%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUN089+1 : TPTP v8.1.2. Released v7.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n023.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 12:51:07 EDT 2023 % Result : Theorem 6.20s 1.57s % Output : Proof 8.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : NUN089+1 : TPTP v8.1.2. Released v7.3.0. % 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n023.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 : Sun Aug 27 09:18:56 EDT 2023 % 0.13/0.35 % CPUTime : % 0.60/0.63 ________ _____ % 0.60/0.63 ___ __ \_________(_)________________________________ % 0.60/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.60/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.60/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.60/0.63 % 0.60/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.60/0.63 (2023-06-19) % 0.60/0.63 % 0.60/0.63 (c) Philipp Rümmer, 2009-2023 % 0.60/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.60/0.63 Amanda Stjerna. % 0.60/0.63 Free software under BSD-3-Clause. % 0.60/0.63 % 0.60/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.60/0.63 % 0.60/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.68/0.64 Running up to 7 provers in parallel. % 0.68/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.68/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.68/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.68/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.68/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.68/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.68/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.97/1.13 Prover 1: Preprocessing ... % 2.97/1.13 Prover 4: Preprocessing ... % 3.48/1.17 Prover 5: Preprocessing ... % 3.48/1.17 Prover 0: Preprocessing ... % 3.48/1.17 Prover 3: Preprocessing ... % 3.48/1.17 Prover 6: Preprocessing ... % 3.48/1.17 Prover 2: Preprocessing ... % 5.02/1.43 Prover 2: Proving ... % 5.02/1.43 Prover 5: Proving ... % 5.71/1.49 Prover 3: Warning: ignoring some quantifiers % 5.71/1.49 Prover 6: Proving ... % 5.71/1.51 Prover 3: Constructing countermodel ... % 6.02/1.52 Prover 1: Warning: ignoring some quantifiers % 6.20/1.54 Prover 1: Constructing countermodel ... % 6.20/1.55 Prover 4: Warning: ignoring some quantifiers % 6.20/1.57 Prover 2: proved (926ms) % 6.20/1.57 % 6.20/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.20/1.57 % 6.20/1.57 Prover 5: proved (914ms) % 6.20/1.57 % 6.20/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.20/1.57 % 6.20/1.57 Prover 3: stopped % 6.20/1.58 Prover 6: stopped % 6.20/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.20/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 6.20/1.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 6.20/1.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 6.20/1.59 Prover 4: Constructing countermodel ... % 6.20/1.60 Prover 0: Proving ... % 6.20/1.62 Prover 0: stopped % 6.79/1.63 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 6.79/1.65 Prover 11: Preprocessing ... % 6.79/1.66 Prover 10: Preprocessing ... % 6.79/1.66 Prover 8: Preprocessing ... % 6.79/1.67 Prover 7: Preprocessing ... % 6.79/1.69 Prover 13: Preprocessing ... % 7.91/1.77 Prover 7: Warning: ignoring some quantifiers % 7.91/1.78 Prover 10: Warning: ignoring some quantifiers % 8.05/1.79 Prover 7: Constructing countermodel ... % 8.05/1.80 Prover 10: Constructing countermodel ... % 8.05/1.80 Prover 13: Warning: ignoring some quantifiers % 8.28/1.82 Prover 1: Found proof (size 14) % 8.28/1.82 Prover 1: proved (1177ms) % 8.28/1.82 Prover 4: stopped % 8.28/1.82 Prover 10: stopped % 8.36/1.83 Prover 13: Constructing countermodel ... % 8.36/1.83 Prover 7: stopped % 8.36/1.84 Prover 13: stopped % 8.36/1.85 Prover 8: Warning: ignoring some quantifiers % 8.36/1.86 Prover 8: Constructing countermodel ... % 8.36/1.87 Prover 8: stopped % 8.36/1.88 Prover 11: Warning: ignoring some quantifiers % 8.36/1.89 Prover 11: Constructing countermodel ... % 8.36/1.90 Prover 11: stopped % 8.36/1.90 % 8.36/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.36/1.90 % 8.36/1.90 % SZS output start Proof for theBenchmark % 8.36/1.91 Assumptions after simplification: % 8.36/1.91 --------------------------------- % 8.36/1.91 % 8.36/1.91 (axiom_7a) % 8.83/1.93 ! [v0: $i] : ! [v1: $i] : ( ~ (r2(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! % 8.83/1.93 [v2: $i] : ( ~ (r1(v2) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 8.83/1.93 id(v2, v1) = v3))) % 8.83/1.93 % 8.83/1.93 (zerounidtwo) % 8.83/1.93 ? [v0: $i] : ($i(v0) & ? [v1: $i] : (r2(v1, v0) = 0 & $i(v1) & ? [v2: $i] : % 8.83/1.93 (r2(v2, v1) = 0 & r1(v2) = 0 & $i(v2))) & ? [v1: $i] : (r1(v1) = 0 & % 8.83/1.93 id(v1, v0) = 0 & $i(v1))) % 8.83/1.93 % 8.83/1.93 (function-axioms) % 8.83/1.94 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 8.83/1.94 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (r4(v4, v3, v2) = v1) | ~ (r4(v4, v3, % 8.83/1.94 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 8.83/1.94 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (r3(v4, v3, v2) = v1) | % 8.83/1.94 ~ (r3(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.83/1.94 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (r2(v3, v2) = % 8.83/1.94 v1) | ~ (r2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.83/1.94 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (id(v3, v2) = % 8.83/1.94 v1) | ~ (id(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 8.83/1.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (r1(v2) = v1) | ~ (r1(v2) % 8.83/1.94 = v0)) % 8.83/1.94 % 8.83/1.94 Further assumptions not needed in the proof: % 8.83/1.94 -------------------------------------------- % 8.83/1.94 axiom_1, axiom_10, axiom_11, axiom_1a, axiom_2, axiom_2a, axiom_3, axiom_3a, % 8.83/1.94 axiom_4, axiom_4a, axiom_5, axiom_5a, axiom_6, axiom_6a, axiom_7, axiom_8, % 8.83/1.94 axiom_9 % 8.83/1.94 % 8.83/1.94 Those formulas are unsatisfiable: % 8.83/1.94 --------------------------------- % 8.83/1.94 % 8.83/1.94 Begin of proof % 8.83/1.94 | % 8.83/1.94 | ALPHA: (function-axioms) implies: % 8.83/1.94 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 8.83/1.94 | ! [v3: $i] : (v1 = v0 | ~ (id(v3, v2) = v1) | ~ (id(v3, v2) = v0)) % 8.83/1.94 | % 8.83/1.95 | DELTA: instantiating (zerounidtwo) with fresh symbol all_19_0 gives: % 8.83/1.95 | (2) $i(all_19_0) & ? [v0: $i] : (r2(v0, all_19_0) = 0 & $i(v0) & ? [v1: % 8.83/1.95 | $i] : (r2(v1, v0) = 0 & r1(v1) = 0 & $i(v1))) & ? [v0: $i] : % 8.83/1.95 | (r1(v0) = 0 & id(v0, all_19_0) = 0 & $i(v0)) % 8.83/1.95 | % 8.83/1.95 | ALPHA: (2) implies: % 8.83/1.95 | (3) $i(all_19_0) % 8.83/1.95 | (4) ? [v0: $i] : (r1(v0) = 0 & id(v0, all_19_0) = 0 & $i(v0)) % 8.83/1.95 | (5) ? [v0: $i] : (r2(v0, all_19_0) = 0 & $i(v0) & ? [v1: $i] : (r2(v1, % 8.83/1.95 | v0) = 0 & r1(v1) = 0 & $i(v1))) % 8.83/1.95 | % 8.83/1.95 | DELTA: instantiating (4) with fresh symbol all_25_0 gives: % 8.83/1.95 | (6) r1(all_25_0) = 0 & id(all_25_0, all_19_0) = 0 & $i(all_25_0) % 8.83/1.95 | % 8.83/1.95 | ALPHA: (6) implies: % 8.83/1.95 | (7) $i(all_25_0) % 8.83/1.95 | (8) id(all_25_0, all_19_0) = 0 % 8.83/1.95 | (9) r1(all_25_0) = 0 % 8.83/1.95 | % 8.83/1.95 | DELTA: instantiating (5) with fresh symbol all_27_0 gives: % 8.83/1.95 | (10) r2(all_27_0, all_19_0) = 0 & $i(all_27_0) & ? [v0: $i] : (r2(v0, % 8.83/1.95 | all_27_0) = 0 & r1(v0) = 0 & $i(v0)) % 8.83/1.95 | % 8.83/1.95 | ALPHA: (10) implies: % 8.83/1.95 | (11) $i(all_27_0) % 8.83/1.95 | (12) r2(all_27_0, all_19_0) = 0 % 8.83/1.95 | % 8.83/1.95 | GROUND_INST: instantiating (axiom_7a) with all_27_0, all_19_0, simplifying % 8.83/1.95 | with (3), (11), (12) gives: % 8.83/1.95 | (13) ! [v0: $i] : ( ~ (r1(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 8.83/1.95 | 0) & id(v0, all_19_0) = v1)) % 8.83/1.95 | % 8.83/1.95 | GROUND_INST: instantiating (13) with all_25_0, simplifying with (7), (9) % 8.83/1.96 | gives: % 8.83/1.96 | (14) ? [v0: int] : ( ~ (v0 = 0) & id(all_25_0, all_19_0) = v0) % 8.83/1.96 | % 8.83/1.96 | DELTA: instantiating (14) with fresh symbol all_45_0 gives: % 8.83/1.96 | (15) ~ (all_45_0 = 0) & id(all_25_0, all_19_0) = all_45_0 % 8.83/1.96 | % 8.83/1.96 | ALPHA: (15) implies: % 8.83/1.96 | (16) ~ (all_45_0 = 0) % 8.83/1.96 | (17) id(all_25_0, all_19_0) = all_45_0 % 8.83/1.96 | % 8.83/1.96 | GROUND_INST: instantiating (1) with 0, all_45_0, all_19_0, all_25_0, % 8.83/1.96 | simplifying with (8), (17) gives: % 8.83/1.96 | (18) all_45_0 = 0 % 8.83/1.96 | % 8.83/1.96 | REDUCE: (16), (18) imply: % 8.83/1.96 | (19) $false % 8.83/1.96 | % 8.83/1.96 | CLOSE: (19) is inconsistent. % 8.83/1.96 | % 8.83/1.96 End of proof % 8.83/1.96 % SZS output end Proof for theBenchmark % 8.83/1.96 % 8.83/1.96 1332ms %------------------------------------------------------------------------------