%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM547+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 : n005.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 11:48:32 EDT 2023 % Result : Theorem 84.05s 11.86s % Output : Proof 84.49s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM547+1 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n005.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 : Fri Aug 25 17:02:53 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.58/1.26 Prover 1: Preprocessing ... % 3.58/1.27 Prover 4: Preprocessing ... % 3.58/1.31 Prover 6: Preprocessing ... % 3.58/1.31 Prover 3: Preprocessing ... % 3.58/1.31 Prover 5: Preprocessing ... % 3.58/1.31 Prover 0: Preprocessing ... % 3.58/1.31 Prover 2: Preprocessing ... % 10.82/2.26 Prover 1: Constructing countermodel ... % 10.82/2.26 Prover 3: Constructing countermodel ... % 11.50/2.37 Prover 6: Proving ... % 11.98/2.42 Prover 5: Constructing countermodel ... % 11.98/2.43 Prover 2: Proving ... % 15.74/2.91 Prover 4: Constructing countermodel ... % 16.55/3.06 Prover 0: Proving ... % 72.06/10.36 Prover 2: stopped % 72.06/10.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.74/10.51 Prover 7: Preprocessing ... % 74.46/10.67 Prover 7: Constructing countermodel ... % 84.05/11.84 Prover 7: Found proof (size 47) % 84.05/11.84 Prover 7: proved (1464ms) % 84.05/11.84 Prover 6: stopped % 84.05/11.85 Prover 3: stopped % 84.05/11.85 Prover 0: stopped % 84.05/11.85 Prover 1: stopped % 84.05/11.85 Prover 4: stopped % 84.05/11.86 Prover 5: stopped % 84.05/11.86 % 84.05/11.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 84.05/11.86 % 84.05/11.87 % SZS output start Proof for theBenchmark % 84.05/11.87 Assumptions after simplification: % 84.05/11.87 --------------------------------- % 84.05/11.87 % 84.05/11.87 (mCountNFin_01) % 84.21/11.88 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 84.21/11.88 % 84.21/11.88 (mDefEmp) % 84.21/11.88 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 84.21/11.88 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 84.21/11.88 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 84.21/11.88 % 84.21/11.88 (mDefSeg) % 84.21/11.90 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 84.21/11.90 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 84.21/11.90 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~ % 84.21/11.90 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 84.21/11.90 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 84.21/11.91 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 84.21/11.91 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 84.21/11.91 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 84.21/11.91 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 84.21/11.91 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 84.21/11.91 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~ % 84.21/11.91 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4: % 84.21/11.91 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) | % 84.21/11.91 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) & % 84.21/11.91 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, % 84.21/11.91 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( % 84.21/11.91 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) % 84.21/11.91 | aSet0(v1)) % 84.21/11.91 % 84.21/11.91 (mDefSel) % 84.21/11.91 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 84.21/11.91 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) | % 84.21/11.91 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ % 84.21/11.91 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 84.21/11.91 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ % 84.21/11.91 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 84.21/11.91 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | % 84.21/11.91 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 84.21/11.91 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 84.21/11.91 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ? % 84.21/11.91 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~ % 84.21/11.91 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) & % 84.21/11.91 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4, % 84.21/11.91 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 84.21/11.91 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~ % 84.21/11.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1, % 84.21/11.91 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 84.21/11.91 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) % 84.21/11.91 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2)) % 84.21/11.91 % 84.21/11.91 (mNATSet) % 84.21/11.91 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 84.21/11.91 % 84.21/11.91 (mSegZero) % 84.21/11.91 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 84.21/11.91 % 84.21/11.91 (mZeroNum) % 84.21/11.91 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 84.21/11.91 % 84.21/11.91 (m__) % 84.21/11.92 $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & ! [v1: % 84.21/11.92 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0))) % 84.21/11.92 % 84.21/11.92 (m__2202) % 84.21/11.92 $i(xk) & $i(szNzAzT0) & aElementOf0(xk, szNzAzT0) % 84.21/11.92 % 84.21/11.92 (m__2202_02) % 84.21/11.92 ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS) % 84.21/11.92 % 84.21/11.92 (m__2227) % 84.21/11.92 $i(xT) & $i(xS) & $i(xk) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = % 84.21/11.92 slcrc0) & slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) & % 84.21/11.92 $i(v0) & aSubsetOf0(v0, v1)) % 84.21/11.92 % 84.21/11.92 (m__2256) % 84.21/11.92 $i(xx) & $i(xS) & aElementOf0(xx, xS) % 84.21/11.92 % 84.21/11.92 (function-axioms) % 84.21/11.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 84.21/11.92 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] % 84.21/11.92 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = % 84.21/11.92 v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 84.21/11.92 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, % 84.21/11.92 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 84.21/11.92 (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 84.21/11.92 ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & % 84.21/11.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) % 84.21/11.92 | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 % 84.21/11.92 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! % 84.21/11.92 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ % 84.21/11.92 (szszuzczcdt0(v2) = v0)) % 84.21/11.92 % 84.21/11.92 Further assumptions not needed in the proof: % 84.21/11.92 -------------------------------------------- % 84.21/11.92 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 84.21/11.92 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 84.21/11.92 mDefDiff, mDefMax, mDefMin, mDefSub, mDiffCons, mEOfElem, mElmSort, mEmpFin, % 84.21/11.92 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, mIHSort, mLessASymm, mLessRefl, % 84.21/11.92 mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatExtra, mNatNSucc, % 84.21/11.92 mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSelCSet, mSelFSet, mSelNSet, % 84.21/11.92 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, % 84.21/11.92 mSuccNum, mZeroLess % 84.21/11.92 % 84.21/11.92 Those formulas are unsatisfiable: % 84.21/11.92 --------------------------------- % 84.21/11.92 % 84.21/11.92 Begin of proof % 84.21/11.92 | % 84.21/11.92 | ALPHA: (mDefEmp) implies: % 84.21/11.92 | (1) aSet0(slcrc0) % 84.21/11.92 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 84.21/11.92 | (3) ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ aSet0(v0) | ? [v1: $i] : % 84.21/11.92 | ($i(v1) & aElementOf0(v1, v0))) % 84.21/11.92 | % 84.21/11.92 | ALPHA: (mCountNFin_01) implies: % 84.21/11.92 | (4) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 84.21/11.92 | % 84.21/11.92 | ALPHA: (mNATSet) implies: % 84.21/11.92 | (5) aSet0(szNzAzT0) % 84.21/11.92 | (6) isCountable0(szNzAzT0) % 84.21/11.93 | % 84.21/11.93 | ALPHA: (mZeroNum) implies: % 84.21/11.93 | (7) aElementOf0(sz00, szNzAzT0) % 84.21/11.93 | % 84.21/11.93 | ALPHA: (mDefSeg) implies: % 84.21/11.93 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = % 84.21/11.93 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ % 84.21/11.93 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3, % 84.21/11.93 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 & % 84.21/11.93 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) | % 84.21/11.93 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) & % 84.21/11.93 | aElementOf0(v3, szNzAzT0))))) % 84.21/11.93 | % 84.21/11.93 | ALPHA: (mSegZero) implies: % 84.21/11.93 | (9) slbdtrb0(sz00) = slcrc0 % 84.21/11.93 | % 84.21/11.93 | ALPHA: (mDefSel) implies: % 84.21/11.93 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = % 84.21/11.93 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, % 84.21/11.93 | szNzAzT0) | ~ aSet0(v0) | aSet0(v2)) % 84.21/11.93 | % 84.21/11.93 | ALPHA: (m__2202) implies: % 84.21/11.93 | (11) aElementOf0(xk, szNzAzT0) % 84.21/11.93 | (12) $i(szNzAzT0) % 84.21/11.93 | % 84.21/11.93 | ALPHA: (m__2202_02) implies: % 84.21/11.93 | (13) aSet0(xS) % 84.21/11.93 | (14) $i(sz00) % 84.21/11.93 | % 84.21/11.93 | ALPHA: (m__2227) implies: % 84.21/11.93 | (15) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = slcrc0) & slbdtsldtrb0(xT, xk) = % 84.21/11.93 | v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0, % 84.21/11.93 | v1)) % 84.21/11.93 | % 84.21/11.93 | ALPHA: (m__2256) implies: % 84.21/11.93 | (16) aElementOf0(xx, xS) % 84.49/11.93 | (17) $i(xx) % 84.49/11.93 | % 84.49/11.93 | ALPHA: (m__) implies: % 84.49/11.93 | (18) $i(xk) % 84.49/11.93 | (19) $i(xS) % 84.49/11.93 | (20) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 84.49/11.93 | $i(v1) | ~ aElementOf0(v1, v0))) % 84.49/11.93 | % 84.49/11.93 | ALPHA: (function-axioms) implies: % 84.49/11.93 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 84.49/11.93 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) % 84.49/11.93 | % 84.49/11.93 | DELTA: instantiating (20) with fresh symbol all_53_0 gives: % 84.49/11.93 | (22) slbdtsldtrb0(xS, xk) = all_53_0 & $i(all_53_0) & ! [v0: $i] : ( ~ % 84.49/11.93 | $i(v0) | ~ aElementOf0(v0, all_53_0)) % 84.49/11.93 | % 84.49/11.93 | ALPHA: (22) implies: % 84.49/11.93 | (23) slbdtsldtrb0(xS, xk) = all_53_0 % 84.49/11.93 | (24) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_53_0)) % 84.49/11.93 | % 84.49/11.93 | DELTA: instantiating (15) with fresh symbols all_56_0, all_56_1 gives: % 84.49/11.93 | (25) ~ (all_56_1 = slcrc0) & slbdtsldtrb0(xT, xk) = all_56_0 & % 84.49/11.93 | slbdtsldtrb0(xS, xk) = all_56_1 & $i(all_56_0) & $i(all_56_1) & % 84.49/11.93 | aSubsetOf0(all_56_1, all_56_0) % 84.49/11.93 | % 84.49/11.93 | ALPHA: (25) implies: % 84.49/11.93 | (26) ~ (all_56_1 = slcrc0) % 84.49/11.93 | (27) $i(all_56_1) % 84.49/11.93 | (28) slbdtsldtrb0(xS, xk) = all_56_1 % 84.49/11.93 | % 84.49/11.93 | BETA: splitting (4) gives: % 84.49/11.93 | % 84.49/11.93 | Case 1: % 84.49/11.93 | | % 84.49/11.93 | | (29) ~ isCountable0(slcrc0) % 84.49/11.93 | | % 84.49/11.94 | | GROUND_INST: instantiating (21) with all_53_0, all_56_1, xk, xS, simplifying % 84.49/11.94 | | with (23), (28) gives: % 84.49/11.94 | | (30) all_56_1 = all_53_0 % 84.49/11.94 | | % 84.49/11.94 | | PRED_UNIFY: (6), (29) imply: % 84.49/11.94 | | (31) ~ (szNzAzT0 = slcrc0) % 84.49/11.94 | | % 84.49/11.94 | | REDUCE: (26), (30) imply: % 84.49/11.94 | | (32) ~ (all_53_0 = slcrc0) % 84.49/11.94 | | % 84.49/11.94 | | REDUCE: (27), (30) imply: % 84.49/11.94 | | (33) $i(all_53_0) % 84.49/11.94 | | % 84.49/11.94 | | GROUND_INST: instantiating (3) with szNzAzT0, simplifying with (5), (12) % 84.49/11.94 | | gives: % 84.49/11.94 | | (34) szNzAzT0 = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 84.49/11.94 | | szNzAzT0)) % 84.49/11.94 | | % 84.49/11.94 | | GROUND_INST: instantiating (2) with xx, simplifying with (17) gives: % 84.49/11.94 | | (35) ~ aElementOf0(xx, slcrc0) % 84.49/11.94 | | % 84.49/11.94 | | GROUND_INST: instantiating (8) with sz00, slcrc0, xS, simplifying with (7), % 84.49/11.94 | | (9), (13), (14), (19) gives: % 84.49/11.94 | | (36) xS = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~ % 84.49/11.94 | | aElementOf0(v0, xS) | ~ aElementOf0(v0, szNzAzT0) | % 84.49/11.94 | | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) & % 84.49/11.94 | | (aElementOf0(v0, xS) | (szszuzczcdt0(v0) = v1 & $i(v1) & % 84.49/11.94 | | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0)))) % 84.49/11.94 | | % 84.49/11.94 | | GROUND_INST: instantiating (10) with xS, xk, all_53_0, simplifying with % 84.49/11.94 | | (11), (13), (18), (19), (23), (33) gives: % 84.49/11.94 | | (37) aSet0(all_53_0) % 84.49/11.94 | | % 84.49/11.94 | | BETA: splitting (34) gives: % 84.49/11.94 | | % 84.49/11.94 | | Case 1: % 84.49/11.94 | | | % 84.49/11.94 | | | (38) szNzAzT0 = slcrc0 % 84.49/11.94 | | | % 84.49/11.94 | | | REDUCE: (31), (38) imply: % 84.49/11.94 | | | (39) $false % 84.49/11.94 | | | % 84.49/11.94 | | | CLOSE: (39) is inconsistent. % 84.49/11.94 | | | % 84.49/11.94 | | Case 2: % 84.49/11.94 | | | % 84.49/11.94 | | | % 84.49/11.94 | | | PRED_UNIFY: (16), (35) imply: % 84.49/11.94 | | | (40) ~ (xS = slcrc0) % 84.49/11.94 | | | % 84.49/11.94 | | | BETA: splitting (36) gives: % 84.49/11.94 | | | % 84.49/11.94 | | | Case 1: % 84.49/11.94 | | | | % 84.49/11.94 | | | | (41) xS = slcrc0 % 84.49/11.94 | | | | % 84.49/11.94 | | | | REDUCE: (40), (41) imply: % 84.49/11.94 | | | | (42) $false % 84.49/11.94 | | | | % 84.49/11.94 | | | | CLOSE: (42) is inconsistent. % 84.49/11.94 | | | | % 84.49/11.94 | | | Case 2: % 84.49/11.94 | | | | % 84.49/11.94 | | | | % 84.49/11.94 | | | | GROUND_INST: instantiating (3) with all_53_0, simplifying with (33), % 84.49/11.94 | | | | (37) gives: % 84.49/11.94 | | | | (43) all_53_0 = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 84.49/11.94 | | | | all_53_0)) % 84.49/11.94 | | | | % 84.49/11.94 | | | | BETA: splitting (43) gives: % 84.49/11.94 | | | | % 84.49/11.94 | | | | Case 1: % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | (44) all_53_0 = slcrc0 % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | REDUCE: (32), (44) imply: % 84.49/11.94 | | | | | (45) $false % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | CLOSE: (45) is inconsistent. % 84.49/11.94 | | | | | % 84.49/11.94 | | | | Case 2: % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | (46) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_53_0)) % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | DELTA: instantiating (46) with fresh symbol all_146_0 gives: % 84.49/11.94 | | | | | (47) $i(all_146_0) & aElementOf0(all_146_0, all_53_0) % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | ALPHA: (47) implies: % 84.49/11.94 | | | | | (48) aElementOf0(all_146_0, all_53_0) % 84.49/11.94 | | | | | (49) $i(all_146_0) % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | GROUND_INST: instantiating (24) with all_146_0, simplifying with (48), % 84.49/11.94 | | | | | (49) gives: % 84.49/11.94 | | | | | (50) $false % 84.49/11.94 | | | | | % 84.49/11.94 | | | | | CLOSE: (50) is inconsistent. % 84.49/11.94 | | | | | % 84.49/11.94 | | | | End of split % 84.49/11.94 | | | | % 84.49/11.94 | | | End of split % 84.49/11.94 | | | % 84.49/11.94 | | End of split % 84.49/11.94 | | % 84.49/11.94 | Case 2: % 84.49/11.94 | | % 84.49/11.95 | | (51) ~ aSet0(slcrc0) % 84.49/11.95 | | % 84.49/11.95 | | PRED_UNIFY: (1), (51) imply: % 84.49/11.95 | | (52) $false % 84.49/11.95 | | % 84.49/11.95 | | CLOSE: (52) is inconsistent. % 84.49/11.95 | | % 84.49/11.95 | End of split % 84.49/11.95 | % 84.49/11.95 End of proof % 84.49/11.95 % SZS output end Proof for theBenchmark % 84.49/11.95 % 84.49/11.95 11328ms %------------------------------------------------------------------------------