%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG100+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 : n011.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 13:57:52 EDT 2023 % Result : Theorem 67.82s 9.65s % Output : Proof 68.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : RNG100+1 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n011.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 : Sun Aug 27 02:33:24 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/sandbox/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.17/1.17 Prover 1: Preprocessing ... % 3.17/1.17 Prover 4: Preprocessing ... % 3.17/1.20 Prover 3: Preprocessing ... % 3.17/1.20 Prover 6: Preprocessing ... % 3.17/1.20 Prover 0: Preprocessing ... % 3.17/1.21 Prover 5: Preprocessing ... % 3.17/1.21 Prover 2: Preprocessing ... % 8.19/1.92 Prover 1: Constructing countermodel ... % 8.75/2.00 Prover 3: Constructing countermodel ... % 8.75/2.03 Prover 5: Proving ... % 8.75/2.06 Prover 6: Proving ... % 9.29/2.12 Prover 2: Proving ... % 10.86/2.25 Prover 4: Constructing countermodel ... % 11.19/2.30 Prover 0: Proving ... % 13.15/2.53 Prover 3: gave up % 13.15/2.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.49/2.61 Prover 7: Preprocessing ... % 14.93/2.78 Prover 1: gave up % 14.93/2.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 15.36/2.84 Prover 8: Preprocessing ... % 15.56/2.87 Prover 7: Constructing countermodel ... % 16.45/3.01 Prover 8: Warning: ignoring some quantifiers % 16.45/3.02 Prover 8: Constructing countermodel ... % 21.82/3.67 Prover 8: gave up % 21.82/3.70 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 22.24/3.73 Prover 9: Preprocessing ... % 23.42/3.98 Prover 9: Constructing countermodel ... % 61.88/8.87 Prover 2: stopped % 61.88/8.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 62.57/8.96 Prover 10: Preprocessing ... % 63.76/9.09 Prover 10: Constructing countermodel ... % 67.82/9.64 Prover 10: Found proof (size 136) % 67.82/9.64 Prover 10: proved (764ms) % 67.82/9.64 Prover 0: stopped % 67.82/9.64 Prover 9: stopped % 67.82/9.64 Prover 5: stopped % 67.82/9.64 Prover 7: stopped % 67.82/9.64 Prover 6: stopped % 67.82/9.65 Prover 4: stopped % 67.82/9.65 % 67.82/9.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 67.82/9.65 % 67.82/9.66 % SZS output start Proof for theBenchmark % 67.82/9.66 Assumptions after simplification: % 67.82/9.66 --------------------------------- % 67.82/9.66 % 67.82/9.66 (mAMDistr) % 68.21/9.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 68.21/9.69 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 68.21/9.69 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 68.21/9.69 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 68.21/9.69 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, % 68.21/9.69 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, % 68.21/9.69 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 68.21/9.69 $i(v5))) % 68.21/9.69 % 68.21/9.69 (mAddComm) % 68.21/9.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 68.21/9.69 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 68.21/9.69 = v2 & $i(v2))) % 68.21/9.69 % 68.21/9.69 (mDefDiv) % 68.21/9.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 68.21/9.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 68.21/9.70 aElement0(v0) | doDivides0(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) % 68.21/9.70 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aElement0(v1) | ~ aElement0(v0) | % 68.21/9.70 ? [v2: $i] : (sdtasdt0(v0, v2) = v1 & $i(v2) & aElement0(v2))) % 68.21/9.70 % 68.21/9.70 (mDefIdeal) % 68.21/9.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1) % 68.21/9.70 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ % 68.21/9.70 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i] % 68.21/9.70 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ % 68.21/9.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | % 68.21/9.70 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 68.21/9.70 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | % 68.21/9.70 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 68.21/9.70 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, % 68.21/9.70 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 68.21/9.70 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 68.21/9.70 aElementOf0(v5, v0))))) % 68.21/9.70 % 68.21/9.70 (mDefPrIdeal) % 68.21/9.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) = % 68.21/9.70 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 68.21/9.70 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & ! % 68.21/9.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~ % 68.21/9.70 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: % 68.21/9.70 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6: % 68.21/9.70 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) & % 68.21/9.70 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 & % 68.21/9.70 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 68.21/9.70 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, % 68.21/9.70 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 68.21/9.70 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 68.21/9.70 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 68.21/9.70 % 68.21/9.70 (mEOfElem) % 68.21/9.71 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 68.21/9.71 ~ aSet0(v0) | aElement0(v1)) % 68.21/9.71 % 68.21/9.71 (mMulAsso) % 68.21/9.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 68.21/9.71 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 68.21/9.71 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 68.21/9.71 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) & % 68.21/9.71 $i(v4))) % 68.21/9.71 % 68.21/9.71 (mMulComm) % 68.21/9.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 68.21/9.71 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 68.21/9.71 = v2 & $i(v2))) % 68.21/9.71 % 68.21/9.71 (mSortsB) % 68.21/9.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 68.21/9.71 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 68.21/9.71 % 68.21/9.71 (mSortsB_02) % 68.21/9.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 68.21/9.71 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 68.21/9.71 % 68.21/9.71 (m__) % 68.21/9.71 $i(xc) & ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & ~ aIdeal0(v0)) % 68.21/9.71 % 68.21/9.71 (m__1905) % 68.21/9.71 $i(xc) & aElement0(xc) % 68.21/9.71 % 68.21/9.71 (function-axioms) % 68.21/9.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.21/9.71 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 68.21/9.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 68.21/9.71 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 68.21/9.71 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 68.21/9.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.21/9.71 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 68.21/9.71 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 68.21/9.71 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 68.21/9.71 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 68.21/9.71 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 68.21/9.71 % 68.21/9.71 Further assumptions not needed in the proof: % 68.21/9.71 -------------------------------------------- % 68.21/9.71 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDvs, mDefGCD, % 68.21/9.71 mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mElmSort, mEucSort, mIdeInt, % 68.21/9.71 mIdeSum, mMulMnOne, mMulUnit, mMulZero, mNatLess, mNatSort, mSetEq, mSetSort, % 68.21/9.71 mSortsC, mSortsC_01, mSortsU, mUnNeZr % 68.21/9.71 % 68.21/9.71 Those formulas are unsatisfiable: % 68.21/9.71 --------------------------------- % 68.21/9.71 % 68.21/9.71 Begin of proof % 68.21/9.71 | % 68.21/9.71 | ALPHA: (mDefIdeal) implies: % 68.21/9.72 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | aIdeal0(v0) | ? [v1: $i] : % 68.21/9.72 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & % 68.21/9.72 | $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 & % 68.21/9.72 | $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 68.21/9.72 | (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 68.21/9.72 | aElementOf0(v5, v0))))) % 68.21/9.72 | % 68.21/9.72 | ALPHA: (mDefDiv) implies: % 68.21/9.72 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, % 68.21/9.72 | v1) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v2: $i] : % 68.21/9.72 | (sdtasdt0(v0, v2) = v1 & $i(v2) & aElement0(v2))) % 68.21/9.72 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | % 68.21/9.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ % 68.21/9.72 | aElement0(v1) | ~ aElement0(v0) | doDivides0(v0, v1)) % 68.21/9.72 | % 68.21/9.72 | ALPHA: (mDefPrIdeal) implies: % 68.21/9.72 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ $i(v1) | ~ % 68.21/9.72 | $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 68.21/9.72 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 68.21/9.72 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 68.21/9.72 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 68.21/9.72 | aElement0(v3))) % 68.21/9.72 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 68.21/9.72 | (slsdtgt0(v0) = v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ % 68.21/9.72 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) % 68.21/9.72 | | aElementOf0(v2, v1)) % 68.21/9.72 | % 68.21/9.72 | ALPHA: (m__1905) implies: % 68.21/9.72 | (7) aElement0(xc) % 68.21/9.72 | % 68.21/9.72 | ALPHA: (m__) implies: % 68.21/9.72 | (8) $i(xc) % 68.21/9.72 | (9) ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & ~ aIdeal0(v0)) % 68.21/9.72 | % 68.21/9.72 | ALPHA: (function-axioms) implies: % 68.21/9.72 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.21/9.72 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 68.21/9.72 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 68.21/9.72 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 68.21/9.72 | % 68.21/9.72 | DELTA: instantiating (9) with fresh symbol all_33_0 gives: % 68.21/9.72 | (12) slsdtgt0(xc) = all_33_0 & $i(all_33_0) & ~ aIdeal0(all_33_0) % 68.21/9.72 | % 68.21/9.72 | ALPHA: (12) implies: % 68.21/9.72 | (13) ~ aIdeal0(all_33_0) % 68.21/9.72 | (14) $i(all_33_0) % 68.21/9.72 | (15) slsdtgt0(xc) = all_33_0 % 68.21/9.72 | % 68.21/9.72 | GROUND_INST: instantiating (4) with xc, all_33_0, simplifying with (7), (8), % 68.21/9.72 | (14), (15) gives: % 68.21/9.72 | (16) aSet0(all_33_0) % 68.21/9.73 | % 68.21/9.73 | GROUND_INST: instantiating (1) with all_33_0, simplifying with (13), (14), % 68.21/9.73 | (16) gives: % 68.21/9.73 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 68.21/9.73 | ($i(v3) & $i(v1) & $i(v0) & aElementOf0(v0, all_33_0) & ((sdtasdt0(v1, % 68.21/9.73 | v0) = v2 & $i(v2) & aElement0(v1) & ~ aElementOf0(v2, % 68.21/9.73 | all_33_0)) | (sdtpldt0(v0, v3) = v4 & $i(v4) & aElementOf0(v3, % 68.21/9.73 | all_33_0) & ~ aElementOf0(v4, all_33_0)))) % 68.21/9.73 | % 68.21/9.73 | DELTA: instantiating (17) with fresh symbols all_49_0, all_49_1, all_49_2, % 68.21/9.73 | all_49_3, all_49_4 gives: % 68.21/9.73 | (18) $i(all_49_1) & $i(all_49_3) & $i(all_49_4) & aElementOf0(all_49_4, % 68.21/9.73 | all_33_0) & ((sdtasdt0(all_49_3, all_49_4) = all_49_2 & $i(all_49_2) % 68.21/9.73 | & aElement0(all_49_3) & ~ aElementOf0(all_49_2, all_33_0)) | % 68.21/9.73 | (sdtpldt0(all_49_4, all_49_1) = all_49_0 & $i(all_49_0) & % 68.21/9.73 | aElementOf0(all_49_1, all_33_0) & ~ aElementOf0(all_49_0, % 68.21/9.73 | all_33_0))) % 68.21/9.73 | % 68.21/9.73 | ALPHA: (18) implies: % 68.21/9.73 | (19) aElementOf0(all_49_4, all_33_0) % 68.21/9.73 | (20) $i(all_49_4) % 68.21/9.73 | (21) $i(all_49_3) % 68.21/9.73 | (22) $i(all_49_1) % 68.21/9.73 | (23) (sdtasdt0(all_49_3, all_49_4) = all_49_2 & $i(all_49_2) & % 68.21/9.73 | aElement0(all_49_3) & ~ aElementOf0(all_49_2, all_33_0)) | % 68.21/9.73 | (sdtpldt0(all_49_4, all_49_1) = all_49_0 & $i(all_49_0) & % 68.21/9.73 | aElementOf0(all_49_1, all_33_0) & ~ aElementOf0(all_49_0, % 68.21/9.73 | all_33_0)) % 68.21/9.73 | % 68.21/9.73 | GROUND_INST: instantiating (5) with xc, all_33_0, all_49_4, simplifying with % 68.21/9.73 | (7), (8), (14), (15), (19), (20) gives: % 68.21/9.73 | (24) ? [v0: $i] : (sdtasdt0(xc, v0) = all_49_4 & $i(v0) & aElement0(v0)) % 68.21/9.73 | % 68.21/9.73 | GROUND_INST: instantiating (mEOfElem) with all_33_0, all_49_4, simplifying % 68.21/9.73 | with (14), (16), (19), (20) gives: % 68.21/9.73 | (25) aElement0(all_49_4) % 68.21/9.73 | % 68.21/9.73 | DELTA: instantiating (24) with fresh symbol all_57_0 gives: % 68.21/9.73 | (26) sdtasdt0(xc, all_57_0) = all_49_4 & $i(all_57_0) & aElement0(all_57_0) % 68.21/9.73 | % 68.21/9.73 | ALPHA: (26) implies: % 68.21/9.73 | (27) aElement0(all_57_0) % 68.21/9.73 | (28) $i(all_57_0) % 68.21/9.73 | (29) sdtasdt0(xc, all_57_0) = all_49_4 % 68.21/9.73 | % 68.21/9.73 | GROUND_INST: instantiating (mMulComm) with xc, all_57_0, all_49_4, simplifying % 68.21/9.73 | with (7), (8), (27), (28), (29) gives: % 68.21/9.73 | (30) sdtasdt0(all_57_0, xc) = all_49_4 & $i(all_49_4) % 68.21/9.73 | % 68.21/9.73 | ALPHA: (30) implies: % 68.21/9.73 | (31) sdtasdt0(all_57_0, xc) = all_49_4 % 68.21/9.73 | % 68.21/9.73 | GROUND_INST: instantiating (3) with xc, all_49_4, all_57_0, simplifying with % 68.21/9.73 | (7), (8), (20), (25), (27), (28), (29) gives: % 68.21/9.73 | (32) doDivides0(xc, all_49_4) % 68.21/9.73 | % 68.21/9.73 | GROUND_INST: instantiating (3) with all_57_0, all_49_4, xc, simplifying with % 68.21/9.73 | (7), (8), (20), (25), (27), (28), (31) gives: % 68.21/9.73 | (33) doDivides0(all_57_0, all_49_4) % 68.21/9.73 | % 68.21/9.73 | DELTA: instantiating (24) with fresh symbol all_71_0 gives: % 68.21/9.73 | (34) sdtasdt0(xc, all_71_0) = all_49_4 & $i(all_71_0) & aElement0(all_71_0) % 68.21/9.73 | % 68.21/9.73 | ALPHA: (34) implies: % 68.21/9.73 | (35) aElement0(all_71_0) % 68.21/9.73 | (36) $i(all_71_0) % 68.21/9.73 | (37) sdtasdt0(xc, all_71_0) = all_49_4 % 68.21/9.73 | % 68.21/9.73 | GROUND_INST: instantiating (2) with all_57_0, all_49_4, simplifying with (20), % 68.21/9.73 | (25), (27), (28), (33) gives: % 68.21/9.74 | (38) ? [v0: $i] : (sdtasdt0(all_57_0, v0) = all_49_4 & $i(v0) & % 68.21/9.74 | aElement0(v0)) % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (mMulComm) with xc, all_71_0, all_49_4, simplifying % 68.21/9.74 | with (7), (8), (35), (36), (37) gives: % 68.21/9.74 | (39) sdtasdt0(all_71_0, xc) = all_49_4 & $i(all_49_4) % 68.21/9.74 | % 68.21/9.74 | ALPHA: (39) implies: % 68.21/9.74 | (40) sdtasdt0(all_71_0, xc) = all_49_4 % 68.21/9.74 | % 68.21/9.74 | DELTA: instantiating (38) with fresh symbol all_79_0 gives: % 68.21/9.74 | (41) sdtasdt0(all_57_0, all_79_0) = all_49_4 & $i(all_79_0) & % 68.21/9.74 | aElement0(all_79_0) % 68.21/9.74 | % 68.21/9.74 | ALPHA: (41) implies: % 68.21/9.74 | (42) aElement0(all_79_0) % 68.21/9.74 | (43) $i(all_79_0) % 68.21/9.74 | (44) sdtasdt0(all_57_0, all_79_0) = all_49_4 % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (mMulComm) with all_57_0, all_79_0, all_49_4, % 68.21/9.74 | simplifying with (27), (28), (42), (43), (44) gives: % 68.21/9.74 | (45) sdtasdt0(all_79_0, all_57_0) = all_49_4 & $i(all_49_4) % 68.21/9.74 | % 68.21/9.74 | ALPHA: (45) implies: % 68.21/9.74 | (46) sdtasdt0(all_79_0, all_57_0) = all_49_4 % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (3) with all_71_0, all_49_4, xc, simplifying with % 68.21/9.74 | (7), (8), (20), (25), (35), (36), (40) gives: % 68.21/9.74 | (47) doDivides0(all_71_0, all_49_4) % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (2) with all_71_0, all_49_4, simplifying with (20), % 68.21/9.74 | (25), (35), (36), (47) gives: % 68.21/9.74 | (48) ? [v0: $i] : (sdtasdt0(all_71_0, v0) = all_49_4 & $i(v0) & % 68.21/9.74 | aElement0(v0)) % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (3) with all_79_0, all_49_4, all_57_0, simplifying % 68.21/9.74 | with (20), (25), (27), (28), (42), (43), (46) gives: % 68.21/9.74 | (49) doDivides0(all_79_0, all_49_4) % 68.21/9.74 | % 68.21/9.74 | DELTA: instantiating (48) with fresh symbol all_93_0 gives: % 68.21/9.74 | (50) sdtasdt0(all_71_0, all_93_0) = all_49_4 & $i(all_93_0) & % 68.21/9.74 | aElement0(all_93_0) % 68.21/9.74 | % 68.21/9.74 | ALPHA: (50) implies: % 68.21/9.74 | (51) aElement0(all_93_0) % 68.21/9.74 | (52) $i(all_93_0) % 68.21/9.74 | (53) sdtasdt0(all_71_0, all_93_0) = all_49_4 % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (2) with all_79_0, all_49_4, simplifying with (20), % 68.21/9.74 | (25), (42), (43), (49) gives: % 68.21/9.74 | (54) ? [v0: $i] : (sdtasdt0(all_79_0, v0) = all_49_4 & $i(v0) & % 68.21/9.74 | aElement0(v0)) % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (mMulComm) with all_71_0, all_93_0, all_49_4, % 68.21/9.74 | simplifying with (35), (36), (51), (52), (53) gives: % 68.21/9.74 | (55) sdtasdt0(all_93_0, all_71_0) = all_49_4 & $i(all_49_4) % 68.21/9.74 | % 68.21/9.74 | ALPHA: (55) implies: % 68.21/9.74 | (56) sdtasdt0(all_93_0, all_71_0) = all_49_4 % 68.21/9.74 | % 68.21/9.74 | DELTA: instantiating (54) with fresh symbol all_101_0 gives: % 68.21/9.74 | (57) sdtasdt0(all_79_0, all_101_0) = all_49_4 & $i(all_101_0) & % 68.21/9.74 | aElement0(all_101_0) % 68.21/9.74 | % 68.21/9.74 | ALPHA: (57) implies: % 68.21/9.74 | (58) aElement0(all_101_0) % 68.21/9.74 | (59) $i(all_101_0) % 68.21/9.74 | (60) sdtasdt0(all_79_0, all_101_0) = all_49_4 % 68.21/9.74 | % 68.21/9.74 | GROUND_INST: instantiating (mMulComm) with all_79_0, all_101_0, all_49_4, % 68.21/9.74 | simplifying with (42), (43), (58), (59), (60) gives: % 68.21/9.74 | (61) sdtasdt0(all_101_0, all_79_0) = all_49_4 & $i(all_49_4) % 68.21/9.74 | % 68.21/9.74 | ALPHA: (61) implies: % 68.21/9.74 | (62) sdtasdt0(all_101_0, all_79_0) = all_49_4 % 68.21/9.74 | % 68.21/9.75 | GROUND_INST: instantiating (3) with all_101_0, all_49_4, all_79_0, simplifying % 68.21/9.75 | with (20), (25), (42), (43), (58), (59), (62) gives: % 68.21/9.75 | (63) doDivides0(all_101_0, all_49_4) % 68.21/9.75 | % 68.21/9.75 | GROUND_INST: instantiating (2) with all_101_0, all_49_4, simplifying with % 68.21/9.75 | (20), (25), (58), (59), (63) gives: % 68.21/9.75 | (64) ? [v0: $i] : (sdtasdt0(all_101_0, v0) = all_49_4 & $i(v0) & % 68.21/9.75 | aElement0(v0)) % 68.21/9.75 | % 68.21/9.75 | DELTA: instantiating (64) with fresh symbol all_123_0 gives: % 68.21/9.75 | (65) sdtasdt0(all_101_0, all_123_0) = all_49_4 & $i(all_123_0) & % 68.21/9.75 | aElement0(all_123_0) % 68.21/9.75 | % 68.21/9.75 | ALPHA: (65) implies: % 68.21/9.75 | (66) aElement0(all_123_0) % 68.21/9.75 | (67) $i(all_123_0) % 68.21/9.75 | (68) sdtasdt0(all_101_0, all_123_0) = all_49_4 % 68.21/9.75 | % 68.21/9.75 | GROUND_INST: instantiating (mMulComm) with all_101_0, all_123_0, all_49_4, % 68.21/9.75 | simplifying with (58), (59), (66), (67), (68) gives: % 68.21/9.75 | (69) sdtasdt0(all_123_0, all_101_0) = all_49_4 & $i(all_49_4) % 68.21/9.75 | % 68.21/9.75 | ALPHA: (69) implies: % 68.21/9.75 | (70) sdtasdt0(all_123_0, all_101_0) = all_49_4 % 68.21/9.75 | % 68.21/9.75 | GROUND_INST: instantiating (3) with all_123_0, all_49_4, all_101_0, % 68.21/9.75 | simplifying with (20), (25), (58), (59), (66), (67), (70) gives: % 68.21/9.75 | (71) doDivides0(all_123_0, all_49_4) % 68.21/9.75 | % 68.21/9.75 | GROUND_INST: instantiating (2) with all_123_0, all_49_4, simplifying with % 68.21/9.75 | (20), (25), (66), (67), (71) gives: % 68.21/9.75 | (72) ? [v0: $i] : (sdtasdt0(all_123_0, v0) = all_49_4 & $i(v0) & % 68.21/9.75 | aElement0(v0)) % 68.21/9.75 | % 68.21/9.75 | DELTA: instantiating (72) with fresh symbol all_145_0 gives: % 68.21/9.75 | (73) sdtasdt0(all_123_0, all_145_0) = all_49_4 & $i(all_145_0) & % 68.21/9.75 | aElement0(all_145_0) % 68.21/9.75 | % 68.21/9.75 | ALPHA: (73) implies: % 68.21/9.75 | (74) aElement0(all_145_0) % 68.21/9.75 | (75) $i(all_145_0) % 68.21/9.75 | (76) sdtasdt0(all_123_0, all_145_0) = all_49_4 % 68.21/9.75 | % 68.21/9.75 | GROUND_INST: instantiating (mMulComm) with all_123_0, all_145_0, all_49_4, % 68.21/9.75 | simplifying with (66), (67), (74), (75), (76) gives: % 68.21/9.75 | (77) sdtasdt0(all_145_0, all_123_0) = all_49_4 & $i(all_49_4) % 68.21/9.75 | % 68.21/9.75 | BETA: splitting (23) gives: % 68.21/9.75 | % 68.21/9.75 | Case 1: % 68.21/9.75 | | % 68.21/9.75 | | (78) sdtasdt0(all_49_3, all_49_4) = all_49_2 & $i(all_49_2) & % 68.21/9.75 | | aElement0(all_49_3) & ~ aElementOf0(all_49_2, all_33_0) % 68.21/9.75 | | % 68.21/9.75 | | ALPHA: (78) implies: % 68.21/9.75 | | (79) ~ aElementOf0(all_49_2, all_33_0) % 68.21/9.75 | | (80) aElement0(all_49_3) % 68.21/9.75 | | (81) sdtasdt0(all_49_3, all_49_4) = all_49_2 % 68.21/9.75 | | % 68.21/9.75 | | GROUND_INST: instantiating (mMulComm) with all_49_3, all_49_4, all_49_2, % 68.21/9.75 | | simplifying with (20), (21), (25), (80), (81) gives: % 68.21/9.75 | | (82) sdtasdt0(all_49_4, all_49_3) = all_49_2 & $i(all_49_2) % 68.21/9.75 | | % 68.21/9.75 | | ALPHA: (82) implies: % 68.21/9.75 | | (83) sdtasdt0(all_49_4, all_49_3) = all_49_2 % 68.21/9.75 | | % 68.21/9.75 | | GROUND_INST: instantiating (mMulAsso) with all_93_0, all_71_0, all_49_3, % 68.21/9.75 | | all_49_4, all_49_2, simplifying with (21), (35), (36), (51), % 68.21/9.75 | | (52), (56), (80), (83) gives: % 68.21/9.76 | | (84) ? [v0: $i] : (sdtasdt0(all_93_0, v0) = all_49_2 & % 68.21/9.76 | | sdtasdt0(all_71_0, all_49_3) = v0 & $i(v0) & $i(all_49_2)) % 68.21/9.76 | | % 68.21/9.76 | | GROUND_INST: instantiating (mMulAsso) with xc, all_71_0, all_49_3, all_49_4, % 68.21/9.76 | | all_49_2, simplifying with (7), (8), (21), (35), (36), (37), % 68.21/9.76 | | (80), (83) gives: % 68.21/9.76 | | (85) ? [v0: $i] : (sdtasdt0(all_71_0, all_49_3) = v0 & sdtasdt0(xc, v0) % 68.21/9.76 | | = all_49_2 & $i(v0) & $i(all_49_2)) % 68.21/9.76 | | % 68.21/9.76 | | DELTA: instantiating (85) with fresh symbol all_179_0 gives: % 68.21/9.76 | | (86) sdtasdt0(all_71_0, all_49_3) = all_179_0 & sdtasdt0(xc, all_179_0) = % 68.21/9.76 | | all_49_2 & $i(all_179_0) & $i(all_49_2) % 68.21/9.76 | | % 68.21/9.76 | | ALPHA: (86) implies: % 68.21/9.76 | | (87) sdtasdt0(xc, all_179_0) = all_49_2 % 68.21/9.76 | | (88) sdtasdt0(all_71_0, all_49_3) = all_179_0 % 68.21/9.76 | | % 68.21/9.76 | | DELTA: instantiating (84) with fresh symbol all_199_0 gives: % 68.21/9.76 | | (89) sdtasdt0(all_93_0, all_199_0) = all_49_2 & sdtasdt0(all_71_0, % 68.21/9.76 | | all_49_3) = all_199_0 & $i(all_199_0) & $i(all_49_2) % 68.21/9.76 | | % 68.21/9.76 | | ALPHA: (89) implies: % 68.21/9.76 | | (90) sdtasdt0(all_71_0, all_49_3) = all_199_0 % 68.21/9.76 | | % 68.21/9.76 | | GROUND_INST: instantiating (11) with all_179_0, all_199_0, all_49_3, % 68.21/9.76 | | all_71_0, simplifying with (88), (90) gives: % 68.21/9.76 | | (91) all_199_0 = all_179_0 % 68.21/9.76 | | % 68.21/9.76 | | GROUND_INST: instantiating (mSortsB_02) with all_71_0, all_49_3, all_179_0, % 68.21/9.76 | | simplifying with (21), (35), (36), (80), (88) gives: % 68.21/9.76 | | (92) aElement0(all_179_0) % 68.21/9.76 | | % 68.21/9.76 | | GROUND_INST: instantiating (mMulComm) with all_71_0, all_49_3, all_179_0, % 68.21/9.76 | | simplifying with (21), (35), (36), (80), (88) gives: % 68.21/9.76 | | (93) sdtasdt0(all_49_3, all_71_0) = all_179_0 & $i(all_179_0) % 68.21/9.76 | | % 68.21/9.76 | | ALPHA: (93) implies: % 68.21/9.76 | | (94) $i(all_179_0) % 68.21/9.76 | | % 68.21/9.76 | | GROUND_INST: instantiating (mMulComm) with xc, all_179_0, all_49_2, % 68.21/9.76 | | simplifying with (7), (8), (87), (92), (94) gives: % 68.21/9.76 | | (95) sdtasdt0(all_179_0, xc) = all_49_2 & $i(all_49_2) % 68.21/9.76 | | % 68.21/9.76 | | ALPHA: (95) implies: % 68.21/9.76 | | (96) $i(all_49_2) % 68.21/9.76 | | % 68.21/9.76 | | GROUND_INST: instantiating (6) with xc, all_33_0, all_49_2, all_179_0, % 68.21/9.76 | | simplifying with (7), (8), (14), (15), (79), (87), (92), (94), % 68.21/9.76 | | (96) gives: % 68.21/9.76 | | (97) $false % 68.21/9.76 | | % 68.21/9.76 | | CLOSE: (97) is inconsistent. % 68.21/9.76 | | % 68.21/9.76 | Case 2: % 68.21/9.76 | | % 68.21/9.76 | | (98) sdtpldt0(all_49_4, all_49_1) = all_49_0 & $i(all_49_0) & % 68.21/9.76 | | aElementOf0(all_49_1, all_33_0) & ~ aElementOf0(all_49_0, all_33_0) % 68.21/9.76 | | % 68.21/9.76 | | ALPHA: (98) implies: % 68.21/9.76 | | (99) ~ aElementOf0(all_49_0, all_33_0) % 68.21/9.76 | | (100) aElementOf0(all_49_1, all_33_0) % 68.21/9.76 | | (101) sdtpldt0(all_49_4, all_49_1) = all_49_0 % 68.21/9.76 | | % 68.21/9.76 | | GROUND_INST: instantiating (5) with xc, all_33_0, all_49_1, simplifying with % 68.21/9.76 | | (7), (8), (14), (15), (22), (100) gives: % 68.21/9.76 | | (102) ? [v0: $i] : (sdtasdt0(xc, v0) = all_49_1 & $i(v0) & % 68.21/9.76 | | aElement0(v0)) % 68.62/9.76 | | % 68.62/9.76 | | GROUND_INST: instantiating (mEOfElem) with all_33_0, all_49_1, simplifying % 68.62/9.76 | | with (14), (16), (22), (100) gives: % 68.62/9.76 | | (103) aElement0(all_49_1) % 68.62/9.76 | | % 68.62/9.76 | | DELTA: instantiating (102) with fresh symbol all_167_0 gives: % 68.62/9.76 | | (104) sdtasdt0(xc, all_167_0) = all_49_1 & $i(all_167_0) & % 68.62/9.76 | | aElement0(all_167_0) % 68.62/9.76 | | % 68.62/9.76 | | ALPHA: (104) implies: % 68.62/9.76 | | (105) aElement0(all_167_0) % 68.62/9.76 | | (106) $i(all_167_0) % 68.62/9.76 | | (107) sdtasdt0(xc, all_167_0) = all_49_1 % 68.62/9.76 | | % 68.62/9.76 | | GROUND_INST: instantiating (mAddComm) with all_49_4, all_49_1, all_49_0, % 68.62/9.76 | | simplifying with (20), (22), (25), (101), (103) gives: % 68.62/9.76 | | (108) sdtpldt0(all_49_1, all_49_4) = all_49_0 & $i(all_49_0) % 68.62/9.76 | | % 68.62/9.76 | | ALPHA: (108) implies: % 68.62/9.76 | | (109) sdtpldt0(all_49_1, all_49_4) = all_49_0 % 68.62/9.76 | | % 68.62/9.77 | | GROUND_INST: instantiating (mAMDistr) with xc, all_71_0, all_167_0, % 68.62/9.77 | | all_49_4, all_49_1, all_49_0, simplifying with (7), (8), (35), % 68.62/9.77 | | (36), (37), (101), (105), (106), (107) gives: % 68.62/9.77 | | (110) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 68.62/9.77 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_167_0, xc) = v3 & % 68.62/9.77 | | sdtasdt0(all_71_0, xc) = v2 & sdtasdt0(xc, v0) = all_49_0 & % 68.62/9.77 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_71_0, all_167_0) = v0 & % 68.62/9.77 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_49_0)) % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (mAMDistr) with xc, all_57_0, all_167_0, % 68.62/9.77 | | all_49_4, all_49_1, all_49_0, simplifying with (7), (8), (27), % 68.62/9.77 | | (28), (29), (101), (105), (106), (107) gives: % 68.62/9.77 | | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 68.62/9.77 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_167_0, xc) = v3 & % 68.62/9.77 | | sdtasdt0(all_57_0, xc) = v2 & sdtasdt0(xc, v0) = all_49_0 & % 68.62/9.77 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_57_0, all_167_0) = v0 & % 68.62/9.77 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_49_0)) % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (mMulComm) with xc, all_167_0, all_49_1, % 68.62/9.77 | | simplifying with (7), (8), (105), (106), (107) gives: % 68.62/9.77 | | (112) sdtasdt0(all_167_0, xc) = all_49_1 & $i(all_49_1) % 68.62/9.77 | | % 68.62/9.77 | | ALPHA: (112) implies: % 68.62/9.77 | | (113) sdtasdt0(all_167_0, xc) = all_49_1 % 68.62/9.77 | | % 68.62/9.77 | | DELTA: instantiating (110) with fresh symbols all_177_0, all_177_1, % 68.62/9.77 | | all_177_2, all_177_3 gives: % 68.62/9.77 | | (114) sdtasdt0(all_177_3, xc) = all_177_2 & sdtasdt0(all_167_0, xc) = % 68.62/9.77 | | all_177_0 & sdtasdt0(all_71_0, xc) = all_177_1 & sdtasdt0(xc, % 68.62/9.77 | | all_177_3) = all_49_0 & sdtpldt0(all_177_1, all_177_0) = % 68.62/9.77 | | all_177_2 & sdtpldt0(all_71_0, all_167_0) = all_177_3 & % 68.62/9.77 | | $i(all_177_0) & $i(all_177_1) & $i(all_177_2) & $i(all_177_3) & % 68.62/9.77 | | $i(all_49_0) % 68.62/9.77 | | % 68.62/9.77 | | ALPHA: (114) implies: % 68.62/9.77 | | (115) sdtpldt0(all_71_0, all_167_0) = all_177_3 % 68.62/9.77 | | (116) sdtpldt0(all_177_1, all_177_0) = all_177_2 % 68.62/9.77 | | (117) sdtasdt0(all_71_0, xc) = all_177_1 % 68.62/9.77 | | (118) sdtasdt0(all_167_0, xc) = all_177_0 % 68.62/9.77 | | (119) sdtasdt0(all_177_3, xc) = all_177_2 % 68.62/9.77 | | % 68.62/9.77 | | DELTA: instantiating (111) with fresh symbols all_179_0, all_179_1, % 68.62/9.77 | | all_179_2, all_179_3 gives: % 68.62/9.77 | | (120) sdtasdt0(all_179_3, xc) = all_179_2 & sdtasdt0(all_167_0, xc) = % 68.62/9.77 | | all_179_0 & sdtasdt0(all_57_0, xc) = all_179_1 & sdtasdt0(xc, % 68.62/9.77 | | all_179_3) = all_49_0 & sdtpldt0(all_179_1, all_179_0) = % 68.62/9.77 | | all_179_2 & sdtpldt0(all_57_0, all_167_0) = all_179_3 & % 68.62/9.77 | | $i(all_179_0) & $i(all_179_1) & $i(all_179_2) & $i(all_179_3) & % 68.62/9.77 | | $i(all_49_0) % 68.62/9.77 | | % 68.62/9.77 | | ALPHA: (120) implies: % 68.62/9.77 | | (121) sdtpldt0(all_57_0, all_167_0) = all_179_3 % 68.62/9.77 | | (122) sdtpldt0(all_179_1, all_179_0) = all_179_2 % 68.62/9.77 | | (123) sdtasdt0(all_57_0, xc) = all_179_1 % 68.62/9.77 | | (124) sdtasdt0(all_167_0, xc) = all_179_0 % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (11) with all_49_4, all_179_1, xc, all_57_0, % 68.62/9.77 | | simplifying with (31), (123) gives: % 68.62/9.77 | | (125) all_179_1 = all_49_4 % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (11) with all_49_4, all_177_1, xc, all_71_0, % 68.62/9.77 | | simplifying with (40), (117) gives: % 68.62/9.77 | | (126) all_177_1 = all_49_4 % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (11) with all_177_0, all_179_0, xc, all_167_0, % 68.62/9.77 | | simplifying with (118), (124) gives: % 68.62/9.77 | | (127) all_179_0 = all_177_0 % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (11) with all_49_1, all_179_0, xc, all_167_0, % 68.62/9.77 | | simplifying with (113), (124) gives: % 68.62/9.77 | | (128) all_179_0 = all_49_1 % 68.62/9.77 | | % 68.62/9.77 | | COMBINE_EQS: (127), (128) imply: % 68.62/9.77 | | (129) all_177_0 = all_49_1 % 68.62/9.77 | | % 68.62/9.77 | | SIMP: (129) implies: % 68.62/9.77 | | (130) all_177_0 = all_49_1 % 68.62/9.77 | | % 68.62/9.77 | | REDUCE: (122), (125), (128) imply: % 68.62/9.77 | | (131) sdtpldt0(all_49_4, all_49_1) = all_179_2 % 68.62/9.77 | | % 68.62/9.77 | | REDUCE: (116), (126), (130) imply: % 68.62/9.77 | | (132) sdtpldt0(all_49_4, all_49_1) = all_177_2 % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (10) with all_49_0, all_179_2, all_49_1, % 68.62/9.77 | | all_49_4, simplifying with (101), (131) gives: % 68.62/9.77 | | (133) all_179_2 = all_49_0 % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (10) with all_177_2, all_179_2, all_49_1, % 68.62/9.77 | | all_49_4, simplifying with (131), (132) gives: % 68.62/9.77 | | (134) all_179_2 = all_177_2 % 68.62/9.77 | | % 68.62/9.77 | | COMBINE_EQS: (133), (134) imply: % 68.62/9.77 | | (135) all_177_2 = all_49_0 % 68.62/9.77 | | % 68.62/9.77 | | REDUCE: (119), (135) imply: % 68.62/9.77 | | (136) sdtasdt0(all_177_3, xc) = all_49_0 % 68.62/9.77 | | % 68.62/9.77 | | GROUND_INST: instantiating (mAMDistr) with xc, all_167_0, all_71_0, % 68.62/9.77 | | all_49_1, all_49_4, all_49_0, simplifying with (7), (8), (35), % 68.62/9.77 | | (36), (37), (105), (106), (107), (109) gives: % 68.62/9.77 | | (137) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 68.62/9.77 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_167_0, xc) = v2 & % 68.62/9.77 | | sdtasdt0(all_71_0, xc) = v3 & sdtasdt0(xc, v0) = all_49_0 & % 68.62/9.77 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_167_0, all_71_0) = v0 & % 68.62/9.77 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_49_0)) % 68.62/9.77 | | % 68.62/9.78 | | GROUND_INST: instantiating (mAMDistr) with xc, all_167_0, all_57_0, % 68.62/9.78 | | all_49_1, all_49_4, all_49_0, simplifying with (7), (8), (27), % 68.62/9.78 | | (28), (29), (105), (106), (107), (109) gives: % 68.62/9.78 | | (138) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 68.62/9.78 | | (sdtasdt0(v0, xc) = v1 & sdtasdt0(all_167_0, xc) = v2 & % 68.62/9.78 | | sdtasdt0(all_57_0, xc) = v3 & sdtasdt0(xc, v0) = all_49_0 & % 68.62/9.78 | | sdtpldt0(v2, v3) = v1 & sdtpldt0(all_167_0, all_57_0) = v0 & % 68.62/9.78 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_49_0)) % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (mSortsB) with all_57_0, all_167_0, all_179_3, % 68.62/9.78 | | simplifying with (27), (28), (105), (106), (121) gives: % 68.62/9.78 | | (139) aElement0(all_179_3) % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (mAddComm) with all_57_0, all_167_0, all_179_3, % 68.62/9.78 | | simplifying with (27), (28), (105), (106), (121) gives: % 68.62/9.78 | | (140) sdtpldt0(all_167_0, all_57_0) = all_179_3 & $i(all_179_3) % 68.62/9.78 | | % 68.62/9.78 | | ALPHA: (140) implies: % 68.62/9.78 | | (141) sdtpldt0(all_167_0, all_57_0) = all_179_3 % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (mAddComm) with all_71_0, all_167_0, all_177_3, % 68.62/9.78 | | simplifying with (35), (36), (105), (106), (115) gives: % 68.62/9.78 | | (142) sdtpldt0(all_167_0, all_71_0) = all_177_3 & $i(all_177_3) % 68.62/9.78 | | % 68.62/9.78 | | ALPHA: (142) implies: % 68.62/9.78 | | (143) sdtpldt0(all_167_0, all_71_0) = all_177_3 % 68.62/9.78 | | % 68.62/9.78 | | DELTA: instantiating (138) with fresh symbols all_205_0, all_205_1, % 68.62/9.78 | | all_205_2, all_205_3 gives: % 68.62/9.78 | | (144) sdtasdt0(all_205_3, xc) = all_205_2 & sdtasdt0(all_167_0, xc) = % 68.62/9.78 | | all_205_1 & sdtasdt0(all_57_0, xc) = all_205_0 & sdtasdt0(xc, % 68.62/9.78 | | all_205_3) = all_49_0 & sdtpldt0(all_205_1, all_205_0) = % 68.62/9.78 | | all_205_2 & sdtpldt0(all_167_0, all_57_0) = all_205_3 & % 68.62/9.78 | | $i(all_205_0) & $i(all_205_1) & $i(all_205_2) & $i(all_205_3) & % 68.62/9.78 | | $i(all_49_0) % 68.62/9.78 | | % 68.62/9.78 | | ALPHA: (144) implies: % 68.62/9.78 | | (145) $i(all_205_3) % 68.62/9.78 | | (146) $i(all_205_2) % 68.62/9.78 | | (147) sdtpldt0(all_167_0, all_57_0) = all_205_3 % 68.62/9.78 | | (148) sdtpldt0(all_205_1, all_205_0) = all_205_2 % 68.62/9.78 | | (149) sdtasdt0(xc, all_205_3) = all_49_0 % 68.62/9.78 | | (150) sdtasdt0(all_57_0, xc) = all_205_0 % 68.62/9.78 | | (151) sdtasdt0(all_167_0, xc) = all_205_1 % 68.62/9.78 | | % 68.62/9.78 | | DELTA: instantiating (137) with fresh symbols all_207_0, all_207_1, % 68.62/9.78 | | all_207_2, all_207_3 gives: % 68.62/9.78 | | (152) sdtasdt0(all_207_3, xc) = all_207_2 & sdtasdt0(all_167_0, xc) = % 68.62/9.78 | | all_207_1 & sdtasdt0(all_71_0, xc) = all_207_0 & sdtasdt0(xc, % 68.62/9.78 | | all_207_3) = all_49_0 & sdtpldt0(all_207_1, all_207_0) = % 68.62/9.78 | | all_207_2 & sdtpldt0(all_167_0, all_71_0) = all_207_3 & % 68.62/9.78 | | $i(all_207_0) & $i(all_207_1) & $i(all_207_2) & $i(all_207_3) & % 68.62/9.78 | | $i(all_49_0) % 68.62/9.78 | | % 68.62/9.78 | | ALPHA: (152) implies: % 68.62/9.78 | | (153) sdtpldt0(all_167_0, all_71_0) = all_207_3 % 68.62/9.78 | | (154) sdtpldt0(all_207_1, all_207_0) = all_207_2 % 68.62/9.78 | | (155) sdtasdt0(all_71_0, xc) = all_207_0 % 68.62/9.78 | | (156) sdtasdt0(all_167_0, xc) = all_207_1 % 68.62/9.78 | | (157) sdtasdt0(all_207_3, xc) = all_207_2 % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (10) with all_179_3, all_205_3, all_57_0, % 68.62/9.78 | | all_167_0, simplifying with (141), (147) gives: % 68.62/9.78 | | (158) all_205_3 = all_179_3 % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (10) with all_177_3, all_207_3, all_71_0, % 68.62/9.78 | | all_167_0, simplifying with (143), (153) gives: % 68.62/9.78 | | (159) all_207_3 = all_177_3 % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (11) with all_49_4, all_205_0, xc, all_57_0, % 68.62/9.78 | | simplifying with (31), (150) gives: % 68.62/9.78 | | (160) all_205_0 = all_49_4 % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (11) with all_49_4, all_207_0, xc, all_71_0, % 68.62/9.78 | | simplifying with (40), (155) gives: % 68.62/9.78 | | (161) all_207_0 = all_49_4 % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (11) with all_49_1, all_207_1, xc, all_167_0, % 68.62/9.78 | | simplifying with (113), (156) gives: % 68.62/9.78 | | (162) all_207_1 = all_49_1 % 68.62/9.78 | | % 68.62/9.78 | | GROUND_INST: instantiating (11) with all_205_1, all_207_1, xc, all_167_0, % 68.62/9.78 | | simplifying with (151), (156) gives: % 68.62/9.78 | | (163) all_207_1 = all_205_1 % 68.62/9.78 | | % 68.62/9.78 | | COMBINE_EQS: (162), (163) imply: % 68.72/9.78 | | (164) all_205_1 = all_49_1 % 68.72/9.78 | | % 68.72/9.78 | | REDUCE: (157), (159) imply: % 68.72/9.78 | | (165) sdtasdt0(all_177_3, xc) = all_207_2 % 68.72/9.78 | | % 68.72/9.78 | | REDUCE: (149), (158) imply: % 68.72/9.78 | | (166) sdtasdt0(xc, all_179_3) = all_49_0 % 68.72/9.78 | | % 68.72/9.78 | | REDUCE: (154), (161), (162) imply: % 68.72/9.78 | | (167) sdtpldt0(all_49_1, all_49_4) = all_207_2 % 68.72/9.78 | | % 68.72/9.78 | | REDUCE: (148), (160), (164) imply: % 68.72/9.78 | | (168) sdtpldt0(all_49_1, all_49_4) = all_205_2 % 68.72/9.78 | | % 68.72/9.78 | | REDUCE: (145), (158) imply: % 68.72/9.78 | | (169) $i(all_179_3) % 68.72/9.78 | | % 68.72/9.78 | | GROUND_INST: instantiating (10) with all_205_2, all_207_2, all_49_4, % 68.72/9.78 | | all_49_1, simplifying with (167), (168) gives: % 68.72/9.78 | | (170) all_207_2 = all_205_2 % 68.72/9.78 | | % 68.72/9.78 | | GROUND_INST: instantiating (11) with all_49_0, all_207_2, xc, all_177_3, % 68.72/9.78 | | simplifying with (136), (165) gives: % 68.72/9.78 | | (171) all_207_2 = all_49_0 % 68.72/9.78 | | % 68.72/9.78 | | COMBINE_EQS: (170), (171) imply: % 68.72/9.78 | | (172) all_205_2 = all_49_0 % 68.72/9.78 | | % 68.72/9.78 | | SIMP: (172) implies: % 68.72/9.78 | | (173) all_205_2 = all_49_0 % 68.72/9.78 | | % 68.72/9.78 | | REDUCE: (146), (173) imply: % 68.72/9.78 | | (174) $i(all_49_0) % 68.72/9.78 | | % 68.72/9.78 | | GROUND_INST: instantiating (6) with xc, all_33_0, all_49_0, all_179_3, % 68.72/9.78 | | simplifying with (7), (8), (14), (15), (99), (139), (166), % 68.72/9.78 | | (169), (174) gives: % 68.72/9.78 | | (175) $false % 68.72/9.78 | | % 68.72/9.78 | | CLOSE: (175) is inconsistent. % 68.72/9.78 | | % 68.72/9.78 | End of split % 68.72/9.78 | % 68.72/9.78 End of proof % 68.72/9.78 % SZS output end Proof for theBenchmark % 68.72/9.78 % 68.72/9.78 9167ms %------------------------------------------------------------------------------