%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM525+3 : 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 11:48:23 EDT 2023 % Result : Theorem 14.59s 2.70s % Output : Proof 30.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM525+3 : TPTP v8.1.2. Released v4.0.0. % 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n002.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Aug 25 09:53:02 EDT 2023 % 0.12/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.27/1.18 Prover 4: Preprocessing ... % 3.27/1.18 Prover 1: Preprocessing ... % 3.91/1.22 Prover 0: Preprocessing ... % 3.91/1.22 Prover 2: Preprocessing ... % 3.91/1.22 Prover 5: Preprocessing ... % 3.91/1.22 Prover 3: Preprocessing ... % 3.91/1.22 Prover 6: Preprocessing ... % 8.55/1.98 Prover 1: Constructing countermodel ... % 10.05/2.10 Prover 3: Constructing countermodel ... % 10.73/2.15 Prover 6: Proving ... % 10.73/2.20 Prover 5: Constructing countermodel ... % 12.29/2.37 Prover 2: Proving ... % 12.68/2.43 Prover 4: Constructing countermodel ... % 13.68/2.56 Prover 0: Proving ... % 14.59/2.70 Prover 3: proved (2085ms) % 14.59/2.70 % 14.59/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.59/2.70 % 14.59/2.70 Prover 5: stopped % 14.59/2.71 Prover 2: stopped % 14.59/2.72 Prover 6: stopped % 14.59/2.72 Prover 0: stopped % 14.59/2.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 14.59/2.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 14.59/2.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.08/2.73 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.08/2.73 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.17/2.79 Prover 7: Preprocessing ... % 15.70/2.86 Prover 8: Preprocessing ... % 15.70/2.86 Prover 13: Preprocessing ... % 15.70/2.86 Prover 11: Preprocessing ... % 16.09/2.87 Prover 10: Preprocessing ... % 17.37/3.04 Prover 10: Constructing countermodel ... % 17.45/3.05 Prover 7: Constructing countermodel ... % 17.95/3.14 Prover 13: Constructing countermodel ... % 17.95/3.14 Prover 8: Warning: ignoring some quantifiers % 18.38/3.16 Prover 8: Constructing countermodel ... % 20.49/3.49 Prover 11: Constructing countermodel ... % 30.18/4.70 Prover 10: Found proof (size 172) % 30.18/4.70 Prover 10: proved (1977ms) % 30.18/4.70 Prover 4: stopped % 30.18/4.70 Prover 11: stopped % 30.18/4.70 Prover 13: stopped % 30.18/4.70 Prover 7: stopped % 30.18/4.70 Prover 1: stopped % 30.18/4.71 Prover 8: stopped % 30.18/4.71 % 30.18/4.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 30.18/4.71 % 30.18/4.73 % SZS output start Proof for theBenchmark % 30.18/4.73 Assumptions after simplification: % 30.18/4.73 --------------------------------- % 30.18/4.73 % 30.18/4.73 (mAddComm) % 30.44/4.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 30.44/4.75 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 30.44/4.75 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 30.44/4.75 % 30.44/4.75 (mDefDiv) % 30.44/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ % 30.44/4.76 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 30.44/4.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0: % 30.44/4.76 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 30.44/4.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0, % 30.44/4.76 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 30.44/4.76 % 30.44/4.76 (mDefLE) % 30.44/4.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 30.44/4.76 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 30.44/4.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 30.44/4.76 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 30.44/4.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 30.44/4.76 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 30.44/4.76 % 30.44/4.76 (mDefPrime) % 30.44/4.76 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 30.44/4.76 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 30.44/4.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 30.44/4.76 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 30.44/4.76 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 30.44/4.76 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 30.44/4.76 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 30.44/4.76 % 30.44/4.76 (mDefQuot) % 30.44/4.76 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 30.44/4.76 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 30.44/4.76 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 30.44/4.76 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 30.44/4.76 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 30.44/4.76 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 30.44/4.76 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 30.44/4.76 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 30.44/4.76 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 30.44/4.76 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 30.44/4.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 30.44/4.76 % 30.44/4.76 (mDivLE) % 30.44/4.76 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 30.44/4.76 doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 30.44/4.76 sdtlseqdt0(v0, v1)) % 30.44/4.77 % 30.44/4.77 (mLENTr) % 30.44/4.77 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 30.44/4.77 aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 30.44/4.77 % 30.44/4.77 (mMonMul2) % 30.44/4.77 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 30.44/4.77 (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | % 30.44/4.77 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) % 30.44/4.77 % 30.44/4.77 (mMulAsso) % 30.44/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 30.44/4.77 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 30.44/4.77 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 30.44/4.77 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 30.44/4.77 v5) = v4 & $i(v5) & $i(v4))) % 30.44/4.77 % 30.44/4.77 (mMulCanc) % 30.44/4.77 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 30.44/4.77 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = % 30.44/4.77 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 30.44/4.77 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( % 30.44/4.77 ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & $i(v6) & % 30.44/4.77 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = % 30.44/4.77 v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | % 30.44/4.77 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 30.44/4.77 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 30.44/4.77 % 30.44/4.77 (mMulComm) % 30.44/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 30.44/4.77 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 30.44/4.77 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 30.44/4.77 % 30.44/4.77 (mSortsB_02) % 30.44/4.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 30.44/4.77 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 30.44/4.77 aNaturalNumber0(v2)) % 30.44/4.77 % 30.44/4.77 (mSortsC_01) % 30.44/4.77 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 30.44/4.77 % 30.44/4.77 (m__) % 30.44/4.77 $i(xq) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 30.44/4.77 $i] : ? [v4: $i] : ( ~ (v4 = v1) & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v3) % 30.44/4.77 = v4 & sdtasdt0(xp, v2) = v3 & sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) = v0 % 30.44/4.77 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 30.44/4.77 % 30.44/4.77 (m__2987) % 30.44/4.77 ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & $i(xp) & $i(xm) & $i(xn) & % 30.44/4.77 $i(sz00) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn) % 30.44/4.77 % 30.44/4.77 (m__3014) % 30.44/4.77 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 % 30.44/4.77 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 30.44/4.77 % 30.44/4.77 (m__3025) % 30.44/4.77 ~ (xp = sz10) & $i(xp) & $i(sz10) & isPrime0(xp) & ! [v0: $i] : ! [v1: $i] % 30.44/4.77 : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ $i(v1) | ~ $i(v0) | % 30.44/4.77 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | % 30.44/4.77 v0 = sz10 | ~ $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) % 30.44/4.77 % 30.44/4.77 (m__3046) % 30.44/4.77 $i(xp) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xp, v2) % 30.44/4.77 = v0 & sdtasdt0(xp, v1) = xn & sdtasdt0(xn, xn) = v0 & $i(v2) & $i(v1) & % 30.44/4.77 $i(v0) & doDivides0(xp, v0) & doDivides0(xp, xn) & aNaturalNumber0(v2) & % 30.44/4.77 aNaturalNumber0(v1)) % 30.44/4.77 % 30.44/4.77 (m__3059) % 30.44/4.78 sdtsldt0(xn, xp) = xq & sdtasdt0(xp, xq) = xn & $i(xq) & $i(xp) & $i(xn) & % 30.44/4.78 aNaturalNumber0(xq) % 30.44/4.78 % 30.44/4.78 (function-axioms) % 30.44/4.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.44/4.78 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 30.44/4.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 30.44/4.78 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 30.44/4.78 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 30.44/4.78 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.44/4.78 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 30.44/4.78 % 30.44/4.78 Further assumptions not needed in the proof: % 30.44/4.78 -------------------------------------------- % 30.44/4.78 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDivAsso, mDivMin, mDivSum, mDivTrans, % 30.44/4.78 mIH, mIH_03, mLEAsym, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mNatSort, % 30.44/4.78 mPDP, mPrimDiv, mSortsB, mSortsC, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, % 30.44/4.78 m_MulZero, m__2963 % 30.44/4.78 % 30.44/4.78 Those formulas are unsatisfiable: % 30.44/4.78 --------------------------------- % 30.44/4.78 % 30.44/4.78 Begin of proof % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mSortsC_01) implies: % 30.44/4.78 | (1) aNaturalNumber0(sz10) % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mMulCanc) implies: % 30.44/4.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = % 30.44/4.78 | sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 30.44/4.78 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 30.44/4.78 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 30.44/4.78 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 30.44/4.78 | (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, % 30.44/4.78 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 30.44/4.78 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) % 30.44/4.78 | | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & % 30.44/4.78 | sdtasdt0(v1, v0) = v5 & $i(v6) & $i(v5))) % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mDefLE) implies: % 30.44/4.78 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, % 30.44/4.78 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 30.44/4.78 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mLENTr) implies: % 30.44/4.78 | (5) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 30.44/4.78 | aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mMonMul2) implies: % 30.44/4.78 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtasdt0(v1, % 30.44/4.78 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 30.44/4.78 | aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mDefDiv) implies: % 30.44/4.78 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, % 30.44/4.78 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 30.44/4.78 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mDefQuot) implies: % 30.44/4.78 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 30.44/4.78 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 30.44/4.78 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 30.44/4.78 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 30.44/4.78 | aNaturalNumber0(v0)) % 30.44/4.78 | % 30.44/4.78 | ALPHA: (mDivLE) implies: % 30.44/4.79 | (9) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~ % 30.44/4.79 | doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) % 30.44/4.79 | | sdtlseqdt0(v0, v1)) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (mDefPrime) implies: % 30.44/4.79 | (10) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (m__2987) implies: % 30.44/4.79 | (11) ~ (xn = sz00) % 30.44/4.79 | (12) ~ (xm = sz00) % 30.44/4.79 | (13) ~ (xp = sz00) % 30.44/4.79 | (14) aNaturalNumber0(xn) % 30.44/4.79 | (15) aNaturalNumber0(xm) % 30.44/4.79 | (16) aNaturalNumber0(xp) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (m__3014) implies: % 30.44/4.79 | (17) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) % 30.44/4.79 | = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (m__3025) implies: % 30.44/4.79 | (18) ~ (xp = sz10) % 30.44/4.79 | (19) $i(sz10) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (m__3046) implies: % 30.44/4.79 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xp, v2) = v0 & % 30.44/4.79 | sdtasdt0(xp, v1) = xn & sdtasdt0(xn, xn) = v0 & $i(v2) & $i(v1) & % 30.44/4.79 | $i(v0) & doDivides0(xp, v0) & doDivides0(xp, xn) & % 30.44/4.79 | aNaturalNumber0(v2) & aNaturalNumber0(v1)) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (m__3059) implies: % 30.44/4.79 | (21) aNaturalNumber0(xq) % 30.44/4.79 | (22) $i(xn) % 30.44/4.79 | (23) sdtasdt0(xp, xq) = xn % 30.44/4.79 | (24) sdtsldt0(xn, xp) = xq % 30.44/4.79 | % 30.44/4.79 | ALPHA: (m__) implies: % 30.44/4.79 | (25) $i(xm) % 30.44/4.79 | (26) $i(xp) % 30.44/4.79 | (27) $i(xq) % 30.44/4.79 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 30.44/4.79 | ( ~ (v4 = v1) & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v3) = v4 & % 30.44/4.79 | sdtasdt0(xp, v2) = v3 & sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) = % 30.44/4.79 | v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (function-axioms) implies: % 30.44/4.79 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 30.44/4.79 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 30.44/4.79 | % 30.44/4.79 | DELTA: instantiating (17) with fresh symbols all_41_0, all_41_1 gives: % 30.44/4.79 | (30) sdtasdt0(xp, all_41_1) = all_41_0 & sdtasdt0(xm, xm) = all_41_1 & % 30.44/4.79 | sdtasdt0(xn, xn) = all_41_0 & $i(all_41_0) & $i(all_41_1) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (30) implies: % 30.44/4.79 | (31) sdtasdt0(xn, xn) = all_41_0 % 30.44/4.79 | (32) sdtasdt0(xm, xm) = all_41_1 % 30.44/4.79 | (33) sdtasdt0(xp, all_41_1) = all_41_0 % 30.44/4.79 | % 30.44/4.79 | DELTA: instantiating (20) with fresh symbols all_43_0, all_43_1, all_43_2 % 30.44/4.79 | gives: % 30.44/4.79 | (34) sdtasdt0(xp, all_43_0) = all_43_2 & sdtasdt0(xp, all_43_1) = xn & % 30.44/4.79 | sdtasdt0(xn, xn) = all_43_2 & $i(all_43_0) & $i(all_43_1) & % 30.44/4.79 | $i(all_43_2) & doDivides0(xp, all_43_2) & doDivides0(xp, xn) & % 30.44/4.79 | aNaturalNumber0(all_43_0) & aNaturalNumber0(all_43_1) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (34) implies: % 30.44/4.79 | (35) aNaturalNumber0(all_43_1) % 30.44/4.79 | (36) aNaturalNumber0(all_43_0) % 30.44/4.79 | (37) doDivides0(xp, xn) % 30.44/4.79 | (38) doDivides0(xp, all_43_2) % 30.44/4.79 | (39) $i(all_43_1) % 30.44/4.79 | (40) $i(all_43_0) % 30.44/4.79 | (41) sdtasdt0(xn, xn) = all_43_2 % 30.44/4.79 | (42) sdtasdt0(xp, all_43_1) = xn % 30.44/4.79 | (43) sdtasdt0(xp, all_43_0) = all_43_2 % 30.44/4.79 | % 30.44/4.79 | DELTA: instantiating (28) with fresh symbols all_45_0, all_45_1, all_45_2, % 30.44/4.79 | all_45_3, all_45_4 gives: % 30.44/4.79 | (44) ~ (all_45_0 = all_45_3) & sdtasdt0(xq, xq) = all_45_2 & sdtasdt0(xp, % 30.44/4.79 | all_45_1) = all_45_0 & sdtasdt0(xp, all_45_2) = all_45_1 & % 30.44/4.79 | sdtasdt0(xp, all_45_4) = all_45_3 & sdtasdt0(xm, xm) = all_45_4 & % 30.44/4.79 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & % 30.44/4.79 | $i(all_45_4) % 30.44/4.79 | % 30.44/4.79 | ALPHA: (44) implies: % 30.44/4.80 | (45) ~ (all_45_0 = all_45_3) % 30.44/4.80 | (46) $i(all_45_4) % 30.44/4.80 | (47) $i(all_45_2) % 30.44/4.80 | (48) sdtasdt0(xm, xm) = all_45_4 % 30.44/4.80 | (49) sdtasdt0(xp, all_45_4) = all_45_3 % 30.44/4.80 | (50) sdtasdt0(xp, all_45_2) = all_45_1 % 30.44/4.80 | (51) sdtasdt0(xp, all_45_1) = all_45_0 % 30.44/4.80 | (52) sdtasdt0(xq, xq) = all_45_2 % 30.44/4.80 | % 30.44/4.80 | BETA: splitting (10) gives: % 30.44/4.80 | % 30.44/4.80 | Case 1: % 30.44/4.80 | | % 30.44/4.80 | | (53) ~ aNaturalNumber0(sz10) % 30.44/4.80 | | % 30.44/4.80 | | PRED_UNIFY: (1), (53) imply: % 30.44/4.80 | | (54) $false % 30.44/4.80 | | % 30.44/4.80 | | CLOSE: (54) is inconsistent. % 30.44/4.80 | | % 30.44/4.80 | Case 2: % 30.44/4.80 | | % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (29) with all_41_0, all_43_2, xn, xn, simplifying % 30.44/4.80 | | with (31), (41) gives: % 30.44/4.80 | | (55) all_43_2 = all_41_0 % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (29) with all_41_1, all_45_4, xm, xm, simplifying % 30.44/4.80 | | with (32), (48) gives: % 30.44/4.80 | | (56) all_45_4 = all_41_1 % 30.44/4.80 | | % 30.44/4.80 | | REDUCE: (49), (56) imply: % 30.44/4.80 | | (57) sdtasdt0(xp, all_41_1) = all_45_3 % 30.44/4.80 | | % 30.44/4.80 | | REDUCE: (43), (55) imply: % 30.44/4.80 | | (58) sdtasdt0(xp, all_43_0) = all_41_0 % 30.44/4.80 | | % 30.44/4.80 | | REDUCE: (46), (56) imply: % 30.44/4.80 | | (59) $i(all_41_1) % 30.44/4.80 | | % 30.44/4.80 | | REDUCE: (38), (55) imply: % 30.44/4.80 | | (60) doDivides0(xp, all_41_0) % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (29) with all_41_0, all_45_3, all_41_1, xp, % 30.44/4.80 | | simplifying with (33), (57) gives: % 30.44/4.80 | | (61) all_45_3 = all_41_0 % 30.44/4.80 | | % 30.44/4.80 | | REDUCE: (45), (61) imply: % 30.44/4.80 | | (62) ~ (all_45_0 = all_41_0) % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (5) with xp, simplifying with (16), (26) gives: % 30.44/4.80 | | (63) xp = sz10 | xp = sz00 | sdtlseqdt0(sz10, xp) % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (9) with xp, xn, simplifying with (14), (16), % 30.44/4.80 | | (22), (26), (37) gives: % 30.44/4.80 | | (64) xn = sz00 | sdtlseqdt0(xp, xn) % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (7) with xp, xn, simplifying with (14), (16), % 30.44/4.80 | | (22), (26), (37) gives: % 30.44/4.80 | | (65) ? [v0: $i] : (sdtasdt0(xp, v0) = xn & $i(v0) & aNaturalNumber0(v0)) % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (mSortsB_02) with xm, xm, all_41_1, simplifying % 30.44/4.80 | | with (15), (25), (32) gives: % 30.44/4.80 | | (66) aNaturalNumber0(all_41_1) % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (6) with xm, xm, all_41_1, simplifying with (15), % 30.44/4.80 | | (25), (32) gives: % 30.44/4.80 | | (67) xm = sz00 | sdtlseqdt0(xm, all_41_1) % 30.44/4.80 | | % 30.44/4.80 | | GROUND_INST: instantiating (mMulAsso) with xp, xq, xn, xn, all_41_0, % 30.44/4.80 | | simplifying with (14), (16), (21), (22), (23), (26), (27), (31) % 30.44/4.80 | | gives: % 30.44/4.81 | | (68) ? [v0: $i] : (sdtasdt0(xq, xn) = v0 & sdtasdt0(xp, v0) = all_41_0 & % 30.44/4.81 | | $i(v0) & $i(all_41_0)) % 30.44/4.81 | | % 30.44/4.81 | | GROUND_INST: instantiating (mMulComm) with xp, xq, xn, simplifying with % 30.44/4.81 | | (16), (21), (23), (26), (27) gives: % 30.44/4.81 | | (69) sdtasdt0(xq, xp) = xn & $i(xn) % 30.44/4.81 | | % 30.44/4.81 | | GROUND_INST: instantiating (mMulAsso) with xp, all_43_1, xn, xn, all_41_0, % 30.44/4.81 | | simplifying with (14), (16), (22), (26), (31), (35), (39), (42) % 30.44/4.81 | | gives: % 30.44/4.81 | | (70) ? [v0: $i] : (sdtasdt0(all_43_1, xn) = v0 & sdtasdt0(xp, v0) = % 30.44/4.81 | | all_41_0 & $i(v0) & $i(all_41_0)) % 30.44/4.81 | | % 30.44/4.81 | | GROUND_INST: instantiating (mMulComm) with xp, all_43_1, xn, simplifying % 30.44/4.81 | | with (16), (26), (35), (39), (42) gives: % 30.44/4.81 | | (71) sdtasdt0(all_43_1, xp) = xn & $i(xn) % 30.44/4.81 | | % 30.44/4.81 | | ALPHA: (71) implies: % 30.44/4.81 | | (72) sdtasdt0(all_43_1, xp) = xn % 30.44/4.81 | | % 30.44/4.81 | | GROUND_INST: instantiating (mSortsB_02) with xp, all_43_0, all_41_0, % 30.44/4.81 | | simplifying with (16), (26), (36), (40), (58) gives: % 30.44/4.81 | | (73) aNaturalNumber0(all_41_0) % 30.44/4.81 | | % 30.44/4.81 | | GROUND_INST: instantiating (mSortsB_02) with xq, xq, all_45_2, simplifying % 30.44/4.81 | | with (21), (27), (52) gives: % 30.44/4.81 | | (74) aNaturalNumber0(all_45_2) % 30.44/4.81 | | % 30.44/4.81 | | GROUND_INST: instantiating (8) with xp, xn, xq, all_43_1, simplifying with % 30.44/4.81 | | (14), (16), (22), (24), (26), (35), (37), (39), (42) gives: % 30.44/4.81 | | (75) all_43_1 = xq | xp = sz00 % 30.44/4.81 | | % 30.44/4.81 | | DELTA: instantiating (65) with fresh symbol all_69_0 gives: % 30.44/4.81 | | (76) sdtasdt0(xp, all_69_0) = xn & $i(all_69_0) & % 30.44/4.81 | | aNaturalNumber0(all_69_0) % 30.44/4.81 | | % 30.44/4.81 | | ALPHA: (76) implies: % 30.44/4.81 | | (77) aNaturalNumber0(all_69_0) % 30.44/4.81 | | (78) $i(all_69_0) % 30.44/4.81 | | (79) sdtasdt0(xp, all_69_0) = xn % 30.44/4.81 | | % 30.44/4.81 | | DELTA: instantiating (68) with fresh symbol all_71_0 gives: % 30.44/4.81 | | (80) sdtasdt0(xq, xn) = all_71_0 & sdtasdt0(xp, all_71_0) = all_41_0 & % 30.44/4.81 | | $i(all_71_0) & $i(all_41_0) % 30.44/4.81 | | % 30.44/4.81 | | ALPHA: (80) implies: % 30.44/4.81 | | (81) sdtasdt0(xq, xn) = all_71_0 % 30.44/4.81 | | % 30.44/4.81 | | DELTA: instantiating (70) with fresh symbol all_73_0 gives: % 30.44/4.81 | | (82) sdtasdt0(all_43_1, xn) = all_73_0 & sdtasdt0(xp, all_73_0) = % 30.44/4.81 | | all_41_0 & $i(all_73_0) & $i(all_41_0) % 30.44/4.81 | | % 30.44/4.81 | | ALPHA: (82) implies: % 30.44/4.81 | | (83) sdtasdt0(all_43_1, xn) = all_73_0 % 30.44/4.81 | | % 30.44/4.81 | | BETA: splitting (67) gives: % 30.44/4.81 | | % 30.44/4.81 | | Case 1: % 30.44/4.81 | | | % 30.44/4.81 | | | (84) sdtlseqdt0(xm, all_41_1) % 30.44/4.81 | | | % 30.44/4.81 | | | BETA: splitting (63) gives: % 30.44/4.81 | | | % 30.44/4.81 | | | Case 1: % 30.44/4.81 | | | | % 30.44/4.81 | | | | (85) sdtlseqdt0(sz10, xp) % 30.44/4.81 | | | | % 30.44/4.81 | | | | BETA: splitting (75) gives: % 30.44/4.81 | | | | % 30.44/4.81 | | | | Case 1: % 30.44/4.81 | | | | | % 30.44/4.81 | | | | | (86) xp = sz00 % 30.44/4.81 | | | | | % 30.44/4.81 | | | | | REDUCE: (13), (86) imply: % 30.44/4.81 | | | | | (87) $false % 30.44/4.81 | | | | | % 30.44/4.81 | | | | | CLOSE: (87) is inconsistent. % 30.44/4.81 | | | | | % 30.44/4.81 | | | | Case 2: % 30.44/4.81 | | | | | % 30.44/4.81 | | | | | (88) all_43_1 = xq % 30.44/4.81 | | | | | % 30.44/4.82 | | | | | REDUCE: (72), (88) imply: % 30.44/4.82 | | | | | (89) sdtasdt0(xq, xp) = xn % 30.44/4.82 | | | | | % 30.44/4.82 | | | | | REDUCE: (83), (88) imply: % 30.44/4.82 | | | | | (90) sdtasdt0(xq, xn) = all_73_0 % 30.44/4.82 | | | | | % 30.44/4.82 | | | | | BETA: splitting (64) gives: % 30.44/4.82 | | | | | % 30.44/4.82 | | | | | Case 1: % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | GROUND_INST: instantiating (29) with all_71_0, all_73_0, xn, xq, % 30.44/4.82 | | | | | | simplifying with (81), (90) gives: % 30.44/4.82 | | | | | | (91) all_73_0 = all_71_0 % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_41_1, all_41_0, % 30.44/4.82 | | | | | | simplifying with (16), (26), (33), (59), (66) gives: % 30.44/4.82 | | | | | | (92) sdtasdt0(all_41_1, xp) = all_41_0 & $i(all_41_0) % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | ALPHA: (92) implies: % 30.44/4.82 | | | | | | (93) $i(all_41_0) % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | GROUND_INST: instantiating (7) with xp, all_41_0, simplifying with % 30.44/4.82 | | | | | | (16), (26), (60), (73), (93) gives: % 30.44/4.82 | | | | | | (94) ? [v0: $i] : (sdtasdt0(xp, v0) = all_41_0 & $i(v0) & % 30.44/4.82 | | | | | | aNaturalNumber0(v0)) % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | GROUND_INST: instantiating (mSortsB_02) with xp, all_45_2, all_45_1, % 30.44/4.82 | | | | | | simplifying with (16), (26), (47), (50), (74) gives: % 30.44/4.82 | | | | | | (95) aNaturalNumber0(all_45_1) % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_45_2, all_45_1, % 30.44/4.82 | | | | | | simplifying with (16), (26), (47), (50), (74) gives: % 30.44/4.82 | | | | | | (96) sdtasdt0(all_45_2, xp) = all_45_1 & $i(all_45_1) % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | ALPHA: (96) implies: % 30.44/4.82 | | | | | | (97) $i(all_45_1) % 30.44/4.82 | | | | | | (98) sdtasdt0(all_45_2, xp) = all_45_1 % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | GROUND_INST: instantiating (4) with sz10, xp, simplifying with (1), % 30.44/4.82 | | | | | | (16), (19), (26), (85) gives: % 30.44/4.82 | | | | | | (99) ? [v0: $i] : (sdtpldt0(sz10, v0) = xp & $i(v0) & % 30.44/4.82 | | | | | | aNaturalNumber0(v0)) % 30.44/4.82 | | | | | | % 30.44/4.82 | | | | | | GROUND_INST: instantiating (4) with xm, all_41_1, simplifying with % 30.44/4.82 | | | | | | (15), (25), (59), (66), (84) gives: % 30.44/4.82 | | | | | | (100) ? [v0: $i] : (sdtpldt0(xm, v0) = all_41_1 & $i(v0) & % 30.44/4.82 | | | | | | aNaturalNumber0(v0)) % 30.44/4.82 | | | | | | % 30.74/4.82 | | | | | | GROUND_INST: instantiating (3) with xp, all_69_0, xq, xn, xn, % 30.74/4.82 | | | | | | simplifying with (16), (21), (23), (26), (27), (77), % 30.74/4.82 | | | | | | (78), (79) gives: % 30.74/4.82 | | | | | | (101) all_69_0 = xq | xp = sz00 | ? [v0: $i] : ? [v1: $i] : ( ~ % 30.74/4.82 | | | | | | (v1 = v0) & sdtasdt0(all_69_0, xp) = v0 & sdtasdt0(xq, % 30.74/4.82 | | | | | | xp) = v1 & $i(v1) & $i(v0)) % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | GROUND_INST: instantiating (2) with xp, all_69_0, xq, xn, % 30.74/4.82 | | | | | | simplifying with (16), (21), (23), (26), (27), (77), % 30.74/4.82 | | | | | | (78), (79) gives: % 30.74/4.82 | | | | | | (102) all_69_0 = xq | xp = sz00 % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | GROUND_INST: instantiating (mMulAsso) with xp, all_69_0, xn, xn, % 30.74/4.82 | | | | | | all_41_0, simplifying with (14), (16), (22), (26), % 30.74/4.82 | | | | | | (31), (77), (78), (79) gives: % 30.74/4.82 | | | | | | (103) ? [v0: $i] : (sdtasdt0(all_69_0, xn) = v0 & sdtasdt0(xp, % 30.74/4.82 | | | | | | v0) = all_41_0 & $i(v0) & $i(all_41_0)) % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_69_0, xn, % 30.74/4.82 | | | | | | simplifying with (16), (26), (77), (78), (79) gives: % 30.74/4.82 | | | | | | (104) sdtasdt0(all_69_0, xp) = xn & $i(xn) % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | ALPHA: (104) implies: % 30.74/4.82 | | | | | | (105) sdtasdt0(all_69_0, xp) = xn % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | GROUND_INST: instantiating (mSortsB_02) with xq, xn, all_71_0, % 30.74/4.82 | | | | | | simplifying with (14), (21), (22), (27), (81) gives: % 30.74/4.82 | | | | | | (106) aNaturalNumber0(all_71_0) % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | GROUND_INST: instantiating (6) with xp, xq, xn, simplifying with % 30.74/4.82 | | | | | | (16), (21), (26), (27), (89) gives: % 30.74/4.82 | | | | | | (107) xp = sz00 | sdtlseqdt0(xq, xn) % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | DELTA: instantiating (94) with fresh symbol all_115_0 gives: % 30.74/4.82 | | | | | | (108) sdtasdt0(xp, all_115_0) = all_41_0 & $i(all_115_0) & % 30.74/4.82 | | | | | | aNaturalNumber0(all_115_0) % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | ALPHA: (108) implies: % 30.74/4.82 | | | | | | (109) aNaturalNumber0(all_115_0) % 30.74/4.82 | | | | | | (110) $i(all_115_0) % 30.74/4.82 | | | | | | (111) sdtasdt0(xp, all_115_0) = all_41_0 % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | DELTA: instantiating (100) with fresh symbol all_125_0 gives: % 30.74/4.82 | | | | | | (112) sdtpldt0(xm, all_125_0) = all_41_1 & $i(all_125_0) & % 30.74/4.82 | | | | | | aNaturalNumber0(all_125_0) % 30.74/4.82 | | | | | | % 30.74/4.82 | | | | | | ALPHA: (112) implies: % 30.74/4.82 | | | | | | (113) aNaturalNumber0(all_125_0) % 30.74/4.82 | | | | | | (114) $i(all_125_0) % 30.74/4.83 | | | | | | (115) sdtpldt0(xm, all_125_0) = all_41_1 % 30.74/4.83 | | | | | | % 30.74/4.83 | | | | | | DELTA: instantiating (99) with fresh symbol all_133_0 gives: % 30.74/4.83 | | | | | | (116) sdtpldt0(sz10, all_133_0) = xp & $i(all_133_0) & % 30.74/4.83 | | | | | | aNaturalNumber0(all_133_0) % 30.74/4.83 | | | | | | % 30.74/4.83 | | | | | | ALPHA: (116) implies: % 30.74/4.83 | | | | | | (117) aNaturalNumber0(all_133_0) % 30.74/4.83 | | | | | | (118) $i(all_133_0) % 30.74/4.83 | | | | | | (119) sdtpldt0(sz10, all_133_0) = xp % 30.74/4.83 | | | | | | % 30.74/4.83 | | | | | | DELTA: instantiating (103) with fresh symbol all_141_0 gives: % 30.74/4.83 | | | | | | (120) sdtasdt0(all_69_0, xn) = all_141_0 & sdtasdt0(xp, % 30.74/4.83 | | | | | | all_141_0) = all_41_0 & $i(all_141_0) & $i(all_41_0) % 30.74/4.83 | | | | | | % 30.74/4.83 | | | | | | ALPHA: (120) implies: % 30.74/4.83 | | | | | | (121) $i(all_141_0) % 30.74/4.83 | | | | | | (122) sdtasdt0(xp, all_141_0) = all_41_0 % 30.74/4.83 | | | | | | (123) sdtasdt0(all_69_0, xn) = all_141_0 % 30.74/4.83 | | | | | | % 30.74/4.83 | | | | | | BETA: splitting (101) gives: % 30.74/4.83 | | | | | | % 30.74/4.83 | | | | | | Case 1: % 30.74/4.83 | | | | | | | % 30.74/4.83 | | | | | | | (124) xp = sz00 % 30.74/4.83 | | | | | | | % 30.74/4.83 | | | | | | | REDUCE: (13), (124) imply: % 30.74/4.83 | | | | | | | (125) $false % 30.74/4.83 | | | | | | | % 30.74/4.83 | | | | | | | CLOSE: (125) is inconsistent. % 30.74/4.83 | | | | | | | % 30.74/4.83 | | | | | | Case 2: % 30.74/4.83 | | | | | | | % 30.74/4.83 | | | | | | | (126) all_69_0 = xq | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) % 30.74/4.83 | | | | | | | & sdtasdt0(all_69_0, xp) = v0 & sdtasdt0(xq, xp) = v1 & % 30.74/4.83 | | | | | | | $i(v1) & $i(v0)) % 30.74/4.83 | | | | | | | % 30.74/4.83 | | | | | | | BETA: splitting (126) gives: % 30.74/4.83 | | | | | | | % 30.74/4.83 | | | | | | | Case 1: % 30.74/4.83 | | | | | | | | % 30.74/4.83 | | | | | | | | (127) all_69_0 = xq % 30.74/4.83 | | | | | | | | % 30.74/4.83 | | | | | | | | REDUCE: (123), (127) imply: % 30.74/4.83 | | | | | | | | (128) sdtasdt0(xq, xn) = all_141_0 % 30.74/4.83 | | | | | | | | % 30.74/4.83 | | | | | | | | BETA: splitting (107) gives: % 30.74/4.83 | | | | | | | | % 30.74/4.83 | | | | | | | | Case 1: % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (29) with all_71_0, all_141_0, xn, % 30.74/4.83 | | | | | | | | | xq, simplifying with (81), (128) gives: % 30.74/4.83 | | | | | | | | | (129) all_141_0 = all_71_0 % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | REDUCE: (122), (129) imply: % 30.74/4.83 | | | | | | | | | (130) sdtasdt0(xp, all_71_0) = all_41_0 % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | REDUCE: (121), (129) imply: % 30.74/4.83 | | | | | | | | | (131) $i(all_71_0) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_45_1, % 30.74/4.83 | | | | | | | | | all_45_0, simplifying with (16), (26), (51), (95), % 30.74/4.83 | | | | | | | | | (97) gives: % 30.74/4.83 | | | | | | | | | (132) sdtasdt0(all_45_1, xp) = all_45_0 & $i(all_45_0) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | ALPHA: (132) implies: % 30.74/4.83 | | | | | | | | | (133) sdtasdt0(all_45_1, xp) = all_45_0 % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (2) with xp, all_41_1, all_71_0, % 30.74/4.83 | | | | | | | | | all_41_0, simplifying with (16), (26), (33), (59), % 30.74/4.83 | | | | | | | | | (66), (106), (130), (131) gives: % 30.74/4.83 | | | | | | | | | (134) all_71_0 = all_41_1 | xp = sz00 % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (mAddComm) with sz10, all_133_0, xp, % 30.74/4.83 | | | | | | | | | simplifying with (1), (19), (117), (118), (119) % 30.74/4.83 | | | | | | | | | gives: % 30.74/4.83 | | | | | | | | | (135) sdtpldt0(all_133_0, sz10) = xp & $i(xp) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (mAddComm) with xm, all_125_0, % 30.74/4.83 | | | | | | | | | all_41_1, simplifying with (15), (25), (113), % 30.74/4.83 | | | | | | | | | (114), (115) gives: % 30.74/4.83 | | | | | | | | | (136) sdtpldt0(all_125_0, xm) = all_41_1 & $i(all_41_1) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (3) with xp, all_71_0, all_115_0, % 30.74/4.83 | | | | | | | | | all_41_0, all_41_0, simplifying with (16), (26), % 30.74/4.83 | | | | | | | | | (106), (109), (110), (111), (130), (131) gives: % 30.74/4.83 | | | | | | | | | (137) all_115_0 = all_71_0 | xp = sz00 | ? [v0: $i] : ? % 30.74/4.83 | | | | | | | | | [v1: $i] : ( ~ (v1 = v0) & sdtasdt0(all_115_0, xp) = % 30.74/4.83 | | | | | | | | | v1 & sdtasdt0(all_71_0, xp) = v0 & $i(v1) & $i(v0)) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (2) with xp, all_115_0, all_41_1, % 30.74/4.83 | | | | | | | | | all_41_0, simplifying with (16), (26), (33), (59), % 30.74/4.83 | | | | | | | | | (66), (109), (110), (111) gives: % 30.74/4.83 | | | | | | | | | (138) all_115_0 = all_41_1 | xp = sz00 % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_115_0, % 30.74/4.83 | | | | | | | | | all_41_0, simplifying with (16), (26), (109), % 30.74/4.83 | | | | | | | | | (110), (111) gives: % 30.74/4.83 | | | | | | | | | (139) sdtasdt0(all_115_0, xp) = all_41_0 & $i(all_41_0) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | ALPHA: (139) implies: % 30.74/4.83 | | | | | | | | | (140) sdtasdt0(all_115_0, xp) = all_41_0 % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xq, xq, xp, % 30.74/4.83 | | | | | | | | | all_45_2, all_45_1, simplifying with (16), (21), % 30.74/4.83 | | | | | | | | | (26), (27), (52), (98) gives: % 30.74/4.83 | | | | | | | | | (141) ? [v0: $i] : (sdtasdt0(xq, v0) = all_45_1 & % 30.74/4.83 | | | | | | | | | sdtasdt0(xq, xp) = v0 & $i(v0) & $i(all_45_1)) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_263_0 gives: % 30.74/4.83 | | | | | | | | | (142) sdtasdt0(xq, all_263_0) = all_45_1 & sdtasdt0(xq, xp) % 30.74/4.83 | | | | | | | | | = all_263_0 & $i(all_263_0) & $i(all_45_1) % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | ALPHA: (142) implies: % 30.74/4.83 | | | | | | | | | (143) sdtasdt0(xq, xp) = all_263_0 % 30.74/4.83 | | | | | | | | | (144) sdtasdt0(xq, all_263_0) = all_45_1 % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | BETA: splitting (137) gives: % 30.74/4.83 | | | | | | | | | % 30.74/4.83 | | | | | | | | | Case 1: % 30.74/4.83 | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | (145) xp = sz00 % 30.74/4.83 | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | REDUCE: (13), (145) imply: % 30.74/4.83 | | | | | | | | | | (146) $false % 30.74/4.83 | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | CLOSE: (146) is inconsistent. % 30.74/4.83 | | | | | | | | | | % 30.74/4.83 | | | | | | | | | Case 2: % 30.74/4.83 | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | (147) all_115_0 = all_71_0 | ? [v0: $i] : ? [v1: $i] : % 30.74/4.83 | | | | | | | | | | ( ~ (v1 = v0) & sdtasdt0(all_115_0, xp) = v1 & % 30.74/4.83 | | | | | | | | | | sdtasdt0(all_71_0, xp) = v0 & $i(v1) & $i(v0)) % 30.74/4.83 | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | BETA: splitting (147) gives: % 30.74/4.83 | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | Case 1: % 30.74/4.83 | | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | | (148) all_115_0 = all_71_0 % 30.74/4.83 | | | | | | | | | | | % 30.74/4.83 | | | | | | | | | | | REDUCE: (140), (148) imply: % 30.74/4.84 | | | | | | | | | | | (149) sdtasdt0(all_71_0, xp) = all_41_0 % 30.74/4.84 | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | BETA: splitting (138) gives: % 30.74/4.84 | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | Case 1: % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | (150) xp = sz00 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (13), (150) imply: % 30.74/4.84 | | | | | | | | | | | | (151) $false % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | CLOSE: (151) is inconsistent. % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | Case 2: % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | (152) all_115_0 = all_41_1 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | COMBINE_EQS: (148), (152) imply: % 30.74/4.84 | | | | | | | | | | | | (153) all_71_0 = all_41_1 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (149), (153) imply: % 30.74/4.84 | | | | | | | | | | | | (154) sdtasdt0(all_41_1, xp) = all_41_0 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (81), (153) imply: % 30.74/4.84 | | | | | | | | | | | | (155) sdtasdt0(xq, xn) = all_41_1 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | GROUND_INST: instantiating (29) with xn, all_263_0, xp, xq, % 30.74/4.84 | | | | | | | | | | | | simplifying with (89), (143) gives: % 30.74/4.84 | | | | | | | | | | | | (156) all_263_0 = xn % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (144), (156) imply: % 30.74/4.84 | | | | | | | | | | | | (157) sdtasdt0(xq, xn) = all_45_1 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_41_1, all_45_1, xn, % 30.74/4.84 | | | | | | | | | | | | xq, simplifying with (155), (157) gives: % 30.74/4.84 | | | | | | | | | | | | (158) all_45_1 = all_41_1 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (133), (158) imply: % 30.74/4.84 | | | | | | | | | | | | (159) sdtasdt0(all_41_1, xp) = all_45_0 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_41_0, all_45_0, xp, % 30.74/4.84 | | | | | | | | | | | | all_41_1, simplifying with (154), (159) gives: % 30.74/4.84 | | | | | | | | | | | | (160) all_45_0 = all_41_0 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (62), (160) imply: % 30.74/4.84 | | | | | | | | | | | | (161) $false % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | CLOSE: (161) is inconsistent. % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | End of split % 30.74/4.84 | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | Case 2: % 30.74/4.84 | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | (162) ~ (all_115_0 = all_71_0) % 30.74/4.84 | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | BETA: splitting (138) gives: % 30.74/4.84 | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | Case 1: % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | (163) xp = sz00 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (13), (163) imply: % 30.74/4.84 | | | | | | | | | | | | (164) $false % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | Case 2: % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | (165) all_115_0 = all_41_1 % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | REDUCE: (162), (165) imply: % 30.74/4.84 | | | | | | | | | | | | (166) ~ (all_71_0 = all_41_1) % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | SIMP: (166) implies: % 30.74/4.84 | | | | | | | | | | | | (167) ~ (all_71_0 = all_41_1) % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | BETA: splitting (134) gives: % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | Case 1: % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | | (168) xp = sz00 % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | | REDUCE: (13), (168) imply: % 30.74/4.84 | | | | | | | | | | | | | (169) $false % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | | CLOSE: (169) is inconsistent. % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | Case 2: % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | | (170) all_71_0 = all_41_1 % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | | REDUCE: (167), (170) imply: % 30.74/4.84 | | | | | | | | | | | | | (171) $false % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | | CLOSE: (171) is inconsistent. % 30.74/4.84 | | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | | End of split % 30.74/4.84 | | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | | End of split % 30.74/4.84 | | | | | | | | | | | % 30.74/4.84 | | | | | | | | | | End of split % 30.74/4.84 | | | | | | | | | | % 30.74/4.84 | | | | | | | | | End of split % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | Case 2: % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | (172) xp = sz00 % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | REDUCE: (13), (172) imply: % 30.74/4.84 | | | | | | | | | (173) $false % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | CLOSE: (173) is inconsistent. % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | End of split % 30.74/4.84 | | | | | | | | % 30.74/4.84 | | | | | | | Case 2: % 30.74/4.84 | | | | | | | | % 30.74/4.84 | | | | | | | | (174) ~ (all_69_0 = xq) % 30.74/4.84 | | | | | | | | % 30.74/4.84 | | | | | | | | BETA: splitting (102) gives: % 30.74/4.84 | | | | | | | | % 30.74/4.84 | | | | | | | | Case 1: % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | (175) xp = sz00 % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | REDUCE: (13), (175) imply: % 30.74/4.84 | | | | | | | | | (176) $false % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | CLOSE: (176) is inconsistent. % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | Case 2: % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | (177) all_69_0 = xq % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | REDUCE: (174), (177) imply: % 30.74/4.84 | | | | | | | | | (178) $false % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | | CLOSE: (178) is inconsistent. % 30.74/4.84 | | | | | | | | | % 30.74/4.84 | | | | | | | | End of split % 30.74/4.84 | | | | | | | | % 30.74/4.84 | | | | | | | End of split % 30.74/4.84 | | | | | | | % 30.74/4.84 | | | | | | End of split % 30.74/4.84 | | | | | | % 30.74/4.84 | | | | | Case 2: % 30.74/4.84 | | | | | | % 30.74/4.84 | | | | | | (179) xn = sz00 % 30.74/4.84 | | | | | | % 30.74/4.84 | | | | | | REDUCE: (11), (179) imply: % 30.74/4.84 | | | | | | (180) $false % 30.74/4.84 | | | | | | % 30.74/4.84 | | | | | | CLOSE: (180) is inconsistent. % 30.74/4.84 | | | | | | % 30.74/4.84 | | | | | End of split % 30.74/4.84 | | | | | % 30.74/4.84 | | | | End of split % 30.74/4.84 | | | | % 30.74/4.84 | | | Case 2: % 30.74/4.84 | | | | % 30.74/4.84 | | | | (181) xp = sz10 | xp = sz00 % 30.74/4.84 | | | | % 30.74/4.84 | | | | BETA: splitting (181) gives: % 30.74/4.84 | | | | % 30.74/4.84 | | | | Case 1: % 30.74/4.84 | | | | | % 30.74/4.84 | | | | | (182) xp = sz00 % 30.74/4.84 | | | | | % 30.74/4.84 | | | | | REDUCE: (13), (182) imply: % 30.74/4.84 | | | | | (183) $false % 30.74/4.84 | | | | | % 30.74/4.84 | | | | | CLOSE: (183) is inconsistent. % 30.74/4.84 | | | | | % 30.74/4.84 | | | | Case 2: % 30.74/4.84 | | | | | % 30.74/4.84 | | | | | (184) xp = sz10 % 30.74/4.84 | | | | | % 30.74/4.84 | | | | | REDUCE: (18), (184) imply: % 30.74/4.84 | | | | | (185) $false % 30.74/4.84 | | | | | % 30.74/4.84 | | | | | CLOSE: (185) is inconsistent. % 30.74/4.84 | | | | | % 30.74/4.84 | | | | End of split % 30.74/4.84 | | | | % 30.74/4.84 | | | End of split % 30.74/4.84 | | | % 30.74/4.84 | | Case 2: % 30.74/4.84 | | | % 30.74/4.84 | | | (186) xm = sz00 % 30.74/4.84 | | | % 30.74/4.84 | | | REDUCE: (12), (186) imply: % 30.74/4.84 | | | (187) $false % 30.74/4.84 | | | % 30.74/4.84 | | | CLOSE: (187) is inconsistent. % 30.74/4.84 | | | % 30.74/4.84 | | End of split % 30.74/4.84 | | % 30.74/4.84 | End of split % 30.74/4.84 | % 30.74/4.84 End of proof % 30.74/4.84 % SZS output end Proof for theBenchmark % 30.74/4.84 % 30.74/4.84 4252ms %------------------------------------------------------------------------------