%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU160+3 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 17:42:54 EDT 2023 % Result : Theorem 3.92s 1.24s % Output : Proof 4.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SEU160+3 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n002.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Wed Aug 23 15:37:16 EDT 2023 % 0.14/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.94/0.96 Prover 4: Preprocessing ... % 1.94/0.96 Prover 1: Preprocessing ... % 1.94/1.00 Prover 6: Preprocessing ... % 1.94/1.00 Prover 3: Preprocessing ... % 1.94/1.00 Prover 5: Preprocessing ... % 1.94/1.00 Prover 2: Preprocessing ... % 2.34/1.01 Prover 0: Preprocessing ... % 2.77/1.10 Prover 1: Warning: ignoring some quantifiers % 2.77/1.10 Prover 3: Warning: ignoring some quantifiers % 2.77/1.11 Prover 1: Constructing countermodel ... % 2.77/1.11 Prover 3: Constructing countermodel ... % 2.77/1.11 Prover 4: Constructing countermodel ... % 2.77/1.12 Prover 6: Proving ... % 2.77/1.12 Prover 2: Proving ... % 2.77/1.12 Prover 5: Proving ... % 2.77/1.12 Prover 0: Proving ... % 3.62/1.23 Prover 3: proved (591ms) % 3.92/1.24 % 3.92/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.92/1.24 % 3.95/1.24 Prover 0: stopped % 3.95/1.24 Prover 2: stopped % 3.95/1.24 Prover 6: stopped % 3.95/1.25 Prover 5: stopped % 3.95/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.95/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.95/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.95/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.95/1.26 Prover 8: Preprocessing ... % 3.95/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.95/1.26 Prover 10: Preprocessing ... % 3.95/1.27 Prover 11: Preprocessing ... % 3.95/1.28 Prover 13: Preprocessing ... % 3.95/1.28 Prover 1: Found proof (size 25) % 3.95/1.28 Prover 1: proved (648ms) % 3.95/1.28 Prover 7: Preprocessing ... % 3.95/1.29 Prover 4: stopped % 3.95/1.29 Prover 8: Warning: ignoring some quantifiers % 3.95/1.30 Prover 10: Warning: ignoring some quantifiers % 3.95/1.30 Prover 10: Constructing countermodel ... % 3.95/1.30 Prover 8: Constructing countermodel ... % 3.95/1.30 Prover 10: stopped % 4.37/1.30 Prover 8: stopped % 4.37/1.31 Prover 11: Constructing countermodel ... % 4.37/1.31 Prover 13: Warning: ignoring some quantifiers % 4.37/1.32 Prover 13: Constructing countermodel ... % 4.37/1.32 Prover 11: stopped % 4.37/1.32 Prover 13: stopped % 4.37/1.32 Prover 7: Warning: ignoring some quantifiers % 4.37/1.32 Prover 7: Constructing countermodel ... % 4.37/1.33 Prover 7: stopped % 4.37/1.33 % 4.37/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.37/1.33 % 4.37/1.33 % SZS output start Proof for theBenchmark % 4.37/1.34 Assumptions after simplification: % 4.37/1.34 --------------------------------- % 4.37/1.34 % 4.37/1.34 (l4_zfmisc_1) % 4.69/1.37 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 4.69/1.37 0 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = v3) | ~ $i(v1) | ~ % 4.69/1.37 $i(v0) | ( ~ (v2 = v0) & ~ (v0 = empty_set))) & ! [v0: $i] : ! [v1: $i] : % 4.69/1.37 ! [v2: $i] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ % 4.69/1.37 (subset(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 4.69/1.37 % 4.69/1.37 (t39_zfmisc_1) % 4.69/1.37 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 4.69/1.37 (singleton(v1) = v2 & subset(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v3 = % 4.69/1.37 0 & ~ (v2 = v0) & ~ (v0 = empty_set)) | ( ~ (v3 = 0) & (v2 = v0 | v0 = % 4.69/1.37 empty_set)))) % 4.69/1.37 % 4.69/1.37 Further assumptions not needed in the proof: % 4.69/1.37 -------------------------------------------- % 4.69/1.37 fc1_xboole_0, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 4.69/1.37 % 4.69/1.37 Those formulas are unsatisfiable: % 4.69/1.37 --------------------------------- % 4.69/1.37 % 4.69/1.37 Begin of proof % 4.69/1.37 | % 4.69/1.37 | ALPHA: (l4_zfmisc_1) implies: % 4.69/1.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 = empty_set | % 4.69/1.38 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0) | ~ $i(v1) | ~ % 4.69/1.38 | $i(v0)) % 4.69/1.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.69/1.38 | (singleton(v1) = v2) | ~ (subset(v0, v2) = v3) | ~ $i(v1) | ~ % 4.69/1.38 | $i(v0) | ( ~ (v2 = v0) & ~ (v0 = empty_set))) % 4.69/1.38 | % 4.69/1.38 | ALPHA: (t39_zfmisc_1) implies: % 4.69/1.38 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (singleton(v1) % 4.69/1.38 | = v2 & subset(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v3 = 0 & ~ % 4.69/1.38 | (v2 = v0) & ~ (v0 = empty_set)) | ( ~ (v3 = 0) & (v2 = v0 | v0 = % 4.69/1.38 | empty_set)))) % 4.69/1.38 | % 4.69/1.38 | DELTA: instantiating (3) with fresh symbols all_11_0, all_11_1, all_11_2, % 4.69/1.38 | all_11_3 gives: % 4.69/1.38 | (4) singleton(all_11_2) = all_11_1 & subset(all_11_3, all_11_1) = all_11_0 % 4.69/1.38 | & $i(all_11_1) & $i(all_11_2) & $i(all_11_3) & ((all_11_0 = 0 & ~ % 4.69/1.38 | (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set)) | ( ~ (all_11_0 % 4.69/1.38 | = 0) & (all_11_1 = all_11_3 | all_11_3 = empty_set))) % 4.69/1.38 | % 4.69/1.38 | ALPHA: (4) implies: % 4.69/1.38 | (5) $i(all_11_3) % 4.69/1.38 | (6) $i(all_11_2) % 4.69/1.38 | (7) subset(all_11_3, all_11_1) = all_11_0 % 4.69/1.39 | (8) singleton(all_11_2) = all_11_1 % 4.69/1.39 | (9) (all_11_0 = 0 & ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set)) | % 4.69/1.39 | ( ~ (all_11_0 = 0) & (all_11_1 = all_11_3 | all_11_3 = empty_set)) % 4.69/1.39 | % 4.69/1.39 | GROUND_INST: instantiating (2) with all_11_3, all_11_2, all_11_1, all_11_0, % 4.69/1.39 | simplifying with (5), (6), (7), (8) gives: % 4.69/1.39 | (10) all_11_0 = 0 | ( ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set)) % 4.69/1.39 | % 4.69/1.39 | BETA: splitting (9) gives: % 4.69/1.39 | % 4.69/1.39 | Case 1: % 4.69/1.39 | | % 4.69/1.39 | | (11) all_11_0 = 0 & ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set) % 4.69/1.39 | | % 4.69/1.39 | | ALPHA: (11) implies: % 4.69/1.39 | | (12) all_11_0 = 0 % 4.69/1.39 | | (13) ~ (all_11_3 = empty_set) % 4.69/1.39 | | (14) ~ (all_11_1 = all_11_3) % 4.69/1.39 | | % 4.69/1.39 | | REDUCE: (7), (12) imply: % 4.69/1.39 | | (15) subset(all_11_3, all_11_1) = 0 % 4.69/1.39 | | % 4.69/1.39 | | GROUND_INST: instantiating (1) with all_11_3, all_11_2, all_11_1, % 4.69/1.39 | | simplifying with (5), (6), (8), (15) gives: % 4.69/1.39 | | (16) all_11_1 = all_11_3 | all_11_3 = empty_set % 4.69/1.39 | | % 4.69/1.39 | | REF_CLOSE: (13), (14), (16) are inconsistent by sub-proof #1. % 4.69/1.39 | | % 4.69/1.39 | Case 2: % 4.69/1.39 | | % 4.69/1.39 | | (17) ~ (all_11_0 = 0) & (all_11_1 = all_11_3 | all_11_3 = empty_set) % 4.69/1.39 | | % 4.69/1.39 | | ALPHA: (17) implies: % 4.69/1.39 | | (18) ~ (all_11_0 = 0) % 4.69/1.39 | | (19) all_11_1 = all_11_3 | all_11_3 = empty_set % 4.69/1.39 | | % 4.69/1.39 | | BETA: splitting (10) gives: % 4.69/1.39 | | % 4.69/1.39 | | Case 1: % 4.69/1.39 | | | % 4.69/1.39 | | | (20) all_11_0 = 0 % 4.69/1.39 | | | % 4.69/1.39 | | | REDUCE: (18), (20) imply: % 4.69/1.39 | | | (21) $false % 4.69/1.39 | | | % 4.69/1.39 | | | CLOSE: (21) is inconsistent. % 4.69/1.39 | | | % 4.69/1.39 | | Case 2: % 4.69/1.39 | | | % 4.69/1.39 | | | (22) ~ (all_11_1 = all_11_3) & ~ (all_11_3 = empty_set) % 4.69/1.39 | | | % 4.69/1.39 | | | ALPHA: (22) implies: % 4.69/1.40 | | | (23) ~ (all_11_3 = empty_set) % 4.69/1.40 | | | (24) ~ (all_11_1 = all_11_3) % 4.69/1.40 | | | % 4.69/1.40 | | | REF_CLOSE: (19), (23), (24) are inconsistent by sub-proof #1. % 4.69/1.40 | | | % 4.69/1.40 | | End of split % 4.69/1.40 | | % 4.69/1.40 | End of split % 4.69/1.40 | % 4.69/1.40 End of proof % 4.69/1.40 % 4.69/1.40 Sub-proof #1 shows that the following formulas are inconsistent: % 4.69/1.40 ---------------------------------------------------------------- % 4.69/1.40 (1) all_11_1 = all_11_3 | all_11_3 = empty_set % 4.69/1.40 (2) ~ (all_11_3 = empty_set) % 4.69/1.40 (3) ~ (all_11_1 = all_11_3) % 4.69/1.40 % 4.69/1.40 Begin of proof % 4.69/1.40 | % 4.69/1.40 | BETA: splitting (1) gives: % 4.69/1.40 | % 4.69/1.40 | Case 1: % 4.69/1.40 | | % 4.69/1.40 | | (4) all_11_3 = empty_set % 4.69/1.40 | | % 4.69/1.40 | | REDUCE: (2), (4) imply: % 4.69/1.40 | | (5) $false % 4.69/1.40 | | % 4.69/1.40 | | CLOSE: (5) is inconsistent. % 4.69/1.40 | | % 4.69/1.40 | Case 2: % 4.69/1.40 | | % 4.69/1.40 | | (6) all_11_1 = all_11_3 % 4.69/1.40 | | % 4.69/1.40 | | REDUCE: (3), (6) imply: % 4.69/1.40 | | (7) $false % 4.69/1.40 | | % 4.69/1.40 | | CLOSE: (7) is inconsistent. % 4.69/1.40 | | % 4.69/1.40 | End of split % 4.69/1.40 | % 4.69/1.40 End of proof % 4.69/1.40 % SZS output end Proof for theBenchmark % 4.69/1.40 % 4.69/1.40 781ms %------------------------------------------------------------------------------