%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU158+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 17:42:52 EDT 2023 % Result : Theorem 3.23s 1.20s % Output : Proof 4.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU158+1 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.17/0.34 % Computer : n028.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Wed Aug 23 15:59:04 EDT 2023 % 0.17/0.34 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.62 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 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.77/0.95 Prover 1: Preprocessing ... % 1.77/0.95 Prover 4: Preprocessing ... % 2.19/1.00 Prover 3: Preprocessing ... % 2.19/1.00 Prover 5: Preprocessing ... % 2.19/1.00 Prover 2: Preprocessing ... % 2.19/1.00 Prover 6: Preprocessing ... % 2.19/1.00 Prover 0: Preprocessing ... % 2.89/1.08 Prover 1: Warning: ignoring some quantifiers % 2.89/1.08 Prover 3: Warning: ignoring some quantifiers % 2.89/1.09 Prover 2: Proving ... % 2.89/1.09 Prover 6: Proving ... % 2.89/1.09 Prover 5: Proving ... % 2.89/1.10 Prover 3: Constructing countermodel ... % 2.89/1.10 Prover 4: Constructing countermodel ... % 2.89/1.10 Prover 1: Constructing countermodel ... % 3.12/1.13 Prover 0: Proving ... % 3.23/1.20 Prover 0: proved (566ms) % 3.23/1.20 % 3.23/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.23/1.20 % 3.23/1.20 Prover 2: proved (565ms) % 3.23/1.20 % 3.23/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.23/1.20 % 3.23/1.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.23/1.20 Prover 5: stopped % 3.23/1.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.23/1.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.23/1.20 Prover 6: stopped % 3.23/1.21 Prover 7: Preprocessing ... % 3.23/1.21 Prover 8: Preprocessing ... % 3.79/1.21 Prover 10: Preprocessing ... % 3.79/1.21 Prover 3: stopped % 3.79/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.79/1.23 Prover 7: Warning: ignoring some quantifiers % 3.79/1.23 Prover 10: Warning: ignoring some quantifiers % 3.79/1.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.79/1.23 Prover 10: Constructing countermodel ... % 3.79/1.23 Prover 11: Preprocessing ... % 3.79/1.24 Prover 7: Constructing countermodel ... % 3.79/1.25 Prover 1: Found proof (size 22) % 3.79/1.25 Prover 1: proved (623ms) % 3.79/1.25 Prover 7: stopped % 3.79/1.26 Prover 10: stopped % 3.79/1.26 Prover 13: Preprocessing ... % 3.79/1.26 Prover 8: Warning: ignoring some quantifiers % 3.79/1.26 Prover 4: stopped % 3.79/1.26 Prover 8: Constructing countermodel ... % 3.79/1.27 Prover 8: stopped % 4.25/1.28 Prover 13: Warning: ignoring some quantifiers % 4.25/1.28 Prover 11: Constructing countermodel ... % 4.25/1.28 Prover 13: Constructing countermodel ... % 4.25/1.29 Prover 11: stopped % 4.25/1.29 Prover 13: stopped % 4.25/1.29 % 4.25/1.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.25/1.29 % 4.25/1.29 % SZS output start Proof for theBenchmark % 4.25/1.30 Assumptions after simplification: % 4.25/1.30 --------------------------------- % 4.25/1.30 % 4.25/1.30 (l2_zfmisc_1) % 4.25/1.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.25/1.32 (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 4.25/1.32 [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : % 4.25/1.33 ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | ~ $i(v1) | % 4.25/1.33 ~ $i(v0) | in(v0, v1) = 0) % 4.25/1.33 % 4.25/1.33 (t37_zfmisc_1) % 4.25/1.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 4.25/1.33 (singleton(v0) = v2 & in(v0, v1) = v4 & subset(v2, v1) = v3 & $i(v2) & $i(v1) % 4.25/1.33 & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 4.25/1.33 % 4.25/1.33 (function-axioms) % 4.25/1.33 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.25/1.33 [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 4.25/1.33 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.25/1.33 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 4.25/1.33 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 4.25/1.33 (singleton(v2) = v0)) % 4.25/1.33 % 4.25/1.33 Further assumptions not needed in the proof: % 4.25/1.33 -------------------------------------------- % 4.25/1.33 antisymmetry_r2_hidden, dt_k1_tarski, reflexivity_r1_tarski % 4.25/1.33 % 4.25/1.33 Those formulas are unsatisfiable: % 4.25/1.33 --------------------------------- % 4.25/1.33 % 4.25/1.33 Begin of proof % 4.25/1.33 | % 4.25/1.33 | ALPHA: (l2_zfmisc_1) implies: % 4.25/1.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ % 4.25/1.33 | (subset(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | in(v0, v1) = 0) % 4.25/1.34 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.25/1.34 | (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ % 4.25/1.34 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 4.25/1.34 | % 4.25/1.34 | ALPHA: (function-axioms) implies: % 4.25/1.34 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.25/1.34 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.25/1.34 | % 4.25/1.34 | DELTA: instantiating (t37_zfmisc_1) with fresh symbols all_7_0, all_7_1, % 4.25/1.34 | all_7_2, all_7_3, all_7_4 gives: % 4.25/1.34 | (4) singleton(all_7_4) = all_7_2 & in(all_7_4, all_7_3) = all_7_0 & % 4.25/1.34 | subset(all_7_2, all_7_3) = all_7_1 & $i(all_7_2) & $i(all_7_3) & % 4.25/1.34 | $i(all_7_4) & ((all_7_0 = 0 & ~ (all_7_1 = 0)) | (all_7_1 = 0 & ~ % 4.25/1.34 | (all_7_0 = 0))) % 4.25/1.34 | % 4.25/1.34 | ALPHA: (4) implies: % 4.25/1.34 | (5) $i(all_7_4) % 4.25/1.34 | (6) $i(all_7_3) % 4.25/1.34 | (7) subset(all_7_2, all_7_3) = all_7_1 % 4.25/1.34 | (8) in(all_7_4, all_7_3) = all_7_0 % 4.25/1.34 | (9) singleton(all_7_4) = all_7_2 % 4.25/1.34 | (10) (all_7_0 = 0 & ~ (all_7_1 = 0)) | (all_7_1 = 0 & ~ (all_7_0 = 0)) % 4.25/1.34 | % 4.25/1.34 | GROUND_INST: instantiating (2) with all_7_4, all_7_3, all_7_2, all_7_1, % 4.25/1.34 | simplifying with (5), (6), (7), (9) gives: % 4.25/1.34 | (11) all_7_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_7_4, all_7_3) = v0) % 4.25/1.34 | % 4.25/1.34 | BETA: splitting (10) gives: % 4.25/1.34 | % 4.25/1.35 | Case 1: % 4.25/1.35 | | % 4.25/1.35 | | (12) all_7_0 = 0 & ~ (all_7_1 = 0) % 4.25/1.35 | | % 4.25/1.35 | | ALPHA: (12) implies: % 4.25/1.35 | | (13) all_7_0 = 0 % 4.25/1.35 | | (14) ~ (all_7_1 = 0) % 4.25/1.35 | | % 4.25/1.35 | | REDUCE: (8), (13) imply: % 4.25/1.35 | | (15) in(all_7_4, all_7_3) = 0 % 4.25/1.35 | | % 4.25/1.35 | | BETA: splitting (11) gives: % 4.25/1.35 | | % 4.25/1.35 | | Case 1: % 4.25/1.35 | | | % 4.25/1.35 | | | (16) all_7_1 = 0 % 4.25/1.35 | | | % 4.25/1.35 | | | REDUCE: (14), (16) imply: % 4.25/1.35 | | | (17) $false % 4.25/1.35 | | | % 4.25/1.35 | | | CLOSE: (17) is inconsistent. % 4.25/1.35 | | | % 4.25/1.35 | | Case 2: % 4.25/1.35 | | | % 4.25/1.35 | | | (18) ? [v0: int] : ( ~ (v0 = 0) & in(all_7_4, all_7_3) = v0) % 4.25/1.35 | | | % 4.25/1.35 | | | DELTA: instantiating (18) with fresh symbol all_20_0 gives: % 4.25/1.35 | | | (19) ~ (all_20_0 = 0) & in(all_7_4, all_7_3) = all_20_0 % 4.25/1.35 | | | % 4.25/1.35 | | | ALPHA: (19) implies: % 4.25/1.35 | | | (20) ~ (all_20_0 = 0) % 4.25/1.35 | | | (21) in(all_7_4, all_7_3) = all_20_0 % 4.25/1.35 | | | % 4.25/1.35 | | | GROUND_INST: instantiating (3) with 0, all_20_0, all_7_3, all_7_4, % 4.25/1.35 | | | simplifying with (15), (21) gives: % 4.25/1.35 | | | (22) all_20_0 = 0 % 4.25/1.35 | | | % 4.25/1.35 | | | REDUCE: (20), (22) imply: % 4.25/1.35 | | | (23) $false % 4.25/1.35 | | | % 4.25/1.35 | | | CLOSE: (23) is inconsistent. % 4.25/1.35 | | | % 4.25/1.35 | | End of split % 4.25/1.35 | | % 4.25/1.35 | Case 2: % 4.25/1.35 | | % 4.25/1.35 | | (24) all_7_1 = 0 & ~ (all_7_0 = 0) % 4.25/1.35 | | % 4.25/1.35 | | ALPHA: (24) implies: % 4.25/1.35 | | (25) all_7_1 = 0 % 4.25/1.35 | | (26) ~ (all_7_0 = 0) % 4.25/1.35 | | % 4.25/1.35 | | REDUCE: (7), (25) imply: % 4.25/1.35 | | (27) subset(all_7_2, all_7_3) = 0 % 4.25/1.35 | | % 4.25/1.35 | | GROUND_INST: instantiating (1) with all_7_4, all_7_3, all_7_2, simplifying % 4.25/1.35 | | with (5), (6), (9), (27) gives: % 4.25/1.35 | | (28) in(all_7_4, all_7_3) = 0 % 4.25/1.35 | | % 4.25/1.35 | | GROUND_INST: instantiating (3) with all_7_0, 0, all_7_3, all_7_4, % 4.25/1.35 | | simplifying with (8), (28) gives: % 4.25/1.35 | | (29) all_7_0 = 0 % 4.25/1.35 | | % 4.25/1.35 | | REDUCE: (26), (29) imply: % 4.25/1.35 | | (30) $false % 4.25/1.35 | | % 4.25/1.35 | | CLOSE: (30) is inconsistent. % 4.25/1.35 | | % 4.25/1.35 | End of split % 4.25/1.35 | % 4.25/1.35 End of proof % 4.25/1.35 % SZS output end Proof for theBenchmark % 4.25/1.35 % 4.25/1.35 743ms %------------------------------------------------------------------------------