%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n020.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 15:26:54 EDT 2023 % Result : Theorem 4.31s 1.34s % Output : Proof 6.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET884+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n020.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 : Sat Aug 26 15:47:59 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.88/0.93 Prover 1: Preprocessing ... % 1.88/0.93 Prover 4: Preprocessing ... % 2.18/0.97 Prover 5: Preprocessing ... % 2.18/0.97 Prover 6: Preprocessing ... % 2.18/0.97 Prover 2: Preprocessing ... % 2.18/0.97 Prover 0: Preprocessing ... % 2.18/0.97 Prover 3: Preprocessing ... % 3.69/1.16 Prover 1: Warning: ignoring some quantifiers % 3.69/1.16 Prover 3: Warning: ignoring some quantifiers % 3.69/1.17 Prover 4: Warning: ignoring some quantifiers % 3.69/1.18 Prover 6: Proving ... % 3.69/1.18 Prover 3: Constructing countermodel ... % 3.69/1.18 Prover 5: Proving ... % 3.69/1.19 Prover 1: Constructing countermodel ... % 3.69/1.19 Prover 4: Constructing countermodel ... % 3.99/1.20 Prover 0: Proving ... % 3.99/1.22 Prover 2: Proving ... % 4.31/1.34 Prover 5: proved (711ms) % 4.31/1.34 % 4.31/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.31/1.34 % 4.31/1.34 Prover 3: stopped % 4.31/1.34 Prover 6: stopped % 4.31/1.34 Prover 2: stopped % 4.31/1.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.31/1.36 Prover 0: stopped % 4.31/1.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.31/1.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.31/1.37 Prover 10: Preprocessing ... % 4.31/1.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.31/1.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.31/1.38 Prover 7: Preprocessing ... % 4.31/1.38 Prover 8: Preprocessing ... % 4.31/1.40 Prover 13: Preprocessing ... % 4.31/1.40 Prover 11: Preprocessing ... % 4.31/1.42 Prover 10: Warning: ignoring some quantifiers % 5.17/1.43 Prover 8: Warning: ignoring some quantifiers % 5.17/1.43 Prover 7: Warning: ignoring some quantifiers % 5.17/1.43 Prover 10: Constructing countermodel ... % 5.17/1.44 Prover 8: Constructing countermodel ... % 5.17/1.44 Prover 7: Constructing countermodel ... % 5.17/1.46 Prover 13: Warning: ignoring some quantifiers % 5.17/1.47 Prover 13: Constructing countermodel ... % 5.17/1.47 Prover 1: gave up % 5.17/1.48 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 5.17/1.49 Prover 11: Warning: ignoring some quantifiers % 6.02/1.49 Prover 16: Preprocessing ... % 6.02/1.51 Prover 11: Constructing countermodel ... % 6.02/1.52 Prover 10: Found proof (size 16) % 6.02/1.52 Prover 10: proved (160ms) % 6.02/1.52 Prover 8: stopped % 6.02/1.52 Prover 4: stopped % 6.02/1.52 Prover 7: stopped % 6.02/1.52 Prover 13: stopped % 6.02/1.52 Prover 11: stopped % 6.02/1.52 Prover 16: stopped % 6.02/1.52 % 6.02/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 6.02/1.52 % 6.02/1.53 % SZS output start Proof for theBenchmark % 6.02/1.53 Assumptions after simplification: % 6.02/1.53 --------------------------------- % 6.02/1.53 % 6.02/1.53 (commutativity_k2_tarski) % 6.02/1.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 6.02/1.55 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 6.02/1.55 % 6.02/1.55 (d1_tarski) % 6.02/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 6.02/1.56 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1: % 6.02/1.56 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ % 6.02/1.56 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | % 6.02/1.56 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | % 6.02/1.56 ~ $i(v1) | ~ $i(v0) | in(v0, v1)) % 6.02/1.56 % 6.02/1.56 (d2_tarski) % 6.02/1.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 6.02/1.56 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 6.02/1.56 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 6.02/1.56 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 6.02/1.56 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ % 6.02/1.56 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1: % 6.02/1.56 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ % 6.02/1.56 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 6.02/1.56 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, % 6.02/1.56 v2)) % 6.02/1.56 % 6.02/1.56 (d3_tarski) % 6.02/1.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 6.02/1.57 ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0: $i] : ? [v1: $i] % 6.02/1.57 : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) & in(v2, v0) % 6.02/1.57 & ~ in(v2, v1))) % 6.02/1.57 % 6.02/1.57 (t25_zfmisc_1) % 6.02/1.57 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v2 % 6.02/1.57 = v0) & ~ (v1 = v0) & singleton(v0) = v3 & unordered_pair(v1, v2) = v4 & % 6.02/1.57 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & subset(v3, v4)) % 6.02/1.57 % 6.02/1.57 Further assumptions not needed in the proof: % 6.02/1.57 -------------------------------------------- % 6.02/1.57 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 6.02/1.57 % 6.02/1.57 Those formulas are unsatisfiable: % 6.02/1.57 --------------------------------- % 6.02/1.57 % 6.02/1.57 Begin of proof % 6.02/1.57 | % 6.02/1.57 | ALPHA: (d1_tarski) implies: % 6.02/1.57 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v1) | ~ % 6.02/1.57 | $i(v0) | in(v0, v1)) % 6.02/1.57 | % 6.02/1.57 | ALPHA: (d2_tarski) implies: % 6.02/1.57 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = % 6.02/1.57 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 6.02/1.57 | $i(v1) | ~ $i(v0) | ~ in(v3, v2)) % 6.02/1.57 | % 6.02/1.57 | ALPHA: (d3_tarski) implies: % 6.02/1.57 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 6.02/1.57 | $i(v0) | ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) % 6.02/1.58 | % 6.02/1.58 | DELTA: instantiating (t25_zfmisc_1) with fresh symbols all_16_0, all_16_1, % 6.02/1.58 | all_16_2, all_16_3, all_16_4 gives: % 6.02/1.58 | (4) ~ (all_16_2 = all_16_4) & ~ (all_16_3 = all_16_4) & % 6.02/1.58 | singleton(all_16_4) = all_16_1 & unordered_pair(all_16_3, all_16_2) = % 6.02/1.58 | all_16_0 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & $i(all_16_3) & % 6.02/1.58 | $i(all_16_4) & subset(all_16_1, all_16_0) % 6.02/1.58 | % 6.02/1.58 | ALPHA: (4) implies: % 6.02/1.58 | (5) ~ (all_16_3 = all_16_4) % 6.02/1.58 | (6) ~ (all_16_2 = all_16_4) % 6.02/1.58 | (7) subset(all_16_1, all_16_0) % 6.02/1.58 | (8) $i(all_16_4) % 6.02/1.58 | (9) $i(all_16_3) % 6.02/1.58 | (10) $i(all_16_2) % 6.02/1.58 | (11) $i(all_16_1) % 6.02/1.58 | (12) unordered_pair(all_16_3, all_16_2) = all_16_0 % 6.02/1.58 | (13) singleton(all_16_4) = all_16_1 % 6.02/1.58 | % 6.02/1.58 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_16_3, all_16_2, % 6.02/1.58 | all_16_0, simplifying with (9), (10), (12) gives: % 6.02/1.58 | (14) unordered_pair(all_16_2, all_16_3) = all_16_0 & $i(all_16_0) % 6.02/1.58 | % 6.02/1.58 | ALPHA: (14) implies: % 6.02/1.58 | (15) $i(all_16_0) % 6.02/1.58 | % 6.02/1.58 | GROUND_INST: instantiating (1) with all_16_4, all_16_1, simplifying with (8), % 6.02/1.58 | (11), (13) gives: % 6.02/1.58 | (16) in(all_16_4, all_16_1) % 6.02/1.58 | % 6.02/1.58 | GROUND_INST: instantiating (3) with all_16_1, all_16_0, all_16_4, simplifying % 6.02/1.58 | with (7), (8), (11), (15), (16) gives: % 6.02/1.58 | (17) in(all_16_4, all_16_0) % 6.02/1.58 | % 6.58/1.59 | GROUND_INST: instantiating (2) with all_16_3, all_16_2, all_16_0, all_16_4, % 6.58/1.59 | simplifying with (8), (9), (10), (12), (15), (17) gives: % 6.58/1.59 | (18) all_16_2 = all_16_4 | all_16_3 = all_16_4 % 6.58/1.59 | % 6.58/1.59 | BETA: splitting (18) gives: % 6.58/1.59 | % 6.58/1.59 | Case 1: % 6.58/1.59 | | % 6.58/1.59 | | (19) all_16_2 = all_16_4 % 6.58/1.59 | | % 6.58/1.59 | | REDUCE: (6), (19) imply: % 6.58/1.59 | | (20) $false % 6.58/1.59 | | % 6.58/1.59 | | CLOSE: (20) is inconsistent. % 6.58/1.59 | | % 6.58/1.59 | Case 2: % 6.58/1.59 | | % 6.58/1.59 | | (21) all_16_3 = all_16_4 % 6.58/1.59 | | % 6.58/1.59 | | REDUCE: (5), (21) imply: % 6.58/1.59 | | (22) $false % 6.58/1.59 | | % 6.58/1.59 | | CLOSE: (22) is inconsistent. % 6.58/1.59 | | % 6.58/1.59 | End of split % 6.58/1.59 | % 6.58/1.59 End of proof % 6.58/1.59 % SZS output end Proof for theBenchmark % 6.58/1.59 % 6.58/1.59 978ms %------------------------------------------------------------------------------