%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG098+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 : n005.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 41.36s 6.32s % Output : Proof 60.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : RNG098+2 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n005.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % 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 01:57:08 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.05/1.11 Prover 1: Preprocessing ... % 3.05/1.11 Prover 4: Preprocessing ... % 3.18/1.14 Prover 3: Preprocessing ... % 3.18/1.14 Prover 2: Preprocessing ... % 3.18/1.14 Prover 0: Preprocessing ... % 3.18/1.14 Prover 5: Preprocessing ... % 3.18/1.14 Prover 6: Preprocessing ... % 8.08/1.88 Prover 6: Proving ... % 8.08/1.90 Prover 1: Constructing countermodel ... % 8.08/1.91 Prover 3: Constructing countermodel ... % 8.08/1.92 Prover 5: Proving ... % 8.91/2.02 Prover 2: Proving ... % 8.91/2.04 Prover 4: Constructing countermodel ... % 8.91/2.07 Prover 0: Proving ... % 41.36/6.31 Prover 0: proved (5665ms) % 41.36/6.31 % 41.36/6.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 41.36/6.32 % 41.36/6.33 Prover 3: stopped % 41.36/6.33 Prover 2: stopped % 41.36/6.33 Prover 5: stopped % 42.09/6.33 Prover 6: stopped % 42.09/6.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 42.09/6.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 42.09/6.34 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 42.09/6.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 42.09/6.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 42.09/6.39 Prover 13: Preprocessing ... % 42.58/6.40 Prover 8: Preprocessing ... % 42.58/6.41 Prover 10: Preprocessing ... % 42.58/6.41 Prover 7: Preprocessing ... % 42.58/6.42 Prover 11: Preprocessing ... % 43.09/6.54 Prover 8: Warning: ignoring some quantifiers % 43.40/6.56 Prover 10: Constructing countermodel ... % 43.40/6.59 Prover 8: Constructing countermodel ... % 43.40/6.59 Prover 13: Warning: ignoring some quantifiers % 44.03/6.60 Prover 7: Constructing countermodel ... % 44.03/6.60 Prover 13: Constructing countermodel ... % 44.30/6.70 Prover 11: Constructing countermodel ... % 60.50/8.73 Prover 7: Found proof (size 88) % 60.50/8.73 Prover 7: proved (2401ms) % 60.50/8.73 Prover 8: stopped % 60.50/8.73 Prover 4: stopped % 60.50/8.73 Prover 10: stopped % 60.55/8.73 Prover 11: stopped % 60.55/8.74 Prover 1: stopped % 60.55/8.74 Prover 13: stopped % 60.55/8.74 % 60.55/8.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 60.55/8.74 % 60.55/8.75 % SZS output start Proof for theBenchmark % 60.55/8.75 Assumptions after simplification: % 60.55/8.75 --------------------------------- % 60.55/8.75 % 60.55/8.75 (mAMDistr) % 60.55/8.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 60.55/8.78 $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ % 60.55/8.78 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 60.55/8.78 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 60.55/8.78 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, % 60.55/8.78 v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, % 60.55/8.78 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 60.55/8.78 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 60.55/8.78 $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) % 60.55/8.78 | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 60.55/8.78 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 60.55/8.78 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, % 60.55/8.78 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, % 60.55/8.78 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 60.55/8.78 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 60.55/8.78 $i] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 60.55/8.78 ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 60.55/8.78 aElement0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 60.55/8.78 [v9: $i] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) % 60.55/8.78 = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = % 60.55/8.79 v4 & sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 60.55/8.79 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 60.55/8.79 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 60.55/8.79 ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 60.55/8.79 aElement0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 60.55/8.79 [v9: $i] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) % 60.55/8.79 = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = % 60.55/8.79 v7 & sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 60.55/8.79 $i(v4))) % 60.55/8.79 % 60.55/8.79 (mAddAsso) % 60.55/8.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 60.55/8.79 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 60.55/8.79 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 60.55/8.79 [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4 & $i(v5) & % 60.55/8.79 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 60.55/8.79 $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v2) | % 60.55/8.79 ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 60.55/8.79 aElement0(v0) | ? [v5: $i] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5 % 60.55/8.79 & $i(v5) & $i(v4))) % 60.55/8.79 % 60.55/8.79 (mAddComm) % 60.55/8.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ % 60.55/8.79 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtpldt0(v0, v1) % 60.55/8.79 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 60.55/8.79 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ % 60.55/8.79 aElement0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2))) % 60.55/8.79 % 60.55/8.79 (mAddInvr) % 60.55/8.79 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 60.55/8.79 aElement0(v0) | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00)) % 60.55/8.79 % 60.55/8.79 (mAddZero) % 60.55/8.79 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) % 60.55/8.79 | ~ $i(v0) | ~ aElement0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ % 60.55/8.79 (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ~ aElement0(v0)) & ! [v0: $i] : ! % 60.55/8.79 [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ $i(v0) | ~ aElement0(v0) | % 60.55/8.79 sdtpldt0(sz00, v0) = v0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(sz00, % 60.55/8.79 v0) = v1) | ~ $i(v0) | ~ aElement0(v0) | sdtpldt0(v0, sz00) = v0) % 60.55/8.79 % 60.55/8.79 (mEOfElem) % 60.55/8.79 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 60.55/8.79 ~ aSet0(v0) | aElement0(v1)) % 60.55/8.79 % 60.55/8.79 (mMulComm) % 60.55/8.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 60.55/8.79 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v0, v1) % 60.55/8.79 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 60.55/8.79 (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ % 60.55/8.79 aElement0(v0) | (sdtasdt0(v1, v0) = v2 & $i(v2))) % 60.55/8.79 % 60.55/8.79 (mMulMnOne) % 60.55/8.79 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 60.55/8.79 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 60.55/8.79 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 60.55/8.79 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 60.55/8.79 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 60.55/8.79 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 60.55/8.79 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2)))) % 60.55/8.79 % 60.55/8.79 (mSortsC) % 60.55/8.80 $i(sz00) & aElement0(sz00) % 60.55/8.80 % 60.55/8.80 (mSortsC_01) % 60.55/8.80 $i(sz10) & aElement0(sz10) % 60.55/8.80 % 60.55/8.80 (mSortsU) % 60.55/8.80 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 60.55/8.80 aElement0(v0) | aElement0(v1)) % 60.55/8.80 % 60.55/8.80 (mUnNeZr) % 60.55/8.80 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) % 60.55/8.80 % 60.55/8.80 (m__) % 60.55/8.80 $i(xw) & $i(xx) & $i(xI) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 % 60.55/8.80 & smndt0(xx) = v0 & $i(v1) & $i(v0) & ~ aElementOf0(v1, xI)) % 60.55/8.80 % 60.55/8.80 (m__1205) % 60.55/8.80 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) & aSet0(xJ) & aSet0(xI) & ! [v0: % 60.55/8.80 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | % 60.55/8.80 ~ $i(v0) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ)) % 60.55/8.80 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 60.55/8.80 $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | % 60.55/8.80 aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 60.55/8.80 (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xJ) | % 60.55/8.80 ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ)) & ! [v0: $i] : ! [v1: $i] : % 60.55/8.80 ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 60.55/8.80 aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI)) % 60.55/8.80 % 60.55/8.80 (m__1217) % 60.55/8.80 $i(xy) & $i(xx) & aElement0(xy) & aElement0(xx) % 60.55/8.80 % 60.55/8.80 (m__1294) % 60.55/8.80 sdtpldt0(xa, xb) = sz10 & $i(xb) & $i(xa) & $i(xJ) & $i(xI) & $i(sz10) & % 60.55/8.80 aElementOf0(xb, xJ) & aElementOf0(xa, xI) % 60.55/8.80 % 60.55/8.80 (m__1319) % 60.55/8.80 $i(xw) & $i(xb) & $i(xa) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : % 60.55/8.80 (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) = v1 & sdtpldt0(v0, v1) = xw & % 60.55/8.80 $i(v1) & $i(v0)) % 60.55/8.80 % 60.55/8.80 (m__1374) % 60.55/8.80 $i(xw) & $i(xb) & $i(xa) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? % 60.55/8.80 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(xy, xa) = v2 & sdtasdt0(xx, % 60.55/8.80 xb) = v3 & sdtpldt0(v3, v0) = v4 & sdtpldt0(v2, v4) = v1 & sdtpldt0(xw, % 60.55/8.80 v0) = v1 & smndt0(xx) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 60.55/8.80 % 60.55/8.80 (m__1393) % 60.55/8.80 $i(xb) & $i(xx) & $i(xI) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 60.55/8.80 : (sdtasdt0(xx, v1) = v2 & sdtpldt0(xb, v0) = v1 & smndt0(sz10) = v0 & $i(v2) % 60.55/8.80 & $i(v1) & $i(v0) & aElementOf0(v2, xI)) % 60.55/8.80 % 60.55/8.80 (function-axioms) % 60.55/8.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 60.55/8.80 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 60.55/8.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 60.55/8.80 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 60.55/8.80 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 60.55/8.80 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 60.55/8.80 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 60.55/8.80 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = % 60.55/8.80 v0)) % 60.55/8.80 % 60.55/8.80 Further assumptions not needed in the proof: % 60.55/8.80 -------------------------------------------- % 60.55/8.80 mCancel, mDefIdeal, mDefMod, mDefSInt, mDefSSum, mElmSort, mIdeInt, mIdeSum, % 60.55/8.80 mMulAsso, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB, mSortsB_02, m__1205_03 % 60.55/8.80 % 60.55/8.80 Those formulas are unsatisfiable: % 60.55/8.80 --------------------------------- % 60.55/8.80 % 60.55/8.80 Begin of proof % 60.55/8.80 | % 60.55/8.80 | ALPHA: (mSortsC) implies: % 60.91/8.81 | (1) aElement0(sz00) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mSortsC_01) implies: % 60.91/8.81 | (2) aElement0(sz10) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mAddComm) implies: % 60.91/8.81 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | % 60.91/8.81 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | % 60.91/8.81 | (sdtpldt0(v1, v0) = v2 & $i(v2))) % 60.91/8.81 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | % 60.91/8.81 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | % 60.91/8.81 | (sdtpldt0(v0, v1) = v2 & $i(v2))) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mAddAsso) implies: % 60.91/8.81 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 60.91/8.81 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 60.91/8.81 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 60.91/8.81 | aElement0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, % 60.91/8.81 | v5) = v4 & $i(v5) & $i(v4))) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mAddZero) implies: % 60.91/8.81 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | % 60.91/8.81 | ~ $i(v0) | ~ aElement0(v0)) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mAddInvr) implies: % 60.91/8.81 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 60.91/8.81 | aElement0(v0) | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00)) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mMulComm) implies: % 60.91/8.81 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | % 60.91/8.81 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | % 60.91/8.81 | (sdtasdt0(v0, v1) = v2 & $i(v2))) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mAMDistr) implies: % 60.91/8.81 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 60.91/8.81 | ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | % 60.91/8.81 | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 60.91/8.81 | aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : % 60.91/8.81 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & % 60.91/8.81 | sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = % 60.91/8.81 | v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & % 60.91/8.81 | $i(v8) & $i(v7) & $i(v6) & $i(v5))) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mMulMnOne) implies: % 60.91/8.81 | (10) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] % 60.91/8.81 | : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 60.91/8.81 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] % 60.91/8.81 | : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ % 60.91/8.81 | aElement0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & % 60.91/8.81 | $i(v2))) & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | % 60.91/8.81 | ~ $i(v1) | ~ aElement0(v1) | (sdtasdt0(v1, v0) = v2 & % 60.91/8.81 | sdtasdt0(v0, v1) = v2 & $i(v2)))) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (mUnNeZr) implies: % 60.91/8.81 | (11) ~ (sz10 = sz00) % 60.91/8.81 | (12) $i(sz00) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (m__1205) implies: % 60.91/8.81 | (13) aSet0(xI) % 60.91/8.81 | (14) aSet0(xJ) % 60.91/8.81 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) % 60.91/8.81 | | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, xI) | ~ % 60.91/8.81 | aElementOf0(v0, xI) | aElementOf0(v2, xI)) % 60.91/8.81 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) % 60.91/8.81 | | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) % 60.91/8.81 | | aElementOf0(v2, xI)) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (m__1217) implies: % 60.91/8.81 | (17) aElement0(xx) % 60.91/8.81 | (18) aElement0(xy) % 60.91/8.81 | % 60.91/8.81 | ALPHA: (m__1294) implies: % 60.91/8.81 | (19) aElementOf0(xa, xI) % 60.91/8.81 | (20) aElementOf0(xb, xJ) % 60.91/8.81 | (21) $i(xJ) % 60.91/8.81 | (22) sdtpldt0(xa, xb) = sz10 % 60.91/8.81 | % 60.91/8.81 | ALPHA: (m__1319) implies: % 60.91/8.82 | (23) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) % 60.91/8.82 | = v1 & sdtpldt0(v0, v1) = xw & $i(v1) & $i(v0)) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (m__1374) implies: % 60.91/8.82 | (24) $i(xy) % 60.91/8.82 | (25) $i(xa) % 60.91/8.82 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 60.91/8.82 | (sdtasdt0(xy, xa) = v2 & sdtasdt0(xx, xb) = v3 & sdtpldt0(v3, v0) = v4 % 60.91/8.82 | & sdtpldt0(v2, v4) = v1 & sdtpldt0(xw, v0) = v1 & smndt0(xx) = v0 & % 60.91/8.82 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (m__1393) implies: % 60.91/8.82 | (27) $i(sz10) % 60.91/8.82 | (28) $i(xb) % 60.91/8.82 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xx, v1) = v2 & % 60.91/8.82 | sdtpldt0(xb, v0) = v1 & smndt0(sz10) = v0 & $i(v2) & $i(v1) & $i(v0) % 60.91/8.82 | & aElementOf0(v2, xI)) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (m__) implies: % 60.91/8.82 | (30) $i(xI) % 60.91/8.82 | (31) $i(xx) % 60.91/8.82 | (32) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 & smndt0(xx) = v0 & % 60.91/8.82 | $i(v1) & $i(v0) & ~ aElementOf0(v1, xI)) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (function-axioms) implies: % 60.91/8.82 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 60.91/8.82 | v1) | ~ (smndt0(v2) = v0)) % 60.91/8.82 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 60.91/8.82 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 60.91/8.82 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 60.91/8.82 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 60.91/8.82 | % 60.91/8.82 | DELTA: instantiating (23) with fresh symbols all_26_0, all_26_1 gives: % 60.91/8.82 | (36) sdtasdt0(xy, xa) = all_26_1 & sdtasdt0(xx, xb) = all_26_0 & % 60.91/8.82 | sdtpldt0(all_26_1, all_26_0) = xw & $i(all_26_0) & $i(all_26_1) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (36) implies: % 60.91/8.82 | (37) sdtasdt0(xx, xb) = all_26_0 % 60.91/8.82 | (38) sdtasdt0(xy, xa) = all_26_1 % 60.91/8.82 | % 60.91/8.82 | DELTA: instantiating (32) with fresh symbols all_28_0, all_28_1 gives: % 60.91/8.82 | (39) sdtpldt0(xw, all_28_1) = all_28_0 & smndt0(xx) = all_28_1 & % 60.91/8.82 | $i(all_28_0) & $i(all_28_1) & ~ aElementOf0(all_28_0, xI) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (39) implies: % 60.91/8.82 | (40) ~ aElementOf0(all_28_0, xI) % 60.91/8.82 | (41) smndt0(xx) = all_28_1 % 60.91/8.82 | (42) sdtpldt0(xw, all_28_1) = all_28_0 % 60.91/8.82 | % 60.91/8.82 | DELTA: instantiating (29) with fresh symbols all_30_0, all_30_1, all_30_2 % 60.91/8.82 | gives: % 60.91/8.82 | (43) sdtasdt0(xx, all_30_1) = all_30_0 & sdtpldt0(xb, all_30_2) = all_30_1 % 60.91/8.82 | & smndt0(sz10) = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) % 60.91/8.82 | & aElementOf0(all_30_0, xI) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (43) implies: % 60.91/8.82 | (44) aElementOf0(all_30_0, xI) % 60.91/8.82 | (45) smndt0(sz10) = all_30_2 % 60.91/8.82 | (46) sdtpldt0(xb, all_30_2) = all_30_1 % 60.91/8.82 | (47) sdtasdt0(xx, all_30_1) = all_30_0 % 60.91/8.82 | % 60.91/8.82 | DELTA: instantiating (26) with fresh symbols all_32_0, all_32_1, all_32_2, % 60.91/8.82 | all_32_3, all_32_4 gives: % 60.91/8.82 | (48) sdtasdt0(xy, xa) = all_32_2 & sdtasdt0(xx, xb) = all_32_1 & % 60.91/8.82 | sdtpldt0(all_32_1, all_32_4) = all_32_0 & sdtpldt0(all_32_2, all_32_0) % 60.91/8.82 | = all_32_3 & sdtpldt0(xw, all_32_4) = all_32_3 & smndt0(xx) = all_32_4 % 60.91/8.82 | & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & % 60.91/8.82 | $i(all_32_4) % 60.91/8.82 | % 60.91/8.82 | ALPHA: (48) implies: % 60.91/8.82 | (49) $i(all_32_0) % 60.91/8.82 | (50) smndt0(xx) = all_32_4 % 60.91/8.82 | (51) sdtpldt0(xw, all_32_4) = all_32_3 % 60.91/8.82 | (52) sdtpldt0(all_32_2, all_32_0) = all_32_3 % 60.91/8.82 | (53) sdtpldt0(all_32_1, all_32_4) = all_32_0 % 60.91/8.82 | (54) sdtasdt0(xx, xb) = all_32_1 % 60.91/8.82 | (55) sdtasdt0(xy, xa) = all_32_2 % 60.91/8.82 | % 60.91/8.82 | DELTA: instantiating (10) with fresh symbol all_37_0 gives: % 60.91/8.83 | (56) smndt0(sz10) = all_37_0 & $i(all_37_0) & ! [v0: $i] : ! [v1: $i] : ( % 60.91/8.83 | ~ (sdtasdt0(v0, all_37_0) = v1) | ~ $i(v0) | ~ aElement0(v0) | % 60.91/8.83 | (sdtasdt0(all_37_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0: % 60.91/8.83 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_37_0, v0) = v1) | ~ $i(v0) | % 60.91/8.83 | ~ aElement0(v0) | (sdtasdt0(v0, all_37_0) = v1 & smndt0(v0) = v1 & % 60.91/8.83 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ % 60.91/8.83 | $i(v0) | ~ aElement0(v0) | (sdtasdt0(v0, all_37_0) = v1 & % 60.91/8.83 | sdtasdt0(all_37_0, v0) = v1 & $i(v1))) % 60.91/8.83 | % 60.91/8.83 | ALPHA: (56) implies: % 60.91/8.83 | (57) smndt0(sz10) = all_37_0 % 60.91/8.83 | (58) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 60.91/8.83 | aElement0(v0) | (sdtasdt0(v0, all_37_0) = v1 & sdtasdt0(all_37_0, % 60.91/8.83 | v0) = v1 & $i(v1))) % 60.91/8.83 | % 60.91/8.83 | GROUND_INST: instantiating (33) with all_30_2, all_37_0, sz10, simplifying % 60.91/8.83 | with (45), (57) gives: % 60.91/8.83 | (59) all_37_0 = all_30_2 % 60.91/8.83 | % 60.91/8.83 | GROUND_INST: instantiating (33) with all_28_1, all_32_4, xx, simplifying with % 60.91/8.83 | (41), (50) gives: % 60.91/8.83 | (60) all_32_4 = all_28_1 % 60.91/8.83 | % 60.91/8.83 | GROUND_INST: instantiating (34) with all_28_0, all_32_3, all_28_1, xw, % 60.91/8.83 | simplifying with (42) gives: % 60.91/8.83 | (61) all_32_3 = all_28_0 | ~ (sdtpldt0(xw, all_28_1) = all_32_3) % 60.91/8.83 | % 60.91/8.83 | GROUND_INST: instantiating (35) with all_26_0, all_32_1, xb, xx, simplifying % 60.91/8.83 | with (37), (54) gives: % 60.91/8.83 | (62) all_32_1 = all_26_0 % 60.91/8.83 | % 60.91/8.83 | GROUND_INST: instantiating (35) with all_26_1, all_32_2, xa, xy, simplifying % 60.91/8.83 | with (38), (55) gives: % 60.91/8.83 | (63) all_32_2 = all_26_1 % 60.91/8.83 | % 60.91/8.83 | REDUCE: (53), (60), (62) imply: % 60.91/8.83 | (64) sdtpldt0(all_26_0, all_28_1) = all_32_0 % 60.91/8.83 | % 60.91/8.83 | REDUCE: (52), (63) imply: % 60.91/8.83 | (65) sdtpldt0(all_26_1, all_32_0) = all_32_3 % 60.91/8.83 | % 60.91/8.83 | REDUCE: (51), (60) imply: % 60.91/8.83 | (66) sdtpldt0(xw, all_28_1) = all_32_3 % 60.91/8.83 | % 60.91/8.83 | BETA: splitting (61) gives: % 60.91/8.83 | % 60.91/8.83 | Case 1: % 60.91/8.83 | | % 60.91/8.83 | | (67) ~ (sdtpldt0(xw, all_28_1) = all_32_3) % 60.91/8.83 | | % 60.91/8.83 | | PRED_UNIFY: (66), (67) imply: % 60.91/8.83 | | (68) $false % 60.91/8.83 | | % 60.91/8.83 | | CLOSE: (68) is inconsistent. % 60.91/8.83 | | % 60.91/8.83 | Case 2: % 60.91/8.83 | | % 60.91/8.83 | | (69) all_32_3 = all_28_0 % 60.91/8.83 | | % 60.91/8.83 | | REDUCE: (65), (69) imply: % 60.91/8.83 | | (70) sdtpldt0(all_26_1, all_32_0) = all_28_0 % 60.91/8.83 | | % 60.91/8.83 | | GROUND_INST: instantiating (mEOfElem) with xI, xa, simplifying with (13), % 60.91/8.83 | | (19), (25), (30) gives: % 60.91/8.83 | | (71) aElement0(xa) % 60.91/8.83 | | % 60.91/8.83 | | GROUND_INST: instantiating (mEOfElem) with xJ, xb, simplifying with (14), % 60.91/8.83 | | (20), (21), (28) gives: % 60.91/8.83 | | (72) aElement0(xb) % 60.91/8.83 | | % 60.91/8.83 | | GROUND_INST: instantiating (mSortsU) with sz10, all_30_2, simplifying with % 60.91/8.83 | | (2), (27), (45) gives: % 60.91/8.83 | | (73) aElement0(all_30_2) % 60.91/8.83 | | % 60.91/8.83 | | GROUND_INST: instantiating (58) with sz10, all_30_2, simplifying with (2), % 60.91/8.83 | | (27), (45) gives: % 60.91/8.83 | | (74) sdtasdt0(all_37_0, sz10) = all_30_2 & sdtasdt0(sz10, all_37_0) = % 60.91/8.83 | | all_30_2 & $i(all_30_2) % 60.91/8.83 | | % 60.91/8.83 | | ALPHA: (74) implies: % 60.91/8.83 | | (75) $i(all_30_2) % 60.91/8.83 | | % 60.91/8.83 | | GROUND_INST: instantiating (7) with sz10, all_30_2, simplifying with (2), % 60.91/8.83 | | (27), (45) gives: % 60.91/8.84 | | (76) sdtpldt0(all_30_2, sz10) = sz00 & sdtpldt0(sz10, all_30_2) = sz00 % 60.91/8.84 | | % 60.91/8.84 | | ALPHA: (76) implies: % 60.91/8.84 | | (77) sdtpldt0(sz10, all_30_2) = sz00 % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (58) with xx, all_28_1, simplifying with (17), % 60.91/8.84 | | (31), (41) gives: % 60.91/8.84 | | (78) sdtasdt0(all_37_0, xx) = all_28_1 & sdtasdt0(xx, all_37_0) = % 60.91/8.84 | | all_28_1 & $i(all_28_1) % 60.91/8.84 | | % 60.91/8.84 | | ALPHA: (78) implies: % 60.91/8.84 | | (79) sdtasdt0(xx, all_37_0) = all_28_1 % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (16) with xa, xy, all_26_1, simplifying with % 60.91/8.84 | | (18), (19), (24), (25), (38) gives: % 60.91/8.84 | | (80) aElementOf0(all_26_1, xI) % 60.91/8.84 | | % 60.91/8.84 | | REDUCE: (59), (79) imply: % 60.91/8.84 | | (81) sdtasdt0(xx, all_30_2) = all_28_1 % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (8) with xa, xy, all_26_1, simplifying with (18), % 60.91/8.84 | | (24), (25), (38), (71) gives: % 60.91/8.84 | | (82) sdtasdt0(xa, xy) = all_26_1 & $i(all_26_1) % 60.91/8.84 | | % 60.91/8.84 | | ALPHA: (82) implies: % 60.91/8.84 | | (83) $i(all_26_1) % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (4) with xb, xa, sz10, simplifying with (22), % 60.91/8.84 | | (25), (28), (71), (72) gives: % 60.91/8.84 | | (84) sdtpldt0(xb, xa) = sz10 & $i(sz10) % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (15) with all_26_1, all_32_0, all_28_0, % 60.91/8.84 | | simplifying with (40), (49), (70), (80), (83) gives: % 60.91/8.84 | | (85) ~ aElementOf0(all_32_0, xI) % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (5) with xa, xb, all_30_2, sz10, sz00, % 60.91/8.84 | | simplifying with (22), (25), (28), (71), (72), (73), (75), (77) % 60.91/8.84 | | gives: % 60.91/8.84 | | (86) ? [v0: $i] : (sdtpldt0(xb, all_30_2) = v0 & sdtpldt0(xa, v0) = sz00 % 60.91/8.84 | | & $i(v0) & $i(sz00)) % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (6) with sz10, sz00, simplifying with (2), (27) % 60.91/8.84 | | gives: % 60.91/8.84 | | (87) sz10 = sz00 | ~ (sdtpldt0(sz10, sz00) = sz00) % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (3) with sz00, sz10, sz00, simplifying with (1), % 60.91/8.84 | | (2), (12), (27) gives: % 60.91/8.84 | | (88) ~ (sdtpldt0(sz00, sz10) = sz00) | sdtpldt0(sz10, sz00) = sz00 % 60.91/8.84 | | % 60.91/8.84 | | GROUND_INST: instantiating (9) with xx, xb, all_30_2, all_26_0, all_28_1, % 60.91/8.84 | | all_32_0, simplifying with (17), (28), (31), (37), (64), (72), % 60.91/8.84 | | (73), (75), (81) gives: % 60.91/8.84 | | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 60.91/8.84 | | (sdtasdt0(v0, xx) = v1 & sdtasdt0(all_30_2, xx) = v3 & sdtasdt0(xb, % 60.91/8.84 | | xx) = v2 & sdtasdt0(xx, v0) = all_32_0 & sdtpldt0(v2, v3) = v1 & % 60.91/8.84 | | sdtpldt0(xb, all_30_2) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 60.91/8.84 | | $i(all_32_0)) % 60.91/8.84 | | % 60.91/8.84 | | DELTA: instantiating (86) with fresh symbol all_86_0 gives: % 60.91/8.84 | | (90) sdtpldt0(xb, all_30_2) = all_86_0 & sdtpldt0(xa, all_86_0) = sz00 & % 60.91/8.84 | | $i(all_86_0) & $i(sz00) % 60.91/8.84 | | % 60.91/8.84 | | ALPHA: (90) implies: % 60.91/8.84 | | (91) sdtpldt0(xb, all_30_2) = all_86_0 % 60.91/8.84 | | % 60.91/8.84 | | DELTA: instantiating (89) with fresh symbols all_106_0, all_106_1, % 60.91/8.84 | | all_106_2, all_106_3 gives: % 60.91/8.84 | | (92) sdtasdt0(all_106_3, xx) = all_106_2 & sdtasdt0(all_30_2, xx) = % 60.91/8.84 | | all_106_0 & sdtasdt0(xb, xx) = all_106_1 & sdtasdt0(xx, all_106_3) = % 60.91/8.84 | | all_32_0 & sdtpldt0(all_106_1, all_106_0) = all_106_2 & sdtpldt0(xb, % 60.91/8.84 | | all_30_2) = all_106_3 & $i(all_106_0) & $i(all_106_1) & % 60.91/8.84 | | $i(all_106_2) & $i(all_106_3) & $i(all_32_0) % 60.91/8.84 | | % 60.91/8.84 | | ALPHA: (92) implies: % 60.91/8.84 | | (93) sdtpldt0(xb, all_30_2) = all_106_3 % 60.91/8.84 | | (94) sdtasdt0(xx, all_106_3) = all_32_0 % 60.91/8.84 | | % 60.91/8.84 | | BETA: splitting (87) gives: % 60.91/8.84 | | % 60.91/8.84 | | Case 1: % 60.91/8.84 | | | % 60.91/8.84 | | | (95) ~ (sdtpldt0(sz10, sz00) = sz00) % 60.91/8.84 | | | % 60.91/8.84 | | | BETA: splitting (88) gives: % 60.91/8.84 | | | % 60.91/8.84 | | | Case 1: % 60.91/8.84 | | | | % 60.91/8.84 | | | | % 60.91/8.84 | | | | GROUND_INST: instantiating (34) with all_30_1, all_106_3, all_30_2, xb, % 60.91/8.84 | | | | simplifying with (46), (93) gives: % 60.91/8.84 | | | | (96) all_106_3 = all_30_1 % 60.91/8.84 | | | | % 60.91/8.84 | | | | GROUND_INST: instantiating (34) with all_86_0, all_106_3, all_30_2, xb, % 60.91/8.84 | | | | simplifying with (91), (93) gives: % 60.91/8.84 | | | | (97) all_106_3 = all_86_0 % 60.91/8.84 | | | | % 60.91/8.84 | | | | GROUND_INST: instantiating (35) with all_30_0, all_32_0, all_30_1, xx, % 60.91/8.84 | | | | simplifying with (47) gives: % 60.91/8.84 | | | | (98) all_32_0 = all_30_0 | ~ (sdtasdt0(xx, all_30_1) = all_32_0) % 60.91/8.84 | | | | % 60.91/8.84 | | | | PRED_UNIFY: (44), (85) imply: % 60.91/8.84 | | | | (99) ~ (all_32_0 = all_30_0) % 60.91/8.84 | | | | % 60.91/8.84 | | | | COMBINE_EQS: (96), (97) imply: % 60.91/8.85 | | | | (100) all_86_0 = all_30_1 % 60.91/8.85 | | | | % 60.91/8.85 | | | | REDUCE: (94), (96) imply: % 60.91/8.85 | | | | (101) sdtasdt0(xx, all_30_1) = all_32_0 % 60.91/8.85 | | | | % 60.91/8.85 | | | | BETA: splitting (98) gives: % 60.91/8.85 | | | | % 60.91/8.85 | | | | Case 1: % 60.91/8.85 | | | | | % 60.91/8.85 | | | | | (102) ~ (sdtasdt0(xx, all_30_1) = all_32_0) % 60.91/8.85 | | | | | % 60.91/8.85 | | | | | PRED_UNIFY: (101), (102) imply: % 60.91/8.85 | | | | | (103) $false % 60.91/8.85 | | | | | % 60.91/8.85 | | | | | CLOSE: (103) is inconsistent. % 60.91/8.85 | | | | | % 60.91/8.85 | | | | Case 2: % 60.91/8.85 | | | | | % 60.91/8.85 | | | | | (104) all_32_0 = all_30_0 % 60.91/8.85 | | | | | % 60.91/8.85 | | | | | REDUCE: (99), (104) imply: % 60.91/8.85 | | | | | (105) $false % 60.91/8.85 | | | | | % 60.91/8.85 | | | | | CLOSE: (105) is inconsistent. % 60.91/8.85 | | | | | % 60.91/8.85 | | | | End of split % 60.91/8.85 | | | | % 60.91/8.85 | | | Case 2: % 60.91/8.85 | | | | % 60.91/8.85 | | | | (106) sdtpldt0(sz10, sz00) = sz00 % 60.91/8.85 | | | | % 60.91/8.85 | | | | PRED_UNIFY: (95), (106) imply: % 60.91/8.85 | | | | (107) $false % 60.91/8.85 | | | | % 60.91/8.85 | | | | CLOSE: (107) is inconsistent. % 60.91/8.85 | | | | % 60.91/8.85 | | | End of split % 60.91/8.85 | | | % 60.91/8.85 | | Case 2: % 60.91/8.85 | | | % 60.91/8.85 | | | (108) sz10 = sz00 % 60.91/8.85 | | | % 60.91/8.85 | | | REDUCE: (11), (108) imply: % 60.91/8.85 | | | (109) $false % 60.91/8.85 | | | % 60.91/8.85 | | | CLOSE: (109) is inconsistent. % 60.91/8.85 | | | % 60.91/8.85 | | End of split % 60.91/8.85 | | % 60.91/8.85 | End of split % 60.91/8.85 | % 60.91/8.85 End of proof % 60.91/8.85 % SZS output end Proof for theBenchmark % 60.91/8.85 % 60.91/8.85 8248ms %------------------------------------------------------------------------------