % 5.83/1.63 | % 5.83/1.63 | DELTA: instantiating (main) with fresh symbol all_4_0 gives: % 5.83/1.64 | (3) p201(all_4_0) = 0 & p101(all_4_0) = 0 & $i(all_4_0) & ! [v0: $i] : ( ~ % 5.83/1.64 | (p201(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (p101(v0) % 5.83/1.64 | = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) & ! % 5.83/1.64 | [v0: $i] : ( ~ (p101(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] % 5.83/1.64 | : (p201(v0) = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = % 5.83/1.64 | 0)))) & ! [v0: $i] : ( ~ (r1(all_4_0, v0) = 0) | ~ $i(v0) | % 5.83/1.64 | ? [v1: any] : ? [v2: any] : (p201(v0) = v1 & p101(v0) = v2 & ( ~ (v2 % 5.83/1.64 | = 0) | ~ (v1 = 0)))) % 5.83/1.64 | % 5.83/1.64 | ALPHA: (3) implies: % 5.83/1.64 | (4) $i(all_4_0) % 5.83/1.64 | (5) p101(all_4_0) = 0 % 5.83/1.64 | (6) p201(all_4_0) = 0 % 5.83/1.64 | (7) ! [v0: $i] : ( ~ (p101(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 5.83/1.64 | any] : (p201(v0) = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~ % 5.83/1.64 | (v1 = 0)))) % 5.83/1.64 | (8) ! [v0: $i] : ( ~ (p201(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: % 5.83/1.64 | any] : (p101(v0) = v2 & r1(all_4_0, v0) = v1 & ( ~ (v2 = 0) | ~ % 5.83/1.64 | (v1 = 0)))) % 5.83/1.65 | % 5.83/1.65 | GROUND_INST: instantiating (7) with all_4_0, simplifying with (4), (5) gives: % 5.83/1.65 | (9) ? [v0: any] : ? [v1: any] : (p201(all_4_0) = v1 & r1(all_4_0, % 5.83/1.65 | all_4_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.83/1.65 | % 5.83/1.65 | GROUND_INST: instantiating (8) with all_4_0, simplifying with (4), (6) gives: % 5.83/1.65 | (10) ? [v0: any] : ? [v1: any] : (p101(all_4_0) = v1 & r1(all_4_0, % 5.83/1.65 | all_4_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 5.83/1.65 | % 5.83/1.65 | DELTA: instantiating (10) with fresh symbols all_12_0, all_12_1 gives: % 5.83/1.65 | (11) p101(all_4_0) = all_12_0 & r1(all_4_0, all_4_0) = all_12_1 & ( ~ % 5.83/1.65 | (all_12_0 = 0) | ~ (all_12_1 = 0)) % 5.83/1.65 | % 5.83/1.65 | ALPHA: (11) implies: % 5.83/1.65 | (12) r1(all_4_0, all_4_0) = all_12_1 % 5.83/1.65 | % 5.83/1.65 | DELTA: instantiating (9) with fresh symbols all_14_0, all_14_1 gives: % 5.83/1.65 | (13) p201(all_4_0) = all_14_0 & r1(all_4_0, all_4_0) = all_14_1 & ( ~ % 5.83/1.65 | (all_14_0 = 0) | ~ (all_14_1 = 0)) % 5.83/1.65 | % 5.83/1.65 | ALPHA: (13) implies: % 5.83/1.65 | (14) r1(all_4_0, all_4_0) = all_14_1 % 5.83/1.65 | (15) p201(all_4_0) = all_14_0 % 5.83/1.65 | (16) ~ (all_14_0 = 0) | ~ (all_14_1 = 0) % 5.83/1.65 | % 5.83/1.65 | GROUND_INST: instantiating (2) with all_12_1, all_14_1, all_4_0, all_4_0, % 5.83/1.65 | simplifying with (12), (14) gives: % 5.83/1.65 | (17) all_14_1 = all_12_1 % 5.83/1.65 | % 5.83/1.65 | GROUND_INST: instantiating (1) with 0, all_14_0, all_4_0, simplifying with % 5.83/1.65 | (6), (15) gives: % 5.83/1.65 | (18) all_14_0 = 0 % 5.83/1.65 | % 5.83/1.65 | BETA: splitting (16) gives: % 5.83/1.66 | % 5.83/1.66 | Case 1: % 5.83/1.66 | | % 5.83/1.66 | | (19) ~ (all_14_0 = 0) % 5.83/1.66 | | % 5.83/1.66 | | REDUCE: (18), (19) imply: % 5.83/1.66 | | (20) $false % 5.83/1.66 | | % 5.83/1.66 | | CLOSE: (20) is inconsistent. % 5.83/1.66 | | % 5.83/1.66 | Case 2: % 5.83/1.66 | | % 5.83/1.66 | | (21) ~ (all_14_1 = 0) % 5.83/1.66 | | % 5.83/1.66 | | REDUCE: (17), (21) imply: % 5.83/1.66 | | (22) ~ (all_12_1 = 0) % 5.83/1.66 | | % 5.83/1.66 | | GROUND_INST: instantiating (reflexivity) with all_4_0, all_12_1, simplifying % 5.83/1.66 | | with (4), (12) gives: % 5.83/1.66 | | (23) all_12_1 = 0 % 5.83/1.66 | | % 5.83/1.66 | | REDUCE: (22), (23) imply: % 5.83/1.66 | | (24) $false % 5.83/1.66 | | % 5.83/1.66 | | CLOSE: (24) is inconsistent. % 5.83/1.66 | | % 5.83/1.66 | End of split % 5.83/1.66 | % 5.83/1.66 End of proof % 5.83/1.66 % SZS output end Proof for theBenchmark % 5.83/1.66 % 5.83/1.66 922ms %------------------------------------------------------------------------------