%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET933+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 : n026.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 15:27:06 EDT 2023 % Result : Theorem 5.13s 1.64s % Output : Proof 5.86s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SET933+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n026.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Sat Aug 26 08:43:33 EDT 2023 % 0.15/0.36 % CPUTime : % 0.21/0.68 ________ _____ % 0.21/0.68 ___ __ \_________(_)________________________________ % 0.21/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.68 % 0.21/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.68 (2023-06-19) % 0.21/0.68 % 0.21/0.68 (c) Philipp Rümmer, 2009-2023 % 0.21/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.68 Amanda Stjerna. % 0.21/0.68 Free software under BSD-3-Clause. % 0.21/0.68 % 0.21/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.68 % 0.21/0.68 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.70 Running up to 7 provers in parallel. % 0.21/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.98/1.08 Prover 1: Preprocessing ... % 1.98/1.08 Prover 4: Preprocessing ... % 1.98/1.13 Prover 5: Preprocessing ... % 1.98/1.13 Prover 3: Preprocessing ... % 1.98/1.13 Prover 6: Preprocessing ... % 1.98/1.13 Prover 0: Preprocessing ... % 1.98/1.13 Prover 2: Preprocessing ... % 3.27/1.38 Prover 3: Warning: ignoring some quantifiers % 3.27/1.39 Prover 1: Warning: ignoring some quantifiers % 3.27/1.40 Prover 1: Constructing countermodel ... % 3.27/1.41 Prover 6: Proving ... % 3.27/1.41 Prover 5: Proving ... % 3.27/1.41 Prover 2: Proving ... % 3.27/1.42 Prover 3: Constructing countermodel ... % 3.27/1.43 Prover 4: Warning: ignoring some quantifiers % 3.27/1.44 Prover 4: Constructing countermodel ... % 3.27/1.45 Prover 0: Proving ... % 5.13/1.64 Prover 0: proved (936ms) % 5.13/1.64 % 5.13/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.13/1.64 % 5.13/1.66 Prover 5: stopped % 5.13/1.66 Prover 6: stopped % 5.13/1.66 Prover 2: stopped % 5.13/1.66 Prover 3: stopped % 5.13/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.13/1.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.13/1.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 5.13/1.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 5.13/1.68 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 5.13/1.70 Prover 8: Preprocessing ... % 5.13/1.71 Prover 7: Preprocessing ... % 5.13/1.71 Prover 10: Preprocessing ... % 5.13/1.71 Prover 13: Preprocessing ... % 5.51/1.72 Prover 11: Preprocessing ... % 5.51/1.73 Prover 4: Found proof (size 21) % 5.51/1.73 Prover 4: proved (1019ms) % 5.51/1.73 Prover 7: Warning: ignoring some quantifiers % 5.51/1.73 Prover 13: stopped % 5.51/1.74 Prover 7: Constructing countermodel ... % 5.51/1.74 Prover 7: stopped % 5.51/1.74 Prover 1: stopped % 5.51/1.75 Prover 8: Warning: ignoring some quantifiers % 5.51/1.75 Prover 10: Warning: ignoring some quantifiers % 5.51/1.75 Prover 10: Constructing countermodel ... % 5.51/1.76 Prover 8: Constructing countermodel ... % 5.51/1.76 Prover 10: stopped % 5.51/1.76 Prover 11: stopped % 5.51/1.76 Prover 8: stopped % 5.51/1.76 % 5.51/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.51/1.76 % 5.51/1.77 % SZS output start Proof for theBenchmark % 5.51/1.77 Assumptions after simplification: % 5.51/1.77 --------------------------------- % 5.51/1.77 % 5.51/1.77 (d1_zfmisc_1) % 5.86/1.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 5.86/1.82 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 5.86/1.82 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : ! % 5.86/1.82 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ % 5.86/1.82 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 5.86/1.82 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 5.86/1.82 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 5.86/1.82 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 5.86/1.82 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 5.86/1.82 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 % 5.86/1.82 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 5.86/1.82 [v4: any] : ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) & % 5.86/1.82 ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 5.86/1.82 % 5.86/1.82 (l2_zfmisc_1) % 5.86/1.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 5.86/1.82 (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 5.86/1.82 [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : % 5.86/1.82 ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 5.86/1.82 $i] : ? [v4: int] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = % 5.86/1.82 v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 5.86/1.82 (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 5.86/1.82 in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ % 5.86/1.82 $i(v1) | ~ $i(v0) | ? [v2: $i] : (singleton(v0) = v2 & subset(v2, v1) = 0 % 5.86/1.82 & $i(v2))) % 5.86/1.82 % 5.86/1.83 (reflexivity_r1_tarski) % 5.86/1.83 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0)) % 5.86/1.83 % 5.86/1.83 (t80_zfmisc_1) % 5.86/1.83 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 5.86/1.83 singleton(v0) = v1 & powerset(v0) = v2 & subset(v1, v2) = v3 & $i(v2) & % 5.86/1.83 $i(v1) & $i(v0)) % 5.86/1.83 % 5.86/1.83 Further assumptions not needed in the proof: % 5.86/1.83 -------------------------------------------- % 5.86/1.83 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0 % 5.86/1.83 % 5.86/1.83 Those formulas are unsatisfiable: % 5.86/1.83 --------------------------------- % 5.86/1.83 % 5.86/1.83 Begin of proof % 5.86/1.83 | % 5.86/1.83 | ALPHA: (d1_zfmisc_1) implies: % 5.86/1.83 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 5.86/1.83 | (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 5.86/1.83 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 5.86/1.83 | % 5.86/1.83 | ALPHA: (l2_zfmisc_1) implies: % 5.86/1.84 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 5.86/1.84 | (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ % 5.86/1.84 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 5.86/1.84 | % 5.86/1.84 | DELTA: instantiating (t80_zfmisc_1) with fresh symbols all_11_0, all_11_1, % 5.86/1.84 | all_11_2, all_11_3 gives: % 5.86/1.84 | (3) ~ (all_11_0 = 0) & singleton(all_11_3) = all_11_2 & powerset(all_11_3) % 5.86/1.84 | = all_11_1 & subset(all_11_2, all_11_1) = all_11_0 & $i(all_11_1) & % 5.86/1.84 | $i(all_11_2) & $i(all_11_3) % 5.86/1.84 | % 5.86/1.84 | ALPHA: (3) implies: % 5.86/1.84 | (4) ~ (all_11_0 = 0) % 5.86/1.84 | (5) $i(all_11_3) % 5.86/1.84 | (6) $i(all_11_1) % 5.86/1.84 | (7) subset(all_11_2, all_11_1) = all_11_0 % 5.86/1.84 | (8) powerset(all_11_3) = all_11_1 % 5.86/1.84 | (9) singleton(all_11_3) = all_11_2 % 5.86/1.84 | % 5.86/1.84 | GROUND_INST: instantiating (2) with all_11_3, all_11_1, all_11_2, all_11_0, % 5.86/1.84 | simplifying with (5), (6), (7), (9) gives: % 5.86/1.84 | (10) all_11_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_11_3, all_11_1) = % 5.86/1.84 | v0) % 5.86/1.84 | % 5.86/1.84 | BETA: splitting (10) gives: % 5.86/1.84 | % 5.86/1.84 | Case 1: % 5.86/1.84 | | % 5.86/1.84 | | (11) all_11_0 = 0 % 5.86/1.84 | | % 5.86/1.84 | | REDUCE: (4), (11) imply: % 5.86/1.84 | | (12) $false % 5.86/1.84 | | % 5.86/1.85 | | CLOSE: (12) is inconsistent. % 5.86/1.85 | | % 5.86/1.85 | Case 2: % 5.86/1.85 | | % 5.86/1.85 | | (13) ? [v0: int] : ( ~ (v0 = 0) & in(all_11_3, all_11_1) = v0) % 5.86/1.85 | | % 5.86/1.85 | | DELTA: instantiating (13) with fresh symbol all_26_0 gives: % 5.86/1.85 | | (14) ~ (all_26_0 = 0) & in(all_11_3, all_11_1) = all_26_0 % 5.86/1.85 | | % 5.86/1.85 | | ALPHA: (14) implies: % 5.86/1.85 | | (15) ~ (all_26_0 = 0) % 5.86/1.85 | | (16) in(all_11_3, all_11_1) = all_26_0 % 5.86/1.85 | | % 5.86/1.85 | | GROUND_INST: instantiating (1) with all_11_3, all_11_1, all_11_3, all_26_0, % 5.86/1.85 | | simplifying with (5), (6), (8), (16) gives: % 5.86/1.85 | | (17) all_26_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_11_3, % 5.86/1.85 | | all_11_3) = v0) % 5.86/1.85 | | % 5.86/1.85 | | BETA: splitting (17) gives: % 5.86/1.85 | | % 5.86/1.85 | | Case 1: % 5.86/1.85 | | | % 5.86/1.85 | | | (18) all_26_0 = 0 % 5.86/1.85 | | | % 5.86/1.85 | | | REDUCE: (15), (18) imply: % 5.86/1.85 | | | (19) $false % 5.86/1.85 | | | % 5.86/1.85 | | | CLOSE: (19) is inconsistent. % 5.86/1.85 | | | % 5.86/1.85 | | Case 2: % 5.86/1.85 | | | % 5.86/1.85 | | | (20) ? [v0: int] : ( ~ (v0 = 0) & subset(all_11_3, all_11_3) = v0) % 5.86/1.85 | | | % 5.86/1.85 | | | DELTA: instantiating (20) with fresh symbol all_41_0 gives: % 5.86/1.85 | | | (21) ~ (all_41_0 = 0) & subset(all_11_3, all_11_3) = all_41_0 % 5.86/1.85 | | | % 5.86/1.85 | | | ALPHA: (21) implies: % 5.86/1.85 | | | (22) ~ (all_41_0 = 0) % 5.86/1.85 | | | (23) subset(all_11_3, all_11_3) = all_41_0 % 5.86/1.85 | | | % 5.86/1.85 | | | GROUND_INST: instantiating (reflexivity_r1_tarski) with all_11_3, % 5.86/1.85 | | | all_41_0, simplifying with (5), (23) gives: % 5.86/1.85 | | | (24) all_41_0 = 0 % 5.86/1.85 | | | % 5.86/1.85 | | | REDUCE: (22), (24) imply: % 5.86/1.85 | | | (25) $false % 5.86/1.85 | | | % 5.86/1.85 | | | CLOSE: (25) is inconsistent. % 5.86/1.85 | | | % 5.86/1.85 | | End of split % 5.86/1.85 | | % 5.86/1.85 | End of split % 5.86/1.85 | % 5.86/1.85 End of proof % 5.86/1.85 % SZS output end Proof for theBenchmark % 5.86/1.85 % 5.86/1.85 1169ms %------------------------------------------------------------------------------