%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG114+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 13:57:57 EDT 2023 % Result : Theorem 39.04s 5.87s % Output : Proof 102.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : RNG114+1 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 02:20:23 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.41/1.14 Prover 4: Preprocessing ... % 3.41/1.14 Prover 1: Preprocessing ... % 3.51/1.18 Prover 6: Preprocessing ... % 3.51/1.18 Prover 2: Preprocessing ... % 3.51/1.19 Prover 0: Preprocessing ... % 3.51/1.19 Prover 5: Preprocessing ... % 3.51/1.19 Prover 3: Preprocessing ... % 8.67/1.93 Prover 3: Constructing countermodel ... % 8.67/1.93 Prover 1: Constructing countermodel ... % 8.67/1.95 Prover 6: Proving ... % 9.33/2.01 Prover 5: Proving ... % 9.81/2.09 Prover 2: Proving ... % 10.51/2.14 Prover 4: Constructing countermodel ... % 11.15/2.24 Prover 0: Proving ... % 39.04/5.85 Prover 3: proved (5215ms) % 39.04/5.87 % 39.04/5.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 39.04/5.87 % 39.04/5.87 Prover 2: stopped % 39.04/5.87 Prover 5: stopped % 39.04/5.88 Prover 6: stopped % 39.04/5.89 Prover 0: stopped % 39.04/5.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 39.04/5.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 39.04/5.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 39.89/5.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 39.89/5.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 40.17/5.95 Prover 7: Preprocessing ... % 40.17/5.97 Prover 8: Preprocessing ... % 40.51/5.99 Prover 11: Preprocessing ... % 40.51/6.03 Prover 10: Preprocessing ... % 41.12/6.07 Prover 13: Preprocessing ... % 41.12/6.07 Prover 7: Constructing countermodel ... % 41.12/6.08 Prover 8: Warning: ignoring some quantifiers % 41.12/6.09 Prover 8: Constructing countermodel ... % 41.57/6.14 Prover 10: Constructing countermodel ... % 42.49/6.28 Prover 13: Warning: ignoring some quantifiers % 42.85/6.29 Prover 13: Constructing countermodel ... % 43.32/6.35 Prover 11: Constructing countermodel ... % 77.25/10.74 Prover 13: stopped % 77.25/10.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 77.71/10.79 Prover 16: Preprocessing ... % 78.50/10.89 Prover 16: Warning: ignoring some quantifiers % 78.50/10.90 Prover 16: Constructing countermodel ... % 102.51/13.94 Prover 10: Found proof (size 47) % 102.51/13.94 Prover 10: proved (8023ms) % 102.51/13.94 Prover 7: stopped % 102.51/13.94 Prover 16: stopped % 102.51/13.95 Prover 1: stopped % 102.51/13.95 Prover 4: stopped % 102.51/13.95 Prover 8: stopped % 102.51/13.95 Prover 11: stopped % 102.51/13.95 % 102.51/13.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 102.51/13.95 % 102.51/13.96 % SZS output start Proof for theBenchmark % 102.51/13.96 Assumptions after simplification: % 102.51/13.96 --------------------------------- % 102.51/13.96 % 102.51/13.96 (mDefPrIdeal) % 102.51/13.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) = % 102.51/13.99 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 102.51/13.99 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & ! % 102.51/13.99 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~ % 102.51/13.99 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: % 102.51/13.99 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6: % 102.51/13.99 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) & % 102.51/13.99 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 & % 102.51/13.99 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 102.51/13.99 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, % 102.51/13.99 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 102.51/13.99 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 102.51/13.99 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 102.51/13.99 % 102.51/13.99 (mDefSSum) % 102.51/14.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 102.51/14.00 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) | % 102.51/14.00 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 102.51/14.00 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 102.51/14.00 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 102.51/14.00 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 102.51/14.00 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ? % 102.51/14.00 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3) % 102.51/14.00 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) | % 102.51/14.00 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & % 102.51/14.00 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, % 102.51/14.00 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 102.51/14.00 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 102.51/14.00 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 102.51/14.00 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 102.51/14.00 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] : % 102.51/14.00 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 102.51/14.00 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 102.51/14.00 % 102.51/14.00 (m__) % 102.51/14.00 $i(xu) & $i(xb) & $i(xa) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 102.51/14.00 $i] : ( ~ (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~ % 102.51/14.00 (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ % 102.51/14.00 aElement0(v0)) % 102.51/14.00 % 102.51/14.00 (m__2091) % 102.51/14.00 $i(xb) & $i(xa) & aElement0(xb) & aElement0(xa) % 102.51/14.00 % 102.51/14.00 (m__2174) % 102.51/14.01 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 102.51/14.01 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI)) % 102.51/14.01 % 102.51/14.01 (m__2203) % 102.51/14.01 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 102.51/14.01 slsdtgt0(xa) = v0 & $i(v1) & $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa, % 102.51/14.01 v0) & aElementOf0(sz00, v1) & aElementOf0(sz00, v0)) % 102.51/14.01 % 102.51/14.01 (m__2228) % 102.51/14.01 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 102.51/14.01 $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, % 102.51/14.01 v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2)) % 102.51/14.01 % 102.51/14.01 (m__2273) % 102.51/14.01 $i(xu) & $i(xI) & $i(sz00) & ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 % 102.51/14.01 & $i(v0) & aElementOf0(xu, xI) & ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 102.51/14.01 (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ iLess0(v2, v0) | ~ aElementOf0(v1, % 102.51/14.01 xI))) % 102.51/14.01 % 102.51/14.01 (function-axioms) % 102.51/14.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 102.51/14.01 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 102.51/14.01 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 102.51/14.01 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 102.51/14.01 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 102.51/14.01 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 102.51/14.01 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 102.51/14.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 102.51/14.01 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 102.51/14.01 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 102.51/14.01 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 102.51/14.01 % 102.51/14.01 Further assumptions not needed in the proof: % 102.51/14.01 -------------------------------------------- % 102.51/14.01 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder, % 102.51/14.01 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDivision, % 102.51/14.01 mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulComm, mMulMnOne, % 102.51/14.01 mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort, mSortsB, % 102.51/14.01 mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2110, m__2129, m__2383 % 102.51/14.01 % 102.51/14.01 Those formulas are unsatisfiable: % 102.51/14.01 --------------------------------- % 102.51/14.01 % 102.51/14.01 Begin of proof % 102.51/14.01 | % 102.51/14.02 | ALPHA: (mDefSSum) implies: % 102.51/14.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 102.51/14.02 | (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 102.51/14.02 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ? % 102.51/14.02 | [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 102.51/14.02 | aElementOf0(v5, v1) & aElementOf0(v4, v0))) % 102.51/14.02 | % 102.51/14.02 | ALPHA: (mDefPrIdeal) implies: % 102.51/14.02 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ $i(v1) | ~ % 102.51/14.02 | $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 102.51/14.02 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 102.51/14.02 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 102.51/14.02 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 102.51/14.02 | aElement0(v3))) % 102.51/14.02 | % 102.51/14.02 | ALPHA: (m__2091) implies: % 102.51/14.02 | (4) aElement0(xa) % 102.51/14.02 | (5) aElement0(xb) % 102.51/14.02 | % 102.51/14.02 | ALPHA: (m__2174) implies: % 102.51/14.02 | (6) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 102.51/14.02 | sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI)) % 102.51/14.02 | % 102.51/14.02 | ALPHA: (m__2203) implies: % 102.51/14.02 | (7) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 102.51/14.02 | $i(v1) & $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa, v0) & % 102.51/14.02 | aElementOf0(sz00, v1) & aElementOf0(sz00, v0)) % 102.51/14.02 | % 102.51/14.02 | ALPHA: (m__2228) implies: % 102.51/14.02 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = sz00) % 102.51/14.02 | & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & % 102.51/14.02 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2)) % 102.51/14.02 | % 102.51/14.02 | ALPHA: (m__2273) implies: % 102.51/14.02 | (9) ? [v0: $i] : ( ~ (xu = sz00) & sbrdtbr0(xu) = v0 & $i(v0) & % 102.51/14.02 | aElementOf0(xu, xI) & ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 102.51/14.02 | (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ iLess0(v2, v0) | ~ % 102.51/14.02 | aElementOf0(v1, xI))) % 102.51/14.02 | % 102.51/14.02 | ALPHA: (m__) implies: % 102.51/14.02 | (10) $i(xa) % 102.51/14.02 | (11) $i(xb) % 102.51/14.02 | (12) $i(xu) % 102.51/14.03 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 102.51/14.03 | (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~ % 102.51/14.03 | (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | % 102.51/14.03 | ~ aElement0(v0)) % 102.51/14.03 | % 102.51/14.03 | ALPHA: (function-axioms) implies: % 102.51/14.03 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) % 102.51/14.03 | = v1) | ~ (slsdtgt0(v2) = v0)) % 102.51/14.03 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 102.51/14.03 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) % 102.51/14.03 | % 102.51/14.03 | DELTA: instantiating (6) with fresh symbols all_35_0, all_35_1 gives: % 102.51/14.03 | (16) slsdtgt0(xb) = all_35_0 & slsdtgt0(xa) = all_35_1 & sdtpldt1(all_35_1, % 102.51/14.03 | all_35_0) = xI & $i(all_35_0) & $i(all_35_1) & aIdeal0(xI) % 102.51/14.03 | % 102.51/14.03 | ALPHA: (16) implies: % 102.51/14.03 | (17) sdtpldt1(all_35_1, all_35_0) = xI % 102.51/14.03 | (18) slsdtgt0(xa) = all_35_1 % 102.51/14.03 | (19) slsdtgt0(xb) = all_35_0 % 102.51/14.03 | % 102.51/14.03 | DELTA: instantiating (7) with fresh symbols all_37_0, all_37_1 gives: % 102.51/14.03 | (20) slsdtgt0(xb) = all_37_0 & slsdtgt0(xa) = all_37_1 & $i(all_37_0) & % 102.51/14.03 | $i(all_37_1) & aElementOf0(xb, all_37_0) & aElementOf0(xa, all_37_1) & % 102.51/14.03 | aElementOf0(sz00, all_37_0) & aElementOf0(sz00, all_37_1) % 102.51/14.03 | % 102.51/14.03 | ALPHA: (20) implies: % 102.51/14.03 | (21) $i(all_37_1) % 102.51/14.03 | (22) $i(all_37_0) % 102.51/14.03 | (23) slsdtgt0(xa) = all_37_1 % 102.51/14.03 | (24) slsdtgt0(xb) = all_37_0 % 102.51/14.03 | % 102.51/14.03 | DELTA: instantiating (9) with fresh symbol all_42_0 gives: % 102.51/14.03 | (25) ~ (xu = sz00) & sbrdtbr0(xu) = all_42_0 & $i(all_42_0) & % 102.51/14.03 | aElementOf0(xu, xI) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ % 102.51/14.03 | (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ iLess0(v1, all_42_0) | ~ % 102.51/14.03 | aElementOf0(v0, xI)) % 102.51/14.03 | % 102.51/14.03 | ALPHA: (25) implies: % 102.51/14.03 | (26) aElementOf0(xu, xI) % 102.51/14.03 | % 102.51/14.03 | DELTA: instantiating (8) with fresh symbols all_45_0, all_45_1, all_45_2, % 102.51/14.03 | all_45_3 gives: % 102.51/14.03 | (27) ~ (all_45_0 = sz00) & slsdtgt0(xb) = all_45_2 & slsdtgt0(xa) = % 102.51/14.03 | all_45_3 & sdtpldt1(all_45_3, all_45_2) = all_45_1 & $i(all_45_0) & % 102.51/14.03 | $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & aElementOf0(all_45_0, % 102.51/14.03 | all_45_1) % 102.51/14.03 | % 102.51/14.03 | ALPHA: (27) implies: % 102.51/14.03 | (28) $i(all_45_1) % 102.51/14.03 | (29) sdtpldt1(all_45_3, all_45_2) = all_45_1 % 102.51/14.03 | (30) slsdtgt0(xa) = all_45_3 % 102.51/14.03 | (31) slsdtgt0(xb) = all_45_2 % 102.51/14.03 | % 102.51/14.03 | GROUND_INST: instantiating (14) with all_37_1, all_45_3, xa, simplifying with % 102.51/14.03 | (23), (30) gives: % 102.51/14.03 | (32) all_45_3 = all_37_1 % 102.51/14.03 | % 102.51/14.03 | GROUND_INST: instantiating (14) with all_35_1, all_45_3, xa, simplifying with % 102.51/14.03 | (18), (30) gives: % 102.51/14.03 | (33) all_45_3 = all_35_1 % 102.51/14.03 | % 102.51/14.03 | GROUND_INST: instantiating (14) with all_37_0, all_45_2, xb, simplifying with % 102.51/14.03 | (24), (31) gives: % 102.51/14.03 | (34) all_45_2 = all_37_0 % 102.51/14.03 | % 102.51/14.03 | GROUND_INST: instantiating (14) with all_35_0, all_45_2, xb, simplifying with % 102.51/14.03 | (19), (31) gives: % 102.51/14.04 | (35) all_45_2 = all_35_0 % 102.51/14.04 | % 102.51/14.04 | COMBINE_EQS: (34), (35) imply: % 102.51/14.04 | (36) all_37_0 = all_35_0 % 102.51/14.04 | % 102.51/14.04 | SIMP: (36) implies: % 102.51/14.04 | (37) all_37_0 = all_35_0 % 102.51/14.04 | % 102.51/14.04 | COMBINE_EQS: (32), (33) imply: % 102.51/14.04 | (38) all_37_1 = all_35_1 % 102.51/14.04 | % 102.51/14.04 | SIMP: (38) implies: % 102.51/14.04 | (39) all_37_1 = all_35_1 % 102.51/14.04 | % 102.51/14.04 | REDUCE: (29), (33), (35) imply: % 102.51/14.04 | (40) sdtpldt1(all_35_1, all_35_0) = all_45_1 % 102.51/14.04 | % 102.51/14.04 | REDUCE: (22), (37) imply: % 102.51/14.04 | (41) $i(all_35_0) % 102.51/14.04 | % 102.51/14.04 | REDUCE: (21), (39) imply: % 102.51/14.04 | (42) $i(all_35_1) % 102.51/14.04 | % 102.51/14.04 | GROUND_INST: instantiating (15) with xI, all_45_1, all_35_0, all_35_1, % 102.51/14.04 | simplifying with (17), (40) gives: % 102.51/14.04 | (43) all_45_1 = xI % 102.51/14.04 | % 102.51/14.04 | REDUCE: (28), (43) imply: % 102.51/14.04 | (44) $i(xI) % 102.51/14.04 | % 102.51/14.04 | GROUND_INST: instantiating (2) with xa, all_35_1, simplifying with (4), (10), % 102.51/14.04 | (18), (42) gives: % 102.51/14.04 | (45) aSet0(all_35_1) % 102.51/14.04 | % 102.51/14.04 | GROUND_INST: instantiating (2) with xb, all_35_0, simplifying with (5), (11), % 102.51/14.04 | (19), (41) gives: % 102.51/14.04 | (46) aSet0(all_35_0) % 102.51/14.04 | % 102.51/14.04 | GROUND_INST: instantiating (1) with all_35_1, all_35_0, xI, xu, simplifying % 102.51/14.04 | with (12), (17), (26), (41), (42), (44), (45), (46) gives: % 102.51/14.04 | (47) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, v1) = xu & $i(v1) & $i(v0) & % 102.51/14.04 | aElementOf0(v1, all_35_0) & aElementOf0(v0, all_35_1)) % 102.51/14.04 | % 102.51/14.04 | DELTA: instantiating (47) with fresh symbols all_83_0, all_83_1 gives: % 102.51/14.04 | (48) sdtpldt0(all_83_1, all_83_0) = xu & $i(all_83_0) & $i(all_83_1) & % 102.51/14.04 | aElementOf0(all_83_0, all_35_0) & aElementOf0(all_83_1, all_35_1) % 102.51/14.04 | % 102.51/14.04 | ALPHA: (48) implies: % 102.51/14.04 | (49) aElementOf0(all_83_1, all_35_1) % 102.51/14.04 | (50) aElementOf0(all_83_0, all_35_0) % 102.51/14.04 | (51) $i(all_83_1) % 102.51/14.04 | (52) $i(all_83_0) % 102.51/14.04 | (53) sdtpldt0(all_83_1, all_83_0) = xu % 102.51/14.04 | % 102.51/14.04 | GROUND_INST: instantiating (3) with xa, all_35_1, all_83_1, simplifying with % 102.51/14.04 | (4), (10), (18), (42), (49), (51) gives: % 102.51/14.04 | (54) ? [v0: $i] : (sdtasdt0(xa, v0) = all_83_1 & $i(v0) & aElement0(v0)) % 102.51/14.04 | % 102.51/14.04 | GROUND_INST: instantiating (3) with xb, all_35_0, all_83_0, simplifying with % 102.51/14.04 | (5), (11), (19), (41), (50), (52) gives: % 102.51/14.04 | (55) ? [v0: $i] : (sdtasdt0(xb, v0) = all_83_0 & $i(v0) & aElement0(v0)) % 102.51/14.04 | % 102.51/14.04 | DELTA: instantiating (55) with fresh symbol all_263_0 gives: % 102.51/14.04 | (56) sdtasdt0(xb, all_263_0) = all_83_0 & $i(all_263_0) & % 102.51/14.04 | aElement0(all_263_0) % 102.51/14.04 | % 102.51/14.04 | ALPHA: (56) implies: % 102.51/14.04 | (57) aElement0(all_263_0) % 102.51/14.04 | (58) $i(all_263_0) % 102.51/14.04 | (59) sdtasdt0(xb, all_263_0) = all_83_0 % 102.51/14.04 | % 102.51/14.04 | DELTA: instantiating (54) with fresh symbol all_267_0 gives: % 102.51/14.05 | (60) sdtasdt0(xa, all_267_0) = all_83_1 & $i(all_267_0) & % 102.51/14.05 | aElement0(all_267_0) % 102.51/14.05 | % 102.51/14.05 | ALPHA: (60) implies: % 102.51/14.05 | (61) aElement0(all_267_0) % 102.51/14.05 | (62) $i(all_267_0) % 102.51/14.05 | (63) sdtasdt0(xa, all_267_0) = all_83_1 % 102.51/14.05 | % 102.51/14.05 | GROUND_INST: instantiating (13) with all_267_0, all_263_0, all_83_1, all_83_0, % 102.51/14.05 | simplifying with (53), (57), (58), (59), (61), (62), (63) gives: % 102.51/14.05 | (64) $false % 102.51/14.05 | % 102.51/14.05 | CLOSE: (64) is inconsistent. % 102.51/14.05 | % 102.51/14.05 End of proof % 102.51/14.05 % SZS output end Proof for theBenchmark % 102.51/14.05 % 102.51/14.05 13429ms %------------------------------------------------------------------------------