%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : RNG098+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 : n002.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 27.69s 4.56s % Output : Proof 30.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : RNG098+1 : TPTP v8.1.2. Released v4.0.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n002.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sun Aug 27 02:23:48 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.86/1.15 Prover 1: Preprocessing ... % 2.86/1.15 Prover 4: Preprocessing ... % 2.86/1.19 Prover 2: Preprocessing ... % 2.86/1.19 Prover 5: Preprocessing ... % 2.86/1.19 Prover 3: Preprocessing ... % 2.86/1.19 Prover 6: Preprocessing ... % 2.86/1.19 Prover 0: Preprocessing ... % 7.73/1.84 Prover 1: Constructing countermodel ... % 7.73/1.85 Prover 3: Constructing countermodel ... % 7.73/1.85 Prover 6: Proving ... % 7.73/1.86 Prover 5: Proving ... % 7.73/1.90 Prover 4: Constructing countermodel ... % 8.49/2.01 Prover 2: Proving ... % 9.78/2.14 Prover 0: Proving ... % 16.56/3.04 Prover 3: gave up % 16.56/3.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.56/3.10 Prover 7: Preprocessing ... % 17.29/3.26 Prover 7: Constructing countermodel ... % 27.69/4.56 Prover 0: proved (3924ms) % 27.69/4.56 % 27.69/4.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 27.69/4.56 % 27.69/4.57 Prover 2: stopped % 27.69/4.61 Prover 5: stopped % 27.69/4.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 27.69/4.61 Prover 6: stopped % 28.67/4.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 28.67/4.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 28.67/4.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 29.03/4.68 Prover 10: Preprocessing ... % 29.03/4.68 Prover 8: Preprocessing ... % 29.03/4.70 Prover 11: Preprocessing ... % 29.03/4.71 Prover 13: Preprocessing ... % 29.62/4.77 Prover 10: Constructing countermodel ... % 29.84/4.81 Prover 7: Found proof (size 106) % 29.84/4.81 Prover 7: proved (1771ms) % 29.84/4.82 Prover 4: stopped % 29.84/4.82 Prover 10: stopped % 29.84/4.82 Prover 1: stopped % 29.84/4.82 Prover 8: Warning: ignoring some quantifiers % 30.25/4.83 Prover 8: Constructing countermodel ... % 30.25/4.83 Prover 8: stopped % 30.37/4.87 Prover 13: Warning: ignoring some quantifiers % 30.37/4.87 Prover 13: Constructing countermodel ... % 30.37/4.88 Prover 11: Constructing countermodel ... % 30.37/4.89 Prover 13: stopped % 30.37/4.89 Prover 11: stopped % 30.37/4.89 % 30.37/4.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 30.37/4.89 % 30.37/4.91 % SZS output start Proof for theBenchmark % 30.37/4.91 Assumptions after simplification: % 30.37/4.91 --------------------------------- % 30.37/4.91 % 30.37/4.91 (mAMDistr) % 30.72/4.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 30.72/4.95 $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ % 30.72/4.95 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.72/4.95 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 30.72/4.95 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, % 30.72/4.95 v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, % 30.72/4.95 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 30.72/4.95 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 30.72/4.95 $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) % 30.72/4.95 | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.72/4.95 aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6: $i] : ? [v7: % 30.72/4.95 $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, % 30.72/4.95 v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, % 30.72/4.95 v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 30.72/4.95 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 30.72/4.95 $i] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 30.72/4.95 ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 30.72/4.95 aElement0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 30.72/4.95 [v9: $i] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) % 30.72/4.95 = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = % 30.72/4.95 v4 & sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 30.72/4.95 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 30.72/4.95 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 30.72/4.95 ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 30.72/4.95 aElement0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? % 30.72/4.95 [v9: $i] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) % 30.72/4.95 = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = % 30.72/4.95 v7 & sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 30.72/4.95 $i(v4))) % 30.72/4.95 % 30.72/4.95 (mDefIdeal) % 30.72/4.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v1) % 30.72/4.95 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ % 30.72/4.95 aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0: $i] % 30.72/4.95 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ % 30.72/4.95 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | % 30.72/4.95 ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 30.72/4.95 aIdeal0(v0) | aSet0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aSet0(v0) | % 30.72/4.95 aIdeal0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? % 30.72/4.95 [v5: $i] : ($i(v4) & $i(v2) & $i(v1) & aElementOf0(v1, v0) & ((sdtasdt0(v2, % 30.72/4.95 v1) = v3 & $i(v3) & aElement0(v2) & ~ aElementOf0(v3, v0)) | % 30.72/4.95 (sdtpldt0(v1, v4) = v5 & $i(v5) & aElementOf0(v4, v0) & ~ % 30.72/4.95 aElementOf0(v5, v0))))) % 30.72/4.95 % 30.72/4.95 (mEOfElem) % 30.72/4.95 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 30.72/4.95 ~ aSet0(v0) | aElement0(v1)) % 30.72/4.95 % 30.72/4.95 (mMulAsso) % 30.72/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 30.72/4.96 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 30.72/4.96 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? % 30.72/4.96 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) & % 30.72/4.96 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 30.72/4.96 $i] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ $i(v2) | % 30.72/4.96 ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 30.72/4.96 aElement0(v0) | ? [v5: $i] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5 % 30.72/4.96 & $i(v5) & $i(v4))) % 30.72/4.96 % 30.72/4.96 (mMulComm) % 30.72/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 30.72/4.96 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v0, v1) % 30.72/4.96 = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 30.72/4.96 (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ % 30.72/4.96 aElement0(v0) | (sdtasdt0(v1, v0) = v2 & $i(v2))) % 30.72/4.96 % 30.72/4.96 (mMulMnOne) % 30.72/4.96 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 30.72/4.96 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 30.72/4.96 (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 30.72/4.96 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 30.72/4.96 (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : ! % 30.72/4.96 [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 30.72/4.96 (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & $i(v2)))) % 30.72/4.96 % 30.72/4.96 (mSortsB) % 30.72/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 30.72/4.96 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) % 30.72/4.96 % 30.72/4.96 (mSortsC_01) % 30.72/4.96 $i(sz10) & aElement0(sz10) % 30.72/4.96 % 30.72/4.96 (mSortsU) % 30.72/4.96 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 30.72/4.96 aElement0(v0) | aElement0(v1)) % 30.72/4.96 % 30.72/4.96 (m__) % 30.72/4.96 $i(xw) & $i(xx) & $i(xI) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 % 30.72/4.96 & smndt0(xx) = v0 & $i(v1) & $i(v0) & ~ aElementOf0(v1, xI)) % 30.72/4.96 % 30.72/4.96 (m__1205) % 30.72/4.96 $i(xJ) & $i(xI) & aIdeal0(xJ) & aIdeal0(xI) % 30.72/4.96 % 30.72/4.96 (m__1217) % 30.72/4.96 $i(xy) & $i(xx) & aElement0(xy) & aElement0(xx) % 30.72/4.96 % 30.72/4.96 (m__1294) % 30.72/4.96 sdtpldt0(xa, xb) = sz10 & $i(xb) & $i(xa) & $i(xJ) & $i(xI) & $i(sz10) & % 30.72/4.96 aElementOf0(xb, xJ) & aElementOf0(xa, xI) % 30.72/4.96 % 30.72/4.96 (m__1319) % 30.72/4.97 $i(xw) & $i(xb) & $i(xa) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : % 30.72/4.97 (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) = v1 & sdtpldt0(v0, v1) = xw & % 30.72/4.97 $i(v1) & $i(v0)) % 30.72/4.97 % 30.72/4.97 (m__1374) % 30.96/4.97 $i(xw) & $i(xb) & $i(xa) & $i(xy) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ? % 30.96/4.97 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(xy, xa) = v2 & sdtasdt0(xx, % 30.96/4.97 xb) = v3 & sdtpldt0(v3, v0) = v4 & sdtpldt0(v2, v4) = v1 & sdtpldt0(xw, % 30.96/4.97 v0) = v1 & smndt0(xx) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 30.96/4.97 % 30.96/4.97 (m__1393) % 30.96/4.97 $i(xb) & $i(xx) & $i(xI) & $i(sz10) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] % 30.96/4.97 : (sdtasdt0(xx, v1) = v2 & sdtpldt0(xb, v0) = v1 & smndt0(sz10) = v0 & $i(v2) % 30.96/4.97 & $i(v1) & $i(v0) & aElementOf0(v2, xI)) % 30.96/4.97 % 30.96/4.97 (function-axioms) % 30.96/4.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.96/4.97 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.96/4.97 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | % 30.96/4.97 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 30.96/4.97 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 30.96/4.97 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.96/4.97 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.96/4.97 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = % 30.96/4.97 v0)) % 30.96/4.97 % 30.96/4.97 Further assumptions not needed in the proof: % 30.96/4.97 -------------------------------------------- % 30.96/4.97 mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mDefMod, mDefSInt, mDefSSum, % 30.96/4.97 mElmSort, mIdeInt, mIdeSum, mMulUnit, mMulZero, mSetEq, mSetSort, mSortsB_02, % 30.96/4.97 mSortsC, mUnNeZr, m__1205_03 % 30.96/4.97 % 30.96/4.97 Those formulas are unsatisfiable: % 30.96/4.97 --------------------------------- % 30.96/4.97 % 30.96/4.97 Begin of proof % 30.96/4.97 | % 30.96/4.97 | ALPHA: (mSortsC_01) implies: % 30.96/4.97 | (1) aElement0(sz10) % 30.96/4.97 | % 30.96/4.97 | ALPHA: (mMulComm) implies: % 30.96/4.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | % 30.96/4.97 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | % 30.96/4.97 | (sdtasdt0(v0, v1) = v2 & $i(v2))) % 30.96/4.97 | % 30.96/4.97 | ALPHA: (mMulAsso) implies: % 30.96/4.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 30.96/4.97 | ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ $i(v2) | % 30.96/4.97 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 30.96/4.97 | aElement0(v0) | ? [v5: $i] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, % 30.96/4.97 | v1) = v5 & $i(v5) & $i(v4))) % 30.96/4.98 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 30.96/4.98 | ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | % 30.96/4.98 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 30.96/4.98 | aElement0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 30.96/4.98 | v5) = v4 & $i(v5) & $i(v4))) % 30.96/4.98 | % 30.96/4.98 | ALPHA: (mAMDistr) implies: % 30.96/4.98 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 30.96/4.98 | ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 30.96/4.98 | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ % 30.96/4.98 | aElement0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 30.96/4.98 | : ? [v9: $i] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & % 30.96/4.98 | sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = % 30.96/4.98 | v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4 & $i(v9) & % 30.96/4.98 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4))) % 30.96/4.98 | % 30.96/4.98 | ALPHA: (mMulMnOne) implies: % 30.96/4.98 | (6) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 30.96/4.98 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ aElement0(v1) | % 30.96/4.98 | (sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))) & ! [v1: $i] : % 30.96/4.98 | ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ % 30.96/4.98 | aElement0(v1) | (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))) % 30.96/4.98 | & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ~ % 30.96/4.98 | aElement0(v1) | (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1) = v2 & % 30.96/4.98 | $i(v2)))) % 30.96/4.98 | % 30.96/4.98 | ALPHA: (mDefIdeal) implies: % 30.96/4.98 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ aIdeal0(v0) | aSet0(v0)) % 30.96/4.98 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 30.96/4.98 | (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.96/4.98 | aIdeal0(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) | % 30.96/4.98 | aElementOf0(v3, v0)) % 30.96/4.98 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 30.96/4.98 | (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.96/4.98 | aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) | % 30.96/4.98 | aElementOf0(v3, v0)) % 30.96/4.98 | % 30.96/4.98 | ALPHA: (m__1205) implies: % 30.96/4.98 | (10) aIdeal0(xI) % 30.96/4.98 | (11) aIdeal0(xJ) % 30.96/4.98 | % 30.96/4.98 | ALPHA: (m__1217) implies: % 30.96/4.98 | (12) aElement0(xx) % 30.96/4.98 | (13) aElement0(xy) % 30.96/4.98 | % 30.96/4.98 | ALPHA: (m__1294) implies: % 30.96/4.98 | (14) aElementOf0(xa, xI) % 30.96/4.98 | (15) aElementOf0(xb, xJ) % 30.96/4.98 | (16) $i(xJ) % 30.96/4.98 | % 30.96/4.98 | ALPHA: (m__1319) implies: % 30.96/4.98 | (17) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xy, xa) = v0 & sdtasdt0(xx, xb) % 30.96/4.98 | = v1 & sdtpldt0(v0, v1) = xw & $i(v1) & $i(v0)) % 30.96/4.98 | % 30.96/4.99 | ALPHA: (m__1374) implies: % 30.96/4.99 | (18) $i(xy) % 30.96/4.99 | (19) $i(xa) % 30.96/4.99 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 30.96/4.99 | (sdtasdt0(xy, xa) = v2 & sdtasdt0(xx, xb) = v3 & sdtpldt0(v3, v0) = v4 % 30.96/4.99 | & sdtpldt0(v2, v4) = v1 & sdtpldt0(xw, v0) = v1 & smndt0(xx) = v0 & % 30.96/4.99 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 30.96/4.99 | % 30.96/4.99 | ALPHA: (m__1393) implies: % 30.96/4.99 | (21) $i(sz10) % 30.96/4.99 | (22) $i(xb) % 30.96/4.99 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xx, v1) = v2 & % 30.96/4.99 | sdtpldt0(xb, v0) = v1 & smndt0(sz10) = v0 & $i(v2) & $i(v1) & $i(v0) % 30.96/4.99 | & aElementOf0(v2, xI)) % 30.96/4.99 | % 30.96/4.99 | ALPHA: (m__) implies: % 30.96/4.99 | (24) $i(xI) % 30.96/4.99 | (25) $i(xx) % 30.96/4.99 | (26) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(xw, v0) = v1 & smndt0(xx) = v0 & % 30.96/4.99 | $i(v1) & $i(v0) & ~ aElementOf0(v1, xI)) % 30.96/4.99 | % 30.96/4.99 | ALPHA: (function-axioms) implies: % 30.96/4.99 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = % 30.96/4.99 | v1) | ~ (smndt0(v2) = v0)) % 30.96/4.99 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.96/4.99 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 30.96/4.99 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.96/4.99 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 30.96/4.99 | % 30.96/4.99 | DELTA: instantiating (26) with fresh symbols all_25_0, all_25_1 gives: % 30.96/4.99 | (30) sdtpldt0(xw, all_25_1) = all_25_0 & smndt0(xx) = all_25_1 & % 30.96/4.99 | $i(all_25_0) & $i(all_25_1) & ~ aElementOf0(all_25_0, xI) % 30.96/4.99 | % 30.96/4.99 | ALPHA: (30) implies: % 30.96/4.99 | (31) ~ aElementOf0(all_25_0, xI) % 30.96/4.99 | (32) smndt0(xx) = all_25_1 % 30.96/4.99 | (33) sdtpldt0(xw, all_25_1) = all_25_0 % 30.96/4.99 | % 30.96/4.99 | DELTA: instantiating (17) with fresh symbols all_30_0, all_30_1 gives: % 30.96/4.99 | (34) sdtasdt0(xy, xa) = all_30_1 & sdtasdt0(xx, xb) = all_30_0 & % 30.96/4.99 | sdtpldt0(all_30_1, all_30_0) = xw & $i(all_30_0) & $i(all_30_1) % 30.96/4.99 | % 30.96/4.99 | ALPHA: (34) implies: % 30.96/4.99 | (35) sdtasdt0(xx, xb) = all_30_0 % 30.96/4.99 | (36) sdtasdt0(xy, xa) = all_30_1 % 30.96/4.99 | % 30.96/4.99 | DELTA: instantiating (23) with fresh symbols all_32_0, all_32_1, all_32_2 % 30.96/4.99 | gives: % 30.96/4.99 | (37) sdtasdt0(xx, all_32_1) = all_32_0 & sdtpldt0(xb, all_32_2) = all_32_1 % 30.96/4.99 | & smndt0(sz10) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) % 30.96/4.99 | & aElementOf0(all_32_0, xI) % 30.96/4.99 | % 30.96/4.99 | ALPHA: (37) implies: % 30.96/4.99 | (38) aElementOf0(all_32_0, xI) % 30.96/4.99 | (39) $i(all_32_0) % 30.96/4.99 | (40) smndt0(sz10) = all_32_2 % 30.96/4.99 | (41) sdtpldt0(xb, all_32_2) = all_32_1 % 30.96/4.99 | (42) sdtasdt0(xx, all_32_1) = all_32_0 % 30.96/4.99 | % 30.96/4.99 | DELTA: instantiating (20) with fresh symbols all_34_0, all_34_1, all_34_2, % 30.96/4.99 | all_34_3, all_34_4 gives: % 30.96/5.00 | (43) sdtasdt0(xy, xa) = all_34_2 & sdtasdt0(xx, xb) = all_34_1 & % 30.96/5.00 | sdtpldt0(all_34_1, all_34_4) = all_34_0 & sdtpldt0(all_34_2, all_34_0) % 30.96/5.00 | = all_34_3 & sdtpldt0(xw, all_34_4) = all_34_3 & smndt0(xx) = all_34_4 % 30.96/5.00 | & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) & $i(all_34_3) & % 30.96/5.00 | $i(all_34_4) % 30.96/5.00 | % 30.96/5.00 | ALPHA: (43) implies: % 30.96/5.00 | (44) $i(all_34_2) % 30.96/5.00 | (45) $i(all_34_1) % 30.96/5.00 | (46) smndt0(xx) = all_34_4 % 30.96/5.00 | (47) sdtpldt0(xw, all_34_4) = all_34_3 % 30.96/5.00 | (48) sdtpldt0(all_34_2, all_34_0) = all_34_3 % 30.96/5.00 | (49) sdtpldt0(all_34_1, all_34_4) = all_34_0 % 30.96/5.00 | (50) sdtasdt0(xx, xb) = all_34_1 % 30.96/5.00 | (51) sdtasdt0(xy, xa) = all_34_2 % 30.96/5.00 | % 30.96/5.00 | DELTA: instantiating (6) with fresh symbol all_36_0 gives: % 30.96/5.00 | (52) smndt0(sz10) = all_36_0 & $i(all_36_0) & ! [v0: $i] : ! [v1: $i] : ( % 30.96/5.00 | ~ (sdtasdt0(v0, all_36_0) = v1) | ~ $i(v0) | ~ aElement0(v0) | % 30.96/5.00 | (sdtasdt0(all_36_0, v0) = v1 & smndt0(v0) = v1 & $i(v1))) & ! [v0: % 30.96/5.00 | $i] : ! [v1: $i] : ( ~ (sdtasdt0(all_36_0, v0) = v1) | ~ $i(v0) | % 30.96/5.00 | ~ aElement0(v0) | (sdtasdt0(v0, all_36_0) = v1 & smndt0(v0) = v1 & % 30.96/5.00 | $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ % 30.96/5.00 | $i(v0) | ~ aElement0(v0) | (sdtasdt0(v0, all_36_0) = v1 & % 30.96/5.00 | sdtasdt0(all_36_0, v0) = v1 & $i(v1))) % 30.96/5.00 | % 30.96/5.00 | ALPHA: (52) implies: % 30.96/5.00 | (53) smndt0(sz10) = all_36_0 % 30.96/5.00 | (54) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~ % 30.96/5.00 | aElement0(v0) | (sdtasdt0(v0, all_36_0) = v1 & sdtasdt0(all_36_0, % 30.96/5.00 | v0) = v1 & $i(v1))) % 30.96/5.00 | % 30.96/5.00 | GROUND_INST: instantiating (27) with all_32_2, all_36_0, sz10, simplifying % 30.96/5.00 | with (40), (53) gives: % 30.96/5.00 | (55) all_36_0 = all_32_2 % 30.96/5.00 | % 30.96/5.00 | GROUND_INST: instantiating (27) with all_25_1, all_34_4, xx, simplifying with % 30.96/5.00 | (32), (46) gives: % 30.96/5.00 | (56) all_34_4 = all_25_1 % 30.96/5.00 | % 30.96/5.00 | GROUND_INST: instantiating (28) with all_25_0, all_34_3, all_25_1, xw, % 30.96/5.00 | simplifying with (33) gives: % 30.96/5.00 | (57) all_34_3 = all_25_0 | ~ (sdtpldt0(xw, all_25_1) = all_34_3) % 30.96/5.00 | % 30.96/5.00 | GROUND_INST: instantiating (29) with all_30_0, all_34_1, xb, xx, simplifying % 30.96/5.00 | with (35), (50) gives: % 30.96/5.00 | (58) all_34_1 = all_30_0 % 30.96/5.00 | % 30.96/5.00 | GROUND_INST: instantiating (29) with all_30_1, all_34_2, xa, xy, simplifying % 30.96/5.00 | with (36), (51) gives: % 30.96/5.00 | (59) all_34_2 = all_30_1 % 30.96/5.00 | % 30.96/5.00 | REDUCE: (49), (56), (58) imply: % 30.96/5.00 | (60) sdtpldt0(all_30_0, all_25_1) = all_34_0 % 30.96/5.00 | % 30.96/5.00 | REDUCE: (48), (59) imply: % 30.96/5.00 | (61) sdtpldt0(all_30_1, all_34_0) = all_34_3 % 30.96/5.00 | % 30.96/5.00 | REDUCE: (47), (56) imply: % 30.96/5.00 | (62) sdtpldt0(xw, all_25_1) = all_34_3 % 30.96/5.00 | % 30.96/5.00 | REDUCE: (45), (58) imply: % 30.96/5.00 | (63) $i(all_30_0) % 30.96/5.00 | % 30.96/5.00 | REDUCE: (44), (59) imply: % 30.96/5.00 | (64) $i(all_30_1) % 30.96/5.00 | % 30.96/5.00 | BETA: splitting (57) gives: % 30.96/5.00 | % 30.96/5.01 | Case 1: % 30.96/5.01 | | % 30.96/5.01 | | (65) ~ (sdtpldt0(xw, all_25_1) = all_34_3) % 30.96/5.01 | | % 30.96/5.01 | | PRED_UNIFY: (62), (65) imply: % 30.96/5.01 | | (66) $false % 30.96/5.01 | | % 30.96/5.01 | | CLOSE: (66) is inconsistent. % 30.96/5.01 | | % 30.96/5.01 | Case 2: % 30.96/5.01 | | % 30.96/5.01 | | (67) all_34_3 = all_25_0 % 30.96/5.01 | | % 30.96/5.01 | | REDUCE: (61), (67) imply: % 30.96/5.01 | | (68) sdtpldt0(all_30_1, all_34_0) = all_25_0 % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (7) with xJ, simplifying with (11), (16) gives: % 30.96/5.01 | | (69) aSet0(xJ) % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (mSortsU) with sz10, all_32_2, simplifying with % 30.96/5.01 | | (1), (21), (40) gives: % 30.96/5.01 | | (70) aElement0(all_32_2) % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (54) with sz10, all_32_2, simplifying with (1), % 30.96/5.01 | | (21), (40) gives: % 30.96/5.01 | | (71) sdtasdt0(all_36_0, sz10) = all_32_2 & sdtasdt0(sz10, all_36_0) = % 30.96/5.01 | | all_32_2 & $i(all_32_2) % 30.96/5.01 | | % 30.96/5.01 | | ALPHA: (71) implies: % 30.96/5.01 | | (72) $i(all_32_2) % 30.96/5.01 | | (73) sdtasdt0(sz10, all_36_0) = all_32_2 % 30.96/5.01 | | (74) sdtasdt0(all_36_0, sz10) = all_32_2 % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (mSortsU) with xx, all_25_1, simplifying with % 30.96/5.01 | | (12), (25), (32) gives: % 30.96/5.01 | | (75) aElement0(all_25_1) % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (54) with xx, all_25_1, simplifying with (12), % 30.96/5.01 | | (25), (32) gives: % 30.96/5.01 | | (76) sdtasdt0(all_36_0, xx) = all_25_1 & sdtasdt0(xx, all_36_0) = % 30.96/5.01 | | all_25_1 & $i(all_25_1) % 30.96/5.01 | | % 30.96/5.01 | | ALPHA: (76) implies: % 30.96/5.01 | | (77) $i(all_25_1) % 30.96/5.01 | | (78) sdtasdt0(xx, all_36_0) = all_25_1 % 30.96/5.01 | | (79) sdtasdt0(all_36_0, xx) = all_25_1 % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (9) with xJ, xb, xx, all_30_0, simplifying with % 30.96/5.01 | | (11), (12), (15), (16), (22), (25), (35) gives: % 30.96/5.01 | | (80) aElementOf0(all_30_0, xJ) % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (9) with xI, xa, xy, all_30_1, simplifying with % 30.96/5.01 | | (10), (13), (14), (18), (19), (24), (36) gives: % 30.96/5.01 | | (81) aElementOf0(all_30_1, xI) % 30.96/5.01 | | % 30.96/5.01 | | REDUCE: (55), (79) imply: % 30.96/5.01 | | (82) sdtasdt0(all_32_2, xx) = all_25_1 % 30.96/5.01 | | % 30.96/5.01 | | REDUCE: (55), (74) imply: % 30.96/5.01 | | (83) sdtasdt0(all_32_2, sz10) = all_32_2 % 30.96/5.01 | | % 30.96/5.01 | | REDUCE: (55), (78) imply: % 30.96/5.01 | | (84) sdtasdt0(xx, all_32_2) = all_25_1 % 30.96/5.01 | | % 30.96/5.01 | | REDUCE: (55), (73) imply: % 30.96/5.01 | | (85) sdtasdt0(sz10, all_32_2) = all_32_2 % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (2) with xb, xx, all_30_0, simplifying with (12), % 30.96/5.01 | | (22), (25), (35) gives: % 30.96/5.01 | | (86) ~ aElement0(xb) | (sdtasdt0(xb, xx) = all_30_0 & $i(all_30_0)) % 30.96/5.01 | | % 30.96/5.01 | | GROUND_INST: instantiating (5) with xx, xb, all_32_2, all_32_1, all_32_0, % 30.96/5.01 | | simplifying with (12), (22), (25), (41), (42), (70), (72) % 30.96/5.01 | | gives: % 30.96/5.02 | | (87) ~ aElement0(xb) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 30.96/5.02 | | $i] : ? [v4: $i] : (sdtasdt0(all_32_1, xx) = v2 & % 30.96/5.02 | | sdtasdt0(all_32_2, xx) = v4 & sdtasdt0(xb, xx) = v3 & sdtasdt0(xx, % 30.96/5.02 | | all_32_2) = v1 & sdtasdt0(xx, xb) = v0 & sdtpldt0(v3, v4) = v2 & % 30.96/5.02 | | sdtpldt0(v0, v1) = all_32_0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 30.96/5.02 | | $i(v0) & $i(all_32_0)) % 30.96/5.02 | | % 30.96/5.02 | | GROUND_INST: instantiating (mSortsB) with all_30_0, all_25_1, all_34_0, % 30.96/5.02 | | simplifying with (60), (63), (75), (77) gives: % 30.96/5.02 | | (88) ~ aElement0(all_30_0) | aElement0(all_34_0) % 30.96/5.02 | | % 30.96/5.02 | | GROUND_INST: instantiating (mEOfElem) with xJ, xb, simplifying with (15), % 30.96/5.02 | | (16), (22), (69) gives: % 30.96/5.02 | | (89) aElement0(xb) % 30.96/5.02 | | % 30.96/5.02 | | GROUND_INST: instantiating (8) with xI, all_30_1, all_32_0, all_25_0, % 30.96/5.02 | | simplifying with (10), (24), (31), (38), (39), (64), (81) % 30.96/5.02 | | gives: % 30.96/5.02 | | (90) ~ (sdtpldt0(all_30_1, all_32_0) = all_25_0) % 30.96/5.02 | | % 30.96/5.02 | | GROUND_INST: instantiating (mEOfElem) with xJ, all_30_0, simplifying with % 30.96/5.02 | | (16), (63), (69), (80) gives: % 30.96/5.02 | | (91) aElement0(all_30_0) % 30.96/5.02 | | % 30.96/5.02 | | GROUND_INST: instantiating (3) with xx, all_32_2, sz10, all_32_2, all_25_1, % 30.96/5.02 | | simplifying with (1), (12), (21), (25), (70), (72), (83), (84) % 30.96/5.02 | | gives: % 30.96/5.02 | | (92) ? [v0: $i] : (sdtasdt0(v0, sz10) = all_25_1 & sdtasdt0(xx, % 30.96/5.02 | | all_32_2) = v0 & $i(v0) & $i(all_25_1)) % 30.96/5.02 | | % 30.96/5.02 | | GROUND_INST: instantiating (4) with sz10, all_32_2, xx, all_32_2, all_25_1, % 30.96/5.02 | | simplifying with (1), (12), (21), (25), (70), (72), (82), (85) % 30.96/5.02 | | gives: % 30.96/5.02 | | (93) ? [v0: $i] : (sdtasdt0(all_32_2, xx) = v0 & sdtasdt0(sz10, v0) = % 30.96/5.02 | | all_25_1 & $i(v0) & $i(all_25_1)) % 30.96/5.02 | | % 30.96/5.02 | | DELTA: instantiating (93) with fresh symbol all_67_0 gives: % 30.96/5.02 | | (94) sdtasdt0(all_32_2, xx) = all_67_0 & sdtasdt0(sz10, all_67_0) = % 30.96/5.02 | | all_25_1 & $i(all_67_0) & $i(all_25_1) % 30.96/5.02 | | % 30.96/5.02 | | ALPHA: (94) implies: % 30.96/5.02 | | (95) sdtasdt0(all_32_2, xx) = all_67_0 % 30.96/5.02 | | % 30.96/5.02 | | DELTA: instantiating (92) with fresh symbol all_73_0 gives: % 30.96/5.02 | | (96) sdtasdt0(all_73_0, sz10) = all_25_1 & sdtasdt0(xx, all_32_2) = % 30.96/5.02 | | all_73_0 & $i(all_73_0) & $i(all_25_1) % 30.96/5.02 | | % 30.96/5.02 | | ALPHA: (96) implies: % 30.96/5.02 | | (97) sdtasdt0(xx, all_32_2) = all_73_0 % 30.96/5.02 | | % 30.96/5.02 | | BETA: splitting (86) gives: % 30.96/5.02 | | % 30.96/5.02 | | Case 1: % 30.96/5.02 | | | % 30.96/5.02 | | | (98) ~ aElement0(xb) % 30.96/5.02 | | | % 30.96/5.02 | | | PRED_UNIFY: (89), (98) imply: % 30.96/5.02 | | | (99) $false % 30.96/5.02 | | | % 30.96/5.02 | | | CLOSE: (99) is inconsistent. % 30.96/5.02 | | | % 30.96/5.02 | | Case 2: % 30.96/5.02 | | | % 30.96/5.02 | | | (100) sdtasdt0(xb, xx) = all_30_0 & $i(all_30_0) % 30.96/5.02 | | | % 30.96/5.02 | | | ALPHA: (100) implies: % 30.96/5.02 | | | (101) sdtasdt0(xb, xx) = all_30_0 % 30.96/5.02 | | | % 30.96/5.02 | | | BETA: splitting (87) gives: % 30.96/5.02 | | | % 30.96/5.02 | | | Case 1: % 30.96/5.02 | | | | % 30.96/5.02 | | | | (102) ~ aElement0(xb) % 30.96/5.02 | | | | % 30.96/5.02 | | | | PRED_UNIFY: (89), (102) imply: % 30.96/5.02 | | | | (103) $false % 30.96/5.02 | | | | % 30.96/5.02 | | | | CLOSE: (103) is inconsistent. % 30.96/5.02 | | | | % 30.96/5.02 | | | Case 2: % 30.96/5.02 | | | | % 30.96/5.02 | | | | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 30.96/5.02 | | | | $i] : (sdtasdt0(all_32_1, xx) = v2 & sdtasdt0(all_32_2, xx) = % 30.96/5.02 | | | | v4 & sdtasdt0(xb, xx) = v3 & sdtasdt0(xx, all_32_2) = v1 & % 30.96/5.02 | | | | sdtasdt0(xx, xb) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, % 30.96/5.02 | | | | v1) = all_32_0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) % 30.96/5.02 | | | | & $i(all_32_0)) % 30.96/5.02 | | | | % 30.96/5.02 | | | | DELTA: instantiating (104) with fresh symbols all_102_0, all_102_1, % 30.96/5.02 | | | | all_102_2, all_102_3, all_102_4 gives: % 30.96/5.02 | | | | (105) sdtasdt0(all_32_1, xx) = all_102_2 & sdtasdt0(all_32_2, xx) = % 30.96/5.02 | | | | all_102_0 & sdtasdt0(xb, xx) = all_102_1 & sdtasdt0(xx, % 30.96/5.02 | | | | all_32_2) = all_102_3 & sdtasdt0(xx, xb) = all_102_4 & % 30.96/5.02 | | | | sdtpldt0(all_102_1, all_102_0) = all_102_2 & % 30.96/5.02 | | | | sdtpldt0(all_102_4, all_102_3) = all_32_0 & $i(all_102_0) & % 30.96/5.02 | | | | $i(all_102_1) & $i(all_102_2) & $i(all_102_3) & $i(all_102_4) & % 30.96/5.02 | | | | $i(all_32_0) % 30.96/5.02 | | | | % 30.96/5.02 | | | | ALPHA: (105) implies: % 30.96/5.02 | | | | (106) sdtpldt0(all_102_4, all_102_3) = all_32_0 % 30.96/5.02 | | | | (107) sdtpldt0(all_102_1, all_102_0) = all_102_2 % 30.96/5.02 | | | | (108) sdtasdt0(xx, xb) = all_102_4 % 30.96/5.02 | | | | (109) sdtasdt0(xx, all_32_2) = all_102_3 % 30.96/5.02 | | | | (110) sdtasdt0(xb, xx) = all_102_1 % 30.96/5.02 | | | | (111) sdtasdt0(all_32_2, xx) = all_102_0 % 30.96/5.02 | | | | % 30.96/5.02 | | | | BETA: splitting (88) gives: % 30.96/5.02 | | | | % 30.96/5.02 | | | | Case 1: % 30.96/5.02 | | | | | % 30.96/5.02 | | | | | (112) ~ aElement0(all_30_0) % 30.96/5.02 | | | | | % 30.96/5.02 | | | | | PRED_UNIFY: (91), (112) imply: % 30.96/5.02 | | | | | (113) $false % 30.96/5.02 | | | | | % 30.96/5.02 | | | | | CLOSE: (113) is inconsistent. % 30.96/5.02 | | | | | % 30.96/5.02 | | | | Case 2: % 30.96/5.02 | | | | | % 30.96/5.02 | | | | | % 30.96/5.02 | | | | | GROUND_INST: instantiating (29) with all_30_0, all_102_4, xb, xx, % 30.96/5.02 | | | | | simplifying with (35), (108) gives: % 30.96/5.02 | | | | | (114) all_102_4 = all_30_0 % 30.96/5.02 | | | | | % 30.96/5.03 | | | | | GROUND_INST: instantiating (29) with all_25_1, all_102_3, all_32_2, % 30.96/5.03 | | | | | xx, simplifying with (84), (109) gives: % 30.96/5.03 | | | | | (115) all_102_3 = all_25_1 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | GROUND_INST: instantiating (29) with all_73_0, all_102_3, all_32_2, % 30.96/5.03 | | | | | xx, simplifying with (97), (109) gives: % 30.96/5.03 | | | | | (116) all_102_3 = all_73_0 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | GROUND_INST: instantiating (29) with all_30_0, all_102_1, xx, xb, % 30.96/5.03 | | | | | simplifying with (101), (110) gives: % 30.96/5.03 | | | | | (117) all_102_1 = all_30_0 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | GROUND_INST: instantiating (29) with all_25_1, all_102_0, xx, % 30.96/5.03 | | | | | all_32_2, simplifying with (82), (111) gives: % 30.96/5.03 | | | | | (118) all_102_0 = all_25_1 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | GROUND_INST: instantiating (29) with all_67_0, all_102_0, xx, % 30.96/5.03 | | | | | all_32_2, simplifying with (95), (111) gives: % 30.96/5.03 | | | | | (119) all_102_0 = all_67_0 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | PRED_UNIFY: (68), (90) imply: % 30.96/5.03 | | | | | (120) ~ (all_34_0 = all_32_0) % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | COMBINE_EQS: (118), (119) imply: % 30.96/5.03 | | | | | (121) all_67_0 = all_25_1 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | COMBINE_EQS: (115), (116) imply: % 30.96/5.03 | | | | | (122) all_73_0 = all_25_1 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | REDUCE: (107), (117), (118) imply: % 30.96/5.03 | | | | | (123) sdtpldt0(all_30_0, all_25_1) = all_102_2 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | REDUCE: (106), (114), (115) imply: % 30.96/5.03 | | | | | (124) sdtpldt0(all_30_0, all_25_1) = all_32_0 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | GROUND_INST: instantiating (28) with all_34_0, all_102_2, all_25_1, % 30.96/5.03 | | | | | all_30_0, simplifying with (60), (123) gives: % 30.96/5.03 | | | | | (125) all_102_2 = all_34_0 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | GROUND_INST: instantiating (28) with all_32_0, all_102_2, all_25_1, % 30.96/5.03 | | | | | all_30_0, simplifying with (123), (124) gives: % 30.96/5.03 | | | | | (126) all_102_2 = all_32_0 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | COMBINE_EQS: (125), (126) imply: % 30.96/5.03 | | | | | (127) all_34_0 = all_32_0 % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | REDUCE: (120), (127) imply: % 30.96/5.03 | | | | | (128) $false % 30.96/5.03 | | | | | % 30.96/5.03 | | | | | CLOSE: (128) is inconsistent. % 30.96/5.03 | | | | | % 30.96/5.03 | | | | End of split % 30.96/5.03 | | | | % 30.96/5.03 | | | End of split % 30.96/5.03 | | | % 30.96/5.03 | | End of split % 30.96/5.03 | | % 30.96/5.03 | End of split % 30.96/5.03 | % 30.96/5.03 End of proof % 30.96/5.03 % SZS output end Proof for theBenchmark % 30.96/5.03 % 30.96/5.03 4410ms %------------------------------------------------------------------------------