%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM592+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 : n013.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 11:48:49 EDT 2023 % Result : Theorem 31.25s 4.93s % Output : Proof 63.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM592+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n013.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 11:31:32 EDT 2023 % 0.12/0.34 % 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. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.40/1.35 Prover 1: Preprocessing ... % 4.40/1.35 Prover 4: Preprocessing ... % 4.40/1.37 Prover 5: Preprocessing ... % 4.40/1.37 Prover 0: Preprocessing ... % 4.40/1.37 Prover 2: Preprocessing ... % 4.40/1.37 Prover 3: Preprocessing ... % 4.40/1.37 Prover 6: Preprocessing ... % 14.19/2.71 Prover 3: Constructing countermodel ... % 14.19/2.72 Prover 1: Constructing countermodel ... % 15.19/2.80 Prover 6: Proving ... % 15.19/2.91 Prover 5: Proving ... % 17.11/3.07 Prover 2: Proving ... % 19.36/3.34 Prover 4: Constructing countermodel ... % 19.97/3.55 Prover 0: Proving ... % 31.25/4.93 Prover 3: proved (4303ms) % 31.25/4.93 % 31.25/4.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.25/4.93 % 31.25/4.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 31.25/4.94 Prover 6: stopped % 31.25/4.94 Prover 0: stopped % 31.25/4.94 Prover 5: stopped % 31.25/4.97 Prover 2: stopped % 31.25/4.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 31.25/4.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 31.25/4.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 31.25/4.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 31.25/5.08 Prover 7: Preprocessing ... % 32.83/5.17 Prover 11: Preprocessing ... % 32.83/5.17 Prover 10: Preprocessing ... % 32.83/5.20 Prover 13: Preprocessing ... % 32.83/5.20 Prover 8: Preprocessing ... % 34.20/5.34 Prover 7: Constructing countermodel ... % 34.82/5.40 Prover 10: Constructing countermodel ... % 35.11/5.44 Prover 8: Warning: ignoring some quantifiers % 35.11/5.48 Prover 8: Constructing countermodel ... % 35.85/5.52 Prover 13: Warning: ignoring some quantifiers % 35.85/5.54 Prover 13: Constructing countermodel ... % 41.23/6.24 Prover 11: Constructing countermodel ... % 63.07/9.08 Prover 7: Found proof (size 34) % 63.07/9.08 Prover 7: proved (4151ms) % 63.07/9.08 Prover 8: stopped % 63.07/9.08 Prover 10: stopped % 63.07/9.08 Prover 11: stopped % 63.07/9.09 Prover 4: stopped % 63.07/9.09 Prover 13: stopped % 63.07/9.09 Prover 1: stopped % 63.07/9.09 % 63.07/9.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 63.07/9.09 % 63.07/9.09 % SZS output start Proof for theBenchmark % 63.07/9.10 Assumptions after simplification: % 63.07/9.10 --------------------------------- % 63.07/9.10 % 63.07/9.10 (m__) % 63.07/9.12 $i(xi) & $i(xC) & $i(xN) & $i(xk) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? % 63.07/9.12 [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xC, xi) = v3 & sdtlpdtrp0(xN, xi) = v0 & % 63.07/9.12 szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & % 63.07/9.12 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) % 63.07/9.12 = v6) | ~ $i(v5) | ~ $i(v4) | ~ aSubsetOf0(v5, v2) | ~ % 63.07/9.12 isCountable0(v5) | ~ aElementOf0(v4, xT) | ? [v7: $i] : ? [v8: $i] : ( % 63.07/9.12 ~ (v8 = v4) & sdtlpdtrp0(v3, v7) = v8 & $i(v8) & $i(v7) & % 63.07/9.12 aElementOf0(v7, v6) & aSet0(v7)))) % 63.07/9.12 % 63.07/9.12 (m__4448_02) % 63.07/9.12 $i(xd) & $i(xY) & $i(xi) & $i(xC) & $i(xN) & ? [v0: $i] : ? [v1: $i] : % 63.07/9.12 (sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & % 63.07/9.12 sdtmndt0(v0, v1) = xY & $i(v1) & $i(v0)) % 63.07/9.12 % 63.07/9.12 (m__4545) % 63.07/9.13 $i(xX) & $i(xu) & $i(xd) & $i(xY) & $i(xk) & $i(xT) & ? [v0: $i] : % 63.07/9.13 (slbdtsldtrb0(xX, xk) = v0 & $i(v0) & aSubsetOf0(xX, xY) & isCountable0(xX) & % 63.07/9.13 aElementOf0(xu, xT) & ! [v1: $i] : ! [v2: $i] : (v2 = xu | ~ % 63.07/9.13 (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ aElementOf0(v1, v0) | ~ % 63.07/9.13 aSet0(v1))) % 63.07/9.13 % 63.07/9.13 (function-axioms) % 63.07/9.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 63.07/9.13 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 63.07/9.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 63.07/9.13 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 63.07/9.13 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 63.07/9.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 63.07/9.13 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 63.07/9.13 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 63.07/9.13 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 63.07/9.13 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 63.07/9.13 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 63.07/9.13 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 63.07/9.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 63.07/9.13 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 63.07/9.13 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 63.07/9.13 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 63.07/9.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 63.07/9.13 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 63.07/9.13 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 63.07/9.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 63.07/9.13 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 63.07/9.13 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 63.07/9.13 v0)) % 63.07/9.13 % 63.07/9.13 Further assumptions not needed in the proof: % 63.07/9.13 -------------------------------------------- % 63.07/9.13 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 63.07/9.13 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 63.07/9.13 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 63.07/9.13 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 63.07/9.13 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 63.07/9.13 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 63.07/9.13 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 63.07/9.13 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 63.07/9.13 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 63.07/9.13 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, % 63.07/9.13 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, % 63.07/9.13 m__3821, m__3965, m__4151, m__4182, m__4331, m__4423, m__4448, m__4482 % 63.07/9.13 % 63.07/9.13 Those formulas are unsatisfiable: % 63.07/9.13 --------------------------------- % 63.07/9.13 % 63.07/9.13 Begin of proof % 63.07/9.13 | % 63.07/9.13 | ALPHA: (m__4448_02) implies: % 63.07/9.13 | (1) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, % 63.07/9.13 | xi) = v0 & szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = xY & $i(v1) & % 63.07/9.13 | $i(v0)) % 63.07/9.13 | % 63.07/9.13 | ALPHA: (m__4545) implies: % 63.07/9.13 | (2) $i(xu) % 63.07/9.13 | (3) $i(xX) % 63.07/9.14 | (4) ? [v0: $i] : (slbdtsldtrb0(xX, xk) = v0 & $i(v0) & aSubsetOf0(xX, xY) % 63.07/9.14 | & isCountable0(xX) & aElementOf0(xu, xT) & ! [v1: $i] : ! [v2: $i] % 63.07/9.14 | : (v2 = xu | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ % 63.07/9.14 | aElementOf0(v1, v0) | ~ aSet0(v1))) % 63.07/9.14 | % 63.07/9.14 | ALPHA: (m__) implies: % 63.07/9.14 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xC, % 63.07/9.14 | xi) = v3 & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & % 63.07/9.14 | sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 63.07/9.14 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | % 63.07/9.14 | ~ $i(v5) | ~ $i(v4) | ~ aSubsetOf0(v5, v2) | ~ isCountable0(v5) % 63.07/9.14 | | ~ aElementOf0(v4, xT) | ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = % 63.07/9.14 | v4) & sdtlpdtrp0(v3, v7) = v8 & $i(v8) & $i(v7) & % 63.07/9.14 | aElementOf0(v7, v6) & aSet0(v7)))) % 63.07/9.14 | % 63.07/9.14 | ALPHA: (function-axioms) implies: % 63.37/9.14 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) % 63.37/9.14 | = v1) | ~ (szmzizndt0(v2) = v0)) % 63.37/9.14 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 63.37/9.14 | (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 63.37/9.14 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 63.37/9.14 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 63.37/9.14 | % 63.37/9.14 | DELTA: instantiating (1) with fresh symbols all_72_0, all_72_1 gives: % 63.37/9.14 | (9) sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, xi) = all_72_1 & % 63.37/9.14 | szmzizndt0(all_72_1) = all_72_0 & sdtmndt0(all_72_1, all_72_0) = xY & % 63.37/9.14 | $i(all_72_0) & $i(all_72_1) % 63.37/9.14 | % 63.37/9.14 | ALPHA: (9) implies: % 63.37/9.14 | (10) sdtmndt0(all_72_1, all_72_0) = xY % 63.37/9.14 | (11) szmzizndt0(all_72_1) = all_72_0 % 63.37/9.14 | (12) sdtlpdtrp0(xN, xi) = all_72_1 % 63.37/9.14 | (13) sdtlpdtrp0(xC, xi) = xd % 63.37/9.14 | % 63.37/9.14 | DELTA: instantiating (4) with fresh symbol all_78_0 gives: % 63.37/9.14 | (14) slbdtsldtrb0(xX, xk) = all_78_0 & $i(all_78_0) & aSubsetOf0(xX, xY) & % 63.37/9.14 | isCountable0(xX) & aElementOf0(xu, xT) & ! [v0: $i] : ! [v1: $i] : % 63.37/9.14 | (v1 = xu | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 63.37/9.14 | aElementOf0(v0, all_78_0) | ~ aSet0(v0)) % 63.37/9.14 | % 63.37/9.14 | ALPHA: (14) implies: % 63.37/9.14 | (15) aElementOf0(xu, xT) % 63.37/9.14 | (16) isCountable0(xX) % 63.37/9.14 | (17) aSubsetOf0(xX, xY) % 63.37/9.14 | (18) slbdtsldtrb0(xX, xk) = all_78_0 % 63.37/9.14 | (19) ! [v0: $i] : ! [v1: $i] : (v1 = xu | ~ (sdtlpdtrp0(xd, v0) = v1) | % 63.37/9.14 | ~ $i(v0) | ~ aElementOf0(v0, all_78_0) | ~ aSet0(v0)) % 63.37/9.14 | % 63.37/9.14 | DELTA: instantiating (5) with fresh symbols all_84_0, all_84_1, all_84_2, % 63.37/9.14 | all_84_3 gives: % 63.37/9.14 | (20) sdtlpdtrp0(xC, xi) = all_84_0 & sdtlpdtrp0(xN, xi) = all_84_3 & % 63.37/9.14 | szmzizndt0(all_84_3) = all_84_2 & sdtmndt0(all_84_3, all_84_2) = % 63.37/9.14 | all_84_1 & $i(all_84_0) & $i(all_84_1) & $i(all_84_2) & $i(all_84_3) & % 63.37/9.14 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xk) = % 63.37/9.14 | v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, all_84_1) | ~ % 63.37/9.14 | isCountable0(v1) | ~ aElementOf0(v0, xT) | ? [v3: $i] : ? [v4: % 63.37/9.14 | $i] : ( ~ (v4 = v0) & sdtlpdtrp0(all_84_0, v3) = v4 & $i(v4) & % 63.37/9.14 | $i(v3) & aElementOf0(v3, v2) & aSet0(v3))) % 63.37/9.14 | % 63.37/9.14 | ALPHA: (20) implies: % 63.37/9.14 | (21) sdtmndt0(all_84_3, all_84_2) = all_84_1 % 63.37/9.14 | (22) szmzizndt0(all_84_3) = all_84_2 % 63.37/9.14 | (23) sdtlpdtrp0(xN, xi) = all_84_3 % 63.37/9.14 | (24) sdtlpdtrp0(xC, xi) = all_84_0 % 63.37/9.14 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xk) = % 63.37/9.14 | v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, all_84_1) | ~ % 63.37/9.14 | isCountable0(v1) | ~ aElementOf0(v0, xT) | ? [v3: $i] : ? [v4: % 63.37/9.14 | $i] : ( ~ (v4 = v0) & sdtlpdtrp0(all_84_0, v3) = v4 & $i(v4) & % 63.37/9.14 | $i(v3) & aElementOf0(v3, v2) & aSet0(v3))) % 63.37/9.14 | % 63.37/9.14 | GROUND_INST: instantiating (6) with all_72_0, all_84_2, all_72_1, simplifying % 63.37/9.14 | with (11) gives: % 63.37/9.15 | (26) all_84_2 = all_72_0 | ~ (szmzizndt0(all_72_1) = all_84_2) % 63.37/9.15 | % 63.37/9.15 | GROUND_INST: instantiating (8) with all_72_1, all_84_3, xi, xN, simplifying % 63.37/9.15 | with (12), (23) gives: % 63.37/9.15 | (27) all_84_3 = all_72_1 % 63.37/9.15 | % 63.37/9.15 | GROUND_INST: instantiating (8) with xd, all_84_0, xi, xC, simplifying with % 63.37/9.15 | (13), (24) gives: % 63.37/9.15 | (28) all_84_0 = xd % 63.37/9.15 | % 63.37/9.15 | REDUCE: (22), (27) imply: % 63.37/9.15 | (29) szmzizndt0(all_72_1) = all_84_2 % 63.37/9.15 | % 63.37/9.15 | REDUCE: (21), (27) imply: % 63.37/9.15 | (30) sdtmndt0(all_72_1, all_84_2) = all_84_1 % 63.37/9.15 | % 63.37/9.15 | BETA: splitting (26) gives: % 63.37/9.15 | % 63.37/9.15 | Case 1: % 63.37/9.15 | | % 63.37/9.15 | | (31) ~ (szmzizndt0(all_72_1) = all_84_2) % 63.37/9.15 | | % 63.37/9.15 | | PRED_UNIFY: (29), (31) imply: % 63.37/9.15 | | (32) $false % 63.37/9.15 | | % 63.37/9.15 | | CLOSE: (32) is inconsistent. % 63.37/9.15 | | % 63.37/9.15 | Case 2: % 63.37/9.15 | | % 63.37/9.15 | | (33) all_84_2 = all_72_0 % 63.37/9.15 | | % 63.37/9.15 | | REDUCE: (30), (33) imply: % 63.37/9.15 | | (34) sdtmndt0(all_72_1, all_72_0) = all_84_1 % 63.37/9.15 | | % 63.37/9.15 | | GROUND_INST: instantiating (7) with xY, all_84_1, all_72_0, all_72_1, % 63.37/9.15 | | simplifying with (10), (34) gives: % 63.37/9.15 | | (35) all_84_1 = xY % 63.37/9.15 | | % 63.37/9.15 | | GROUND_INST: instantiating (25) with xu, xX, all_78_0, simplifying with (2), % 63.37/9.15 | | (3), (15), (16), (18) gives: % 63.37/9.15 | | (36) ~ aSubsetOf0(xX, all_84_1) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 63.37/9.15 | | xu) & sdtlpdtrp0(all_84_0, v0) = v1 & $i(v1) & $i(v0) & % 63.37/9.15 | | aElementOf0(v0, all_78_0) & aSet0(v0)) % 63.37/9.15 | | % 63.37/9.15 | | BETA: splitting (36) gives: % 63.37/9.15 | | % 63.37/9.15 | | Case 1: % 63.37/9.15 | | | % 63.37/9.15 | | | (37) ~ aSubsetOf0(xX, all_84_1) % 63.37/9.15 | | | % 63.37/9.15 | | | REDUCE: (35), (37) imply: % 63.37/9.15 | | | (38) ~ aSubsetOf0(xX, xY) % 63.37/9.15 | | | % 63.37/9.15 | | | PRED_UNIFY: (17), (38) imply: % 63.37/9.15 | | | (39) $false % 63.37/9.15 | | | % 63.37/9.15 | | | CLOSE: (39) is inconsistent. % 63.37/9.15 | | | % 63.37/9.15 | | Case 2: % 63.37/9.15 | | | % 63.37/9.15 | | | (40) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xu) & sdtlpdtrp0(all_84_0, % 63.37/9.15 | | | v0) = v1 & $i(v1) & $i(v0) & aElementOf0(v0, all_78_0) & % 63.37/9.15 | | | aSet0(v0)) % 63.37/9.15 | | | % 63.37/9.15 | | | DELTA: instantiating (40) with fresh symbols all_166_0, all_166_1 gives: % 63.37/9.15 | | | (41) ~ (all_166_0 = xu) & sdtlpdtrp0(all_84_0, all_166_1) = all_166_0 % 63.37/9.15 | | | & $i(all_166_0) & $i(all_166_1) & aElementOf0(all_166_1, all_78_0) % 63.37/9.15 | | | & aSet0(all_166_1) % 63.37/9.15 | | | % 63.37/9.15 | | | ALPHA: (41) implies: % 63.37/9.15 | | | (42) ~ (all_166_0 = xu) % 63.37/9.15 | | | (43) aSet0(all_166_1) % 63.37/9.15 | | | (44) aElementOf0(all_166_1, all_78_0) % 63.37/9.15 | | | (45) $i(all_166_1) % 63.37/9.15 | | | (46) sdtlpdtrp0(all_84_0, all_166_1) = all_166_0 % 63.37/9.15 | | | % 63.37/9.15 | | | REDUCE: (28), (46) imply: % 63.37/9.15 | | | (47) sdtlpdtrp0(xd, all_166_1) = all_166_0 % 63.37/9.15 | | | % 63.37/9.15 | | | GROUND_INST: instantiating (19) with all_166_1, all_166_0, simplifying % 63.37/9.15 | | | with (43), (44), (45), (47) gives: % 63.37/9.15 | | | (48) all_166_0 = xu % 63.37/9.15 | | | % 63.37/9.15 | | | REDUCE: (42), (48) imply: % 63.37/9.15 | | | (49) $false % 63.37/9.15 | | | % 63.37/9.15 | | | CLOSE: (49) is inconsistent. % 63.37/9.15 | | | % 63.37/9.15 | | End of split % 63.37/9.15 | | % 63.37/9.15 | End of split % 63.37/9.15 | % 63.37/9.15 End of proof % 63.37/9.15 % SZS output end Proof for theBenchmark % 63.37/9.15 % 63.37/9.15 8557ms %------------------------------------------------------------------------------