%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET878+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 : n032.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 15:26:53 EDT 2023 % Result : Theorem 3.92s 1.29s % Output : Proof 5.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET878+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.31 % Computer : n032.cluster.edu % 0.13/0.31 % Model : x86_64 x86_64 % 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.31 % Memory : 8042.1875MB % 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.31 % CPULimit : 300 % 0.13/0.31 % WCLimit : 300 % 0.13/0.31 % DateTime : Sat Aug 26 09:46:28 EDT 2023 % 0.13/0.31 % CPUTime : % 0.16/0.52 ________ _____ % 0.16/0.52 ___ __ \_________(_)________________________________ % 0.16/0.52 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.52 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.52 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.52 % 0.16/0.52 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.52 (2023-06-19) % 0.16/0.52 % 0.16/0.52 (c) Philipp Rümmer, 2009-2023 % 0.16/0.52 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.52 Amanda Stjerna. % 0.16/0.52 Free software under BSD-3-Clause. % 0.16/0.52 % 0.16/0.52 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.52 % 0.16/0.52 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.16/0.53 Running up to 7 provers in parallel. % 0.16/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.16/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.37/0.86 Prover 4: Preprocessing ... % 1.37/0.87 Prover 1: Preprocessing ... % 1.97/0.91 Prover 2: Preprocessing ... % 1.97/0.91 Prover 6: Preprocessing ... % 1.97/0.91 Prover 3: Preprocessing ... % 1.97/0.91 Prover 0: Preprocessing ... % 1.97/0.91 Prover 5: Preprocessing ... % 3.15/1.09 Prover 3: Warning: ignoring some quantifiers % 3.15/1.10 Prover 6: Proving ... % 3.19/1.10 Prover 5: Proving ... % 3.23/1.11 Prover 1: Warning: ignoring some quantifiers % 3.23/1.11 Prover 3: Constructing countermodel ... % 3.23/1.11 Prover 1: Constructing countermodel ... % 3.23/1.12 Prover 4: Warning: ignoring some quantifiers % 3.23/1.12 Prover 0: Proving ... % 3.23/1.13 Prover 4: Constructing countermodel ... % 3.23/1.14 Prover 2: Proving ... % 3.92/1.28 Prover 3: proved (741ms) % 3.92/1.28 % 3.92/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.92/1.29 % 3.92/1.29 Prover 0: proved (755ms) % 3.92/1.29 % 3.92/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.92/1.29 % 3.92/1.29 Prover 5: stopped % 3.92/1.29 Prover 6: stopped % 3.92/1.29 Prover 2: proved (755ms) % 3.92/1.29 % 3.92/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.92/1.29 % 4.59/1.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.59/1.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.59/1.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.59/1.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.59/1.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.59/1.32 Prover 13: Preprocessing ... % 4.59/1.32 Prover 10: Preprocessing ... % 4.59/1.33 Prover 7: Preprocessing ... % 4.59/1.33 Prover 8: Preprocessing ... % 4.59/1.34 Prover 11: Preprocessing ... % 4.59/1.35 Prover 1: Found proof (size 19) % 4.59/1.35 Prover 4: Found proof (size 20) % 4.59/1.35 Prover 1: proved (810ms) % 4.59/1.35 Prover 4: proved (805ms) % 4.59/1.35 Prover 11: stopped % 4.59/1.37 Prover 10: Warning: ignoring some quantifiers % 4.59/1.37 Prover 7: Warning: ignoring some quantifiers % 4.59/1.37 Prover 8: Warning: ignoring some quantifiers % 4.59/1.38 Prover 10: Constructing countermodel ... % 4.59/1.38 Prover 13: Warning: ignoring some quantifiers % 4.59/1.38 Prover 7: Constructing countermodel ... % 4.59/1.38 Prover 10: stopped % 4.59/1.38 Prover 8: Constructing countermodel ... % 4.59/1.38 Prover 7: stopped % 4.59/1.38 Prover 13: Constructing countermodel ... % 4.59/1.39 Prover 8: stopped % 4.59/1.39 Prover 13: stopped % 4.59/1.39 % 4.59/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.59/1.39 % 5.22/1.39 % SZS output start Proof for theBenchmark % 5.22/1.39 Assumptions after simplification: % 5.22/1.39 --------------------------------- % 5.22/1.39 % 5.22/1.39 (commutativity_k2_tarski) % 5.22/1.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 5.22/1.42 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 5.22/1.42 % 5.22/1.42 (commutativity_k3_xboole_0) % 5.22/1.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 5.22/1.43 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 5.22/1.43 % 5.22/1.43 (d2_tarski) % 5.22/1.43 ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ % 5.22/1.43 (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 5.22/1.43 $i] : ? [v5: any] : (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = % 5.22/1.43 v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0: $i] % 5.22/1.43 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | % 5.22/1.43 ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, % 5.22/1.43 v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1) & ~ (v3 = v0))) & ! [v3: $i] % 5.22/1.43 : (v3 = v1 | v3 = v0 | ~ (in(v3, v2) = 0) | ~ $i(v3)))) % 5.22/1.43 % 5.22/1.43 (l32_zfmisc_1) % 5.22/1.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 5.22/1.44 (singleton(v0) = v2) | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v1) | ~ % 5.22/1.44 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 5.22/1.44 % 5.22/1.44 (t19_zfmisc_1) % 5.22/1.44 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4 % 5.22/1.44 = v2) & singleton(v0) = v2 & set_intersection2(v2, v3) = v4 & % 5.22/1.44 unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.22/1.44 % 5.22/1.44 Further assumptions not needed in the proof: % 5.22/1.44 -------------------------------------------- % 5.22/1.44 antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0 % 5.22/1.44 % 5.22/1.44 Those formulas are unsatisfiable: % 5.22/1.44 --------------------------------- % 5.22/1.44 % 5.22/1.44 Begin of proof % 5.22/1.44 | % 5.22/1.44 | ALPHA: (d2_tarski) implies: % 5.22/1.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 5.22/1.44 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: % 5.22/1.44 | int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ( ~ (v3 = v1) % 5.22/1.44 | & ~ (v3 = v0))) & ! [v3: $i] : (v3 = v1 | v3 = v0 | ~ % 5.22/1.44 | (in(v3, v2) = 0) | ~ $i(v3)))) % 5.22/1.44 | % 5.22/1.44 | DELTA: instantiating (t19_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 5.22/1.44 | all_14_2, all_14_3, all_14_4 gives: % 5.22/1.45 | (2) ~ (all_14_0 = all_14_2) & singleton(all_14_4) = all_14_2 & % 5.22/1.45 | set_intersection2(all_14_2, all_14_1) = all_14_0 & % 5.22/1.45 | unordered_pair(all_14_4, all_14_3) = all_14_1 & $i(all_14_0) & % 5.22/1.45 | $i(all_14_1) & $i(all_14_2) & $i(all_14_3) & $i(all_14_4) % 5.22/1.45 | % 5.22/1.45 | ALPHA: (2) implies: % 5.22/1.45 | (3) ~ (all_14_0 = all_14_2) % 5.22/1.45 | (4) $i(all_14_4) % 5.22/1.45 | (5) $i(all_14_3) % 5.22/1.45 | (6) $i(all_14_2) % 5.22/1.45 | (7) unordered_pair(all_14_4, all_14_3) = all_14_1 % 5.22/1.45 | (8) set_intersection2(all_14_2, all_14_1) = all_14_0 % 5.22/1.45 | (9) singleton(all_14_4) = all_14_2 % 5.22/1.45 | % 5.22/1.45 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_14_4, all_14_3, % 5.22/1.45 | all_14_1, simplifying with (4), (5), (7) gives: % 5.22/1.45 | (10) unordered_pair(all_14_3, all_14_4) = all_14_1 & $i(all_14_1) % 5.22/1.45 | % 5.22/1.45 | ALPHA: (10) implies: % 5.22/1.45 | (11) $i(all_14_1) % 5.22/1.45 | (12) unordered_pair(all_14_3, all_14_4) = all_14_1 % 5.22/1.45 | % 5.22/1.45 | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_2, % 5.22/1.45 | all_14_1, all_14_0, simplifying with (6), (8), (11) gives: % 5.22/1.45 | (13) set_intersection2(all_14_1, all_14_2) = all_14_0 & $i(all_14_0) % 5.22/1.45 | % 5.22/1.45 | ALPHA: (13) implies: % 5.22/1.45 | (14) set_intersection2(all_14_1, all_14_2) = all_14_0 % 5.22/1.45 | % 5.22/1.45 | GROUND_INST: instantiating (1) with all_14_3, all_14_4, all_14_1, simplifying % 5.22/1.45 | with (4), (5), (11), (12) gives: % 5.22/1.46 | (15) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_14_1) = v1) | ~ % 5.22/1.46 | $i(v0) | ( ~ (v0 = all_14_3) & ~ (v0 = all_14_4))) & ! [v0: any] : % 5.22/1.46 | (v0 = all_14_3 | v0 = all_14_4 | ~ (in(v0, all_14_1) = 0) | ~ % 5.22/1.46 | $i(v0)) % 5.22/1.46 | % 5.22/1.46 | ALPHA: (15) implies: % 5.22/1.46 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_14_1) = v1) | ~ % 5.22/1.46 | $i(v0) | ( ~ (v0 = all_14_3) & ~ (v0 = all_14_4))) % 5.22/1.46 | % 5.22/1.46 | GROUND_INST: instantiating (l32_zfmisc_1) with all_14_4, all_14_1, all_14_2, % 5.22/1.46 | all_14_0, simplifying with (4), (9), (11), (14) gives: % 5.22/1.46 | (17) all_14_0 = all_14_2 | ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4, % 5.22/1.46 | all_14_1) = v0) % 5.22/1.46 | % 5.22/1.46 | BETA: splitting (17) gives: % 5.22/1.46 | % 5.22/1.46 | Case 1: % 5.22/1.46 | | % 5.22/1.46 | | (18) all_14_0 = all_14_2 % 5.22/1.46 | | % 5.22/1.46 | | REDUCE: (3), (18) imply: % 5.22/1.46 | | (19) $false % 5.22/1.46 | | % 5.22/1.46 | | CLOSE: (19) is inconsistent. % 5.22/1.46 | | % 5.22/1.46 | Case 2: % 5.22/1.46 | | % 5.22/1.46 | | (20) ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4, all_14_1) = v0) % 5.22/1.46 | | % 5.22/1.46 | | DELTA: instantiating (20) with fresh symbol all_39_0 gives: % 5.22/1.46 | | (21) ~ (all_39_0 = 0) & in(all_14_4, all_14_1) = all_39_0 % 5.22/1.46 | | % 5.22/1.46 | | ALPHA: (21) implies: % 5.22/1.46 | | (22) ~ (all_39_0 = 0) % 5.22/1.46 | | (23) in(all_14_4, all_14_1) = all_39_0 % 5.22/1.46 | | % 5.22/1.46 | | GROUND_INST: instantiating (16) with all_14_4, all_39_0, simplifying with % 5.22/1.46 | | (4), (23) gives: % 5.22/1.46 | | (24) all_39_0 = 0 % 5.22/1.46 | | % 5.22/1.46 | | REDUCE: (22), (24) imply: % 5.22/1.46 | | (25) $false % 5.22/1.46 | | % 5.22/1.46 | | CLOSE: (25) is inconsistent. % 5.22/1.46 | | % 5.22/1.47 | End of split % 5.22/1.47 | % 5.22/1.47 End of proof % 5.22/1.47 % SZS output end Proof for theBenchmark % 5.22/1.47 % 5.22/1.47 946ms %------------------------------------------------------------------------------