%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET924+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 : n012.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 15:27:03 EDT 2023 % Result : Theorem 3.79s 1.27s % Output : Proof 4.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET924+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 12:45:40 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.83/0.96 Prover 1: Preprocessing ... % 1.83/0.96 Prover 4: Preprocessing ... % 1.83/1.01 Prover 2: Preprocessing ... % 1.83/1.01 Prover 6: Preprocessing ... % 1.83/1.01 Prover 3: Preprocessing ... % 1.83/1.01 Prover 5: Preprocessing ... % 1.83/1.01 Prover 0: Preprocessing ... % 2.70/1.13 Prover 1: Constructing countermodel ... % 2.70/1.13 Prover 4: Constructing countermodel ... % 2.70/1.13 Prover 3: Constructing countermodel ... % 2.70/1.14 Prover 6: Constructing countermodel ... % 2.70/1.14 Prover 5: Proving ... % 3.15/1.15 Prover 2: Proving ... % 3.23/1.17 Prover 0: Proving ... % 3.79/1.27 Prover 5: proved (641ms) % 3.79/1.27 % 3.79/1.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.79/1.27 % 3.79/1.28 Prover 3: stopped % 3.79/1.28 Prover 0: stopped % 3.79/1.28 Prover 2: stopped % 3.79/1.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.79/1.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.79/1.28 Prover 6: stopped % 3.79/1.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.79/1.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.79/1.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.79/1.30 Prover 10: Preprocessing ... % 3.79/1.31 Prover 13: Preprocessing ... % 3.79/1.31 Prover 8: Preprocessing ... % 3.79/1.31 Prover 11: Preprocessing ... % 3.79/1.31 Prover 7: Preprocessing ... % 3.79/1.33 Prover 10: Constructing countermodel ... % 4.40/1.34 Prover 7: Constructing countermodel ... % 4.40/1.35 Prover 8: Warning: ignoring some quantifiers % 4.40/1.35 Prover 1: Found proof (size 22) % 4.40/1.35 Prover 1: proved (732ms) % 4.40/1.35 Prover 10: stopped % 4.40/1.35 Prover 4: stopped % 4.40/1.35 Prover 7: stopped % 4.40/1.35 Prover 8: Constructing countermodel ... % 4.40/1.36 Prover 8: stopped % 4.40/1.37 Prover 11: Constructing countermodel ... % 4.40/1.37 Prover 11: stopped % 4.40/1.37 Prover 13: Warning: ignoring some quantifiers % 4.40/1.37 Prover 13: Constructing countermodel ... % 4.40/1.38 Prover 13: stopped % 4.40/1.38 % 4.40/1.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.40/1.38 % 4.40/1.38 % SZS output start Proof for theBenchmark % 4.40/1.39 Assumptions after simplification: % 4.40/1.39 --------------------------------- % 4.40/1.39 % 4.40/1.39 (l34_zfmisc_1) % 4.40/1.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 4.40/1.42 (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ $i(v1) | ~ % 4.40/1.42 $i(v0) | in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 4.40/1.42 (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v2) | ~ $i(v1) | ~ % 4.40/1.42 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 4.40/1.42 % 4.40/1.42 (t67_zfmisc_1) % 4.40/1.43 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : % 4.40/1.43 (singleton(v0) = v2 & set_difference(v2, v1) = v3 & in(v0, v1) = v4 & $i(v3) & % 4.40/1.43 $i(v2) & $i(v1) & $i(v0) & ((v4 = 0 & v3 = v2) | ( ~ (v4 = 0) & ~ (v3 = % 4.40/1.43 v2)))) % 4.40/1.43 % 4.40/1.43 (function-axioms) % 4.40/1.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 4.40/1.43 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 4.40/1.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 4.40/1.43 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! % 4.40/1.43 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ % 4.40/1.43 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 4.40/1.43 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 4.40/1.43 (empty(v2) = v0)) % 4.40/1.43 % 4.40/1.43 Further assumptions not needed in the proof: % 4.40/1.43 -------------------------------------------- % 4.40/1.43 antisymmetry_r2_hidden, rc1_xboole_0, rc2_xboole_0 % 4.40/1.43 % 4.40/1.43 Those formulas are unsatisfiable: % 4.40/1.43 --------------------------------- % 4.40/1.43 % 4.40/1.43 Begin of proof % 4.40/1.43 | % 4.40/1.43 | ALPHA: (l34_zfmisc_1) implies: % 4.40/1.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (singleton(v0) = v2) | ~ % 4.40/1.43 | (set_difference(v2, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] % 4.40/1.43 | : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 4.40/1.44 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 4.40/1.44 | (singleton(v0) = v2) | ~ (set_difference(v2, v1) = v3) | ~ $i(v1) | % 4.40/1.44 | ~ $i(v0) | in(v0, v1) = 0) % 4.40/1.44 | % 4.40/1.44 | ALPHA: (function-axioms) implies: % 4.40/1.44 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.40/1.44 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 4.40/1.44 | % 4.40/1.44 | DELTA: instantiating (t67_zfmisc_1) with fresh symbols all_9_0, all_9_1, % 4.40/1.44 | all_9_2, all_9_3, all_9_4 gives: % 4.40/1.44 | (4) singleton(all_9_4) = all_9_2 & set_difference(all_9_2, all_9_3) = % 4.40/1.44 | all_9_1 & in(all_9_4, all_9_3) = all_9_0 & $i(all_9_1) & $i(all_9_2) & % 4.40/1.44 | $i(all_9_3) & $i(all_9_4) & ((all_9_0 = 0 & all_9_1 = all_9_2) | ( ~ % 4.40/1.44 | (all_9_0 = 0) & ~ (all_9_1 = all_9_2))) % 4.40/1.44 | % 4.40/1.44 | ALPHA: (4) implies: % 4.40/1.44 | (5) $i(all_9_4) % 4.40/1.44 | (6) $i(all_9_3) % 4.40/1.44 | (7) in(all_9_4, all_9_3) = all_9_0 % 4.40/1.44 | (8) set_difference(all_9_2, all_9_3) = all_9_1 % 4.40/1.44 | (9) singleton(all_9_4) = all_9_2 % 4.40/1.44 | (10) (all_9_0 = 0 & all_9_1 = all_9_2) | ( ~ (all_9_0 = 0) & ~ (all_9_1 = % 4.40/1.44 | all_9_2)) % 4.40/1.44 | % 4.40/1.44 | GROUND_INST: instantiating (2) with all_9_4, all_9_3, all_9_2, all_9_1, % 4.40/1.44 | simplifying with (5), (6), (8), (9) gives: % 4.40/1.44 | (11) all_9_1 = all_9_2 | in(all_9_4, all_9_3) = 0 % 4.40/1.44 | % 4.40/1.44 | BETA: splitting (10) gives: % 4.40/1.44 | % 4.40/1.44 | Case 1: % 4.40/1.44 | | % 4.40/1.44 | | (12) all_9_0 = 0 & all_9_1 = all_9_2 % 4.40/1.44 | | % 4.40/1.44 | | ALPHA: (12) implies: % 4.40/1.44 | | (13) all_9_1 = all_9_2 % 4.40/1.45 | | (14) all_9_0 = 0 % 4.40/1.45 | | % 4.40/1.45 | | REDUCE: (8), (13) imply: % 4.40/1.45 | | (15) set_difference(all_9_2, all_9_3) = all_9_2 % 4.40/1.45 | | % 4.40/1.45 | | REDUCE: (7), (14) imply: % 4.40/1.45 | | (16) in(all_9_4, all_9_3) = 0 % 4.40/1.45 | | % 4.40/1.45 | | GROUND_INST: instantiating (1) with all_9_4, all_9_3, all_9_2, simplifying % 4.40/1.45 | | with (5), (6), (9), (15) gives: % 4.40/1.45 | | (17) ? [v0: int] : ( ~ (v0 = 0) & in(all_9_4, all_9_3) = v0) % 4.40/1.45 | | % 4.40/1.45 | | DELTA: instantiating (17) with fresh symbol all_23_0 gives: % 4.40/1.45 | | (18) ~ (all_23_0 = 0) & in(all_9_4, all_9_3) = all_23_0 % 4.40/1.45 | | % 4.40/1.45 | | ALPHA: (18) implies: % 4.40/1.45 | | (19) ~ (all_23_0 = 0) % 4.40/1.45 | | (20) in(all_9_4, all_9_3) = all_23_0 % 4.40/1.45 | | % 4.40/1.45 | | GROUND_INST: instantiating (3) with 0, all_23_0, all_9_3, all_9_4, % 4.40/1.45 | | simplifying with (16), (20) gives: % 4.40/1.45 | | (21) all_23_0 = 0 % 4.40/1.45 | | % 4.40/1.45 | | REDUCE: (19), (21) imply: % 4.40/1.45 | | (22) $false % 4.40/1.45 | | % 4.40/1.45 | | CLOSE: (22) is inconsistent. % 4.40/1.45 | | % 4.40/1.45 | Case 2: % 4.40/1.45 | | % 4.40/1.45 | | (23) ~ (all_9_0 = 0) & ~ (all_9_1 = all_9_2) % 4.40/1.45 | | % 4.40/1.45 | | ALPHA: (23) implies: % 4.40/1.45 | | (24) ~ (all_9_1 = all_9_2) % 4.40/1.45 | | (25) ~ (all_9_0 = 0) % 4.40/1.45 | | % 4.40/1.45 | | BETA: splitting (11) gives: % 4.40/1.45 | | % 4.40/1.45 | | Case 1: % 4.40/1.45 | | | % 4.40/1.45 | | | (26) in(all_9_4, all_9_3) = 0 % 4.40/1.45 | | | % 4.40/1.45 | | | GROUND_INST: instantiating (3) with all_9_0, 0, all_9_3, all_9_4, % 4.40/1.45 | | | simplifying with (7), (26) gives: % 4.40/1.45 | | | (27) all_9_0 = 0 % 4.40/1.45 | | | % 4.40/1.45 | | | REDUCE: (25), (27) imply: % 4.40/1.45 | | | (28) $false % 4.40/1.45 | | | % 4.40/1.45 | | | CLOSE: (28) is inconsistent. % 4.40/1.45 | | | % 4.40/1.45 | | Case 2: % 4.40/1.45 | | | % 4.40/1.45 | | | (29) all_9_1 = all_9_2 % 4.40/1.45 | | | % 4.40/1.45 | | | REDUCE: (24), (29) imply: % 4.40/1.45 | | | (30) $false % 4.40/1.45 | | | % 4.40/1.45 | | | CLOSE: (30) is inconsistent. % 4.40/1.45 | | | % 4.40/1.45 | | End of split % 4.40/1.45 | | % 4.40/1.45 | End of split % 4.40/1.45 | % 4.40/1.45 End of proof % 4.40/1.45 % SZS output end Proof for theBenchmark % 4.40/1.45 % 4.40/1.45 854ms %------------------------------------------------------------------------------