%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG105+2 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.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 13:57:55 EDT 2023 % Result : Theorem 24.04s 4.33s % Output : Proof 31.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG105+2 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n026.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sun Aug 27 03:02:18 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.67 ________ _____ % 0.20/0.67 ___ __ \_________(_)________________________________ % 0.20/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.67 % 0.20/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.67 (2023-06-19) % 0.20/0.67 % 0.20/0.67 (c) Philipp Rümmer, 2009-2023 % 0.20/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.67 Amanda Stjerna. % 0.20/0.67 Free software under BSD-3-Clause. % 0.20/0.67 % 0.20/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.67 % 0.20/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.69 Running up to 7 provers in parallel. % 0.20/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.16/1.32 Prover 1: Preprocessing ... % 3.16/1.32 Prover 4: Preprocessing ... % 3.16/1.36 Prover 3: Preprocessing ... % 3.16/1.36 Prover 5: Preprocessing ... % 3.16/1.36 Prover 6: Preprocessing ... % 3.16/1.36 Prover 2: Preprocessing ... % 3.16/1.36 Prover 0: Preprocessing ... % 8.44/2.18 Prover 1: Constructing countermodel ... % 8.44/2.18 Prover 3: Constructing countermodel ... % 8.44/2.19 Prover 5: Proving ... % 8.44/2.19 Prover 6: Proving ... % 9.94/2.21 Prover 2: Proving ... % 10.31/2.28 Prover 4: Constructing countermodel ... % 11.13/2.38 Prover 0: Proving ... % 24.04/4.33 Prover 3: proved (3622ms) % 24.04/4.33 % 24.04/4.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 24.04/4.33 % 24.99/4.34 Prover 0: stopped % 24.99/4.34 Prover 2: stopped % 24.99/4.34 Prover 6: stopped % 24.99/4.34 Prover 5: stopped % 24.99/4.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 24.99/4.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 24.99/4.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 24.99/4.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 24.99/4.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 26.89/4.46 Prover 10: Preprocessing ... % 26.89/4.48 Prover 8: Preprocessing ... % 26.89/4.49 Prover 11: Preprocessing ... % 26.89/4.50 Prover 13: Preprocessing ... % 26.89/4.50 Prover 7: Preprocessing ... % 27.94/4.60 Prover 10: Constructing countermodel ... % 27.94/4.63 Prover 7: Constructing countermodel ... % 28.54/4.66 Prover 8: Warning: ignoring some quantifiers % 28.70/4.67 Prover 8: Constructing countermodel ... % 28.70/4.70 Prover 13: Warning: ignoring some quantifiers % 29.04/4.72 Prover 13: Constructing countermodel ... % 29.74/4.90 Prover 11: Constructing countermodel ... % 29.74/4.92 Prover 10: Found proof (size 102) % 29.74/4.92 Prover 10: proved (583ms) % 29.74/4.92 Prover 7: stopped % 29.74/4.92 Prover 8: stopped % 29.74/4.92 Prover 13: stopped % 29.74/4.92 Prover 1: stopped % 29.74/4.92 Prover 11: stopped % 29.74/4.93 Prover 4: stopped % 29.74/4.93 % 29.74/4.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 29.74/4.93 % 29.74/4.96 % SZS output start Proof for theBenchmark % 29.74/4.97 Assumptions after simplification: % 29.74/4.97 --------------------------------- % 29.74/4.97 % 29.74/4.97 (mAMDistr) % 29.74/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 29.74/5.00 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 29.74/5.00 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 29.74/5.00 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 29.74/5.00 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, % 29.74/5.00 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, % 29.74/5.00 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 29.74/5.00 $i(v5))) % 29.74/5.00 % 29.74/5.00 (mAddComm) % 29.74/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 29.74/5.00 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 29.74/5.00 = v2 & $i(v2))) % 29.74/5.00 % 29.74/5.00 (mDefPrIdeal) % 30.41/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) = % 30.41/5.00 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 30.41/5.00 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & ! % 30.41/5.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~ % 30.41/5.00 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: % 30.41/5.00 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6: % 30.41/5.00 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) & % 30.41/5.00 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 & % 30.41/5.00 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 30.41/5.00 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, % 30.41/5.00 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 30.41/5.00 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 30.41/5.00 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 30.41/5.00 % 30.41/5.00 (mMulComm) % 30.41/5.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 30.41/5.01 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 30.41/5.01 = v2 & $i(v2))) % 30.41/5.01 % 30.41/5.01 (mSortsB) % 30.41/5.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 30.41/5.01 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 30.41/5.01 % 30.41/5.01 (mSortsB_02) % 30.41/5.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 30.41/5.01 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 30.41/5.01 % 30.41/5.01 (m__) % 30.41/5.01 $i(xz) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 30.41/5.01 (slsdtgt0(xc) = v1 & $i(v1) & ((sdtasdt0(xz, xx) = v2 & $i(v2) & ~ % 30.41/5.01 aElementOf0(v2, v1) & ! [v3: $i] : ( ~ (sdtasdt0(xc, v3) = v2) | ~ % 30.41/5.01 $i(v3) | ~ aElement0(v3))) | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~ % 30.41/5.01 aElementOf0(v0, v1) & ! [v3: $i] : ( ~ (sdtasdt0(xc, v3) = v0) | ~ % 30.41/5.01 $i(v3) | ~ aElement0(v3))))) % 30.41/5.01 % 30.41/5.01 (m__1905) % 30.41/5.01 $i(xc) & aElement0(xc) % 30.41/5.01 % 30.41/5.01 (m__1933) % 30.41/5.01 $i(xz) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 30.41/5.01 (slsdtgt0(xc) = v0 & sdtasdt0(xc, v2) = xx & sdtasdt0(xc, v1) = xy & $i(v2) & % 30.41/5.01 $i(v1) & $i(v0) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(v2) % 30.41/5.01 & aElement0(v1) & aElement0(xz)) % 30.41/5.01 % 30.41/5.01 (m__1956) % 30.41/5.02 sdtasdt0(xc, xu) = xx & $i(xu) & $i(xx) & $i(xc) & aElement0(xu) % 30.41/5.02 % 30.41/5.02 (m__1979) % 30.41/5.02 sdtasdt0(xc, xv) = xy & $i(xv) & $i(xy) & $i(xc) & aElement0(xv) % 30.41/5.02 % 30.41/5.02 (m__2010) % 30.41/5.02 $i(xv) & $i(xu) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : % 30.41/5.02 (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) = v0 & % 30.41/5.02 $i(v1) & $i(v0)) % 30.41/5.02 % 30.41/5.02 (m__2043) % 30.41/5.02 $i(xu) & $i(xz) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xu, % 30.41/5.02 xz) = v1 & sdtasdt0(xz, xx) = v0 & sdtasdt0(xc, v1) = v0 & $i(v1) & % 30.41/5.02 $i(v0)) % 30.41/5.02 % 30.41/5.02 (function-axioms) % 30.41/5.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.41/5.02 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.41/5.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 30.41/5.02 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 30.41/5.02 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 30.41/5.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.41/5.02 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.41/5.02 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 30.41/5.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 30.41/5.02 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 30.41/5.02 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 30.41/5.02 % 30.41/5.02 Further assumptions not needed in the proof: % 30.41/5.02 -------------------------------------------- % 30.41/5.02 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv, mDefDvs, % 30.41/5.02 mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mEOfElem, % 30.41/5.02 mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulMnOne, mMulUnit, mMulZero, % 30.41/5.02 mNatLess, mNatSort, mSetEq, mSetSort, mSortsC, mSortsC_01, mSortsU, mUnNeZr % 30.41/5.02 % 30.41/5.02 Those formulas are unsatisfiable: % 30.41/5.02 --------------------------------- % 30.41/5.02 % 30.41/5.02 Begin of proof % 30.41/5.03 | % 30.41/5.03 | ALPHA: (mDefPrIdeal) implies: % 30.41/5.03 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 30.41/5.03 | (slsdtgt0(v0) = v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ % 30.41/5.03 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) % 30.41/5.03 | | aElementOf0(v2, v1)) % 30.41/5.03 | % 30.41/5.03 | ALPHA: (m__1905) implies: % 30.41/5.03 | (2) aElement0(xc) % 30.41/5.03 | % 30.41/5.03 | ALPHA: (m__1933) implies: % 30.41/5.03 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slsdtgt0(xc) = v0 & % 30.41/5.03 | sdtasdt0(xc, v2) = xx & sdtasdt0(xc, v1) = xy & $i(v2) & $i(v1) & % 30.41/5.03 | $i(v0) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(v2) & % 30.41/5.03 | aElement0(v1) & aElement0(xz)) % 30.41/5.03 | % 30.41/5.03 | ALPHA: (m__1956) implies: % 30.41/5.03 | (4) aElement0(xu) % 30.41/5.03 | (5) sdtasdt0(xc, xu) = xx % 30.41/5.03 | % 30.41/5.03 | ALPHA: (m__1979) implies: % 30.41/5.03 | (6) aElement0(xv) % 30.41/5.03 | (7) sdtasdt0(xc, xv) = xy % 30.41/5.03 | % 30.41/5.03 | ALPHA: (m__2010) implies: % 30.41/5.03 | (8) $i(xv) % 30.41/5.03 | (9) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) = % 30.41/5.03 | v1 & sdtpldt0(xx, xy) = v0 & $i(v1) & $i(v0)) % 30.41/5.03 | % 30.41/5.03 | ALPHA: (m__2043) implies: % 30.41/5.03 | (10) $i(xu) % 30.41/5.03 | (11) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xu, xz) = v1 & sdtasdt0(xz, xx) % 30.41/5.03 | = v0 & sdtasdt0(xc, v1) = v0 & $i(v1) & $i(v0)) % 30.41/5.03 | % 30.41/5.03 | ALPHA: (m__) implies: % 30.41/5.03 | (12) $i(xc) % 30.41/5.03 | (13) $i(xz) % 30.41/5.03 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (slsdtgt0(xc) = v1 & $i(v1) % 30.41/5.03 | & ((sdtasdt0(xz, xx) = v2 & $i(v2) & ~ aElementOf0(v2, v1) & ! % 30.41/5.03 | [v3: $i] : ( ~ (sdtasdt0(xc, v3) = v2) | ~ $i(v3) | ~ % 30.41/5.03 | aElement0(v3))) | (sdtpldt0(xx, xy) = v0 & $i(v0) & ~ % 30.41/5.03 | aElementOf0(v0, v1) & ! [v3: $i] : ( ~ (sdtasdt0(xc, v3) = v0) % 30.41/5.03 | | ~ $i(v3) | ~ aElement0(v3))))) % 30.41/5.03 | % 30.41/5.03 | ALPHA: (function-axioms) implies: % 30.41/5.04 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) % 30.41/5.04 | = v1) | ~ (slsdtgt0(v2) = v0)) % 30.41/5.04 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.41/5.04 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 30.41/5.04 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.41/5.04 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 30.41/5.04 | % 30.41/5.04 | DELTA: instantiating (9) with fresh symbols all_33_0, all_33_1 gives: % 30.41/5.04 | (18) sdtasdt0(xc, all_33_0) = all_33_1 & sdtpldt0(xu, xv) = all_33_0 & % 30.41/5.04 | sdtpldt0(xx, xy) = all_33_1 & $i(all_33_0) & $i(all_33_1) % 30.41/5.04 | % 30.41/5.04 | ALPHA: (18) implies: % 30.41/5.04 | (19) sdtpldt0(xx, xy) = all_33_1 % 30.41/5.04 | (20) sdtpldt0(xu, xv) = all_33_0 % 30.41/5.04 | % 30.41/5.04 | DELTA: instantiating (11) with fresh symbols all_35_0, all_35_1 gives: % 30.41/5.04 | (21) sdtasdt0(xu, xz) = all_35_0 & sdtasdt0(xz, xx) = all_35_1 & % 30.41/5.04 | sdtasdt0(xc, all_35_0) = all_35_1 & $i(all_35_0) & $i(all_35_1) % 30.41/5.04 | % 30.41/5.04 | ALPHA: (21) implies: % 30.41/5.04 | (22) sdtasdt0(xc, all_35_0) = all_35_1 % 30.41/5.04 | (23) sdtasdt0(xz, xx) = all_35_1 % 30.41/5.04 | (24) sdtasdt0(xu, xz) = all_35_0 % 30.41/5.04 | % 30.41/5.04 | DELTA: instantiating (3) with fresh symbols all_40_0, all_40_1, all_40_2 % 30.41/5.04 | gives: % 30.41/5.04 | (25) slsdtgt0(xc) = all_40_2 & sdtasdt0(xc, all_40_0) = xx & sdtasdt0(xc, % 30.41/5.04 | all_40_1) = xy & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) & % 30.41/5.04 | aElementOf0(xy, all_40_2) & aElementOf0(xx, all_40_2) & % 30.41/5.04 | aElement0(all_40_0) & aElement0(all_40_1) & aElement0(xz) % 30.41/5.04 | % 30.41/5.04 | ALPHA: (25) implies: % 30.41/5.04 | (26) aElement0(xz) % 30.41/5.04 | (27) aElement0(all_40_1) % 30.41/5.04 | (28) aElement0(all_40_0) % 30.41/5.04 | (29) $i(all_40_1) % 30.41/5.04 | (30) $i(all_40_0) % 30.41/5.04 | (31) sdtasdt0(xc, all_40_1) = xy % 30.41/5.04 | (32) sdtasdt0(xc, all_40_0) = xx % 30.41/5.04 | (33) slsdtgt0(xc) = all_40_2 % 30.41/5.04 | % 30.41/5.04 | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1, all_42_2 % 30.41/5.04 | gives: % 30.41/5.04 | (34) slsdtgt0(xc) = all_42_1 & $i(all_42_1) & ((sdtasdt0(xz, xx) = all_42_0 % 30.41/5.04 | & $i(all_42_0) & ~ aElementOf0(all_42_0, all_42_1) & ! [v0: $i] % 30.41/5.04 | : ( ~ (sdtasdt0(xc, v0) = all_42_0) | ~ $i(v0) | ~ % 30.41/5.04 | aElement0(v0))) | (sdtpldt0(xx, xy) = all_42_2 & $i(all_42_2) & % 30.41/5.04 | ~ aElementOf0(all_42_2, all_42_1) & ! [v0: $i] : ( ~ % 30.41/5.04 | (sdtasdt0(xc, v0) = all_42_2) | ~ $i(v0) | ~ aElement0(v0)))) % 30.41/5.04 | % 30.41/5.04 | ALPHA: (34) implies: % 30.41/5.04 | (35) $i(all_42_1) % 30.41/5.04 | (36) slsdtgt0(xc) = all_42_1 % 30.41/5.04 | (37) (sdtasdt0(xz, xx) = all_42_0 & $i(all_42_0) & ~ aElementOf0(all_42_0, % 30.41/5.04 | all_42_1) & ! [v0: $i] : ( ~ (sdtasdt0(xc, v0) = all_42_0) | ~ % 30.41/5.04 | $i(v0) | ~ aElement0(v0))) | (sdtpldt0(xx, xy) = all_42_2 & % 30.41/5.04 | $i(all_42_2) & ~ aElementOf0(all_42_2, all_42_1) & ! [v0: $i] : ( % 30.41/5.04 | ~ (sdtasdt0(xc, v0) = all_42_2) | ~ $i(v0) | ~ aElement0(v0))) % 30.41/5.04 | % 30.41/5.05 | GROUND_INST: instantiating (15) with all_40_2, all_42_1, xc, simplifying with % 30.41/5.05 | (33), (36) gives: % 30.41/5.05 | (38) all_42_1 = all_40_2 % 30.41/5.05 | % 30.41/5.05 | REDUCE: (35), (38) imply: % 30.41/5.05 | (39) $i(all_40_2) % 30.41/5.05 | % 30.41/5.05 | GROUND_INST: instantiating (mSortsB) with xu, xv, all_33_0, simplifying with % 30.41/5.05 | (4), (6), (8), (10), (20) gives: % 30.41/5.05 | (40) aElement0(all_33_0) % 30.41/5.05 | % 30.41/5.05 | GROUND_INST: instantiating (mMulComm) with xc, xu, xx, simplifying with (2), % 30.41/5.05 | (4), (5), (10), (12) gives: % 30.41/5.05 | (41) sdtasdt0(xu, xc) = xx & $i(xx) % 30.41/5.05 | % 30.41/5.05 | ALPHA: (41) implies: % 30.41/5.05 | (42) sdtasdt0(xu, xc) = xx % 30.41/5.05 | % 30.41/5.05 | GROUND_INST: instantiating (mAMDistr) with xc, xu, xv, xx, xy, all_33_1, % 30.41/5.05 | simplifying with (2), (4), (5), (6), (7), (8), (10), (12), (19) % 30.41/5.05 | gives: % 30.41/5.05 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 30.41/5.05 | xc) = v1 & sdtasdt0(xv, xc) = v3 & sdtasdt0(xu, xc) = v2 & % 30.41/5.05 | sdtasdt0(xc, v0) = all_33_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu, % 30.41/5.05 | xv) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_33_1)) % 30.41/5.05 | % 30.41/5.05 | GROUND_INST: instantiating (mMulComm) with xc, xv, xy, simplifying with (2), % 30.41/5.05 | (6), (7), (8), (12) gives: % 30.41/5.05 | (44) sdtasdt0(xv, xc) = xy & $i(xy) % 30.41/5.05 | % 30.41/5.05 | ALPHA: (44) implies: % 30.41/5.05 | (45) sdtasdt0(xv, xc) = xy % 30.41/5.05 | % 30.41/5.05 | GROUND_INST: instantiating (mAMDistr) with xc, xu, all_40_1, xx, xy, all_33_1, % 30.41/5.05 | simplifying with (2), (4), (5), (10), (12), (19), (27), (29), % 30.41/5.05 | (31) gives: % 30.41/5.05 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 30.41/5.05 | xc) = v1 & sdtasdt0(all_40_1, xc) = v3 & sdtasdt0(xu, xc) = v2 & % 30.41/5.05 | sdtasdt0(xc, v0) = all_33_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu, % 30.41/5.05 | all_40_1) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_33_1)) % 30.41/5.05 | % 30.41/5.05 | GROUND_INST: instantiating (mSortsB_02) with xc, all_40_1, xy, simplifying % 30.41/5.05 | with (2), (12), (27), (29), (31) gives: % 30.41/5.05 | (47) aElement0(xy) % 30.41/5.05 | % 30.41/5.05 | GROUND_INST: instantiating (mMulComm) with xc, all_40_1, xy, simplifying with % 30.41/5.05 | (2), (12), (27), (29), (31) gives: % 30.41/5.05 | (48) sdtasdt0(all_40_1, xc) = xy & $i(xy) % 30.41/5.05 | % 30.41/5.05 | ALPHA: (48) implies: % 30.41/5.05 | (49) sdtasdt0(all_40_1, xc) = xy % 30.41/5.05 | % 30.41/5.06 | GROUND_INST: instantiating (mAMDistr) with xc, all_40_0, all_40_1, xx, xy, % 30.41/5.06 | all_33_1, simplifying with (2), (12), (19), (27), (28), (29), % 30.41/5.06 | (30), (31), (32) gives: % 30.41/5.06 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 30.41/5.06 | xc) = v1 & sdtasdt0(all_40_0, xc) = v2 & sdtasdt0(all_40_1, xc) = % 30.41/5.06 | v3 & sdtasdt0(xc, v0) = all_33_1 & sdtpldt0(v2, v3) = v1 & % 30.41/5.06 | sdtpldt0(all_40_0, all_40_1) = v0 & $i(v3) & $i(v2) & $i(v1) & % 30.41/5.06 | $i(v0) & $i(all_33_1)) % 30.41/5.06 | % 30.41/5.06 | GROUND_INST: instantiating (mAMDistr) with xc, all_40_0, xv, xx, xy, all_33_1, % 30.41/5.06 | simplifying with (2), (6), (7), (8), (12), (19), (28), (30), (32) % 30.41/5.06 | gives: % 30.41/5.06 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 30.41/5.06 | xc) = v1 & sdtasdt0(all_40_0, xc) = v2 & sdtasdt0(xv, xc) = v3 & % 30.41/5.06 | sdtasdt0(xc, v0) = all_33_1 & sdtpldt0(v2, v3) = v1 & % 30.41/5.06 | sdtpldt0(all_40_0, xv) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 30.41/5.06 | $i(all_33_1)) % 30.41/5.06 | % 30.41/5.06 | GROUND_INST: instantiating (mSortsB_02) with xc, all_40_0, xx, simplifying % 30.41/5.06 | with (2), (12), (28), (30), (32) gives: % 30.41/5.06 | (52) aElement0(xx) % 30.41/5.06 | % 30.41/5.06 | GROUND_INST: instantiating (mMulComm) with xc, all_40_0, xx, simplifying with % 30.41/5.06 | (2), (12), (28), (30), (32) gives: % 30.41/5.06 | (53) sdtasdt0(all_40_0, xc) = xx & $i(xx) % 30.41/5.06 | % 30.41/5.06 | ALPHA: (53) implies: % 30.41/5.06 | (54) sdtasdt0(all_40_0, xc) = xx % 30.41/5.06 | % 30.41/5.06 | GROUND_INST: instantiating (mSortsB_02) with xu, xz, all_35_0, simplifying % 30.41/5.06 | with (4), (10), (13), (24), (26) gives: % 30.41/5.06 | (55) aElement0(all_35_0) % 30.41/5.06 | % 30.41/5.06 | GROUND_INST: instantiating (mMulComm) with xu, xz, all_35_0, simplifying with % 30.41/5.06 | (4), (10), (13), (24), (26) gives: % 30.41/5.06 | (56) sdtasdt0(xz, xu) = all_35_0 & $i(all_35_0) % 30.41/5.06 | % 30.41/5.06 | ALPHA: (56) implies: % 30.41/5.06 | (57) $i(all_35_0) % 30.41/5.06 | % 30.41/5.06 | DELTA: instantiating (51) with fresh symbols all_58_0, all_58_1, all_58_2, % 30.41/5.06 | all_58_3 gives: % 30.41/5.06 | (58) sdtasdt0(all_58_3, xc) = all_58_2 & sdtasdt0(all_40_0, xc) = all_58_1 % 30.41/5.06 | & sdtasdt0(xv, xc) = all_58_0 & sdtasdt0(xc, all_58_3) = all_33_1 & % 30.41/5.06 | sdtpldt0(all_58_1, all_58_0) = all_58_2 & sdtpldt0(all_40_0, xv) = % 30.41/5.06 | all_58_3 & $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) & % 30.41/5.06 | $i(all_33_1) % 30.41/5.06 | % 30.41/5.06 | ALPHA: (58) implies: % 30.41/5.06 | (59) $i(all_58_1) % 30.41/5.06 | (60) $i(all_58_0) % 30.41/5.06 | (61) sdtpldt0(all_58_1, all_58_0) = all_58_2 % 30.41/5.06 | (62) sdtasdt0(xv, xc) = all_58_0 % 30.41/5.06 | (63) sdtasdt0(all_40_0, xc) = all_58_1 % 30.41/5.06 | % 30.41/5.06 | DELTA: instantiating (46) with fresh symbols all_60_0, all_60_1, all_60_2, % 30.41/5.06 | all_60_3 gives: % 30.41/5.06 | (64) sdtasdt0(all_60_3, xc) = all_60_2 & sdtasdt0(all_40_1, xc) = all_60_0 % 30.41/5.06 | & sdtasdt0(xu, xc) = all_60_1 & sdtasdt0(xc, all_60_3) = all_33_1 & % 30.41/5.06 | sdtpldt0(all_60_1, all_60_0) = all_60_2 & sdtpldt0(xu, all_40_1) = % 30.41/5.06 | all_60_3 & $i(all_60_0) & $i(all_60_1) & $i(all_60_2) & $i(all_60_3) & % 30.41/5.06 | $i(all_33_1) % 30.41/5.06 | % 30.41/5.06 | ALPHA: (64) implies: % 30.41/5.06 | (65) sdtpldt0(all_60_1, all_60_0) = all_60_2 % 30.41/5.06 | (66) sdtasdt0(xu, xc) = all_60_1 % 30.41/5.07 | (67) sdtasdt0(all_40_1, xc) = all_60_0 % 30.41/5.07 | % 30.41/5.07 | DELTA: instantiating (43) with fresh symbols all_62_0, all_62_1, all_62_2, % 30.41/5.07 | all_62_3 gives: % 30.41/5.07 | (68) sdtasdt0(all_62_3, xc) = all_62_2 & sdtasdt0(xv, xc) = all_62_0 & % 30.41/5.07 | sdtasdt0(xu, xc) = all_62_1 & sdtasdt0(xc, all_62_3) = all_33_1 & % 30.41/5.07 | sdtpldt0(all_62_1, all_62_0) = all_62_2 & sdtpldt0(xu, xv) = all_62_3 % 30.41/5.07 | & $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & $i(all_62_3) & % 30.41/5.07 | $i(all_33_1) % 30.41/5.07 | % 30.41/5.07 | ALPHA: (68) implies: % 30.41/5.07 | (69) $i(all_62_3) % 30.41/5.07 | (70) sdtpldt0(xu, xv) = all_62_3 % 30.41/5.07 | (71) sdtpldt0(all_62_1, all_62_0) = all_62_2 % 30.41/5.07 | (72) sdtasdt0(xc, all_62_3) = all_33_1 % 30.41/5.07 | (73) sdtasdt0(xu, xc) = all_62_1 % 30.41/5.07 | (74) sdtasdt0(xv, xc) = all_62_0 % 30.41/5.07 | % 30.41/5.07 | DELTA: instantiating (50) with fresh symbols all_64_0, all_64_1, all_64_2, % 30.41/5.07 | all_64_3 gives: % 30.41/5.07 | (75) sdtasdt0(all_64_3, xc) = all_64_2 & sdtasdt0(all_40_0, xc) = all_64_1 % 30.41/5.07 | & sdtasdt0(all_40_1, xc) = all_64_0 & sdtasdt0(xc, all_64_3) = % 30.41/5.07 | all_33_1 & sdtpldt0(all_64_1, all_64_0) = all_64_2 & % 30.41/5.07 | sdtpldt0(all_40_0, all_40_1) = all_64_3 & $i(all_64_0) & $i(all_64_1) % 30.41/5.07 | & $i(all_64_2) & $i(all_64_3) & $i(all_33_1) % 30.41/5.07 | % 30.41/5.07 | ALPHA: (75) implies: % 30.41/5.07 | (76) sdtpldt0(all_64_1, all_64_0) = all_64_2 % 30.41/5.07 | (77) sdtasdt0(all_40_1, xc) = all_64_0 % 30.41/5.07 | (78) sdtasdt0(all_40_0, xc) = all_64_1 % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (16) with all_33_0, all_62_3, xv, xu, simplifying % 30.41/5.07 | with (20), (70) gives: % 30.41/5.07 | (79) all_62_3 = all_33_0 % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with all_60_1, all_62_1, xc, xu, simplifying % 30.41/5.07 | with (66), (73) gives: % 30.41/5.07 | (80) all_62_1 = all_60_1 % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with xx, all_62_1, xc, xu, simplifying with % 30.41/5.07 | (42), (73) gives: % 30.41/5.07 | (81) all_62_1 = xx % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with all_58_0, all_62_0, xc, xv, simplifying % 30.41/5.07 | with (62), (74) gives: % 30.41/5.07 | (82) all_62_0 = all_58_0 % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with xy, all_62_0, xc, xv, simplifying with % 30.41/5.07 | (45), (74) gives: % 30.41/5.07 | (83) all_62_0 = xy % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with all_60_0, all_64_0, xc, all_40_1, % 30.41/5.07 | simplifying with (67), (77) gives: % 30.41/5.07 | (84) all_64_0 = all_60_0 % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with xy, all_64_0, xc, all_40_1, simplifying % 30.41/5.07 | with (49), (77) gives: % 30.41/5.07 | (85) all_64_0 = xy % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with all_58_1, all_64_1, xc, all_40_0, % 30.41/5.07 | simplifying with (63), (78) gives: % 30.41/5.07 | (86) all_64_1 = all_58_1 % 30.41/5.07 | % 30.41/5.07 | GROUND_INST: instantiating (17) with xx, all_64_1, xc, all_40_0, simplifying % 30.41/5.07 | with (54), (78) gives: % 30.41/5.07 | (87) all_64_1 = xx % 30.41/5.07 | % 30.41/5.07 | COMBINE_EQS: (84), (85) imply: % 30.41/5.07 | (88) all_60_0 = xy % 30.41/5.07 | % 30.41/5.07 | SIMP: (88) implies: % 30.41/5.07 | (89) all_60_0 = xy % 30.41/5.07 | % 30.41/5.07 | COMBINE_EQS: (86), (87) imply: % 30.41/5.07 | (90) all_58_1 = xx % 30.41/5.07 | % 30.41/5.07 | SIMP: (90) implies: % 30.41/5.07 | (91) all_58_1 = xx % 30.41/5.07 | % 30.41/5.07 | COMBINE_EQS: (82), (83) imply: % 30.41/5.07 | (92) all_58_0 = xy % 30.41/5.07 | % 30.41/5.07 | COMBINE_EQS: (80), (81) imply: % 30.41/5.07 | (93) all_60_1 = xx % 30.41/5.07 | % 30.41/5.07 | SIMP: (93) implies: % 30.41/5.07 | (94) all_60_1 = xx % 30.41/5.07 | % 30.41/5.07 | REDUCE: (72), (79) imply: % 30.41/5.07 | (95) sdtasdt0(xc, all_33_0) = all_33_1 % 30.41/5.07 | % 30.41/5.07 | REDUCE: (76), (85), (87) imply: % 30.41/5.07 | (96) sdtpldt0(xx, xy) = all_64_2 % 30.41/5.07 | % 30.41/5.07 | REDUCE: (71), (81), (83) imply: % 30.41/5.07 | (97) sdtpldt0(xx, xy) = all_62_2 % 30.41/5.07 | % 30.41/5.07 | REDUCE: (65), (89), (94) imply: % 30.41/5.07 | (98) sdtpldt0(xx, xy) = all_60_2 % 30.41/5.07 | % 30.41/5.07 | REDUCE: (61), (91), (92) imply: % 30.41/5.08 | (99) sdtpldt0(xx, xy) = all_58_2 % 30.41/5.08 | % 30.41/5.08 | REDUCE: (69), (79) imply: % 30.41/5.08 | (100) $i(all_33_0) % 30.41/5.08 | % 30.41/5.08 | REDUCE: (60), (92) imply: % 30.41/5.08 | (101) $i(xy) % 30.41/5.08 | % 30.41/5.08 | REDUCE: (59), (91) imply: % 30.41/5.08 | (102) $i(xx) % 30.41/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (16) with all_33_1, all_64_2, xy, xx, simplifying % 31.21/5.08 | with (19), (96) gives: % 31.21/5.08 | (103) all_64_2 = all_33_1 % 31.21/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (16) with all_62_2, all_64_2, xy, xx, simplifying % 31.21/5.08 | with (96), (97) gives: % 31.21/5.08 | (104) all_64_2 = all_62_2 % 31.21/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (16) with all_60_2, all_64_2, xy, xx, simplifying % 31.21/5.08 | with (96), (98) gives: % 31.21/5.08 | (105) all_64_2 = all_60_2 % 31.21/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (16) with all_58_2, all_64_2, xy, xx, simplifying % 31.21/5.08 | with (96), (99) gives: % 31.21/5.08 | (106) all_64_2 = all_58_2 % 31.21/5.08 | % 31.21/5.08 | COMBINE_EQS: (104), (106) imply: % 31.21/5.08 | (107) all_62_2 = all_58_2 % 31.21/5.08 | % 31.21/5.08 | COMBINE_EQS: (103), (104) imply: % 31.21/5.08 | (108) all_62_2 = all_33_1 % 31.21/5.08 | % 31.21/5.08 | COMBINE_EQS: (104), (105) imply: % 31.21/5.08 | (109) all_62_2 = all_60_2 % 31.21/5.08 | % 31.21/5.08 | COMBINE_EQS: (107), (109) imply: % 31.21/5.08 | (110) all_60_2 = all_58_2 % 31.21/5.08 | % 31.21/5.08 | COMBINE_EQS: (108), (109) imply: % 31.21/5.08 | (111) all_60_2 = all_33_1 % 31.21/5.08 | % 31.21/5.08 | COMBINE_EQS: (110), (111) imply: % 31.21/5.08 | (112) all_58_2 = all_33_1 % 31.21/5.08 | % 31.21/5.08 | SIMP: (112) implies: % 31.21/5.08 | (113) all_58_2 = all_33_1 % 31.21/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (mAddComm) with xx, xy, all_33_1, simplifying with % 31.21/5.08 | (19), (47), (52), (101), (102) gives: % 31.21/5.08 | (114) sdtpldt0(xy, xx) = all_33_1 & $i(all_33_1) % 31.21/5.08 | % 31.21/5.08 | ALPHA: (114) implies: % 31.21/5.08 | (115) $i(all_33_1) % 31.21/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (1) with xc, all_40_2, all_33_1, all_33_0, % 31.21/5.08 | simplifying with (2), (12), (33), (39), (40), (95), (100), (115) % 31.21/5.08 | gives: % 31.21/5.08 | (116) aElementOf0(all_33_1, all_40_2) % 31.21/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (mMulComm) with xc, all_35_0, all_35_1, simplifying % 31.21/5.08 | with (2), (12), (22), (55), (57) gives: % 31.21/5.08 | (117) sdtasdt0(all_35_0, xc) = all_35_1 & $i(all_35_1) % 31.21/5.08 | % 31.21/5.08 | ALPHA: (117) implies: % 31.21/5.08 | (118) $i(all_35_1) % 31.21/5.08 | % 31.21/5.08 | GROUND_INST: instantiating (1) with xc, all_40_2, all_35_1, all_35_0, % 31.21/5.08 | simplifying with (2), (12), (22), (33), (39), (55), (57), (118) % 31.21/5.08 | gives: % 31.21/5.08 | (119) aElementOf0(all_35_1, all_40_2) % 31.21/5.08 | % 31.21/5.08 | BETA: splitting (37) gives: % 31.21/5.08 | % 31.21/5.08 | Case 1: % 31.21/5.08 | | % 31.21/5.08 | | (120) sdtasdt0(xz, xx) = all_42_0 & $i(all_42_0) & ~ % 31.21/5.08 | | aElementOf0(all_42_0, all_42_1) & ! [v0: $i] : ( ~ (sdtasdt0(xc, % 31.21/5.08 | | v0) = all_42_0) | ~ $i(v0) | ~ aElement0(v0)) % 31.21/5.08 | | % 31.21/5.08 | | ALPHA: (120) implies: % 31.21/5.09 | | (121) ~ aElementOf0(all_42_0, all_42_1) % 31.21/5.09 | | (122) sdtasdt0(xz, xx) = all_42_0 % 31.21/5.09 | | % 31.21/5.09 | | REDUCE: (38), (121) imply: % 31.21/5.09 | | (123) ~ aElementOf0(all_42_0, all_40_2) % 31.21/5.09 | | % 31.21/5.09 | | GROUND_INST: instantiating (17) with all_35_1, all_42_0, xx, xz, simplifying % 31.21/5.09 | | with (23), (122) gives: % 31.21/5.09 | | (124) all_42_0 = all_35_1 % 31.21/5.09 | | % 31.21/5.09 | | REDUCE: (123), (124) imply: % 31.21/5.09 | | (125) ~ aElementOf0(all_35_1, all_40_2) % 31.21/5.09 | | % 31.21/5.09 | | PRED_UNIFY: (119), (125) imply: % 31.21/5.09 | | (126) $false % 31.21/5.09 | | % 31.21/5.09 | | CLOSE: (126) is inconsistent. % 31.21/5.09 | | % 31.21/5.09 | Case 2: % 31.21/5.09 | | % 31.21/5.09 | | (127) sdtpldt0(xx, xy) = all_42_2 & $i(all_42_2) & ~ % 31.21/5.09 | | aElementOf0(all_42_2, all_42_1) & ! [v0: $i] : ( ~ (sdtasdt0(xc, % 31.21/5.09 | | v0) = all_42_2) | ~ $i(v0) | ~ aElement0(v0)) % 31.21/5.09 | | % 31.21/5.09 | | ALPHA: (127) implies: % 31.21/5.09 | | (128) ~ aElementOf0(all_42_2, all_42_1) % 31.21/5.09 | | (129) sdtpldt0(xx, xy) = all_42_2 % 31.21/5.09 | | % 31.21/5.09 | | REDUCE: (38), (128) imply: % 31.21/5.09 | | (130) ~ aElementOf0(all_42_2, all_40_2) % 31.21/5.09 | | % 31.21/5.09 | | GROUND_INST: instantiating (16) with all_33_1, all_42_2, xy, xx, simplifying % 31.21/5.09 | | with (19), (129) gives: % 31.21/5.09 | | (131) all_42_2 = all_33_1 % 31.21/5.09 | | % 31.21/5.09 | | REDUCE: (130), (131) imply: % 31.21/5.09 | | (132) ~ aElementOf0(all_33_1, all_40_2) % 31.21/5.09 | | % 31.21/5.09 | | PRED_UNIFY: (116), (132) imply: % 31.21/5.09 | | (133) $false % 31.21/5.09 | | % 31.21/5.09 | | CLOSE: (133) is inconsistent. % 31.21/5.09 | | % 31.21/5.09 | End of split % 31.21/5.09 | % 31.21/5.09 End of proof % 31.21/5.09 % SZS output end Proof for theBenchmark % 31.21/5.09 % 31.21/5.09 4418ms %------------------------------------------------------------------------------