%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET813+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 : n004.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 15:26:33 EDT 2023 % Result : Theorem 9.93s 2.22s % Output : Proof 12.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET813+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 : n004.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 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 12:58:08 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 ... % 0.20/0.62 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 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 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 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 % 2.83/1.13 Prover 1: Preprocessing ... % 2.83/1.13 Prover 4: Preprocessing ... % 2.83/1.17 Prover 2: Preprocessing ... % 2.83/1.17 Prover 3: Preprocessing ... % 2.83/1.17 Prover 5: Preprocessing ... % 2.83/1.17 Prover 6: Preprocessing ... % 2.83/1.17 Prover 0: Preprocessing ... % 7.19/1.73 Prover 6: Proving ... % 7.19/1.74 Prover 5: Proving ... % 7.19/1.74 Prover 1: Constructing countermodel ... % 7.19/1.75 Prover 3: Constructing countermodel ... % 7.19/1.75 Prover 2: Proving ... % 7.72/1.85 Prover 3: gave up % 7.72/1.86 Prover 6: gave up % 7.72/1.86 Prover 1: gave up % 8.39/1.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.39/1.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.39/1.87 Prover 4: Constructing countermodel ... % 8.39/1.87 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.83/1.94 Prover 7: Preprocessing ... % 8.83/1.94 Prover 0: Proving ... % 8.83/1.94 Prover 8: Preprocessing ... % 8.83/1.95 Prover 9: Preprocessing ... % 9.93/2.09 Prover 7: Warning: ignoring some quantifiers % 9.93/2.13 Prover 7: Constructing countermodel ... % 9.93/2.13 Prover 8: Warning: ignoring some quantifiers % 9.93/2.16 Prover 8: Constructing countermodel ... % 9.93/2.21 Prover 0: proved (1586ms) % 9.93/2.21 % 9.93/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.93/2.22 % 9.93/2.23 Prover 5: stopped % 9.93/2.24 Prover 2: stopped % 9.93/2.24 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.93/2.24 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.93/2.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.93/2.27 Prover 10: Preprocessing ... % 11.22/2.30 Prover 13: Preprocessing ... % 11.22/2.31 Prover 11: Preprocessing ... % 11.48/2.32 Prover 8: gave up % 11.48/2.33 Prover 10: Warning: ignoring some quantifiers % 11.48/2.34 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.69/2.35 Prover 10: Constructing countermodel ... % 11.69/2.37 Prover 9: Constructing countermodel ... % 11.69/2.37 Prover 16: Preprocessing ... % 11.69/2.38 Prover 4: Found proof (size 24) % 11.69/2.38 Prover 4: proved (1740ms) % 11.69/2.38 Prover 9: stopped % 11.69/2.38 Prover 7: stopped % 11.69/2.38 Prover 10: stopped % 11.69/2.38 Prover 13: stopped % 11.69/2.38 Prover 11: stopped % 11.69/2.39 Prover 16: stopped % 11.69/2.39 % 11.69/2.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.69/2.39 % 11.69/2.39 % SZS output start Proof for theBenchmark % 11.69/2.40 Assumptions after simplification: % 11.69/2.40 --------------------------------- % 11.69/2.40 % 11.69/2.40 (singleton) % 11.69/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | % 11.69/2.42 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 11.69/2.42 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~ % 11.69/2.42 $i(v1) | ~ $i(v0)) % 11.69/2.42 % 11.69/2.42 (successor) % 12.19/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.19/2.43 | ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) = % 12.19/2.43 v4) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 12.19/2.43 suc(v0) = v5 & member(v1, v5) = v6 & $i(v5))) & ! [v0: $i] : ! [v1: $i] % 12.19/2.43 : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (suc(v0) = v2) | ~ (member(v1, % 12.19/2.43 v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: % 12.19/2.43 int] : ( ~ (v6 = 0) & singleton(v0) = v4 & union(v0, v4) = v5 & member(v1, % 12.19/2.43 v5) = v6 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.19/2.43 ! [v3: $i] : ( ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ % 12.19/2.43 (member(v1, v3) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (suc(v0) = v4 & % 12.19/2.43 member(v1, v4) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 12.19/2.43 ( ~ (suc(v0) = v2) | ~ (member(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 12.19/2.43 $i] : ? [v4: $i] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1, % 12.19/2.43 v4) = 0 & $i(v4) & $i(v3))) % 12.19/2.43 % 12.19/2.43 (thV12) % 12.19/2.43 $i(on) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & suc(v0) = % 12.19/2.43 v1 & member(v0, v1) = v2 & member(v0, on) = 0 & $i(v1) & $i(v0)) % 12.19/2.43 % 12.19/2.43 (union) % 12.19/2.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 12.19/2.44 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 12.19/2.44 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 12.19/2.44 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 12.19/2.44 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 12.19/2.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.19/2.44 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 12.19/2.44 % 12.19/2.44 Further assumptions not needed in the proof: % 12.19/2.44 -------------------------------------------- % 12.19/2.44 difference, empty_set, equal_set, initial_segment, intersection, least, % 12.19/2.44 ordinal_number, power_set, product, rel_member, set_member, strict_order, % 12.19/2.44 strict_well_order, subset, sum, unordered_pair % 12.19/2.44 % 12.19/2.44 Those formulas are unsatisfiable: % 12.19/2.44 --------------------------------- % 12.19/2.44 % 12.19/2.44 Begin of proof % 12.19/2.44 | % 12.19/2.44 | ALPHA: (union) implies: % 12.19/2.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 12.19/2.44 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 12.19/2.44 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 12.19/2.44 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 12.19/2.44 | v5)) % 12.19/2.44 | % 12.19/2.44 | ALPHA: (singleton) implies: % 12.19/2.45 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) % 12.19/2.45 | = v1) | ~ (member(v0, v1) = v2) | ~ $i(v0)) % 12.19/2.45 | % 12.19/2.45 | ALPHA: (successor) implies: % 12.19/2.45 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 12.19/2.45 | (suc(v0) = v2) | ~ (member(v1, v2) = v3) | ~ $i(v1) | ~ $i(v0) | % 12.19/2.45 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & % 12.19/2.45 | singleton(v0) = v4 & union(v0, v4) = v5 & member(v1, v5) = v6 & % 12.19/2.45 | $i(v5) & $i(v4))) % 12.19/2.45 | % 12.19/2.45 | ALPHA: (thV12) implies: % 12.19/2.45 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & suc(v0) = v1 % 12.19/2.45 | & member(v0, v1) = v2 & member(v0, on) = 0 & $i(v1) & $i(v0)) % 12.19/2.45 | % 12.19/2.45 | DELTA: instantiating (4) with fresh symbols all_23_0, all_23_1, all_23_2 % 12.19/2.45 | gives: % 12.19/2.45 | (5) ~ (all_23_0 = 0) & suc(all_23_2) = all_23_1 & member(all_23_2, % 12.19/2.45 | all_23_1) = all_23_0 & member(all_23_2, on) = 0 & $i(all_23_1) & % 12.19/2.45 | $i(all_23_2) % 12.19/2.45 | % 12.19/2.45 | ALPHA: (5) implies: % 12.19/2.45 | (6) ~ (all_23_0 = 0) % 12.19/2.45 | (7) $i(all_23_2) % 12.19/2.45 | (8) member(all_23_2, all_23_1) = all_23_0 % 12.19/2.45 | (9) suc(all_23_2) = all_23_1 % 12.19/2.45 | % 12.19/2.45 | GROUND_INST: instantiating (3) with all_23_2, all_23_2, all_23_1, all_23_0, % 12.19/2.45 | simplifying with (7), (8), (9) gives: % 12.19/2.46 | (10) all_23_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) % 12.19/2.46 | & singleton(all_23_2) = v0 & union(all_23_2, v0) = v1 & % 12.19/2.46 | member(all_23_2, v1) = v2 & $i(v1) & $i(v0)) % 12.19/2.46 | % 12.19/2.46 | BETA: splitting (10) gives: % 12.19/2.46 | % 12.19/2.46 | Case 1: % 12.19/2.46 | | % 12.19/2.46 | | (11) all_23_0 = 0 % 12.19/2.46 | | % 12.19/2.46 | | REDUCE: (6), (11) imply: % 12.19/2.46 | | (12) $false % 12.19/2.46 | | % 12.19/2.46 | | CLOSE: (12) is inconsistent. % 12.19/2.46 | | % 12.19/2.46 | Case 2: % 12.19/2.46 | | % 12.19/2.46 | | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & % 12.19/2.46 | | singleton(all_23_2) = v0 & union(all_23_2, v0) = v1 & % 12.19/2.46 | | member(all_23_2, v1) = v2 & $i(v1) & $i(v0)) % 12.19/2.46 | | % 12.19/2.46 | | DELTA: instantiating (13) with fresh symbols all_40_0, all_40_1, all_40_2 % 12.19/2.46 | | gives: % 12.19/2.46 | | (14) ~ (all_40_0 = 0) & singleton(all_23_2) = all_40_2 & union(all_23_2, % 12.19/2.46 | | all_40_2) = all_40_1 & member(all_23_2, all_40_1) = all_40_0 & % 12.19/2.46 | | $i(all_40_1) & $i(all_40_2) % 12.19/2.46 | | % 12.19/2.46 | | ALPHA: (14) implies: % 12.19/2.46 | | (15) ~ (all_40_0 = 0) % 12.19/2.46 | | (16) $i(all_40_2) % 12.19/2.46 | | (17) member(all_23_2, all_40_1) = all_40_0 % 12.19/2.46 | | (18) union(all_23_2, all_40_2) = all_40_1 % 12.19/2.46 | | (19) singleton(all_23_2) = all_40_2 % 12.19/2.46 | | % 12.19/2.46 | | GROUND_INST: instantiating (1) with all_23_2, all_23_2, all_40_2, all_40_1, % 12.19/2.46 | | all_40_0, simplifying with (7), (16), (17), (18) gives: % 12.19/2.46 | | (20) all_40_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 12.19/2.46 | | 0) & member(all_23_2, all_40_2) = v1 & member(all_23_2, % 12.19/2.46 | | all_23_2) = v0) % 12.19/2.46 | | % 12.19/2.46 | | BETA: splitting (20) gives: % 12.19/2.46 | | % 12.19/2.46 | | Case 1: % 12.19/2.46 | | | % 12.19/2.46 | | | (21) all_40_0 = 0 % 12.19/2.46 | | | % 12.19/2.46 | | | REDUCE: (15), (21) imply: % 12.19/2.46 | | | (22) $false % 12.19/2.46 | | | % 12.19/2.46 | | | CLOSE: (22) is inconsistent. % 12.19/2.46 | | | % 12.19/2.46 | | Case 2: % 12.19/2.46 | | | % 12.19/2.46 | | | (23) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 12.19/2.46 | | | member(all_23_2, all_40_2) = v1 & member(all_23_2, all_23_2) = % 12.19/2.46 | | | v0) % 12.19/2.46 | | | % 12.19/2.46 | | | DELTA: instantiating (23) with fresh symbols all_65_0, all_65_1 gives: % 12.19/2.46 | | | (24) ~ (all_65_0 = 0) & ~ (all_65_1 = 0) & member(all_23_2, all_40_2) % 12.19/2.46 | | | = all_65_0 & member(all_23_2, all_23_2) = all_65_1 % 12.19/2.46 | | | % 12.19/2.46 | | | ALPHA: (24) implies: % 12.19/2.47 | | | (25) ~ (all_65_0 = 0) % 12.19/2.47 | | | (26) member(all_23_2, all_40_2) = all_65_0 % 12.19/2.47 | | | % 12.19/2.47 | | | GROUND_INST: instantiating (2) with all_23_2, all_40_2, all_65_0, % 12.19/2.47 | | | simplifying with (7), (19), (26) gives: % 12.19/2.47 | | | (27) all_65_0 = 0 % 12.19/2.47 | | | % 12.19/2.47 | | | REDUCE: (25), (27) imply: % 12.19/2.47 | | | (28) $false % 12.19/2.47 | | | % 12.19/2.47 | | | CLOSE: (28) is inconsistent. % 12.19/2.47 | | | % 12.19/2.47 | | End of split % 12.19/2.47 | | % 12.19/2.47 | End of split % 12.19/2.47 | % 12.19/2.47 End of proof % 12.19/2.47 % SZS output end Proof for theBenchmark % 12.19/2.47 % 12.19/2.47 1858ms %------------------------------------------------------------------------------