%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG090+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 : n022.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 13:57:48 EDT 2023 % Result : Theorem 130.95s 18.44s % Output : Proof 132.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : RNG090+2 : TPTP v8.1.2. Released v4.0.0. % 0.10/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.36 % Computer : n022.cluster.edu % 0.13/0.36 % Model : x86_64 x86_64 % 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.36 % Memory : 8042.1875MB % 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.36 % CPULimit : 300 % 0.13/0.36 % WCLimit : 300 % 0.13/0.36 % DateTime : Sun Aug 27 02:16:39 EDT 2023 % 0.13/0.36 % CPUTime : % 0.19/0.65 ________ _____ % 0.19/0.66 ___ __ \_________(_)________________________________ % 0.19/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.66 % 0.19/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.66 (2023-06-19) % 0.19/0.66 % 0.19/0.66 (c) Philipp Rümmer, 2009-2023 % 0.19/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.66 Amanda Stjerna. % 0.19/0.66 Free software under BSD-3-Clause. % 0.19/0.66 % 0.19/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.66 % 0.19/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.67 Running up to 7 provers in parallel. % 0.19/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.98/1.31 Prover 1: Preprocessing ... % 2.98/1.31 Prover 4: Preprocessing ... % 2.98/1.36 Prover 5: Preprocessing ... % 2.98/1.36 Prover 6: Preprocessing ... % 2.98/1.36 Prover 2: Preprocessing ... % 2.98/1.36 Prover 0: Preprocessing ... % 2.98/1.36 Prover 3: Preprocessing ... % 10.36/2.34 Prover 1: Constructing countermodel ... % 11.06/2.40 Prover 3: Constructing countermodel ... % 11.06/2.41 Prover 6: Proving ... % 11.06/2.48 Prover 5: Proving ... % 11.64/2.52 Prover 4: Constructing countermodel ... % 12.39/2.75 Prover 2: Proving ... % 12.60/2.82 Prover 0: Proving ... % 70.15/10.52 Prover 2: stopped % 70.71/10.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.66/10.64 Prover 7: Preprocessing ... % 74.36/10.87 Prover 7: Constructing countermodel ... % 97.85/14.02 Prover 5: stopped % 97.85/14.02 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 98.59/14.07 Prover 8: Preprocessing ... % 99.09/14.18 Prover 8: Warning: ignoring some quantifiers % 99.09/14.19 Prover 8: Constructing countermodel ... % 112.60/16.06 Prover 1: stopped % 112.60/16.08 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 112.89/16.13 Prover 9: Preprocessing ... % 117.50/16.58 Prover 9: Constructing countermodel ... % 127.26/17.98 Prover 6: stopped % 127.91/17.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 127.91/18.07 Prover 10: Preprocessing ... % 128.72/18.21 Prover 10: Constructing countermodel ... % 130.95/18.42 Prover 10: Found proof (size 54) % 130.95/18.42 Prover 10: proved (428ms) % 130.95/18.42 Prover 0: stopped % 130.95/18.42 Prover 7: stopped % 130.95/18.42 Prover 8: stopped % 130.95/18.42 Prover 9: stopped % 130.95/18.44 Prover 3: stopped % 130.95/18.44 Prover 4: stopped % 130.95/18.44 % 130.95/18.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 130.95/18.44 % 130.95/18.46 % SZS output start Proof for theBenchmark % 130.95/18.46 Assumptions after simplification: % 130.95/18.46 --------------------------------- % 130.95/18.46 % 130.95/18.46 (mAddAsso) % 131.42/18.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 131.42/18.51 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 131.42/18.51 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 131.42/18.51 [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4 & $i(v5) & % 131.42/18.51 $i(v4))) % 131.42/18.51 % 131.42/18.51 (mAddComm) % 131.42/18.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 131.42/18.52 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 131.42/18.52 = v2 & $i(v2))) % 131.42/18.52 % 131.42/18.52 (mDefSSum) % 131.42/18.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 131.42/18.53 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) | % 131.42/18.53 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 131.42/18.53 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 131.42/18.53 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 131.42/18.53 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 131.42/18.53 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ? % 131.42/18.53 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3) % 131.42/18.53 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) | % 131.42/18.53 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & % 131.42/18.53 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, % 131.42/18.53 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 131.42/18.53 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 131.42/18.53 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 131.42/18.53 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 131.42/18.53 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] : % 131.42/18.53 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 131.42/18.53 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 131.42/18.53 % 131.42/18.53 (mEOfElem) % 131.42/18.53 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 131.42/18.53 ~ aSet0(v0) | aElement0(v1)) % 131.42/18.53 % 131.42/18.53 (m__) % 131.42/18.53 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: % 131.42/18.53 $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v0) & sdtpldt0(v1, v2) = v3 & % 131.42/18.53 sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = v1 & sdtpldt0(xx, xy) = v0 & % 131.42/18.53 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 131.42/18.53 % 131.42/18.53 (m__1021) % 131.42/18.53 $i(xl) & $i(xk) & $i(xz) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : % 131.42/18.53 (sdtasdt0(xz, xl) = v1 & sdtasdt0(xz, xk) = v0 & $i(v1) & $i(v0) & % 131.42/18.53 aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 131.42/18.53 % 131.42/18.53 (m__870) % 131.42/18.54 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) & aSet0(xJ) & aSet0(xI) & ! [v0: % 131.42/18.54 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | % 131.42/18.54 ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ)) % 131.42/18.54 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 131.42/18.54 $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | % 131.42/18.54 aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 131.42/18.54 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | % 131.42/18.54 ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ)) & ! [v0: $i] : ! [v1: $i] : % 131.42/18.54 ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 131.42/18.54 aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI)) % 131.42/18.54 % 131.42/18.54 (m__901) % 131.42/18.54 $i(xz) & $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: $i] : ? % 131.42/18.54 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtpldt1(xI, xJ) = v0 & sdtpldt0(v3, % 131.42/18.54 v4) = xx & sdtpldt0(v1, v2) = xy & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 131.42/18.54 $i(v0) & aElementOf0(v4, xJ) & aElementOf0(v3, xI) & aElementOf0(v2, xJ) & % 131.42/18.54 aElementOf0(v1, xI) & aElementOf0(xy, v0) & aElementOf0(xx, v0) & % 131.42/18.54 aElement0(xz)) % 131.42/18.54 % 131.42/18.54 (m__934) % 131.42/18.54 sdtpldt0(xk, xl) = xx & $i(xl) & $i(xk) & $i(xx) & $i(xJ) & $i(xI) & % 131.42/18.54 aElementOf0(xl, xJ) & aElementOf0(xk, xI) % 131.42/18.54 % 131.42/18.54 (m__967) % 131.42/18.54 sdtpldt0(xm, xn) = xy & $i(xn) & $i(xm) & $i(xy) & $i(xJ) & $i(xI) & % 131.42/18.54 aElementOf0(xn, xJ) & aElementOf0(xm, xI) % 131.42/18.54 % 131.42/18.54 (m__994) % 131.42/18.54 $i(xn) & $i(xm) & $i(xl) & $i(xk) & $i(xJ) & $i(xI) & ? [v0: $i] : ? [v1: % 131.42/18.54 $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) = v0 & $i(v1) & $i(v0) & % 131.42/18.54 aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 131.42/18.54 % 131.42/18.54 (function-axioms) % 131.42/18.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.42/18.55 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 131.42/18.55 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 131.42/18.55 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 131.42/18.55 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 131.42/18.55 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.42/18.55 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 131.42/18.55 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = % 131.42/18.55 v0)) % 131.42/18.55 % 131.42/18.55 Further assumptions not needed in the proof: % 131.42/18.55 -------------------------------------------- % 131.42/18.55 mAMDistr, mAddInvr, mAddZero, mCancel, mDefIdeal, mDefSInt, mElmSort, mMulAsso, % 131.42/18.55 mMulComm, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02, % 131.42/18.55 mSortsC, mSortsC_01, mSortsU, mUnNeZr % 131.42/18.55 % 131.42/18.55 Those formulas are unsatisfiable: % 131.42/18.55 --------------------------------- % 131.42/18.55 % 131.42/18.55 Begin of proof % 131.42/18.55 | % 131.42/18.55 | ALPHA: (mDefSSum) implies: % 131.42/18.55 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | % 131.42/18.55 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 131.42/18.55 | aSet0(v2)) % 131.42/18.55 | % 131.42/18.55 | ALPHA: (m__870) implies: % 131.42/18.55 | (2) aSet0(xI) % 131.42/18.55 | (3) aSet0(xJ) % 131.42/18.55 | % 131.42/18.55 | ALPHA: (m__901) implies: % 131.42/18.55 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 131.42/18.56 | (sdtpldt1(xI, xJ) = v0 & sdtpldt0(v3, v4) = xx & sdtpldt0(v1, v2) = xy % 131.42/18.56 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v4, xJ) & % 131.42/18.56 | aElementOf0(v3, xI) & aElementOf0(v2, xJ) & aElementOf0(v1, xI) & % 131.42/18.56 | aElementOf0(xy, v0) & aElementOf0(xx, v0) & aElement0(xz)) % 131.42/18.56 | % 131.42/18.56 | ALPHA: (m__934) implies: % 131.42/18.56 | (5) aElementOf0(xk, xI) % 131.42/18.56 | (6) aElementOf0(xl, xJ) % 131.42/18.56 | (7) sdtpldt0(xk, xl) = xx % 131.42/18.56 | % 131.42/18.56 | ALPHA: (m__967) implies: % 131.42/18.56 | (8) aElementOf0(xm, xI) % 131.42/18.56 | (9) aElementOf0(xn, xJ) % 131.42/18.56 | (10) sdtpldt0(xm, xn) = xy % 131.42/18.56 | % 131.42/18.56 | ALPHA: (m__994) implies: % 131.42/18.56 | (11) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xl, xn) = v1 & sdtpldt0(xk, xm) % 131.42/18.56 | = v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 131.42/18.56 | % 131.42/18.56 | ALPHA: (m__1021) implies: % 131.42/18.56 | (12) $i(xI) % 131.42/18.56 | (13) $i(xJ) % 131.42/18.56 | % 131.42/18.56 | ALPHA: (m__) implies: % 131.42/18.56 | (14) $i(xk) % 131.42/18.56 | (15) $i(xl) % 131.42/18.56 | (16) $i(xm) % 131.42/18.56 | (17) $i(xn) % 131.42/18.56 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v0) % 131.42/18.56 | & sdtpldt0(v1, v2) = v3 & sdtpldt0(xl, xn) = v2 & sdtpldt0(xk, xm) = % 131.42/18.56 | v1 & sdtpldt0(xx, xy) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 131.42/18.56 | % 131.42/18.56 | ALPHA: (function-axioms) implies: % 131.42/18.56 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 131.42/18.56 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 131.42/18.56 | % 131.42/18.56 | DELTA: instantiating (11) with fresh symbols all_23_0, all_23_1 gives: % 131.42/18.56 | (20) sdtpldt0(xl, xn) = all_23_0 & sdtpldt0(xk, xm) = all_23_1 & % 131.42/18.56 | $i(all_23_0) & $i(all_23_1) & aElementOf0(all_23_0, xJ) & % 131.42/18.56 | aElementOf0(all_23_1, xI) % 131.42/18.56 | % 131.42/18.56 | ALPHA: (20) implies: % 131.42/18.56 | (21) aElementOf0(all_23_0, xJ) % 131.42/18.56 | (22) sdtpldt0(xk, xm) = all_23_1 % 131.42/18.56 | (23) sdtpldt0(xl, xn) = all_23_0 % 131.42/18.56 | % 131.42/18.56 | DELTA: instantiating (18) with fresh symbols all_30_0, all_30_1, all_30_2, % 131.42/18.56 | all_30_3 gives: % 131.42/18.57 | (24) ~ (all_30_0 = all_30_3) & sdtpldt0(all_30_2, all_30_1) = all_30_0 & % 131.42/18.57 | sdtpldt0(xl, xn) = all_30_1 & sdtpldt0(xk, xm) = all_30_2 & % 131.42/18.57 | sdtpldt0(xx, xy) = all_30_3 & $i(all_30_0) & $i(all_30_1) & % 131.42/18.57 | $i(all_30_2) & $i(all_30_3) % 131.42/18.57 | % 131.42/18.57 | ALPHA: (24) implies: % 131.42/18.57 | (25) ~ (all_30_0 = all_30_3) % 131.42/18.57 | (26) $i(all_30_1) % 131.42/18.57 | (27) sdtpldt0(xx, xy) = all_30_3 % 131.42/18.57 | (28) sdtpldt0(xk, xm) = all_30_2 % 131.42/18.57 | (29) sdtpldt0(xl, xn) = all_30_1 % 131.42/18.57 | (30) sdtpldt0(all_30_2, all_30_1) = all_30_0 % 131.42/18.57 | % 131.42/18.57 | DELTA: instantiating (4) with fresh symbols all_32_0, all_32_1, all_32_2, % 131.42/18.57 | all_32_3, all_32_4 gives: % 131.42/18.57 | (31) sdtpldt1(xI, xJ) = all_32_4 & sdtpldt0(all_32_1, all_32_0) = xx & % 131.42/18.57 | sdtpldt0(all_32_3, all_32_2) = xy & $i(all_32_0) & $i(all_32_1) & % 131.42/18.57 | $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & aElementOf0(all_32_0, xJ) % 131.42/18.57 | & aElementOf0(all_32_1, xI) & aElementOf0(all_32_2, xJ) & % 131.42/18.57 | aElementOf0(all_32_3, xI) & aElementOf0(xy, all_32_4) & % 131.42/18.57 | aElementOf0(xx, all_32_4) & aElement0(xz) % 131.42/18.57 | % 131.42/18.57 | ALPHA: (31) implies: % 131.42/18.57 | (32) aElementOf0(xy, all_32_4) % 131.42/18.57 | (33) aElementOf0(all_32_3, xI) % 131.42/18.57 | (34) aElementOf0(all_32_2, xJ) % 131.42/18.57 | (35) $i(all_32_4) % 131.42/18.57 | (36) $i(all_32_3) % 131.42/18.57 | (37) $i(all_32_2) % 131.42/18.57 | (38) sdtpldt0(all_32_3, all_32_2) = xy % 131.42/18.57 | (39) sdtpldt1(xI, xJ) = all_32_4 % 131.42/18.57 | % 131.42/18.57 | GROUND_INST: instantiating (19) with all_23_1, all_30_2, xm, xk, simplifying % 131.42/18.57 | with (22), (28) gives: % 131.42/18.57 | (40) all_30_2 = all_23_1 % 131.42/18.57 | % 131.42/18.57 | GROUND_INST: instantiating (19) with all_23_0, all_30_1, xn, xl, simplifying % 131.42/18.57 | with (23), (29) gives: % 131.42/18.57 | (41) all_30_1 = all_23_0 % 131.42/18.57 | % 131.42/18.57 | REDUCE: (30), (40), (41) imply: % 131.42/18.57 | (42) sdtpldt0(all_23_1, all_23_0) = all_30_0 % 131.42/18.57 | % 131.42/18.57 | REDUCE: (26), (41) imply: % 131.42/18.57 | (43) $i(all_23_0) % 131.42/18.57 | % 131.42/18.57 | GROUND_INST: instantiating (mEOfElem) with xI, xk, simplifying with (2), (5), % 131.42/18.57 | (12), (14) gives: % 131.42/18.58 | (44) aElement0(xk) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (mEOfElem) with xJ, xl, simplifying with (3), (6), % 131.42/18.58 | (13), (15) gives: % 131.42/18.58 | (45) aElement0(xl) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (mEOfElem) with xI, xm, simplifying with (2), (8), % 131.42/18.58 | (12), (16) gives: % 131.42/18.58 | (46) aElement0(xm) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (mEOfElem) with xJ, xn, simplifying with (3), (9), % 131.42/18.58 | (13), (17) gives: % 131.42/18.58 | (47) aElement0(xn) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (mEOfElem) with xJ, all_23_0, simplifying with (3), % 131.42/18.58 | (13), (21), (43) gives: % 131.42/18.58 | (48) aElement0(all_23_0) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (mEOfElem) with xI, all_32_3, simplifying with (2), % 131.42/18.58 | (12), (33), (36) gives: % 131.42/18.58 | (49) aElement0(all_32_3) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (mEOfElem) with xJ, all_32_2, simplifying with (3), % 131.42/18.58 | (13), (34), (37) gives: % 131.42/18.58 | (50) aElement0(all_32_2) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (1) with xI, xJ, all_32_4, simplifying with (2), % 131.42/18.58 | (3), (12), (13), (35), (39) gives: % 131.42/18.58 | (51) aSet0(all_32_4) % 131.42/18.58 | % 131.42/18.58 | GROUND_INST: instantiating (mAddComm) with xm, xn, xy, simplifying with (10), % 131.42/18.58 | (16), (17), (46), (47) gives: % 131.42/18.58 | (52) sdtpldt0(xn, xm) = xy & $i(xy) % 131.42/18.58 | % 131.42/18.58 | ALPHA: (52) implies: % 131.89/18.58 | (53) sdtpldt0(xn, xm) = xy % 131.89/18.58 | % 131.89/18.59 | GROUND_INST: instantiating (mAddComm) with xl, xn, all_23_0, simplifying with % 131.89/18.59 | (15), (17), (23), (45), (47) gives: % 131.89/18.59 | (54) sdtpldt0(xn, xl) = all_23_0 & $i(all_23_0) % 131.89/18.59 | % 131.89/18.59 | GROUND_INST: instantiating (mAddAsso) with xk, xm, all_23_0, all_23_1, % 131.89/18.59 | all_30_0, simplifying with (14), (16), (22), (42), (43), (44), % 131.89/18.59 | (46), (48) gives: % 131.89/18.59 | (55) ? [v0: $i] : (sdtpldt0(xm, all_23_0) = v0 & sdtpldt0(xk, v0) = % 131.89/18.59 | all_30_0 & $i(v0) & $i(all_30_0)) % 131.89/18.59 | % 131.89/18.59 | GROUND_INST: instantiating (mAddComm) with all_32_3, all_32_2, xy, simplifying % 131.89/18.59 | with (36), (37), (38), (49), (50) gives: % 131.89/18.59 | (56) sdtpldt0(all_32_2, all_32_3) = xy & $i(xy) % 131.89/18.59 | % 131.89/18.59 | ALPHA: (56) implies: % 131.89/18.59 | (57) $i(xy) % 131.89/18.59 | % 131.89/18.59 | GROUND_INST: instantiating (mEOfElem) with all_32_4, xy, simplifying with % 131.89/18.59 | (32), (35), (51), (57) gives: % 131.89/18.59 | (58) aElement0(xy) % 131.89/18.59 | % 131.89/18.59 | DELTA: instantiating (55) with fresh symbol all_54_0 gives: % 131.89/18.59 | (59) sdtpldt0(xm, all_23_0) = all_54_0 & sdtpldt0(xk, all_54_0) = all_30_0 % 131.89/18.59 | & $i(all_54_0) & $i(all_30_0) % 131.89/18.59 | % 131.89/18.59 | ALPHA: (59) implies: % 131.89/18.59 | (60) sdtpldt0(xk, all_54_0) = all_30_0 % 131.89/18.59 | (61) sdtpldt0(xm, all_23_0) = all_54_0 % 131.89/18.59 | % 131.93/18.59 | GROUND_INST: instantiating (mAddAsso) with xk, xl, xy, xx, all_30_3, % 131.93/18.59 | simplifying with (7), (14), (15), (27), (44), (45), (57), (58) % 131.93/18.59 | gives: % 131.93/18.60 | (62) ? [v0: $i] : (sdtpldt0(xl, xy) = v0 & sdtpldt0(xk, v0) = all_30_3 & % 131.93/18.60 | $i(v0) & $i(all_30_3)) % 131.93/18.60 | % 131.93/18.60 | GROUND_INST: instantiating (mAddComm) with xm, all_23_0, all_54_0, simplifying % 131.93/18.60 | with (16), (43), (46), (48), (61) gives: % 131.93/18.60 | (63) sdtpldt0(all_23_0, xm) = all_54_0 & $i(all_54_0) % 131.93/18.60 | % 131.93/18.60 | ALPHA: (63) implies: % 131.93/18.60 | (64) sdtpldt0(all_23_0, xm) = all_54_0 % 131.93/18.60 | % 131.93/18.60 | DELTA: instantiating (62) with fresh symbol all_64_0 gives: % 131.93/18.60 | (65) sdtpldt0(xl, xy) = all_64_0 & sdtpldt0(xk, all_64_0) = all_30_3 & % 131.93/18.60 | $i(all_64_0) & $i(all_30_3) % 131.93/18.60 | % 131.93/18.60 | ALPHA: (65) implies: % 131.93/18.60 | (66) sdtpldt0(xk, all_64_0) = all_30_3 % 131.93/18.60 | (67) sdtpldt0(xl, xy) = all_64_0 % 131.93/18.60 | % 131.93/18.60 | GROUND_INST: instantiating (mAddAsso) with xl, xn, xm, all_23_0, all_54_0, % 131.93/18.60 | simplifying with (15), (16), (17), (23), (45), (46), (47), (64) % 131.93/18.60 | gives: % 131.93/18.60 | (68) ? [v0: $i] : (sdtpldt0(xn, xm) = v0 & sdtpldt0(xl, v0) = all_54_0 & % 131.93/18.60 | $i(v0) & $i(all_54_0)) % 131.93/18.60 | % 131.93/18.60 | DELTA: instantiating (68) with fresh symbol all_86_0 gives: % 131.93/18.60 | (69) sdtpldt0(xn, xm) = all_86_0 & sdtpldt0(xl, all_86_0) = all_54_0 & % 131.93/18.60 | $i(all_86_0) & $i(all_54_0) % 131.93/18.60 | % 131.93/18.60 | ALPHA: (69) implies: % 131.93/18.60 | (70) sdtpldt0(xl, all_86_0) = all_54_0 % 131.93/18.60 | (71) sdtpldt0(xn, xm) = all_86_0 % 131.93/18.60 | % 131.93/18.60 | GROUND_INST: instantiating (19) with xy, all_86_0, xm, xn, simplifying with % 131.93/18.60 | (53), (71) gives: % 131.93/18.60 | (72) all_86_0 = xy % 131.93/18.60 | % 131.93/18.60 | REDUCE: (70), (72) imply: % 131.93/18.61 | (73) sdtpldt0(xl, xy) = all_54_0 % 131.93/18.61 | % 131.93/18.61 | GROUND_INST: instantiating (19) with all_64_0, all_54_0, xy, xl, simplifying % 131.99/18.61 | with (67), (73) gives: % 131.99/18.61 | (74) all_64_0 = all_54_0 % 131.99/18.61 | % 131.99/18.61 | REDUCE: (66), (74) imply: % 131.99/18.61 | (75) sdtpldt0(xk, all_54_0) = all_30_3 % 131.99/18.61 | % 131.99/18.61 | GROUND_INST: instantiating (19) with all_30_0, all_30_3, all_54_0, xk, % 131.99/18.61 | simplifying with (60), (75) gives: % 131.99/18.61 | (76) all_30_0 = all_30_3 % 131.99/18.61 | % 131.99/18.61 | REDUCE: (25), (76) imply: % 132.00/18.61 | (77) $false % 132.00/18.61 | % 132.00/18.61 | CLOSE: (77) is inconsistent. % 132.00/18.61 | % 132.00/18.61 End of proof % 132.00/18.61 % SZS output end Proof for theBenchmark % 132.00/18.61 % 132.00/18.61 17950ms %------------------------------------------------------------------------------