%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM538+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n014.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 77.26s 11.12s % Output : Proof 77.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM538+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.34 % Computer : n014.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Fri Aug 25 13:34:03 EDT 2023 % 0.16/0.34 % CPUTime : % 0.19/0.61 ________ _____ % 0.19/0.61 ___ __ \_________(_)________________________________ % 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.61 % 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.61 (2023-06-19) % 0.19/0.61 % 0.19/0.61 (c) Philipp Rümmer, 2009-2023 % 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.99/1.16 Prover 4: Preprocessing ... % 2.99/1.16 Prover 1: Preprocessing ... % 2.99/1.20 Prover 0: Preprocessing ... % 2.99/1.20 Prover 5: Preprocessing ... % 2.99/1.20 Prover 2: Preprocessing ... % 2.99/1.20 Prover 6: Preprocessing ... % 3.52/1.20 Prover 3: Preprocessing ... % 8.13/1.92 Prover 5: Constructing countermodel ... % 8.13/1.93 Prover 1: Constructing countermodel ... % 8.70/1.96 Prover 2: Proving ... % 8.70/1.96 Prover 3: Constructing countermodel ... % 8.70/1.96 Prover 6: Proving ... % 9.18/2.19 Prover 4: Constructing countermodel ... % 10.18/2.29 Prover 0: Proving ... % 71.55/10.35 Prover 2: stopped % 71.55/10.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.57/10.39 Prover 7: Preprocessing ... % 73.00/10.46 Prover 7: Constructing countermodel ... % 76.52/10.94 Prover 7: Found proof (size 46) % 76.52/10.94 Prover 7: proved (597ms) % 76.52/10.95 Prover 0: stopped % 76.52/10.95 Prover 4: stopped % 76.52/10.95 Prover 1: stopped % 76.52/10.95 Prover 6: stopped % 76.86/10.98 Prover 5: stopped % 77.26/11.12 Prover 3: stopped % 77.26/11.12 % 77.26/11.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 77.26/11.12 % 77.26/11.12 % SZS output start Proof for theBenchmark % 77.26/11.12 Assumptions after simplification: % 77.26/11.12 --------------------------------- % 77.26/11.12 % 77.26/11.12 (mCardCons) % 77.44/11.16 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 77.44/11.16 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2) % 77.44/11.16 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~ % 77.44/11.16 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0)))) % 77.44/11.16 % 77.44/11.16 (mCardEmpty) % 77.44/11.16 $i(sz00) & $i(slcrc0) & ! [v0: $i] : (v0 = sz00 | ~ (sbrdtbr0(slcrc0) = v0) % 77.44/11.16 | ~ aSet0(slcrc0)) & ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00) % 77.44/11.16 | ~ $i(v0) | ~ aSet0(v0)) % 77.44/11.16 % 77.44/11.16 (mConsDiff) % 77.44/11.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ % 77.44/11.16 $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | ~ aSet0(v0) | sdtpldt0(v2, % 77.44/11.16 v1) = v0) % 77.44/11.16 % 77.44/11.17 (mCountNFin_01) % 77.44/11.17 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 77.44/11.17 % 77.44/11.17 (mDefDiff) % 77.44/11.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~ % 77.44/11.18 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ % 77.44/11.18 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 = % 77.44/11.18 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)) % 77.44/11.18 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) & % 77.44/11.18 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 77.44/11.18 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 77.44/11.18 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ % 77.44/11.18 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 77.44/11.18 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | % 77.44/11.18 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) % 77.44/11.18 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 77.44/11.18 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 77.44/11.18 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ % 77.44/11.18 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 77.44/11.18 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 77.44/11.18 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : ! % 77.44/11.18 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | % 77.44/11.18 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2)) % 77.44/11.18 % 77.44/11.18 (mDefEmp) % 77.44/11.19 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 77.44/11.19 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 77.44/11.19 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 77.44/11.19 % 77.44/11.19 (mEOfElem) % 77.44/11.19 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 77.44/11.19 ~ aSet0(v0) | aElement0(v1)) % 77.44/11.19 % 77.44/11.19 (mFDiffSet) % 77.44/11.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ % 77.44/11.19 $i(v1) | ~ $i(v0) | ~ isFinite0(v1) | ~ aElement0(v0) | ~ aSet0(v1) | % 77.44/11.19 isFinite0(v2)) % 77.44/11.19 % 77.44/11.19 (m__) % 77.44/11.19 $i(xx) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ % 77.44/11.19 (v3 = v2) & sbrdtbr0(v0) = v1 & sbrdtbr0(xS) = v3 & szszuzczcdt0(v1) = v2 & % 77.44/11.19 sdtmndt0(xS, xx) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 77.44/11.19 % 77.44/11.20 (m__1522) % 77.44/11.20 $i(xS) & aSet0(xS) % 77.44/11.20 % 77.44/11.20 (m__1522_02) % 77.44/11.20 $i(xx) & $i(xS) & isFinite0(xS) & aElementOf0(xx, xS) % 77.44/11.20 % 77.44/11.20 (function-axioms) % 77.44/11.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 77.44/11.20 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 77.44/11.20 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 77.44/11.20 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 77.44/11.20 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! % 77.44/11.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 77.44/11.20 (szszuzczcdt0(v2) = v0)) % 77.44/11.20 % 77.44/11.20 Further assumptions not needed in the proof: % 77.44/11.20 -------------------------------------------- % 77.44/11.20 mCConsSet, mCDiffSet, mCardNum, mCardS, mCntRel, mCountNFin, mDefCons, mDefSub, % 77.44/11.20 mDiffCons, mElmSort, mEmpFin, mFConsSet, mFinRel, mIH, mIHSort, mLessASymm, % 77.44/11.20 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mNATSet, mNatExtra, % 77.44/11.20 mNatNSucc, mNoScLessZr, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 77.44/11.20 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum % 77.44/11.20 % 77.44/11.20 Those formulas are unsatisfiable: % 77.44/11.20 --------------------------------- % 77.44/11.20 % 77.44/11.20 Begin of proof % 77.44/11.20 | % 77.44/11.20 | ALPHA: (mDefEmp) implies: % 77.44/11.20 | (1) aSet0(slcrc0) % 77.44/11.21 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 77.44/11.21 | % 77.44/11.21 | ALPHA: (mCountNFin_01) implies: % 77.44/11.21 | (3) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 77.44/11.21 | % 77.44/11.21 | ALPHA: (mDefDiff) implies: % 77.44/11.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | % 77.44/11.21 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | % 77.44/11.21 | aSet0(v2)) % 77.44/11.21 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | % 77.44/11.21 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v2) | ~ % 77.44/11.21 | aElement0(v1) | ~ aSet0(v0)) % 77.44/11.21 | % 77.44/11.21 | ALPHA: (mCardEmpty) implies: % 77.44/11.21 | (6) ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~ % 77.44/11.21 | aSet0(v0)) % 77.44/11.21 | % 77.44/11.21 | ALPHA: (m__1522) implies: % 77.44/11.21 | (7) aSet0(xS) % 77.44/11.21 | % 77.44/11.21 | ALPHA: (m__1522_02) implies: % 77.44/11.21 | (8) aElementOf0(xx, xS) % 77.44/11.21 | (9) isFinite0(xS) % 77.44/11.21 | % 77.44/11.21 | ALPHA: (m__) implies: % 77.44/11.21 | (10) $i(xS) % 77.44/11.21 | (11) $i(xx) % 77.44/11.21 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) % 77.44/11.21 | & sbrdtbr0(v0) = v1 & sbrdtbr0(xS) = v3 & szszuzczcdt0(v1) = v2 & % 77.44/11.21 | sdtmndt0(xS, xx) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 77.44/11.21 | % 77.44/11.21 | ALPHA: (function-axioms) implies: % 77.72/11.21 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 77.72/11.21 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 77.72/11.22 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) % 77.72/11.22 | = v1) | ~ (sbrdtbr0(v2) = v0)) % 77.72/11.22 | % 77.72/11.22 | DELTA: instantiating (12) with fresh symbols all_37_0, all_37_1, all_37_2, % 77.72/11.22 | all_37_3 gives: % 77.72/11.22 | (15) ~ (all_37_0 = all_37_1) & sbrdtbr0(all_37_3) = all_37_2 & % 77.72/11.22 | sbrdtbr0(xS) = all_37_0 & szszuzczcdt0(all_37_2) = all_37_1 & % 77.72/11.22 | sdtmndt0(xS, xx) = all_37_3 & $i(all_37_0) & $i(all_37_1) & % 77.72/11.22 | $i(all_37_2) & $i(all_37_3) % 77.72/11.22 | % 77.72/11.22 | ALPHA: (15) implies: % 77.72/11.22 | (16) ~ (all_37_0 = all_37_1) % 77.72/11.22 | (17) $i(all_37_3) % 77.72/11.22 | (18) sdtmndt0(xS, xx) = all_37_3 % 77.72/11.22 | (19) szszuzczcdt0(all_37_2) = all_37_1 % 77.72/11.22 | (20) sbrdtbr0(xS) = all_37_0 % 77.72/11.22 | (21) sbrdtbr0(all_37_3) = all_37_2 % 77.72/11.22 | % 77.72/11.22 | BETA: splitting (3) gives: % 77.72/11.22 | % 77.72/11.22 | Case 1: % 77.72/11.22 | | % 77.72/11.22 | | (22) ~ aSet0(slcrc0) % 77.72/11.22 | | % 77.72/11.22 | | PRED_UNIFY: (1), (22) imply: % 77.72/11.22 | | (23) $false % 77.72/11.22 | | % 77.72/11.22 | | CLOSE: (23) is inconsistent. % 77.72/11.22 | | % 77.72/11.22 | Case 2: % 77.72/11.22 | | % 77.72/11.22 | | % 77.72/11.22 | | GROUND_INST: instantiating (mEOfElem) with xS, xx, simplifying with (7), % 77.72/11.22 | | (8), (10), (11) gives: % 77.72/11.22 | | (24) aElement0(xx) % 77.72/11.22 | | % 77.72/11.22 | | GROUND_INST: instantiating (2) with xx, simplifying with (11) gives: % 77.72/11.22 | | (25) ~ aElementOf0(xx, slcrc0) % 77.72/11.22 | | % 77.72/11.22 | | GROUND_INST: instantiating (mConsDiff) with xS, xx, all_37_3, simplifying % 77.72/11.22 | | with (7), (8), (10), (11), (18) gives: % 77.72/11.22 | | (26) sdtpldt0(all_37_3, xx) = xS % 77.72/11.22 | | % 77.72/11.22 | | GROUND_INST: instantiating (6) with xS, simplifying with (7), (10) gives: % 77.72/11.23 | | (27) xS = slcrc0 | ~ (sbrdtbr0(xS) = sz00) % 77.72/11.23 | | % 77.72/11.23 | | PRED_UNIFY: (8), (25) imply: % 77.72/11.23 | | (28) ~ (xS = slcrc0) % 77.72/11.23 | | % 77.72/11.23 | | BETA: splitting (27) gives: % 77.72/11.23 | | % 77.72/11.23 | | Case 1: % 77.72/11.23 | | | % 77.72/11.23 | | | % 77.72/11.23 | | | GROUND_INST: instantiating (4) with xS, xx, all_37_3, simplifying with % 77.72/11.23 | | | (7), (10), (11), (17), (18), (24) gives: % 77.72/11.23 | | | (29) aSet0(all_37_3) % 77.72/11.23 | | | % 77.72/11.23 | | | GROUND_INST: instantiating (mFDiffSet) with xx, xS, all_37_3, simplifying % 77.72/11.23 | | | with (7), (9), (10), (11), (18), (24) gives: % 77.72/11.23 | | | (30) isFinite0(all_37_3) % 77.72/11.23 | | | % 77.72/11.23 | | | GROUND_INST: instantiating (13) with all_37_1, all_37_0, all_37_2, % 77.72/11.23 | | | simplifying with (19) gives: % 77.72/11.23 | | | (31) all_37_0 = all_37_1 | ~ (szszuzczcdt0(all_37_2) = all_37_0) % 77.72/11.23 | | | % 77.72/11.23 | | | GROUND_INST: instantiating (mCardCons) with all_37_3, all_37_2, % 77.72/11.23 | | | simplifying with (17), (21), (29), (30) gives: % 77.72/11.23 | | | (32) ? [v0: $i] : (szszuzczcdt0(all_37_2) = v0 & $i(v0) & ! [v1: $i] % 77.72/11.23 | | | : ! [v2: $i] : ( ~ (sdtpldt0(all_37_3, v1) = v2) | ~ $i(v1) | % 77.72/11.23 | | | ~ aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, % 77.72/11.23 | | | all_37_3))) % 77.72/11.23 | | | % 77.72/11.23 | | | DELTA: instantiating (32) with fresh symbol all_108_0 gives: % 77.72/11.23 | | | (33) szszuzczcdt0(all_37_2) = all_108_0 & $i(all_108_0) & ! [v0: $i] : % 77.72/11.23 | | | ! [v1: $i] : ( ~ (sdtpldt0(all_37_3, v0) = v1) | ~ $i(v0) | ~ % 77.72/11.23 | | | aElement0(v0) | sbrdtbr0(v1) = all_108_0 | aElementOf0(v0, % 77.72/11.23 | | | all_37_3)) % 77.72/11.23 | | | % 77.72/11.23 | | | ALPHA: (33) implies: % 77.72/11.23 | | | (34) szszuzczcdt0(all_37_2) = all_108_0 % 77.72/11.23 | | | (35) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(all_37_3, v0) = v1) | ~ % 77.72/11.23 | | | $i(v0) | ~ aElement0(v0) | sbrdtbr0(v1) = all_108_0 | % 77.72/11.23 | | | aElementOf0(v0, all_37_3)) % 77.72/11.23 | | | % 77.72/11.23 | | | GROUND_INST: instantiating (35) with xx, xS, simplifying with (11), (24), % 77.72/11.23 | | | (26) gives: % 77.72/11.23 | | | (36) sbrdtbr0(xS) = all_108_0 | aElementOf0(xx, all_37_3) % 77.72/11.23 | | | % 77.72/11.23 | | | BETA: splitting (31) gives: % 77.72/11.23 | | | % 77.72/11.23 | | | Case 1: % 77.72/11.23 | | | | % 77.72/11.24 | | | | (37) ~ (szszuzczcdt0(all_37_2) = all_37_0) % 77.72/11.24 | | | | % 77.72/11.24 | | | | GROUND_INST: instantiating (13) with all_37_1, all_108_0, all_37_2, % 77.72/11.24 | | | | simplifying with (19), (34) gives: % 77.72/11.24 | | | | (38) all_108_0 = all_37_1 % 77.72/11.24 | | | | % 77.72/11.24 | | | | PRED_UNIFY: (34), (37) imply: % 77.72/11.24 | | | | (39) ~ (all_108_0 = all_37_0) % 77.72/11.24 | | | | % 77.72/11.24 | | | | REDUCE: (38), (39) imply: % 77.72/11.24 | | | | (40) ~ (all_37_0 = all_37_1) % 77.72/11.24 | | | | % 77.72/11.24 | | | | BETA: splitting (36) gives: % 77.72/11.24 | | | | % 77.72/11.24 | | | | Case 1: % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | (41) sbrdtbr0(xS) = all_108_0 % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | REDUCE: (38), (41) imply: % 77.72/11.24 | | | | | (42) sbrdtbr0(xS) = all_37_1 % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | GROUND_INST: instantiating (14) with all_37_0, all_37_1, xS, % 77.72/11.24 | | | | | simplifying with (20), (42) gives: % 77.72/11.24 | | | | | (43) all_37_0 = all_37_1 % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | REDUCE: (16), (43) imply: % 77.72/11.24 | | | | | (44) $false % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | CLOSE: (44) is inconsistent. % 77.72/11.24 | | | | | % 77.72/11.24 | | | | Case 2: % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | (45) aElementOf0(xx, all_37_3) % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | GROUND_INST: instantiating (5) with xS, xx, all_37_3, simplifying with % 77.72/11.24 | | | | | (7), (10), (11), (17), (18), (24), (45) gives: % 77.72/11.24 | | | | | (46) $false % 77.72/11.24 | | | | | % 77.72/11.24 | | | | | CLOSE: (46) is inconsistent. % 77.72/11.24 | | | | | % 77.72/11.24 | | | | End of split % 77.72/11.24 | | | | % 77.72/11.24 | | | Case 2: % 77.72/11.24 | | | | % 77.72/11.24 | | | | (47) all_37_0 = all_37_1 % 77.72/11.24 | | | | % 77.72/11.24 | | | | REDUCE: (16), (47) imply: % 77.72/11.24 | | | | (48) $false % 77.72/11.24 | | | | % 77.72/11.24 | | | | CLOSE: (48) is inconsistent. % 77.72/11.24 | | | | % 77.72/11.24 | | | End of split % 77.72/11.24 | | | % 77.72/11.24 | | Case 2: % 77.72/11.24 | | | % 77.72/11.24 | | | (49) xS = slcrc0 % 77.72/11.24 | | | % 77.72/11.24 | | | REDUCE: (28), (49) imply: % 77.72/11.24 | | | (50) $false % 77.72/11.24 | | | % 77.72/11.24 | | | CLOSE: (50) is inconsistent. % 77.72/11.24 | | | % 77.72/11.24 | | End of split % 77.72/11.24 | | % 77.72/11.24 | End of split % 77.72/11.24 | % 77.72/11.24 End of proof % 77.72/11.24 % SZS output end Proof for theBenchmark % 77.72/11.24 % 77.72/11.24 10634ms %------------------------------------------------------------------------------