%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM537+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.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 11:48:28 EDT 2023 % Result : Theorem 18.39s 3.36s % Output : Proof 21.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : NUM537+2 : TPTP v8.1.2. Released v4.0.0. % 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n011.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 : Fri Aug 25 10:53:38 EDT 2023 % 0.14/0.36 % CPUTime : % 0.22/0.62 ________ _____ % 0.22/0.62 ___ __ \_________(_)________________________________ % 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.62 % 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.62 (2023-06-19) % 0.22/0.62 % 0.22/0.62 (c) Philipp Rümmer, 2009-2023 % 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.62 Amanda Stjerna. % 0.22/0.62 Free software under BSD-3-Clause. % 0.22/0.62 % 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.62 % 0.22/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.64 Running up to 7 provers in parallel. % 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.87/1.12 Prover 1: Preprocessing ... % 2.87/1.12 Prover 4: Preprocessing ... % 2.91/1.16 Prover 0: Preprocessing ... % 2.91/1.16 Prover 3: Preprocessing ... % 2.91/1.16 Prover 2: Preprocessing ... % 2.91/1.16 Prover 5: Preprocessing ... % 2.91/1.16 Prover 6: Preprocessing ... % 6.81/1.70 Prover 5: Constructing countermodel ... % 6.81/1.72 Prover 1: Constructing countermodel ... % 7.07/1.74 Prover 3: Constructing countermodel ... % 7.07/1.75 Prover 2: Proving ... % 7.07/1.75 Prover 6: Proving ... % 8.09/1.98 Prover 4: Constructing countermodel ... % 8.09/2.01 Prover 0: Proving ... % 18.39/3.36 Prover 0: proved (2703ms) % 18.39/3.36 % 18.39/3.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 18.39/3.36 % 18.39/3.36 Prover 3: stopped % 18.39/3.36 Prover 5: stopped % 18.39/3.38 Prover 2: stopped % 18.39/3.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 18.39/3.38 Prover 6: stopped % 19.30/3.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 19.30/3.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 19.30/3.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 19.30/3.40 Prover 7: Preprocessing ... % 19.30/3.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.30/3.44 Prover 11: Preprocessing ... % 19.30/3.44 Prover 13: Preprocessing ... % 19.30/3.44 Prover 8: Preprocessing ... % 19.30/3.47 Prover 10: Preprocessing ... % 20.22/3.52 Prover 10: Constructing countermodel ... % 20.22/3.52 Prover 7: Constructing countermodel ... % 20.22/3.52 Prover 13: Constructing countermodel ... % 20.84/3.64 Prover 8: Warning: ignoring some quantifiers % 20.84/3.64 Prover 8: Constructing countermodel ... % 20.84/3.65 Prover 10: Found proof (size 22) % 20.84/3.65 Prover 10: proved (263ms) % 20.84/3.65 Prover 13: stopped % 20.84/3.65 Prover 7: stopped % 20.84/3.65 Prover 8: stopped % 20.84/3.65 Prover 4: stopped % 20.84/3.65 Prover 1: stopped % 21.38/3.70 Prover 11: Constructing countermodel ... % 21.38/3.71 Prover 11: stopped % 21.38/3.71 % 21.38/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.38/3.71 % 21.38/3.71 % SZS output start Proof for theBenchmark % 21.38/3.71 Assumptions after simplification: % 21.38/3.71 --------------------------------- % 21.38/3.71 % 21.38/3.71 (mEOfElem) % 21.38/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 21.38/3.72 ~ aSet0(v0) | aElement0(v1)) % 21.38/3.72 % 21.38/3.72 (m__) % 21.38/3.74 $i(xS) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v0, xx) % 21.38/3.74 = v1 & sdtpldt0(xS, xx) = v0 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & % 21.38/3.74 aSet0(v0) & ~ aElementOf0(xx, v1) & ! [v3: $i] : (v3 = xx | ~ $i(v3) | ~ % 21.38/3.74 aElementOf0(v3, v0) | ~ aElement0(v3) | aElementOf0(v3, v1)) & ! [v3: % 21.38/3.74 $i] : (v3 = xx | ~ $i(v3) | ~ aElementOf0(v3, v0) | aElementOf0(v3, xS)) % 21.38/3.74 & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v1) | aElementOf0(v3, v0)) & % 21.38/3.74 ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v1) | aElement0(v3)) & ! [v3: % 21.38/3.74 $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aElement0(v3)) & ! [v3: $i] : % 21.38/3.74 ( ~ $i(v3) | ~ aElementOf0(v3, xS) | ~ aElement0(v3) | aElementOf0(v3, % 21.38/3.74 v0)) & ( ~ aElement0(xx) | aElementOf0(xx, v0)) & ((aElementOf0(v2, v1) % 21.38/3.74 & ~ aSubsetOf0(v1, xS) & ~ aElementOf0(v2, xS)) | (aElementOf0(v2, xS) % 21.38/3.74 & ~ aSubsetOf0(xS, v1) & ~ aElementOf0(v2, v1)))) % 21.38/3.74 % 21.38/3.74 (m__679) % 21.38/3.74 $i(xS) & $i(xx) & aElement0(xx) & aSet0(xS) % 21.38/3.74 % 21.38/3.74 (m__679_02) % 21.38/3.74 $i(xS) & $i(xx) & ~ aElementOf0(xx, xS) % 21.38/3.74 % 21.38/3.74 Further assumptions not needed in the proof: % 21.38/3.74 -------------------------------------------- % 21.38/3.74 mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons, mDefDiff, mDefEmp, % 21.38/3.74 mDefSub, mElmSort, mEmpFin, mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl, % 21.38/3.74 mSubTrans % 21.38/3.74 % 21.38/3.74 Those formulas are unsatisfiable: % 21.38/3.74 --------------------------------- % 21.38/3.74 % 21.38/3.74 Begin of proof % 21.38/3.75 | % 21.38/3.75 | ALPHA: (m__679) implies: % 21.38/3.75 | (1) aSet0(xS) % 21.38/3.75 | % 21.38/3.75 | ALPHA: (m__679_02) implies: % 21.38/3.75 | (2) ~ aElementOf0(xx, xS) % 21.38/3.75 | % 21.38/3.75 | ALPHA: (m__) implies: % 21.38/3.75 | (3) $i(xS) % 21.38/3.75 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v0, xx) = v1 & % 21.38/3.75 | sdtpldt0(xS, xx) = v0 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & % 21.38/3.75 | aSet0(v0) & ~ aElementOf0(xx, v1) & ! [v3: $i] : (v3 = xx | ~ % 21.38/3.75 | $i(v3) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | % 21.38/3.75 | aElementOf0(v3, v1)) & ! [v3: $i] : (v3 = xx | ~ $i(v3) | ~ % 21.38/3.75 | aElementOf0(v3, v0) | aElementOf0(v3, xS)) & ! [v3: $i] : ( ~ % 21.38/3.75 | $i(v3) | ~ aElementOf0(v3, v1) | aElementOf0(v3, v0)) & ! [v3: % 21.38/3.75 | $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v1) | aElement0(v3)) & ! % 21.38/3.75 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aElement0(v3)) & ! % 21.38/3.75 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, xS) | ~ aElement0(v3) | % 21.38/3.75 | aElementOf0(v3, v0)) & ( ~ aElement0(xx) | aElementOf0(xx, v0)) & % 21.38/3.75 | ((aElementOf0(v2, v1) & ~ aSubsetOf0(v1, xS) & ~ aElementOf0(v2, % 21.38/3.75 | xS)) | (aElementOf0(v2, xS) & ~ aSubsetOf0(xS, v1) & ~ % 21.38/3.75 | aElementOf0(v2, v1)))) % 21.38/3.75 | % 21.38/3.75 | DELTA: instantiating (4) with fresh symbols all_15_0, all_15_1, all_15_2 % 21.38/3.75 | gives: % 21.38/3.76 | (5) sdtmndt0(all_15_2, xx) = all_15_1 & sdtpldt0(xS, xx) = all_15_2 & % 21.38/3.76 | $i(all_15_0) & $i(all_15_1) & $i(all_15_2) & aSet0(all_15_1) & % 21.38/3.76 | aSet0(all_15_2) & ~ aElementOf0(xx, all_15_1) & ! [v0: $i] : (v0 = xx % 21.38/3.76 | | ~ $i(v0) | ~ aElementOf0(v0, all_15_2) | ~ aElement0(v0) | % 21.38/3.76 | aElementOf0(v0, all_15_1)) & ! [v0: $i] : (v0 = xx | ~ $i(v0) | ~ % 21.38/3.76 | aElementOf0(v0, all_15_2) | aElementOf0(v0, xS)) & ! [v0: $i] : ( ~ % 21.38/3.76 | $i(v0) | ~ aElementOf0(v0, all_15_1) | aElementOf0(v0, all_15_2)) & % 21.38/3.76 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_15_1) | aElement0(v0)) % 21.38/3.76 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_15_2) | % 21.38/3.76 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | % 21.38/3.76 | ~ aElement0(v0) | aElementOf0(v0, all_15_2)) & ( ~ aElement0(xx) | % 21.38/3.76 | aElementOf0(xx, all_15_2)) & ((aElementOf0(all_15_0, all_15_1) & ~ % 21.38/3.76 | aSubsetOf0(all_15_1, xS) & ~ aElementOf0(all_15_0, xS)) | % 21.38/3.76 | (aElementOf0(all_15_0, xS) & ~ aSubsetOf0(xS, all_15_1) & ~ % 21.38/3.76 | aElementOf0(all_15_0, all_15_1))) % 21.38/3.76 | % 21.38/3.76 | ALPHA: (5) implies: % 21.38/3.76 | (6) ~ aElementOf0(xx, all_15_1) % 21.38/3.76 | (7) $i(all_15_0) % 21.38/3.76 | (8) (aElementOf0(all_15_0, all_15_1) & ~ aSubsetOf0(all_15_1, xS) & ~ % 21.38/3.76 | aElementOf0(all_15_0, xS)) | (aElementOf0(all_15_0, xS) & ~ % 21.38/3.76 | aSubsetOf0(xS, all_15_1) & ~ aElementOf0(all_15_0, all_15_1)) % 21.38/3.76 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) | ~ aElement0(v0) | % 21.38/3.76 | aElementOf0(v0, all_15_2)) % 21.38/3.76 | (10) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_15_1) | % 21.38/3.76 | aElementOf0(v0, all_15_2)) % 21.38/3.76 | (11) ! [v0: $i] : (v0 = xx | ~ $i(v0) | ~ aElementOf0(v0, all_15_2) | % 21.38/3.76 | aElementOf0(v0, xS)) % 21.38/3.76 | (12) ! [v0: $i] : (v0 = xx | ~ $i(v0) | ~ aElementOf0(v0, all_15_2) | ~ % 21.38/3.76 | aElement0(v0) | aElementOf0(v0, all_15_1)) % 21.38/3.76 | % 21.38/3.76 | BETA: splitting (8) gives: % 21.38/3.76 | % 21.38/3.76 | Case 1: % 21.38/3.76 | | % 21.38/3.76 | | (13) aElementOf0(all_15_0, all_15_1) & ~ aSubsetOf0(all_15_1, xS) & ~ % 21.38/3.76 | | aElementOf0(all_15_0, xS) % 21.38/3.76 | | % 21.38/3.76 | | ALPHA: (13) implies: % 21.38/3.76 | | (14) ~ aElementOf0(all_15_0, xS) % 21.38/3.76 | | (15) aElementOf0(all_15_0, all_15_1) % 21.38/3.76 | | % 21.38/3.76 | | GROUND_INST: instantiating (10) with all_15_0, simplifying with (7), (15) % 21.38/3.76 | | gives: % 21.38/3.76 | | (16) aElementOf0(all_15_0, all_15_2) % 21.38/3.76 | | % 21.38/3.76 | | GROUND_INST: instantiating (11) with all_15_0, simplifying with (7), (14), % 21.38/3.76 | | (16) gives: % 21.38/3.76 | | (17) all_15_0 = xx % 21.38/3.76 | | % 21.38/3.76 | | REDUCE: (15), (17) imply: % 21.38/3.76 | | (18) aElementOf0(xx, all_15_1) % 21.38/3.76 | | % 21.38/3.76 | | PRED_UNIFY: (6), (18) imply: % 21.38/3.76 | | (19) $false % 21.38/3.76 | | % 21.38/3.76 | | CLOSE: (19) is inconsistent. % 21.38/3.76 | | % 21.38/3.76 | Case 2: % 21.38/3.76 | | % 21.38/3.76 | | (20) aElementOf0(all_15_0, xS) & ~ aSubsetOf0(xS, all_15_1) & ~ % 21.38/3.76 | | aElementOf0(all_15_0, all_15_1) % 21.38/3.77 | | % 21.38/3.77 | | ALPHA: (20) implies: % 21.38/3.77 | | (21) ~ aElementOf0(all_15_0, all_15_1) % 21.38/3.77 | | (22) aElementOf0(all_15_0, xS) % 21.38/3.77 | | % 21.38/3.77 | | GROUND_INST: instantiating (mEOfElem) with xS, all_15_0, simplifying with % 21.38/3.77 | | (1), (3), (7), (22) gives: % 21.38/3.77 | | (23) aElement0(all_15_0) % 21.38/3.77 | | % 21.38/3.77 | | GROUND_INST: instantiating (9) with all_15_0, simplifying with (7), (22), % 21.38/3.77 | | (23) gives: % 21.38/3.77 | | (24) aElementOf0(all_15_0, all_15_2) % 21.38/3.77 | | % 21.38/3.77 | | GROUND_INST: instantiating (12) with all_15_0, simplifying with (7), (21), % 21.38/3.77 | | (23), (24) gives: % 21.38/3.77 | | (25) all_15_0 = xx % 21.38/3.77 | | % 21.38/3.77 | | REDUCE: (22), (25) imply: % 21.38/3.77 | | (26) aElementOf0(xx, xS) % 21.38/3.77 | | % 21.38/3.77 | | PRED_UNIFY: (2), (26) imply: % 21.38/3.77 | | (27) $false % 21.38/3.77 | | % 21.38/3.77 | | CLOSE: (27) is inconsistent. % 21.38/3.77 | | % 21.38/3.77 | End of split % 21.38/3.77 | % 21.38/3.77 End of proof % 21.38/3.77 % SZS output end Proof for theBenchmark % 21.38/3.77 % 21.38/3.77 3145ms %------------------------------------------------------------------------------