%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG104+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 : n012.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 13:57:54 EDT 2023 % Result : Theorem 15.63s 2.92s % Output : Proof 22.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG104+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n012.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sun Aug 27 02:14:40 EDT 2023 % 0.19/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.11/1.12 Prover 1: Preprocessing ... % 3.11/1.12 Prover 4: Preprocessing ... % 3.57/1.16 Prover 3: Preprocessing ... % 3.57/1.16 Prover 6: Preprocessing ... % 3.57/1.16 Prover 5: Preprocessing ... % 3.57/1.16 Prover 2: Preprocessing ... % 3.57/1.17 Prover 0: Preprocessing ... % 8.90/2.02 Prover 3: Constructing countermodel ... % 8.90/2.02 Prover 6: Proving ... % 8.90/2.05 Prover 1: Constructing countermodel ... % 8.90/2.11 Prover 5: Proving ... % 11.13/2.30 Prover 2: Proving ... % 11.62/2.40 Prover 4: Constructing countermodel ... % 12.25/2.47 Prover 0: Proving ... % 15.63/2.92 Prover 0: proved (2306ms) % 15.63/2.92 % 15.63/2.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.63/2.92 % 15.63/2.92 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 15.63/2.92 Prover 5: stopped % 15.63/2.92 Prover 3: stopped % 16.09/2.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 16.09/2.93 Prover 2: stopped % 16.09/2.95 Prover 6: stopped % 16.09/2.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 16.09/2.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 16.09/2.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 16.30/3.01 Prover 8: Preprocessing ... % 16.30/3.02 Prover 7: Preprocessing ... % 16.79/3.03 Prover 10: Preprocessing ... % 17.07/3.06 Prover 13: Preprocessing ... % 17.07/3.07 Prover 11: Preprocessing ... % 18.43/3.24 Prover 7: Constructing countermodel ... % 18.64/3.26 Prover 10: Constructing countermodel ... % 19.07/3.33 Prover 8: Warning: ignoring some quantifiers % 19.07/3.34 Prover 8: Constructing countermodel ... % 19.07/3.35 Prover 13: Warning: ignoring some quantifiers % 19.07/3.36 Prover 13: Constructing countermodel ... % 21.05/3.62 Prover 11: Constructing countermodel ... % 21.87/3.70 Prover 10: Found proof (size 60) % 21.87/3.70 Prover 10: proved (768ms) % 21.87/3.70 Prover 13: stopped % 21.87/3.70 Prover 1: stopped % 21.87/3.70 Prover 7: stopped % 21.87/3.70 Prover 4: stopped % 21.87/3.70 Prover 11: stopped % 21.87/3.70 Prover 8: stopped % 21.87/3.70 % 21.87/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 21.87/3.70 % 21.87/3.72 % SZS output start Proof for theBenchmark % 21.87/3.72 Assumptions after simplification: % 21.87/3.72 --------------------------------- % 21.87/3.72 % 21.87/3.72 (mAMDistr) % 21.87/3.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.87/3.74 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 21.87/3.75 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 21.87/3.75 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 21.87/3.75 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, % 21.87/3.75 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, % 21.87/3.75 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 21.87/3.75 $i(v5))) % 21.87/3.75 % 21.87/3.75 (mAddComm) % 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 21.87/3.75 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 21.87/3.75 = v2 & $i(v2))) % 21.87/3.75 % 21.87/3.75 (mDefPrIdeal) % 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) = % 21.87/3.75 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 21.87/3.75 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & ! % 21.87/3.75 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~ % 21.87/3.75 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4: % 21.87/3.75 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6: % 21.87/3.75 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) & % 21.87/3.75 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 & % 21.87/3.75 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 21.87/3.75 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, % 21.87/3.75 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 21.87/3.75 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 21.87/3.75 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1)) % 21.87/3.75 % 21.87/3.75 (mMulAsso) % 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 21.87/3.75 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 21.87/3.75 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 21.87/3.75 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) & % 21.87/3.75 $i(v4))) % 21.87/3.75 % 21.87/3.75 (mMulComm) % 21.87/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 21.87/3.75 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 21.87/3.75 = v2 & $i(v2))) % 21.87/3.75 % 21.87/3.76 (mSortsB_02) % 21.87/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 21.87/3.76 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 21.87/3.76 % 21.87/3.76 (m__) % 21.87/3.76 $i(xu) & $i(xz) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 21.87/3.76 ( ~ (v2 = v0) & sdtasdt0(xu, xz) = v1 & sdtasdt0(xz, xx) = v0 & sdtasdt0(xc, % 21.87/3.76 v1) = v2 & $i(v2) & $i(v1) & $i(v0)) % 21.87/3.76 % 21.87/3.76 (m__1905) % 21.87/3.76 $i(xc) & aElement0(xc) % 21.87/3.76 % 21.87/3.76 (m__1933) % 21.87/3.76 $i(xz) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) % 21.87/3.76 & aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz)) % 21.87/3.76 % 21.87/3.76 (m__1956) % 22.17/3.76 sdtasdt0(xc, xu) = xx & $i(xu) & $i(xx) & $i(xc) & aElement0(xu) % 22.17/3.76 % 22.17/3.76 (m__1979) % 22.17/3.76 sdtasdt0(xc, xv) = xy & $i(xv) & $i(xy) & $i(xc) & aElement0(xv) % 22.17/3.76 % 22.17/3.76 (m__2010) % 22.17/3.76 $i(xv) & $i(xu) & $i(xy) & $i(xx) & $i(xc) & ? [v0: $i] : ? [v1: $i] : % 22.17/3.76 (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) = v1 & sdtpldt0(xx, xy) = v0 & % 22.17/3.76 $i(v1) & $i(v0)) % 22.17/3.76 % 22.17/3.76 (function-axioms) % 22.17/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.17/3.76 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 22.17/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 22.17/3.76 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 22.17/3.76 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 22.17/3.76 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.17/3.76 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 22.17/3.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2) % 22.17/3.76 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 22.17/3.76 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 22.17/3.76 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) % 22.17/3.76 % 22.17/3.76 Further assumptions not needed in the proof: % 22.17/3.76 -------------------------------------------- % 22.17/3.76 mAddAsso, mAddInvr, mAddZero, mCancel, mChineseRemainder, mDefDiv, mDefDvs, % 22.17/3.76 mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum, mDivision, mEOfElem, % 22.17/3.76 mElmSort, mEucSort, mIdeInt, mIdeSum, mMulMnOne, mMulUnit, mMulZero, mNatLess, % 22.17/3.76 mNatSort, mSetEq, mSetSort, mSortsB, mSortsC, mSortsC_01, mSortsU, mUnNeZr % 22.17/3.76 % 22.17/3.76 Those formulas are unsatisfiable: % 22.17/3.76 --------------------------------- % 22.17/3.76 % 22.17/3.76 Begin of proof % 22.17/3.76 | % 22.17/3.76 | ALPHA: (mDefPrIdeal) implies: % 22.17/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~ % 22.17/3.77 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 22.17/3.77 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) & % 22.17/3.77 | aElement0(v3))) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (m__1905) implies: % 22.17/3.77 | (2) aElement0(xc) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (m__1933) implies: % 22.17/3.77 | (3) ? [v0: $i] : (slsdtgt0(xc) = v0 & $i(v0) & aElementOf0(xy, v0) & % 22.17/3.77 | aElementOf0(xx, v0) & aElement0(xz)) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (m__1956) implies: % 22.17/3.77 | (4) aElement0(xu) % 22.17/3.77 | (5) sdtasdt0(xc, xu) = xx % 22.17/3.77 | % 22.17/3.77 | ALPHA: (m__1979) implies: % 22.17/3.77 | (6) aElement0(xv) % 22.17/3.77 | (7) sdtasdt0(xc, xv) = xy % 22.17/3.77 | % 22.17/3.77 | ALPHA: (m__2010) implies: % 22.17/3.77 | (8) $i(xv) % 22.17/3.77 | (9) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = v0 & sdtpldt0(xu, xv) = % 22.17/3.77 | v1 & sdtpldt0(xx, xy) = v0 & $i(v1) & $i(v0)) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (m__) implies: % 22.17/3.77 | (10) $i(xc) % 22.17/3.77 | (11) $i(xz) % 22.17/3.77 | (12) $i(xu) % 22.17/3.77 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & sdtasdt0(xu, % 22.17/3.77 | xz) = v1 & sdtasdt0(xz, xx) = v0 & sdtasdt0(xc, v1) = v2 & $i(v2) % 22.17/3.77 | & $i(v1) & $i(v0)) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (function-axioms) implies: % 22.17/3.77 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.17/3.77 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 22.17/3.77 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.17/3.77 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 22.17/3.77 | % 22.17/3.77 | DELTA: instantiating (3) with fresh symbol all_33_0 gives: % 22.17/3.77 | (16) slsdtgt0(xc) = all_33_0 & $i(all_33_0) & aElementOf0(xy, all_33_0) & % 22.17/3.77 | aElementOf0(xx, all_33_0) & aElement0(xz) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (16) implies: % 22.17/3.77 | (17) aElement0(xz) % 22.17/3.77 | (18) aElementOf0(xy, all_33_0) % 22.17/3.77 | (19) $i(all_33_0) % 22.17/3.77 | (20) slsdtgt0(xc) = all_33_0 % 22.17/3.77 | % 22.17/3.77 | DELTA: instantiating (9) with fresh symbols all_35_0, all_35_1 gives: % 22.17/3.77 | (21) sdtasdt0(xc, all_35_0) = all_35_1 & sdtpldt0(xu, xv) = all_35_0 & % 22.17/3.77 | sdtpldt0(xx, xy) = all_35_1 & $i(all_35_0) & $i(all_35_1) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (21) implies: % 22.17/3.77 | (22) sdtpldt0(xx, xy) = all_35_1 % 22.17/3.77 | % 22.17/3.77 | DELTA: instantiating (13) with fresh symbols all_37_0, all_37_1, all_37_2 % 22.17/3.77 | gives: % 22.17/3.77 | (23) ~ (all_37_0 = all_37_2) & sdtasdt0(xu, xz) = all_37_1 & sdtasdt0(xz, % 22.17/3.77 | xx) = all_37_2 & sdtasdt0(xc, all_37_1) = all_37_0 & $i(all_37_0) & % 22.17/3.77 | $i(all_37_1) & $i(all_37_2) % 22.17/3.77 | % 22.17/3.77 | ALPHA: (23) implies: % 22.17/3.77 | (24) ~ (all_37_0 = all_37_2) % 22.17/3.77 | (25) sdtasdt0(xc, all_37_1) = all_37_0 % 22.17/3.77 | (26) sdtasdt0(xz, xx) = all_37_2 % 22.17/3.77 | (27) sdtasdt0(xu, xz) = all_37_1 % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (mSortsB_02) with xc, xu, xx, simplifying with (2), % 22.17/3.78 | (4), (5), (10), (12) gives: % 22.17/3.78 | (28) aElement0(xx) % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (mMulComm) with xc, xu, xx, simplifying with (2), % 22.17/3.78 | (4), (5), (10), (12) gives: % 22.17/3.78 | (29) sdtasdt0(xu, xc) = xx & $i(xx) % 22.17/3.78 | % 22.17/3.78 | ALPHA: (29) implies: % 22.17/3.78 | (30) sdtasdt0(xu, xc) = xx % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (mAMDistr) with xc, xu, xv, xx, xy, all_35_1, % 22.17/3.78 | simplifying with (2), (4), (5), (6), (7), (8), (10), (12), (22) % 22.17/3.78 | gives: % 22.17/3.78 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 22.17/3.78 | xc) = v1 & sdtasdt0(xv, xc) = v3 & sdtasdt0(xu, xc) = v2 & % 22.17/3.78 | sdtasdt0(xc, v0) = all_35_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu, % 22.17/3.78 | xv) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_35_1)) % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (mSortsB_02) with xc, xv, xy, simplifying with (2), % 22.17/3.78 | (6), (7), (8), (10) gives: % 22.17/3.78 | (32) aElement0(xy) % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (mMulComm) with xc, xv, xy, simplifying with (2), % 22.17/3.78 | (6), (7), (8), (10) gives: % 22.17/3.78 | (33) sdtasdt0(xv, xc) = xy & $i(xy) % 22.17/3.78 | % 22.17/3.78 | ALPHA: (33) implies: % 22.17/3.78 | (34) $i(xy) % 22.17/3.78 | (35) sdtasdt0(xv, xc) = xy % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (mSortsB_02) with xu, xz, all_37_1, simplifying % 22.17/3.78 | with (4), (11), (12), (17), (27) gives: % 22.17/3.78 | (36) aElement0(all_37_1) % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (mMulComm) with xu, xz, all_37_1, simplifying with % 22.17/3.78 | (4), (11), (12), (17), (27) gives: % 22.17/3.78 | (37) sdtasdt0(xz, xu) = all_37_1 & $i(all_37_1) % 22.17/3.78 | % 22.17/3.78 | ALPHA: (37) implies: % 22.17/3.78 | (38) $i(all_37_1) % 22.17/3.78 | (39) sdtasdt0(xz, xu) = all_37_1 % 22.17/3.78 | % 22.17/3.78 | GROUND_INST: instantiating (1) with xc, all_33_0, xy, simplifying with (2), % 22.17/3.78 | (10), (18), (19), (20), (34) gives: % 22.17/3.78 | (40) ? [v0: $i] : (sdtasdt0(xc, v0) = xy & $i(v0) & aElement0(v0)) % 22.17/3.78 | % 22.17/3.78 | DELTA: instantiating (40) with fresh symbol all_50_0 gives: % 22.17/3.78 | (41) sdtasdt0(xc, all_50_0) = xy & $i(all_50_0) & aElement0(all_50_0) % 22.17/3.78 | % 22.17/3.78 | ALPHA: (41) implies: % 22.17/3.78 | (42) aElement0(all_50_0) % 22.17/3.78 | (43) $i(all_50_0) % 22.17/3.79 | (44) sdtasdt0(xc, all_50_0) = xy % 22.17/3.79 | % 22.17/3.79 | DELTA: instantiating (31) with fresh symbols all_52_0, all_52_1, all_52_2, % 22.17/3.79 | all_52_3 gives: % 22.17/3.79 | (45) sdtasdt0(all_52_3, xc) = all_52_2 & sdtasdt0(xv, xc) = all_52_0 & % 22.17/3.79 | sdtasdt0(xu, xc) = all_52_1 & sdtasdt0(xc, all_52_3) = all_35_1 & % 22.17/3.79 | sdtpldt0(all_52_1, all_52_0) = all_52_2 & sdtpldt0(xu, xv) = all_52_3 % 22.17/3.79 | & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3) & % 22.17/3.79 | $i(all_35_1) % 22.17/3.79 | % 22.17/3.79 | ALPHA: (45) implies: % 22.17/3.79 | (46) $i(all_52_1) % 22.17/3.79 | (47) $i(all_52_0) % 22.17/3.79 | (48) sdtpldt0(all_52_1, all_52_0) = all_52_2 % 22.17/3.79 | (49) sdtasdt0(xu, xc) = all_52_1 % 22.17/3.79 | (50) sdtasdt0(xv, xc) = all_52_0 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (15) with xx, all_52_1, xc, xu, simplifying with % 22.17/3.79 | (30), (49) gives: % 22.17/3.79 | (51) all_52_1 = xx % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (15) with xy, all_52_0, xc, xv, simplifying with % 22.17/3.79 | (35), (50) gives: % 22.17/3.79 | (52) all_52_0 = xy % 22.17/3.79 | % 22.17/3.79 | REDUCE: (48), (51), (52) imply: % 22.17/3.79 | (53) sdtpldt0(xx, xy) = all_52_2 % 22.17/3.79 | % 22.17/3.79 | REDUCE: (46), (51) imply: % 22.17/3.79 | (54) $i(xx) % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (14) with all_35_1, all_52_2, xy, xx, simplifying % 22.17/3.79 | with (22), (53) gives: % 22.17/3.79 | (55) all_52_2 = all_35_1 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (mAddComm) with xx, xy, all_35_1, simplifying with % 22.17/3.79 | (22), (28), (32), (34), (54) gives: % 22.17/3.79 | (56) sdtpldt0(xy, xx) = all_35_1 & $i(all_35_1) % 22.17/3.79 | % 22.17/3.79 | ALPHA: (56) implies: % 22.17/3.79 | (57) sdtpldt0(xy, xx) = all_35_1 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (mMulComm) with xc, all_37_1, all_37_0, simplifying % 22.17/3.79 | with (2), (10), (25), (36), (38) gives: % 22.17/3.79 | (58) sdtasdt0(all_37_1, xc) = all_37_0 & $i(all_37_0) % 22.17/3.79 | % 22.17/3.79 | ALPHA: (58) implies: % 22.17/3.79 | (59) sdtasdt0(all_37_1, xc) = all_37_0 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (mAMDistr) with xc, xu, all_50_0, xx, xy, all_35_1, % 22.17/3.79 | simplifying with (2), (4), (5), (10), (12), (22), (42), (43), % 22.17/3.79 | (44) gives: % 22.17/3.79 | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 22.17/3.79 | xc) = v1 & sdtasdt0(all_50_0, xc) = v3 & sdtasdt0(xu, xc) = v2 & % 22.17/3.79 | sdtasdt0(xc, v0) = all_35_1 & sdtpldt0(v2, v3) = v1 & sdtpldt0(xu, % 22.17/3.79 | all_50_0) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_35_1)) % 22.17/3.79 | % 22.17/3.79 | DELTA: instantiating (60) with fresh symbols all_70_0, all_70_1, all_70_2, % 22.17/3.79 | all_70_3 gives: % 22.17/3.79 | (61) sdtasdt0(all_70_3, xc) = all_70_2 & sdtasdt0(all_50_0, xc) = all_70_0 % 22.17/3.79 | & sdtasdt0(xu, xc) = all_70_1 & sdtasdt0(xc, all_70_3) = all_35_1 & % 22.17/3.79 | sdtpldt0(all_70_1, all_70_0) = all_70_2 & sdtpldt0(xu, all_50_0) = % 22.17/3.79 | all_70_3 & $i(all_70_0) & $i(all_70_1) & $i(all_70_2) & $i(all_70_3) & % 22.17/3.79 | $i(all_35_1) % 22.17/3.79 | % 22.17/3.79 | ALPHA: (61) implies: % 22.17/3.79 | (62) sdtasdt0(xu, xc) = all_70_1 % 22.17/3.79 | % 22.17/3.79 | GROUND_INST: instantiating (15) with xx, all_70_1, xc, xu, simplifying with % 22.17/3.79 | (30), (62) gives: % 22.17/3.79 | (63) all_70_1 = xx % 22.17/3.79 | % 22.17/3.80 | GROUND_INST: instantiating (mAMDistr) with xc, all_50_0, xu, xy, xx, all_35_1, % 22.17/3.80 | simplifying with (2), (4), (5), (10), (12), (42), (43), (44), % 22.17/3.80 | (57) gives: % 22.17/3.80 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v0, % 22.17/3.80 | xc) = v1 & sdtasdt0(all_50_0, xc) = v2 & sdtasdt0(xu, xc) = v3 & % 22.17/3.80 | sdtasdt0(xc, v0) = all_35_1 & sdtpldt0(v2, v3) = v1 & % 22.17/3.80 | sdtpldt0(all_50_0, xu) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 22.17/3.80 | $i(all_35_1)) % 22.17/3.80 | % 22.17/3.80 | GROUND_INST: instantiating (mMulAsso) with xz, xu, xc, all_37_1, all_37_0, % 22.17/3.80 | simplifying with (2), (4), (10), (11), (12), (17), (39), (59) % 22.17/3.80 | gives: % 22.17/3.80 | (65) ? [v0: $i] : (sdtasdt0(xu, xc) = v0 & sdtasdt0(xz, v0) = all_37_0 & % 22.17/3.80 | $i(v0) & $i(all_37_0)) % 22.17/3.80 | % 22.17/3.80 | DELTA: instantiating (65) with fresh symbol all_108_0 gives: % 22.17/3.80 | (66) sdtasdt0(xu, xc) = all_108_0 & sdtasdt0(xz, all_108_0) = all_37_0 & % 22.17/3.80 | $i(all_108_0) & $i(all_37_0) % 22.17/3.80 | % 22.17/3.80 | ALPHA: (66) implies: % 22.17/3.80 | (67) sdtasdt0(xz, all_108_0) = all_37_0 % 22.17/3.80 | (68) sdtasdt0(xu, xc) = all_108_0 % 22.17/3.80 | % 22.17/3.80 | DELTA: instantiating (64) with fresh symbols all_116_0, all_116_1, all_116_2, % 22.17/3.80 | all_116_3 gives: % 22.17/3.80 | (69) sdtasdt0(all_116_3, xc) = all_116_2 & sdtasdt0(all_50_0, xc) = % 22.17/3.80 | all_116_1 & sdtasdt0(xu, xc) = all_116_0 & sdtasdt0(xc, all_116_3) = % 22.17/3.80 | all_35_1 & sdtpldt0(all_116_1, all_116_0) = all_116_2 & % 22.17/3.80 | sdtpldt0(all_50_0, xu) = all_116_3 & $i(all_116_0) & $i(all_116_1) & % 22.17/3.80 | $i(all_116_2) & $i(all_116_3) & $i(all_35_1) % 22.17/3.80 | % 22.17/3.80 | ALPHA: (69) implies: % 22.17/3.80 | (70) sdtasdt0(xu, xc) = all_116_0 % 22.17/3.80 | % 22.17/3.80 | GROUND_INST: instantiating (15) with xx, all_116_0, xc, xu, simplifying with % 22.17/3.80 | (30), (70) gives: % 22.17/3.80 | (71) all_116_0 = xx % 22.17/3.80 | % 22.17/3.80 | GROUND_INST: instantiating (15) with all_108_0, all_116_0, xc, xu, simplifying % 22.17/3.80 | with (68), (70) gives: % 22.17/3.80 | (72) all_116_0 = all_108_0 % 22.17/3.80 | % 22.17/3.80 | COMBINE_EQS: (71), (72) imply: % 22.17/3.80 | (73) all_108_0 = xx % 22.17/3.80 | % 22.17/3.80 | SIMP: (73) implies: % 22.17/3.80 | (74) all_108_0 = xx % 22.17/3.80 | % 22.17/3.80 | REDUCE: (67), (74) imply: % 22.17/3.80 | (75) sdtasdt0(xz, xx) = all_37_0 % 22.17/3.80 | % 22.17/3.80 | GROUND_INST: instantiating (15) with all_37_2, all_37_0, xx, xz, simplifying % 22.17/3.80 | with (26), (75) gives: % 22.17/3.80 | (76) all_37_0 = all_37_2 % 22.17/3.80 | % 22.17/3.80 | REDUCE: (24), (76) imply: % 22.17/3.80 | (77) $false % 22.17/3.80 | % 22.17/3.80 | CLOSE: (77) is inconsistent. % 22.17/3.80 | % 22.17/3.80 End of proof % 22.17/3.80 % SZS output end Proof for theBenchmark % 22.17/3.80 % 22.17/3.80 3212ms %------------------------------------------------------------------------------