%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG099+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 : n029.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 13:57:51 EDT 2023 % Result : Theorem 12.43s 2.48s % Output : Proof 18.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG099+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.34 % Computer : n029.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Sun Aug 27 02:05:10 EDT 2023 % 0.15/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.63/1.10 Prover 4: Preprocessing ... % 2.63/1.11 Prover 1: Preprocessing ... % 3.12/1.14 Prover 2: Preprocessing ... % 3.12/1.14 Prover 5: Preprocessing ... % 3.12/1.14 Prover 3: Preprocessing ... % 3.12/1.15 Prover 6: Preprocessing ... % 3.12/1.15 Prover 0: Preprocessing ... % 7.83/1.80 Prover 1: Constructing countermodel ... % 8.35/1.84 Prover 3: Constructing countermodel ... % 8.35/1.86 Prover 6: Proving ... % 9.00/1.93 Prover 5: Proving ... % 9.20/2.00 Prover 2: Proving ... % 9.20/2.00 Prover 4: Constructing countermodel ... % 9.87/2.13 Prover 0: Proving ... % 12.43/2.48 Prover 3: proved (1851ms) % 12.43/2.48 % 12.43/2.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.43/2.48 % 12.94/2.49 Prover 5: stopped % 12.94/2.49 Prover 6: stopped % 12.94/2.51 Prover 2: stopped % 12.94/2.51 Prover 0: stopped % 12.94/2.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.94/2.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.94/2.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.94/2.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.94/2.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.94/2.55 Prover 7: Preprocessing ... % 13.55/2.57 Prover 8: Preprocessing ... % 13.86/2.61 Prover 10: Preprocessing ... % 13.86/2.61 Prover 13: Preprocessing ... % 13.86/2.63 Prover 11: Preprocessing ... % 13.99/2.70 Prover 7: Constructing countermodel ... % 13.99/2.71 Prover 8: Warning: ignoring some quantifiers % 14.65/2.73 Prover 8: Constructing countermodel ... % 15.13/2.81 Prover 13: Warning: ignoring some quantifiers % 15.13/2.82 Prover 10: Constructing countermodel ... % 15.13/2.83 Prover 13: Constructing countermodel ... % 15.87/2.98 Prover 11: Constructing countermodel ... % 17.58/3.18 Prover 10: Found proof (size 48) % 17.58/3.18 Prover 10: proved (675ms) % 17.58/3.18 Prover 13: stopped % 17.58/3.18 Prover 8: stopped % 17.58/3.18 Prover 1: stopped % 17.58/3.19 Prover 4: stopped % 17.58/3.19 Prover 7: stopped % 17.58/3.19 Prover 11: stopped % 17.58/3.19 % 17.58/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 17.58/3.19 % 17.58/3.20 % SZS output start Proof for theBenchmark % 17.58/3.20 Assumptions after simplification: % 17.58/3.20 --------------------------------- % 17.58/3.20 % 17.58/3.20 (mAddComm) % 18.22/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 18.22/3.23 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v1, v0) % 18.22/3.23 = v2 & $i(v2))) % 18.22/3.23 % 18.22/3.23 (mDefIdeal) % 18.22/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1) % 18.22/3.23 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ % 18.22/3.23 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i] % 18.22/3.23 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ % 18.22/3.23 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | % 18.22/3.23 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 18.22/3.23 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | % 18.22/3.23 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 18.22/3.23 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, % 18.22/3.23 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 18.22/3.23 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 18.22/3.23 aElementOf0(v5, v0))))) % 18.22/3.23 % 18.22/3.23 (mDefMod) % 18.22/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 18.22/3.24 (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.22/3.24 $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, v1, v2) | ~ aIdeal0(v2) | ~ % 18.22/3.24 aElement0(v1) | ~ aElement0(v0) | aElementOf0(v4, v2)) & ! [v0: $i] : ! % 18.22/3.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = % 18.22/3.24 v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 18.22/3.24 aIdeal0(v2) | ~ aElementOf0(v4, v2) | ~ aElement0(v1) | ~ aElement0(v0) | % 18.22/3.24 sdteqdtlpzmzozddtrp0(v0, v1, v2)) % 18.22/3.24 % 18.22/3.24 (mDefSSum) % 18.22/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 18.22/3.24 $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ $i(v5) | % 18.22/3.24 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 18.22/3.24 aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | % 18.22/3.24 aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 18.22/3.24 : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 18.22/3.24 ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4: $i] : ? [v5: $i] : ? % 18.22/3.24 [v6: $i] : ? [v7: $i] : ($i(v6) & $i(v5) & $i(v4) & ( ~ aElementOf0(v4, v3) % 18.22/3.24 | ! [v8: $i] : ! [v9: $i] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ $i(v9) | % 18.22/3.24 ~ $i(v8) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & % 18.22/3.24 (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, % 18.22/3.24 v1) & aElementOf0(v5, v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 18.22/3.24 $i] : ! [v3: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 18.22/3.24 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | % 18.22/3.24 ? [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 18.22/3.24 aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0: $i] : ! [v1: $i] : % 18.22/3.24 ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 18.22/3.24 ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) % 18.22/3.24 % 18.22/3.25 (mEOfElem) % 18.22/3.25 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 18.22/3.25 ~ aSet0(v0) | aElement0(v1)) % 18.22/3.25 % 18.22/3.25 (mIdeSum) % 18.22/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ % 18.22/3.25 $i(v1) | ~ $i(v0) | ~ aIdeal0(v1) | ~ aIdeal0(v0) | aIdeal0(v2)) % 18.22/3.25 % 18.22/3.25 (mMulComm) % 18.22/3.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 18.22/3.25 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0) % 18.22/3.25 = v2 & $i(v2))) % 18.22/3.25 % 18.22/3.25 (m__) % 18.22/3.25 $i(xy) & $i(xx) & $i(xJ) & $i(xI) & ! [v0: $i] : ( ~ $i(v0) | ~ % 18.22/3.25 sdteqdtlpzmzozddtrp0(v0, xy, xJ) | ~ sdteqdtlpzmzozddtrp0(v0, xx, xI) | ~ % 18.22/3.25 aElement0(v0)) % 18.22/3.25 % 18.22/3.25 (m__1205) % 18.22/3.25 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) % 18.22/3.25 % 18.22/3.25 (m__1205_03) % 18.22/3.25 $i(xJ) & $i(xI) & ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i] % 18.22/3.25 : ( ~ $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0))) % 18.22/3.25 % 18.22/3.25 (m__1217) % 18.22/3.25 $i(xy) & $i(xx) & aElement0(xy) & aElement0(xx) % 18.22/3.25 % 18.22/3.25 (m__1294) % 18.22/3.25 sdtpldt0(xa, xb) = sz10 & $i(xb) & $i(xa) & $i(xJ) & $i(xI) & $i(sz10) & % 18.22/3.25 aElementOf0(xb, xJ) & aElementOf0(xa, xI) % 18.22/3.25 % 18.22/3.25 (m__1319) % 18.22/3.25 $i(xw) & $i(xb) & $i(xa) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : % 18.22/3.25 (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) = v1 & sdtpldt0(v0, v1) = xw & % 18.22/3.25 $i(v1) & $i(v0)) % 18.22/3.25 % 18.22/3.25 (m__1332) % 18.22/3.25 $i(xw) & $i(xx) & $i(xI) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 % 18.22/3.25 & smndt0(xx) = v0 & $i(v1) & $i(v0) & aElementOf0(v1, xI)) % 18.22/3.25 % 18.22/3.25 (m__1409) % 18.22/3.25 $i(xw) & $i(xy) & $i(xJ) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 % 18.22/3.25 & smndt0(xy) = v0 & $i(v1) & $i(v0) & aElementOf0(v1, xJ)) % 18.22/3.25 % 18.22/3.25 Further assumptions not needed in the proof: % 18.22/3.25 -------------------------------------------- % 18.22/3.25 mAMDistr, mAddAsso, mAddInvr, mAddZero, mCancel, mDefSInt, mElmSort, mIdeInt, % 18.22/3.25 mMulAsso, mMulMnOne, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02, % 18.22/3.25 mSortsC, mSortsC_01, mSortsU, mUnNeZr % 18.22/3.25 % 18.22/3.25 Those formulas are unsatisfiable: % 18.22/3.25 --------------------------------- % 18.22/3.25 % 18.22/3.25 Begin of proof % 18.22/3.25 | % 18.22/3.25 | ALPHA: (mDefSSum) implies: % 18.22/3.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.22/3.26 | (sdtpldt1(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 18.22/3.26 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ? % 18.22/3.26 | [v4: $i] : ? [v5: $i] : (sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) & % 18.22/3.26 | aElementOf0(v5, v1) & aElementOf0(v4, v0))) % 18.22/3.26 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.22/3.26 | ! [v5: $i] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | % 18.22/3.26 | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 18.22/3.26 | | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ % 18.22/3.26 | aSet0(v0) | aElementOf0(v3, v2)) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (mDefIdeal) implies: % 18.22/3.26 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0)) % 18.22/3.26 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 18.22/3.26 | (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 18.22/3.26 | aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) | % 18.22/3.26 | aElementOf0(v3, v0)) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (mDefMod) implies: % 18.22/3.26 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 18.22/3.26 | ~ (sdtpldt0(v0, v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ % 18.22/3.26 | $i(v1) | ~ $i(v0) | ~ aIdeal0(v2) | ~ aElementOf0(v4, v2) | ~ % 18.22/3.26 | aElement0(v1) | ~ aElement0(v0) | sdteqdtlpzmzozddtrp0(v0, v1, v2)) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__1205) implies: % 18.22/3.26 | (6) aIdeal0(xI) % 18.22/3.26 | (7) aIdeal0(xJ) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__1205_03) implies: % 18.22/3.26 | (8) ? [v0: $i] : (sdtpldt1(xI, xJ) = v0 & $i(v0) & ! [v1: $i] : ( ~ % 18.22/3.26 | $i(v1) | ~ aElement0(v1) | aElementOf0(v1, v0))) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__1217) implies: % 18.22/3.26 | (9) aElement0(xx) % 18.22/3.26 | (10) aElement0(xy) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__1294) implies: % 18.22/3.26 | (11) aElementOf0(xa, xI) % 18.22/3.26 | (12) aElementOf0(xb, xJ) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__1319) implies: % 18.22/3.26 | (13) $i(xa) % 18.22/3.26 | (14) $i(xb) % 18.22/3.26 | (15) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) % 18.22/3.26 | = v1 & sdtpldt0(v0, v1) = xw & $i(v1) & $i(v0)) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__1332) implies: % 18.22/3.26 | (16) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 & smndt0(xx) = v0 & % 18.22/3.26 | $i(v1) & $i(v0) & aElementOf0(v1, xI)) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__1409) implies: % 18.22/3.26 | (17) $i(xw) % 18.22/3.26 | (18) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 & smndt0(xy) = v0 & % 18.22/3.26 | $i(v1) & $i(v0) & aElementOf0(v1, xJ)) % 18.22/3.26 | % 18.22/3.26 | ALPHA: (m__) implies: % 18.22/3.26 | (19) $i(xI) % 18.22/3.26 | (20) $i(xJ) % 18.22/3.26 | (21) $i(xx) % 18.22/3.26 | (22) $i(xy) % 18.22/3.26 | (23) ! [v0: $i] : ( ~ $i(v0) | ~ sdteqdtlpzmzozddtrp0(v0, xy, xJ) | ~ % 18.22/3.26 | sdteqdtlpzmzozddtrp0(v0, xx, xI) | ~ aElement0(v0)) % 18.22/3.26 | % 18.22/3.27 | DELTA: instantiating (16) with fresh symbols all_26_0, all_26_1 gives: % 18.22/3.27 | (24) sdtpldt0(xw, all_26_1) = all_26_0 & smndt0(xx) = all_26_1 & % 18.22/3.27 | $i(all_26_0) & $i(all_26_1) & aElementOf0(all_26_0, xI) % 18.22/3.27 | % 18.22/3.27 | ALPHA: (24) implies: % 18.22/3.27 | (25) aElementOf0(all_26_0, xI) % 18.22/3.27 | (26) smndt0(xx) = all_26_1 % 18.22/3.27 | (27) sdtpldt0(xw, all_26_1) = all_26_0 % 18.22/3.27 | % 18.22/3.27 | DELTA: instantiating (18) with fresh symbols all_28_0, all_28_1 gives: % 18.22/3.27 | (28) sdtpldt0(xw, all_28_1) = all_28_0 & smndt0(xy) = all_28_1 & % 18.22/3.27 | $i(all_28_0) & $i(all_28_1) & aElementOf0(all_28_0, xJ) % 18.22/3.27 | % 18.22/3.27 | ALPHA: (28) implies: % 18.22/3.27 | (29) aElementOf0(all_28_0, xJ) % 18.22/3.27 | (30) smndt0(xy) = all_28_1 % 18.22/3.27 | (31) sdtpldt0(xw, all_28_1) = all_28_0 % 18.22/3.27 | % 18.22/3.27 | DELTA: instantiating (8) with fresh symbol all_30_0 gives: % 18.22/3.27 | (32) sdtpldt1(xI, xJ) = all_30_0 & $i(all_30_0) & ! [v0: $i] : ( ~ $i(v0) % 18.22/3.27 | | ~ aElement0(v0) | aElementOf0(v0, all_30_0)) % 18.22/3.27 | % 18.22/3.27 | ALPHA: (32) implies: % 18.22/3.27 | (33) $i(all_30_0) % 18.22/3.27 | (34) sdtpldt1(xI, xJ) = all_30_0 % 18.22/3.27 | % 18.22/3.27 | DELTA: instantiating (15) with fresh symbols all_33_0, all_33_1 gives: % 18.22/3.27 | (35) sdtasdt0(xy, xa) = all_33_1 & sdtasdt0(xx, xb) = all_33_0 & % 18.22/3.27 | sdtpldt0(all_33_1, all_33_0) = xw & $i(all_33_0) & $i(all_33_1) % 18.22/3.27 | % 18.22/3.27 | ALPHA: (35) implies: % 18.22/3.27 | (36) $i(all_33_1) % 18.22/3.27 | (37) $i(all_33_0) % 18.22/3.27 | (38) sdtpldt0(all_33_1, all_33_0) = xw % 18.22/3.27 | (39) sdtasdt0(xx, xb) = all_33_0 % 18.22/3.27 | (40) sdtasdt0(xy, xa) = all_33_1 % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (3) with xI, simplifying with (6), (19) gives: % 18.22/3.27 | (41) aSet0(xI) % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (3) with xJ, simplifying with (7), (20) gives: % 18.22/3.27 | (42) aSet0(xJ) % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (4) with xJ, xb, xx, all_33_0, simplifying with % 18.22/3.27 | (7), (9), (12), (14), (20), (21), (39) gives: % 18.22/3.27 | (43) aElementOf0(all_33_0, xJ) % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (4) with xI, xa, xy, all_33_1, simplifying with % 18.22/3.27 | (6), (10), (11), (13), (19), (22), (40) gives: % 18.22/3.27 | (44) aElementOf0(all_33_1, xI) % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (mIdeSum) with xI, xJ, all_30_0, simplifying with % 18.22/3.27 | (6), (7), (19), (20), (34) gives: % 18.22/3.27 | (45) aIdeal0(all_30_0) % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (mEOfElem) with xI, xa, simplifying with (11), % 18.22/3.27 | (13), (19), (41) gives: % 18.22/3.27 | (46) aElement0(xa) % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (mEOfElem) with xJ, xb, simplifying with (12), % 18.22/3.27 | (14), (20), (42) gives: % 18.22/3.27 | (47) aElement0(xb) % 18.22/3.27 | % 18.22/3.27 | GROUND_INST: instantiating (mEOfElem) with xI, all_33_1, simplifying with % 18.22/3.27 | (19), (36), (41), (44) gives: % 18.22/3.27 | (48) aElement0(all_33_1) % 18.22/3.27 | % 18.22/3.28 | GROUND_INST: instantiating (2) with xI, xJ, all_30_0, xw, all_33_1, all_33_0, % 18.22/3.28 | simplifying with (17), (19), (20), (33), (34), (36), (37), (38), % 18.22/3.28 | (41), (42), (43), (44) gives: % 18.22/3.28 | (49) aElementOf0(xw, all_30_0) % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (mEOfElem) with xJ, all_33_0, simplifying with % 18.22/3.28 | (20), (37), (42), (43) gives: % 18.22/3.28 | (50) aElement0(all_33_0) % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (3) with all_30_0, simplifying with (33), (45) % 18.22/3.28 | gives: % 18.22/3.28 | (51) aSet0(all_30_0) % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (mMulComm) with xy, xa, all_33_1, simplifying with % 18.22/3.28 | (10), (13), (22), (40), (46) gives: % 18.22/3.28 | (52) sdtasdt0(xa, xy) = all_33_1 & $i(all_33_1) % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (mMulComm) with xx, xb, all_33_0, simplifying with % 18.22/3.28 | (9), (14), (21), (39), (47) gives: % 18.22/3.28 | (53) sdtasdt0(xb, xx) = all_33_0 & $i(all_33_0) % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (mAddComm) with all_33_1, all_33_0, xw, simplifying % 18.22/3.28 | with (36), (37), (38), (48), (50) gives: % 18.22/3.28 | (54) sdtpldt0(all_33_0, all_33_1) = xw & $i(xw) % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (1) with xI, xJ, all_30_0, xw, simplifying with % 18.22/3.28 | (17), (19), (20), (33), (34), (41), (42), (49) gives: % 18.22/3.28 | (55) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, v1) = xw & $i(v1) & $i(v0) & % 18.22/3.28 | aElementOf0(v1, xJ) & aElementOf0(v0, xI)) % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (mEOfElem) with all_30_0, xw, simplifying with % 18.22/3.28 | (17), (33), (49), (51) gives: % 18.22/3.28 | (56) aElement0(xw) % 18.22/3.28 | % 18.22/3.28 | DELTA: instantiating (55) with fresh symbols all_72_0, all_72_1 gives: % 18.22/3.28 | (57) sdtpldt0(all_72_1, all_72_0) = xw & $i(all_72_0) & $i(all_72_1) & % 18.22/3.28 | aElementOf0(all_72_0, xJ) & aElementOf0(all_72_1, xI) % 18.22/3.28 | % 18.22/3.28 | ALPHA: (57) implies: % 18.22/3.28 | (58) aElementOf0(all_72_1, xI) % 18.22/3.28 | (59) aElementOf0(all_72_0, xJ) % 18.22/3.28 | (60) $i(all_72_1) % 18.22/3.28 | (61) $i(all_72_0) % 18.22/3.28 | (62) sdtpldt0(all_72_1, all_72_0) = xw % 18.22/3.28 | % 18.22/3.28 | GROUND_INST: instantiating (5) with xw, xy, xJ, all_28_1, all_28_0, % 18.22/3.28 | simplifying with (7), (10), (17), (20), (22), (29), (30), (31), % 18.22/3.28 | (56) gives: % 18.22/3.28 | (63) sdteqdtlpzmzozddtrp0(xw, xy, xJ) % 18.22/3.28 | % 18.62/3.28 | GROUND_INST: instantiating (5) with xw, xx, xI, all_26_1, all_26_0, % 18.62/3.28 | simplifying with (6), (9), (17), (19), (21), (25), (26), (27), % 18.62/3.28 | (56) gives: % 18.62/3.28 | (64) sdteqdtlpzmzozddtrp0(xw, xx, xI) % 18.62/3.28 | % 18.62/3.29 | GROUND_INST: instantiating (mEOfElem) with xI, all_72_1, simplifying with % 18.62/3.29 | (19), (41), (58), (60) gives: % 18.62/3.29 | (65) aElement0(all_72_1) % 18.62/3.29 | % 18.62/3.29 | GROUND_INST: instantiating (mEOfElem) with xJ, all_72_0, simplifying with % 18.62/3.29 | (20), (42), (59), (61) gives: % 18.62/3.29 | (66) aElement0(all_72_0) % 18.62/3.29 | % 18.62/3.29 | GROUND_INST: instantiating (mAddComm) with all_72_1, all_72_0, xw, simplifying % 18.62/3.29 | with (60), (61), (62), (65), (66) gives: % 18.62/3.29 | (67) sdtpldt0(all_72_0, all_72_1) = xw & $i(xw) % 18.62/3.29 | % 18.62/3.29 | GROUND_INST: instantiating (23) with xw, simplifying with (17), (56), (63), % 18.62/3.29 | (64) gives: % 18.62/3.29 | (68) $false % 18.62/3.29 | % 18.62/3.29 | CLOSE: (68) is inconsistent. % 18.62/3.29 | % 18.62/3.29 End of proof % 18.62/3.29 % SZS output end Proof for theBenchmark % 18.62/3.29 % 18.62/3.29 2688ms %------------------------------------------------------------------------------