%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 266.11s 36.41s % Output : Proof 267.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG112+4 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n007.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 01:19:42 EDT 2023 % 0.13/0.35 % 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 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 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 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 % 3.48/1.27 Prover 4: Preprocessing ... % 3.48/1.27 Prover 1: Preprocessing ... % 3.85/1.32 Prover 6: Preprocessing ... % 3.85/1.32 Prover 2: Preprocessing ... % 3.85/1.32 Prover 5: Preprocessing ... % 3.85/1.33 Prover 0: Preprocessing ... % 3.85/1.33 Prover 3: Preprocessing ... % 11.51/2.38 Prover 1: Constructing countermodel ... % 11.51/2.39 Prover 6: Proving ... % 11.51/2.40 Prover 5: Proving ... % 11.51/2.41 Prover 3: Constructing countermodel ... % 12.36/2.51 Prover 2: Proving ... % 13.35/2.64 Prover 0: Proving ... % 13.35/2.66 Prover 4: Constructing countermodel ... % 72.89/10.38 Prover 2: stopped % 72.89/10.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.99/10.52 Prover 7: Preprocessing ... % 75.74/10.76 Prover 7: Constructing countermodel ... % 100.01/13.98 Prover 5: stopped % 100.01/14.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.77/14.06 Prover 8: Preprocessing ... % 102.66/14.28 Prover 8: Warning: ignoring some quantifiers % 102.80/14.29 Prover 8: Constructing countermodel ... % 115.59/15.98 Prover 1: stopped % 115.59/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.59/16.08 Prover 9: Preprocessing ... % 118.15/16.31 Prover 9: Constructing countermodel ... % 129.68/17.89 Prover 6: stopped % 129.68/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 130.50/17.98 Prover 10: Preprocessing ... % 131.22/18.12 Prover 10: Constructing countermodel ... % 220.66/30.23 Prover 7: stopped % 220.66/30.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 221.28/30.30 Prover 11: Preprocessing ... % 223.59/30.59 Prover 11: Constructing countermodel ... % 266.11/36.40 Prover 10: Found proof (size 56) % 266.11/36.40 Prover 10: proved (18510ms) % 266.11/36.40 Prover 9: stopped % 266.11/36.40 Prover 0: stopped % 266.11/36.40 Prover 3: stopped % 266.11/36.41 Prover 8: stopped % 266.11/36.41 Prover 4: stopped % 266.11/36.41 Prover 11: stopped % 266.11/36.41 % 266.11/36.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 266.11/36.41 % 266.11/36.42 % SZS output start Proof for theBenchmark % 266.11/36.42 Assumptions after simplification: % 266.11/36.42 --------------------------------- % 266.11/36.42 % 266.11/36.42 (m__) % 267.17/36.46 $i(xI) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : % 267.17/36.46 (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 267.17/36.46 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v2 = sz00 | ~ (sbrdtbr0(v2) = v3) | % 267.17/36.46 ~ (sdtpldt0(v4, v5) = v2) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ % 267.17/36.46 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ? [v6: $i] : ? [v7: $i] : % 267.17/36.46 ? [v8: $i] : ? [v9: $i] : ( ~ (v6 = sz00) & sbrdtbr0(v6) = v7 & % 267.17/36.46 sdtpldt0(v8, v9) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & iLess0(v7, % 267.17/36.46 v3) & aElementOf0(v9, v1) & aElementOf0(v8, v0) & aElementOf0(v6, % 267.22/36.46 xI))) & ! [v2: $i] : ! [v3: $i] : (v2 = sz00 | ~ (sbrdtbr0(v2) = % 267.22/36.46 v3) | ~ $i(v2) | ~ aElementOf0(v2, xI) | ? [v4: $i] : ? [v5: $i] : % 267.22/36.46 ? [v6: $i] : ? [v7: $i] : ( ~ (v4 = sz00) & sbrdtbr0(v4) = v5 & % 267.22/36.46 sdtpldt0(v6, v7) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & iLess0(v5, % 267.22/36.46 v3) & aElementOf0(v7, v1) & aElementOf0(v6, v0) & aElementOf0(v4, % 267.22/36.46 xI)))) % 267.22/36.46 % 267.22/36.46 (m__2174) % 267.22/36.46 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & % 267.22/36.46 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI) & % 267.22/36.46 aSet0(xI) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v2) % 267.22/36.46 = v4) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v2, xI) | ~ % 267.22/36.46 aElement0(v3) | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ! [v4: % 267.22/36.46 $i] : ( ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 267.22/36.46 aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) | aElementOf0(v2, xI)) & ! % 267.22/36.47 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ % 267.22/36.47 $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xI) | ~ aElementOf0(v2, xI) | % 267.22/36.47 aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(xb, v3) = % 267.22/36.47 v2) | ~ $i(v3) | ~ $i(v2) | ~ aElement0(v3) | aElementOf0(v2, v1)) & % 267.22/36.47 ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(xa, v3) = v2) | ~ $i(v3) | ~ % 267.22/36.47 $i(v2) | ~ aElement0(v3) | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ % 267.22/36.47 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtasdt0(xb, v3) = v2 & % 267.22/36.47 $i(v3) & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 267.22/36.47 v0) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & $i(v3) & aElement0(v3))) & % 267.22/36.47 ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xI) | ? [v3: $i] : ? [v4: $i] % 267.22/36.47 : (sdtpldt0(v3, v4) = v2 & $i(v4) & $i(v3) & aElementOf0(v4, v1) & % 267.22/36.47 aElementOf0(v3, v0)))) % 267.22/36.47 % 267.22/36.47 (m__2203) % 267.22/36.47 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 267.22/36.47 $i] : ? [v4: $i] : ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 267.22/36.47 sdtasdt0(xb, v3) = sz00 & sdtasdt0(xb, v2) = xb & sdtasdt0(xa, v5) = sz00 & % 267.22/36.47 sdtasdt0(xa, v4) = xa & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 267.22/36.47 & aElementOf0(xb, v1) & aElementOf0(xa, v0) & aElementOf0(sz00, v1) & % 267.22/36.47 aElementOf0(sz00, v0) & aElement0(v5) & aElement0(v4) & aElement0(v3) & % 267.22/36.47 aElement0(v2)) % 267.22/36.47 % 267.22/36.47 (m__2228) % 267.22/36.47 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 267.22/36.47 $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & % 267.22/36.47 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & sdtpldt0(v4, v5) = v3 & $i(v5) & % 267.22/36.47 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v1) & % 267.22/36.47 aElementOf0(v4, v0) & aElementOf0(v3, v2) & ! [v6: $i] : ! [v7: $i] : ( ~ % 267.22/36.47 (sdtasdt0(xb, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v7) | % 267.22/36.47 aElementOf0(v6, v1)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtasdt0(xa, v7) = % 267.22/36.47 v6) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v7) | aElementOf0(v6, v0)) & % 267.22/36.47 ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v1) | ? [v7: $i] : % 267.22/36.47 (sdtasdt0(xb, v7) = v6 & $i(v7) & aElement0(v7))) & ! [v6: $i] : ( ~ % 267.22/36.47 $i(v6) | ~ aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xa, v7) = v6 & % 267.22/36.47 $i(v7) & aElement0(v7)))) % 267.22/36.48 % 267.22/36.48 (m__2351) % 267.22/36.48 $i(xI) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : % 267.22/36.48 (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! % 267.22/36.48 [v3: $i] : ! [v4: $i] : (v2 = sz00 | ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) % 267.22/36.48 | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) % 267.22/36.48 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v5 = sz00) % 267.22/36.48 & sbrdtbr0(v5) = v6 & sdtpldt0(v7, v8) = v5 & $i(v8) & $i(v7) & $i(v6) & % 267.22/36.48 $i(v5) & aElementOf0(v8, v1) & aElementOf0(v7, v0) & aElementOf0(v5, xI) % 267.22/36.48 & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : ! [v12: $i] : (v9 = sz00 % 267.22/36.48 | ~ (sbrdtbr0(v9) = v10) | ~ (sdtpldt0(v11, v12) = v9) | ~ $i(v12) % 267.22/36.48 | ~ $i(v11) | ~ $i(v9) | ~ iLess0(v10, v6) | ~ aElementOf0(v12, % 267.22/36.48 v1) | ~ aElementOf0(v11, v0)) & ! [v9: $i] : ! [v10: $i] : (v9 = % 267.22/36.48 sz00 | ~ (sbrdtbr0(v9) = v10) | ~ $i(v9) | ~ iLess0(v10, v6) | ~ % 267.22/36.48 aElementOf0(v9, xI)))) & ! [v2: $i] : (v2 = sz00 | ~ $i(v2) | ~ % 267.22/36.48 aElementOf0(v2, xI) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 267.22/36.48 $i] : ( ~ (v3 = sz00) & sbrdtbr0(v3) = v4 & sdtpldt0(v5, v6) = v3 & % 267.22/36.48 $i(v6) & $i(v5) & $i(v4) & $i(v3) & aElementOf0(v6, v1) & % 267.22/36.48 aElementOf0(v5, v0) & aElementOf0(v3, xI) & ! [v7: $i] : ! [v8: $i] : % 267.22/36.48 ! [v9: $i] : ! [v10: $i] : (v7 = sz00 | ~ (sbrdtbr0(v7) = v8) | ~ % 267.22/36.48 (sdtpldt0(v9, v10) = v7) | ~ $i(v10) | ~ $i(v9) | ~ $i(v7) | ~ % 267.22/36.48 iLess0(v8, v4) | ~ aElementOf0(v10, v1) | ~ aElementOf0(v9, v0)) & % 267.22/36.48 ! [v7: $i] : ! [v8: $i] : (v7 = sz00 | ~ (sbrdtbr0(v7) = v8) | ~ % 267.22/36.48 $i(v7) | ~ iLess0(v8, v4) | ~ aElementOf0(v7, xI))))) % 267.22/36.48 % 267.22/36.48 (function-axioms) % 267.22/36.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 267.22/36.49 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 267.22/36.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 267.22/36.49 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 267.22/36.49 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 267.22/36.49 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 267.22/36.49 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 267.22/36.49 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 267.22/36.49 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 267.22/36.49 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 267.22/36.49 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 267.22/36.49 % 267.22/36.49 Further assumptions not needed in the proof: % 267.22/36.49 -------------------------------------------- % 267.22/36.49 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder, % 267.22/36.49 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefPrIdeal, mDefRel, mDefSInt, % 267.22/36.49 mDefSSum, mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, % 267.22/36.49 mMulComm, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, % 267.22/36.49 mSetSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2091, % 267.22/36.49 m__2110, m__2129 % 267.22/36.49 % 267.22/36.49 Those formulas are unsatisfiable: % 267.22/36.49 --------------------------------- % 267.22/36.49 % 267.22/36.49 Begin of proof % 267.22/36.49 | % 267.22/36.49 | ALPHA: (m__2174) implies: % 267.22/36.50 | (1) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 267.22/36.50 | sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI) & aSet0(xI) & % 267.22/36.50 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v2) = v4) % 267.22/36.50 | | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v2, xI) | ~ aElement0(v3) % 267.22/36.50 | | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 267.22/36.50 | ( ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 267.22/36.50 | aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) | aElementOf0(v2, xI)) % 267.22/36.50 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v2, v3) = % 267.22/36.50 | v4) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xI) | ~ % 267.22/36.50 | aElementOf0(v2, xI) | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: % 267.22/36.50 | $i] : ( ~ (sdtasdt0(xb, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 267.22/36.50 | aElement0(v3) | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] : % 267.22/36.50 | ( ~ (sdtasdt0(xa, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 267.22/36.50 | aElement0(v3) | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) | % 267.22/36.50 | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtasdt0(xb, v3) = v2 & % 267.22/36.50 | $i(v3) & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ % 267.22/36.50 | aElementOf0(v2, v0) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & $i(v3) % 267.22/36.50 | & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, % 267.22/36.50 | xI) | ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v3, v4) = v2 & $i(v4) % 267.22/36.50 | & $i(v3) & aElementOf0(v4, v1) & aElementOf0(v3, v0)))) % 267.22/36.50 | % 267.22/36.50 | ALPHA: (m__2203) implies: % 267.22/36.50 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 267.22/36.50 | ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtasdt0(xb, v3) % 267.22/36.50 | = sz00 & sdtasdt0(xb, v2) = xb & sdtasdt0(xa, v5) = sz00 & % 267.22/36.50 | sdtasdt0(xa, v4) = xa & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 267.22/36.50 | $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa, v0) & % 267.22/36.50 | aElementOf0(sz00, v1) & aElementOf0(sz00, v0) & aElement0(v5) & % 267.22/36.50 | aElement0(v4) & aElement0(v3) & aElement0(v2)) % 267.22/36.50 | % 267.22/36.50 | ALPHA: (m__2228) implies: % 267.22/36.50 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 267.22/36.50 | ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 267.22/36.50 | sdtpldt1(v0, v1) = v2 & sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 267.22/36.50 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v1) & % 267.22/36.50 | aElementOf0(v4, v0) & aElementOf0(v3, v2) & ! [v6: $i] : ! [v7: $i] % 267.22/36.50 | : ( ~ (sdtasdt0(xb, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~ % 267.22/36.50 | aElement0(v7) | aElementOf0(v6, v1)) & ! [v6: $i] : ! [v7: $i] : % 267.22/36.50 | ( ~ (sdtasdt0(xa, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~ % 267.22/36.50 | aElement0(v7) | aElementOf0(v6, v0)) & ! [v6: $i] : ( ~ $i(v6) | % 267.22/36.50 | ~ aElementOf0(v6, v1) | ? [v7: $i] : (sdtasdt0(xb, v7) = v6 & % 267.22/36.50 | $i(v7) & aElement0(v7))) & ! [v6: $i] : ( ~ $i(v6) | ~ % 267.22/36.50 | aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xa, v7) = v6 & $i(v7) % 267.22/36.50 | & aElement0(v7)))) % 267.22/36.50 | % 267.22/36.50 | ALPHA: (m__2351) implies: % 267.22/36.51 | (4) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 267.22/36.51 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = % 267.22/36.51 | sz00 | ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ % 267.22/36.51 | $i(v2) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) | ? [v5: % 267.22/36.51 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v5 = sz00) & % 267.22/36.51 | sbrdtbr0(v5) = v6 & sdtpldt0(v7, v8) = v5 & $i(v8) & $i(v7) & % 267.22/36.51 | $i(v6) & $i(v5) & aElementOf0(v8, v1) & aElementOf0(v7, v0) & % 267.22/36.51 | aElementOf0(v5, xI) & ! [v9: $i] : ! [v10: $i] : ! [v11: $i] : % 267.22/36.51 | ! [v12: $i] : (v9 = sz00 | ~ (sbrdtbr0(v9) = v10) | ~ % 267.22/36.51 | (sdtpldt0(v11, v12) = v9) | ~ $i(v12) | ~ $i(v11) | ~ $i(v9) % 267.22/36.51 | | ~ iLess0(v10, v6) | ~ aElementOf0(v12, v1) | ~ % 267.22/36.51 | aElementOf0(v11, v0)) & ! [v9: $i] : ! [v10: $i] : (v9 = sz00 % 267.22/36.51 | | ~ (sbrdtbr0(v9) = v10) | ~ $i(v9) | ~ iLess0(v10, v6) | ~ % 267.22/36.51 | aElementOf0(v9, xI)))) & ! [v2: $i] : (v2 = sz00 | ~ $i(v2) | % 267.22/36.51 | ~ aElementOf0(v2, xI) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 267.22/36.51 | ? [v6: $i] : ( ~ (v3 = sz00) & sbrdtbr0(v3) = v4 & sdtpldt0(v5, v6) % 267.22/36.51 | = v3 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & aElementOf0(v6, v1) & % 267.22/36.51 | aElementOf0(v5, v0) & aElementOf0(v3, xI) & ! [v7: $i] : ! [v8: % 267.22/36.51 | $i] : ! [v9: $i] : ! [v10: $i] : (v7 = sz00 | ~ % 267.22/36.51 | (sbrdtbr0(v7) = v8) | ~ (sdtpldt0(v9, v10) = v7) | ~ $i(v10) % 267.22/36.51 | | ~ $i(v9) | ~ $i(v7) | ~ iLess0(v8, v4) | ~ % 267.22/36.51 | aElementOf0(v10, v1) | ~ aElementOf0(v9, v0)) & ! [v7: $i] : % 267.22/36.51 | ! [v8: $i] : (v7 = sz00 | ~ (sbrdtbr0(v7) = v8) | ~ $i(v7) | ~ % 267.22/36.51 | iLess0(v8, v4) | ~ aElementOf0(v7, xI))))) % 267.22/36.51 | % 267.43/36.51 | ALPHA: (m__) implies: % 267.43/36.51 | (5) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & % 267.43/36.51 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 267.43/36.51 | $i] : (v2 = sz00 | ~ (sbrdtbr0(v2) = v3) | ~ (sdtpldt0(v4, v5) = % 267.43/36.51 | v2) | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v5, v1) % 267.43/36.51 | | ~ aElementOf0(v4, v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 267.43/36.51 | : ? [v9: $i] : ( ~ (v6 = sz00) & sbrdtbr0(v6) = v7 & sdtpldt0(v8, % 267.43/36.51 | v9) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & iLess0(v7, v3) & % 267.43/36.51 | aElementOf0(v9, v1) & aElementOf0(v8, v0) & aElementOf0(v6, xI))) % 267.43/36.51 | & ! [v2: $i] : ! [v3: $i] : (v2 = sz00 | ~ (sbrdtbr0(v2) = v3) | % 267.43/36.51 | ~ $i(v2) | ~ aElementOf0(v2, xI) | ? [v4: $i] : ? [v5: $i] : ? % 267.43/36.51 | [v6: $i] : ? [v7: $i] : ( ~ (v4 = sz00) & sbrdtbr0(v4) = v5 & % 267.43/36.51 | sdtpldt0(v6, v7) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 267.43/36.51 | iLess0(v5, v3) & aElementOf0(v7, v1) & aElementOf0(v6, v0) & % 267.43/36.51 | aElementOf0(v4, xI)))) % 267.43/36.51 | % 267.43/36.51 | ALPHA: (function-axioms) implies: % 267.43/36.51 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = % 267.43/36.51 | v1) | ~ (slsdtgt0(v2) = v0)) % 267.43/36.51 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 267.43/36.51 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) % 267.43/36.51 | % 267.43/36.51 | DELTA: instantiating (2) with fresh symbols all_37_0, all_37_1, all_37_2, % 267.43/36.51 | all_37_3, all_37_4, all_37_5 gives: % 267.43/36.51 | (8) slsdtgt0(xb) = all_37_4 & slsdtgt0(xa) = all_37_5 & sdtasdt0(xb, % 267.43/36.51 | all_37_2) = sz00 & sdtasdt0(xb, all_37_3) = xb & sdtasdt0(xa, % 267.43/36.51 | all_37_0) = sz00 & sdtasdt0(xa, all_37_1) = xa & $i(all_37_0) & % 267.43/36.51 | $i(all_37_1) & $i(all_37_2) & $i(all_37_3) & $i(all_37_4) & % 267.43/36.51 | $i(all_37_5) & aElementOf0(xb, all_37_4) & aElementOf0(xa, all_37_5) & % 267.43/36.51 | aElementOf0(sz00, all_37_4) & aElementOf0(sz00, all_37_5) & % 267.43/36.51 | aElement0(all_37_0) & aElement0(all_37_1) & aElement0(all_37_2) & % 267.43/36.51 | aElement0(all_37_3) % 267.43/36.51 | % 267.43/36.51 | ALPHA: (8) implies: % 267.43/36.51 | (9) slsdtgt0(xa) = all_37_5 % 267.43/36.51 | (10) slsdtgt0(xb) = all_37_4 % 267.43/36.51 | % 267.43/36.51 | DELTA: instantiating (3) with fresh symbols all_39_0, all_39_1, all_39_2, % 267.43/36.51 | all_39_3, all_39_4, all_39_5 gives: % 267.43/36.52 | (11) ~ (all_39_2 = sz00) & slsdtgt0(xb) = all_39_4 & slsdtgt0(xa) = % 267.43/36.52 | all_39_5 & sdtpldt1(all_39_5, all_39_4) = all_39_3 & % 267.43/36.52 | sdtpldt0(all_39_1, all_39_0) = all_39_2 & $i(all_39_0) & $i(all_39_1) % 267.43/36.52 | & $i(all_39_2) & $i(all_39_3) & $i(all_39_4) & $i(all_39_5) & % 267.43/36.52 | aElementOf0(all_39_0, all_39_4) & aElementOf0(all_39_1, all_39_5) & % 267.43/36.52 | aElementOf0(all_39_2, all_39_3) & ! [v0: $i] : ! [v1: $i] : ( ~ % 267.43/36.52 | (sdtasdt0(xb, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | % 267.43/36.52 | aElementOf0(v0, all_39_4)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 267.43/36.52 | (sdtasdt0(xa, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | % 267.43/36.52 | aElementOf0(v0, all_39_5)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 267.43/36.52 | aElementOf0(v0, all_39_4) | ? [v1: $i] : (sdtasdt0(xb, v1) = v0 & % 267.43/36.52 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 267.43/36.52 | aElementOf0(v0, all_39_5) | ? [v1: $i] : (sdtasdt0(xa, v1) = v0 & % 267.43/36.52 | $i(v1) & aElement0(v1))) % 267.43/36.52 | % 267.43/36.52 | ALPHA: (11) implies: % 267.43/36.52 | (12) ~ (all_39_2 = sz00) % 267.43/36.52 | (13) aElementOf0(all_39_2, all_39_3) % 267.43/36.52 | (14) $i(all_39_2) % 267.43/36.52 | (15) sdtpldt1(all_39_5, all_39_4) = all_39_3 % 267.43/36.52 | (16) slsdtgt0(xa) = all_39_5 % 267.43/36.52 | (17) slsdtgt0(xb) = all_39_4 % 267.43/36.52 | % 267.43/36.52 | DELTA: instantiating (5) with fresh symbols all_42_0, all_42_1 gives: % 267.43/36.52 | (18) slsdtgt0(xb) = all_42_0 & slsdtgt0(xa) = all_42_1 & $i(all_42_0) & % 267.43/36.52 | $i(all_42_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 267.43/36.52 | (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ (sdtpldt0(v2, v3) = v0) | ~ % 267.43/36.52 | $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v3, all_42_0) | ~ % 267.43/36.52 | aElementOf0(v2, all_42_1) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 267.43/36.52 | : ? [v7: $i] : ( ~ (v4 = sz00) & sbrdtbr0(v4) = v5 & sdtpldt0(v6, % 267.43/36.52 | v7) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & iLess0(v5, v1) & % 267.43/36.52 | aElementOf0(v7, all_42_0) & aElementOf0(v6, all_42_1) & % 267.43/36.52 | aElementOf0(v4, xI))) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | % 267.43/36.52 | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ? [v2: % 267.43/36.52 | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v2 = sz00) & % 267.43/36.52 | sbrdtbr0(v2) = v3 & sdtpldt0(v4, v5) = v2 & $i(v5) & $i(v4) & % 267.43/36.52 | $i(v3) & $i(v2) & iLess0(v3, v1) & aElementOf0(v5, all_42_0) & % 267.43/36.52 | aElementOf0(v4, all_42_1) & aElementOf0(v2, xI))) % 267.43/36.52 | % 267.43/36.52 | ALPHA: (18) implies: % 267.43/36.52 | (19) slsdtgt0(xa) = all_42_1 % 267.43/36.52 | (20) slsdtgt0(xb) = all_42_0 % 267.43/36.52 | (21) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ % 267.43/36.52 | $i(v0) | ~ aElementOf0(v0, xI) | ? [v2: $i] : ? [v3: $i] : ? % 267.43/36.52 | [v4: $i] : ? [v5: $i] : ( ~ (v2 = sz00) & sbrdtbr0(v2) = v3 & % 267.43/36.52 | sdtpldt0(v4, v5) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 267.43/36.52 | iLess0(v3, v1) & aElementOf0(v5, all_42_0) & aElementOf0(v4, % 267.43/36.52 | all_42_1) & aElementOf0(v2, xI))) % 267.43/36.52 | % 267.43/36.52 | DELTA: instantiating (1) with fresh symbols all_45_0, all_45_1 gives: % 267.43/36.52 | (22) slsdtgt0(xb) = all_45_0 & slsdtgt0(xa) = all_45_1 & sdtpldt1(all_45_1, % 267.43/36.52 | all_45_0) = xI & $i(all_45_0) & $i(all_45_1) & aIdeal0(xI) & % 267.43/36.52 | aSet0(xI) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 267.43/36.52 | (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, % 267.43/36.52 | xI) | ~ aElement0(v1) | aElementOf0(v2, xI)) & ! [v0: $i] : ! % 267.43/36.52 | [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v2) = v0) | ~ $i(v2) | ~ % 267.43/36.52 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, all_45_0) | ~ % 267.43/36.52 | aElementOf0(v1, all_45_1) | aElementOf0(v0, xI)) & ! [v0: $i] : ! % 267.43/36.52 | [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ % 267.43/36.52 | $i(v0) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | % 267.43/36.52 | aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(xb, % 267.43/36.52 | v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | % 267.43/36.52 | aElementOf0(v0, all_45_0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 267.43/36.52 | (sdtasdt0(xa, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | % 267.43/36.52 | aElementOf0(v0, all_45_1)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 267.43/36.52 | aElementOf0(v0, all_45_0) | ? [v1: $i] : (sdtasdt0(xb, v1) = v0 & % 267.43/36.52 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 267.43/36.53 | aElementOf0(v0, all_45_1) | ? [v1: $i] : (sdtasdt0(xa, v1) = v0 & % 267.43/36.53 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ % 267.43/36.53 | aElementOf0(v0, xI) | ? [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v2) % 267.43/36.53 | = v0 & $i(v2) & $i(v1) & aElementOf0(v2, all_45_0) & % 267.43/36.53 | aElementOf0(v1, all_45_1))) % 267.43/36.53 | % 267.43/36.53 | ALPHA: (22) implies: % 267.43/36.53 | (23) sdtpldt1(all_45_1, all_45_0) = xI % 267.43/36.53 | (24) slsdtgt0(xa) = all_45_1 % 267.43/36.53 | (25) slsdtgt0(xb) = all_45_0 % 267.43/36.53 | % 267.43/36.53 | DELTA: instantiating (4) with fresh symbols all_48_0, all_48_1 gives: % 267.43/36.53 | (26) slsdtgt0(xb) = all_48_0 & slsdtgt0(xa) = all_48_1 & $i(all_48_0) & % 267.43/36.53 | $i(all_48_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | % 267.43/36.53 | ~ (sdtpldt0(v1, v2) = v0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 267.43/36.53 | aElementOf0(v2, all_48_0) | ~ aElementOf0(v1, all_48_1) | ? [v3: % 267.43/36.53 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v3 = sz00) & % 267.43/36.53 | sbrdtbr0(v3) = v4 & sdtpldt0(v5, v6) = v3 & $i(v6) & $i(v5) & % 267.43/36.53 | $i(v4) & $i(v3) & aElementOf0(v6, all_48_0) & aElementOf0(v5, % 267.43/36.53 | all_48_1) & aElementOf0(v3, xI) & ! [v7: $i] : ! [v8: $i] : ! % 267.43/36.53 | [v9: $i] : ! [v10: $i] : (v7 = sz00 | ~ (sbrdtbr0(v7) = v8) | ~ % 267.43/36.53 | (sdtpldt0(v9, v10) = v7) | ~ $i(v10) | ~ $i(v9) | ~ $i(v7) | % 267.43/36.53 | ~ iLess0(v8, v4) | ~ aElementOf0(v10, all_48_0) | ~ % 267.43/36.53 | aElementOf0(v9, all_48_1)) & ! [v7: $i] : ! [v8: $i] : (v7 = % 267.43/36.53 | sz00 | ~ (sbrdtbr0(v7) = v8) | ~ $i(v7) | ~ iLess0(v8, v4) | % 267.43/36.53 | ~ aElementOf0(v7, xI)))) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) % 267.43/36.53 | | ~ aElementOf0(v0, xI) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 267.43/36.53 | ? [v4: $i] : ( ~ (v1 = sz00) & sbrdtbr0(v1) = v2 & sdtpldt0(v3, v4) % 267.43/36.53 | = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & aElementOf0(v4, % 267.43/36.53 | all_48_0) & aElementOf0(v3, all_48_1) & aElementOf0(v1, xI) & ! % 267.43/36.53 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v5 = sz00 | % 267.43/36.53 | ~ (sbrdtbr0(v5) = v6) | ~ (sdtpldt0(v7, v8) = v5) | ~ $i(v8) | % 267.43/36.53 | ~ $i(v7) | ~ $i(v5) | ~ iLess0(v6, v2) | ~ aElementOf0(v8, % 267.43/36.53 | all_48_0) | ~ aElementOf0(v7, all_48_1)) & ! [v5: $i] : ! % 267.43/36.53 | [v6: $i] : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ $i(v5) | ~ % 267.43/36.53 | iLess0(v6, v2) | ~ aElementOf0(v5, xI)))) % 267.43/36.53 | % 267.43/36.53 | ALPHA: (26) implies: % 267.43/36.53 | (27) slsdtgt0(xa) = all_48_1 % 267.43/36.53 | (28) slsdtgt0(xb) = all_48_0 % 267.43/36.53 | (29) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, xI) | ? % 267.43/36.53 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v1 = sz00) % 267.43/36.53 | & sbrdtbr0(v1) = v2 & sdtpldt0(v3, v4) = v1 & $i(v4) & $i(v3) & % 267.43/36.53 | $i(v2) & $i(v1) & aElementOf0(v4, all_48_0) & aElementOf0(v3, % 267.43/36.53 | all_48_1) & aElementOf0(v1, xI) & ! [v5: $i] : ! [v6: $i] : ! % 267.43/36.53 | [v7: $i] : ! [v8: $i] : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ % 267.43/36.53 | (sdtpldt0(v7, v8) = v5) | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ % 267.43/36.53 | iLess0(v6, v2) | ~ aElementOf0(v8, all_48_0) | ~ % 267.43/36.53 | aElementOf0(v7, all_48_1)) & ! [v5: $i] : ! [v6: $i] : (v5 = % 267.43/36.53 | sz00 | ~ (sbrdtbr0(v5) = v6) | ~ $i(v5) | ~ iLess0(v6, v2) | % 267.43/36.53 | ~ aElementOf0(v5, xI)))) % 267.43/36.53 | % 267.43/36.53 | GROUND_INST: instantiating (6) with all_42_1, all_45_1, xa, simplifying with % 267.43/36.53 | (19), (24) gives: % 267.43/36.53 | (30) all_45_1 = all_42_1 % 267.43/36.53 | % 267.43/36.53 | GROUND_INST: instantiating (6) with all_39_5, all_45_1, xa, simplifying with % 267.43/36.53 | (16), (24) gives: % 267.43/36.53 | (31) all_45_1 = all_39_5 % 267.43/36.53 | % 267.43/36.53 | GROUND_INST: instantiating (6) with all_42_1, all_48_1, xa, simplifying with % 267.43/36.53 | (19), (27) gives: % 267.43/36.53 | (32) all_48_1 = all_42_1 % 267.43/36.53 | % 267.43/36.53 | GROUND_INST: instantiating (6) with all_37_5, all_48_1, xa, simplifying with % 267.43/36.53 | (9), (27) gives: % 267.43/36.53 | (33) all_48_1 = all_37_5 % 267.43/36.53 | % 267.43/36.54 | GROUND_INST: instantiating (6) with all_39_4, all_42_0, xb, simplifying with % 267.43/36.54 | (17), (20) gives: % 267.43/36.54 | (34) all_42_0 = all_39_4 % 267.43/36.54 | % 267.43/36.54 | GROUND_INST: instantiating (6) with all_42_0, all_45_0, xb, simplifying with % 267.43/36.54 | (20), (25) gives: % 267.43/36.54 | (35) all_45_0 = all_42_0 % 267.43/36.54 | % 267.43/36.54 | GROUND_INST: instantiating (6) with all_45_0, all_48_0, xb, simplifying with % 267.43/36.54 | (25), (28) gives: % 267.43/36.54 | (36) all_48_0 = all_45_0 % 267.43/36.54 | % 267.43/36.54 | GROUND_INST: instantiating (6) with all_37_4, all_48_0, xb, simplifying with % 267.43/36.54 | (10), (28) gives: % 267.43/36.54 | (37) all_48_0 = all_37_4 % 267.43/36.54 | % 267.43/36.54 | COMBINE_EQS: (36), (37) imply: % 267.43/36.54 | (38) all_45_0 = all_37_4 % 267.43/36.54 | % 267.43/36.54 | SIMP: (38) implies: % 267.43/36.54 | (39) all_45_0 = all_37_4 % 267.43/36.54 | % 267.43/36.54 | COMBINE_EQS: (32), (33) imply: % 267.43/36.54 | (40) all_42_1 = all_37_5 % 267.43/36.54 | % 267.43/36.54 | SIMP: (40) implies: % 267.43/36.54 | (41) all_42_1 = all_37_5 % 267.43/36.54 | % 267.43/36.54 | COMBINE_EQS: (35), (39) imply: % 267.43/36.54 | (42) all_42_0 = all_37_4 % 267.43/36.54 | % 267.43/36.54 | SIMP: (42) implies: % 267.43/36.54 | (43) all_42_0 = all_37_4 % 267.43/36.54 | % 267.43/36.54 | COMBINE_EQS: (30), (31) imply: % 267.43/36.54 | (44) all_42_1 = all_39_5 % 267.43/36.54 | % 267.43/36.54 | SIMP: (44) implies: % 267.43/36.54 | (45) all_42_1 = all_39_5 % 267.43/36.54 | % 267.43/36.54 | COMBINE_EQS: (34), (43) imply: % 267.43/36.54 | (46) all_39_4 = all_37_4 % 267.43/36.54 | % 267.43/36.54 | SIMP: (46) implies: % 267.43/36.54 | (47) all_39_4 = all_37_4 % 267.43/36.54 | % 267.43/36.54 | COMBINE_EQS: (41), (45) imply: % 267.43/36.54 | (48) all_39_5 = all_37_5 % 267.43/36.54 | % 267.43/36.54 | COMBINE_EQS: (31), (48) imply: % 267.43/36.54 | (49) all_45_1 = all_37_5 % 267.43/36.54 | % 267.43/36.54 | REDUCE: (23), (39), (49) imply: % 267.43/36.54 | (50) sdtpldt1(all_37_5, all_37_4) = xI % 267.43/36.54 | % 267.43/36.54 | REDUCE: (15), (47), (48) imply: % 267.43/36.54 | (51) sdtpldt1(all_37_5, all_37_4) = all_39_3 % 267.43/36.54 | % 267.43/36.54 | GROUND_INST: instantiating (7) with xI, all_39_3, all_37_4, all_37_5, % 267.43/36.54 | simplifying with (50), (51) gives: % 267.43/36.54 | (52) all_39_3 = xI % 267.43/36.54 | % 267.43/36.54 | REDUCE: (13), (52) imply: % 267.43/36.54 | (53) aElementOf0(all_39_2, xI) % 267.43/36.54 | % 267.43/36.54 | GROUND_INST: instantiating (29) with all_39_2, simplifying with (14), (53) % 267.43/36.54 | gives: % 267.43/36.54 | (54) all_39_2 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 267.43/36.54 | $i] : ( ~ (v0 = sz00) & sbrdtbr0(v0) = v1 & sdtpldt0(v2, v3) = v0 & % 267.43/36.54 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, all_48_0) & % 267.43/36.54 | aElementOf0(v2, all_48_1) & aElementOf0(v0, xI) & ! [v4: $i] : ! % 267.43/36.54 | [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = sz00 | ~ (sbrdtbr0(v4) % 267.43/36.54 | = v5) | ~ (sdtpldt0(v6, v7) = v4) | ~ $i(v7) | ~ $i(v6) | ~ % 267.43/36.54 | $i(v4) | ~ iLess0(v5, v1) | ~ aElementOf0(v7, all_48_0) | ~ % 267.43/36.54 | aElementOf0(v6, all_48_1)) & ! [v4: $i] : ! [v5: $i] : (v4 = % 267.43/36.54 | sz00 | ~ (sbrdtbr0(v4) = v5) | ~ $i(v4) | ~ iLess0(v5, v1) | ~ % 267.43/36.54 | aElementOf0(v4, xI))) % 267.43/36.54 | % 267.43/36.54 | BETA: splitting (54) gives: % 267.43/36.54 | % 267.43/36.54 | Case 1: % 267.43/36.54 | | % 267.43/36.54 | | (55) all_39_2 = sz00 % 267.43/36.54 | | % 267.43/36.54 | | REDUCE: (12), (55) imply: % 267.43/36.54 | | (56) $false % 267.43/36.55 | | % 267.43/36.55 | | CLOSE: (56) is inconsistent. % 267.43/36.55 | | % 267.43/36.55 | Case 2: % 267.43/36.55 | | % 267.62/36.55 | | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v0 = % 267.62/36.55 | | sz00) & sbrdtbr0(v0) = v1 & sdtpldt0(v2, v3) = v0 & $i(v3) & % 267.62/36.55 | | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, all_48_0) & % 267.62/36.55 | | aElementOf0(v2, all_48_1) & aElementOf0(v0, xI) & ! [v4: $i] : ! % 267.62/36.55 | | [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v4 = sz00 | ~ % 267.62/36.55 | | (sbrdtbr0(v4) = v5) | ~ (sdtpldt0(v6, v7) = v4) | ~ $i(v7) | % 267.62/36.55 | | ~ $i(v6) | ~ $i(v4) | ~ iLess0(v5, v1) | ~ aElementOf0(v7, % 267.62/36.55 | | all_48_0) | ~ aElementOf0(v6, all_48_1)) & ! [v4: $i] : ! % 267.62/36.55 | | [v5: $i] : (v4 = sz00 | ~ (sbrdtbr0(v4) = v5) | ~ $i(v4) | ~ % 267.62/36.55 | | iLess0(v5, v1) | ~ aElementOf0(v4, xI))) % 267.62/36.55 | | % 267.62/36.55 | | DELTA: instantiating (57) with fresh symbols all_108_0, all_108_1, % 267.62/36.55 | | all_108_2, all_108_3 gives: % 267.62/36.55 | | (58) ~ (all_108_3 = sz00) & sbrdtbr0(all_108_3) = all_108_2 & % 267.62/36.55 | | sdtpldt0(all_108_1, all_108_0) = all_108_3 & $i(all_108_0) & % 267.62/36.55 | | $i(all_108_1) & $i(all_108_2) & $i(all_108_3) & % 267.62/36.55 | | aElementOf0(all_108_0, all_48_0) & aElementOf0(all_108_1, all_48_1) % 267.62/36.55 | | & aElementOf0(all_108_3, xI) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 267.62/36.55 | | $i] : ! [v3: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ % 267.62/36.55 | | (sdtpldt0(v2, v3) = v0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ % 267.62/36.55 | | iLess0(v1, all_108_2) | ~ aElementOf0(v3, all_48_0) | ~ % 267.62/36.55 | | aElementOf0(v2, all_48_1)) & ! [v0: $i] : ! [v1: $i] : (v0 = % 267.62/36.55 | | sz00 | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ iLess0(v1, % 267.62/36.55 | | all_108_2) | ~ aElementOf0(v0, xI)) % 267.62/36.55 | | % 267.62/36.55 | | ALPHA: (58) implies: % 267.62/36.55 | | (59) ~ (all_108_3 = sz00) % 267.62/36.55 | | (60) aElementOf0(all_108_3, xI) % 267.62/36.55 | | (61) $i(all_108_3) % 267.62/36.55 | | (62) sbrdtbr0(all_108_3) = all_108_2 % 267.62/36.55 | | (63) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ % 267.62/36.55 | | $i(v0) | ~ iLess0(v1, all_108_2) | ~ aElementOf0(v0, xI)) % 267.62/36.55 | | % 267.62/36.55 | | GROUND_INST: instantiating (21) with all_108_3, all_108_2, simplifying with % 267.62/36.55 | | (60), (61), (62) gives: % 267.62/36.55 | | (64) all_108_3 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 267.62/36.55 | | $i] : ( ~ (v0 = sz00) & sbrdtbr0(v0) = v1 & sdtpldt0(v2, v3) = v0 % 267.62/36.55 | | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & iLess0(v1, all_108_2) & % 267.62/36.55 | | aElementOf0(v3, all_42_0) & aElementOf0(v2, all_42_1) & % 267.62/36.55 | | aElementOf0(v0, xI)) % 267.62/36.55 | | % 267.62/36.55 | | BETA: splitting (64) gives: % 267.62/36.55 | | % 267.62/36.55 | | Case 1: % 267.62/36.55 | | | % 267.62/36.55 | | | (65) all_108_3 = sz00 % 267.62/36.55 | | | % 267.62/36.55 | | | REDUCE: (59), (65) imply: % 267.62/36.55 | | | (66) $false % 267.62/36.55 | | | % 267.62/36.55 | | | CLOSE: (66) is inconsistent. % 267.62/36.55 | | | % 267.62/36.55 | | Case 2: % 267.62/36.55 | | | % 267.62/36.55 | | | (67) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v0 = % 267.62/36.55 | | | sz00) & sbrdtbr0(v0) = v1 & sdtpldt0(v2, v3) = v0 & $i(v3) & % 267.62/36.55 | | | $i(v2) & $i(v1) & $i(v0) & iLess0(v1, all_108_2) & % 267.62/36.55 | | | aElementOf0(v3, all_42_0) & aElementOf0(v2, all_42_1) & % 267.62/36.55 | | | aElementOf0(v0, xI)) % 267.62/36.55 | | | % 267.62/36.55 | | | DELTA: instantiating (67) with fresh symbols all_1219_0, all_1219_1, % 267.62/36.55 | | | all_1219_2, all_1219_3 gives: % 267.62/36.55 | | | (68) ~ (all_1219_3 = sz00) & sbrdtbr0(all_1219_3) = all_1219_2 & % 267.62/36.55 | | | sdtpldt0(all_1219_1, all_1219_0) = all_1219_3 & $i(all_1219_0) & % 267.62/36.55 | | | $i(all_1219_1) & $i(all_1219_2) & $i(all_1219_3) & % 267.62/36.55 | | | iLess0(all_1219_2, all_108_2) & aElementOf0(all_1219_0, all_42_0) % 267.62/36.55 | | | & aElementOf0(all_1219_1, all_42_1) & aElementOf0(all_1219_3, xI) % 267.62/36.55 | | | % 267.62/36.55 | | | ALPHA: (68) implies: % 267.62/36.55 | | | (69) ~ (all_1219_3 = sz00) % 267.62/36.55 | | | (70) aElementOf0(all_1219_3, xI) % 267.62/36.55 | | | (71) iLess0(all_1219_2, all_108_2) % 267.62/36.55 | | | (72) $i(all_1219_3) % 267.62/36.56 | | | (73) sbrdtbr0(all_1219_3) = all_1219_2 % 267.62/36.56 | | | % 267.62/36.56 | | | GROUND_INST: instantiating (63) with all_1219_3, all_1219_2, simplifying % 267.62/36.56 | | | with (70), (71), (72), (73) gives: % 267.62/36.56 | | | (74) all_1219_3 = sz00 % 267.62/36.56 | | | % 267.62/36.56 | | | REDUCE: (69), (74) imply: % 267.62/36.56 | | | (75) $false % 267.62/36.56 | | | % 267.62/36.56 | | | CLOSE: (75) is inconsistent. % 267.62/36.56 | | | % 267.62/36.56 | | End of split % 267.62/36.56 | | % 267.62/36.56 | End of split % 267.62/36.56 | % 267.62/36.56 End of proof % 267.62/36.56 % SZS output end Proof for theBenchmark % 267.62/36.56 % 267.62/36.56 35939ms %------------------------------------------------------------------------------