%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM525+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 : n010.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 13.42s 2.54s % Output : Proof 26.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM525+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n010.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 16:09:35 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.52/1.18 Prover 1: Preprocessing ... % 3.52/1.18 Prover 4: Preprocessing ... % 3.87/1.22 Prover 3: Preprocessing ... % 3.87/1.22 Prover 0: Preprocessing ... % 3.87/1.22 Prover 5: Preprocessing ... % 3.87/1.22 Prover 6: Preprocessing ... % 3.87/1.22 Prover 2: Preprocessing ... % 8.94/1.95 Prover 1: Constructing countermodel ... % 8.94/1.97 Prover 3: Constructing countermodel ... % 10.13/2.10 Prover 6: Proving ... % 10.64/2.17 Prover 5: Constructing countermodel ... % 11.61/2.32 Prover 2: Proving ... % 12.34/2.38 Prover 4: Constructing countermodel ... % 13.42/2.53 Prover 0: Proving ... % 13.42/2.54 Prover 3: proved (1918ms) % 13.42/2.54 % 13.42/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.42/2.54 % 13.42/2.55 Prover 5: stopped % 13.42/2.55 Prover 2: stopped % 13.42/2.57 Prover 6: stopped % 13.42/2.57 Prover 0: stopped % 13.42/2.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 13.42/2.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 13.42/2.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 13.42/2.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 13.42/2.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 13.42/2.71 Prover 7: Preprocessing ... % 13.98/2.72 Prover 8: Preprocessing ... % 13.98/2.73 Prover 11: Preprocessing ... % 13.98/2.74 Prover 10: Preprocessing ... % 13.98/2.75 Prover 13: Preprocessing ... % 15.56/2.88 Prover 10: Constructing countermodel ... % 16.16/2.94 Prover 8: Warning: ignoring some quantifiers % 16.16/2.95 Prover 8: Constructing countermodel ... % 16.16/2.96 Prover 7: Constructing countermodel ... % 16.16/2.96 Prover 13: Constructing countermodel ... % 17.86/3.19 Prover 11: Constructing countermodel ... % 25.08/4.17 Prover 1: Found proof (size 423) % 25.08/4.17 Prover 1: proved (3564ms) % 25.08/4.17 Prover 11: stopped % 25.08/4.17 Prover 13: stopped % 25.08/4.17 Prover 7: stopped % 25.08/4.17 Prover 8: stopped % 25.08/4.17 Prover 4: stopped % 25.08/4.18 Prover 10: stopped % 25.08/4.18 % 25.08/4.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 25.08/4.18 % 25.96/4.25 % SZS output start Proof for theBenchmark % 25.96/4.25 Assumptions after simplification: % 25.96/4.25 --------------------------------- % 25.96/4.25 % 25.96/4.25 (mDefDiv) % 25.96/4.28 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 25.96/4.28 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 25.96/4.28 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 25.96/4.28 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 25.96/4.28 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 25.96/4.28 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 25.96/4.28 % 25.96/4.28 (mDefPrime) % 25.96/4.28 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | % 25.96/4.28 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ % 25.96/4.28 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | % 25.96/4.28 v2 = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] : % 25.96/4.28 ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = 0 | v0 = sz10 | % 25.96/4.28 v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) & % 25.96/4.28 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & $i(v2))))) % 25.96/4.28 % 25.96/4.28 (mDefQuot) % 25.96/4.29 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 25.96/4.29 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 25.96/4.29 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 25.96/4.29 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 25.96/4.29 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4: % 25.96/4.29 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 25.96/4.29 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = % 25.96/4.29 0)))) % 25.96/4.29 % 25.96/4.29 (mMulAsso) % 25.96/4.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 25.96/4.29 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 25.96/4.29 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 25.96/4.29 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & % 25.96/4.29 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 25.96/4.29 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 25.96/4.29 v4))) % 25.96/4.29 % 25.96/4.29 (mMulCanc) % 25.96/4.29 $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) % 25.96/4.29 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ % 25.96/4.29 (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ % 25.96/4.29 $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 25.96/4.29 (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 % 25.96/4.29 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 25.96/4.29 0) | ( ~ (v8 = v7) & ~ (v4 = v3)))))) % 25.96/4.29 % 25.96/4.29 (mMulComm) % 25.96/4.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 25.96/4.29 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 25.96/4.29 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 25.96/4.29 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 25.96/4.29 % 25.96/4.29 (mPDP) % 25.96/4.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (doDivides0(v2, % 25.96/4.30 v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 25.96/4.30 $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 25.96/4.30 any] : ? [v9: any] : (isPrime0(v2) = v7 & doDivides0(v2, v1) = v9 & % 25.96/4.30 doDivides0(v2, v0) = v8 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = % 25.96/4.30 v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | % 25.96/4.30 ~ (v4 = 0) | v9 = 0 | v8 = 0))) % 25.96/4.30 % 25.96/4.30 (mPrimDiv) % 25.96/4.30 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ % 25.96/4.30 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & % 25.96/4.30 doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0 & $i(v1))) % 25.96/4.30 % 25.96/4.30 (mSortsB_02) % 25.96/4.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 25.96/4.30 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 25.96/4.30 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 25.96/4.30 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 25.96/4.30 % 25.96/4.30 (m__) % 25.96/4.30 $i(xq) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 25.96/4.30 $i] : ? [v4: $i] : ( ~ (v4 = v1) & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v3) % 25.96/4.30 = v4 & sdtasdt0(xp, v2) = v3 & sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) = v0 % 25.96/4.30 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 25.96/4.30 % 25.96/4.30 (m__2987) % 25.96/4.30 ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & aNaturalNumber0(xp) = 0 & % 25.96/4.30 aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & $i(xp) & $i(xm) & $i(xn) & % 25.96/4.30 $i(sz00) % 25.96/4.30 % 25.96/4.30 (m__3014) % 25.96/4.30 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 % 25.96/4.30 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 25.96/4.30 % 25.96/4.30 (m__3025) % 25.96/4.30 isPrime0(xp) = 0 & $i(xp) % 25.96/4.30 % 25.96/4.30 (m__3046) % 25.96/4.30 $i(xp) & $i(xn) & ? [v0: $i] : (doDivides0(xp, v0) = 0 & doDivides0(xp, xn) = % 25.96/4.30 0 & sdtasdt0(xn, xn) = v0 & $i(v0)) % 25.96/4.30 % 25.96/4.30 (m__3059) % 25.96/4.30 sdtsldt0(xn, xp) = xq & $i(xq) & $i(xp) & $i(xn) % 25.96/4.30 % 25.96/4.30 (function-axioms) % 25.96/4.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.96/4.31 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 25.96/4.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.96/4.31 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 25.96/4.31 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 25.96/4.31 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 25.96/4.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.96/4.31 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 25.96/4.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 25.96/4.31 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 25.96/4.31 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 25.96/4.31 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 25.96/4.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 25.96/4.31 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.96/4.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 25.96/4.31 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 25.96/4.31 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 25.96/4.31 | ~ (aNaturalNumber0(v2) = v0)) % 25.96/4.31 % 25.96/4.31 Further assumptions not needed in the proof: % 25.96/4.31 -------------------------------------------- % 25.96/4.31 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDivAsso, mDivLE, % 25.96/4.31 mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, % 25.96/4.31 mLETran, mMonAdd, mMonMul, mMonMul2, mNatSort, mSortsB, mSortsC, mSortsC_01, % 25.96/4.31 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__2963 % 25.96/4.31 % 25.96/4.31 Those formulas are unsatisfiable: % 25.96/4.31 --------------------------------- % 25.96/4.31 % 25.96/4.31 Begin of proof % 25.96/4.31 | % 25.96/4.31 | ALPHA: (mMulCanc) implies: % 25.96/4.31 | (1) ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | % 25.96/4.31 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ % 25.96/4.31 | (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | % 25.96/4.31 | ~ $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] % 25.96/4.31 | : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & % 25.96/4.31 | aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & $i(v8) & % 25.96/4.31 | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = % 25.96/4.31 | v3)))))) % 25.96/4.31 | % 25.96/4.31 | ALPHA: (mDefQuot) implies: % 26.42/4.31 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 26.42/4.31 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 26.42/4.31 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 26.42/4.31 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 26.42/4.31 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | % 26.42/4.31 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = % 26.42/4.31 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | % 26.42/4.31 | (v3 = v1 & aNaturalNumber0(v2) = 0)))) % 26.42/4.31 | % 26.42/4.31 | ALPHA: (mDefPrime) implies: % 26.42/4.32 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | ~ $i(v0) | ? % 26.42/4.32 | [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ (v1 = 0) % 26.42/4.32 | | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | v2 % 26.42/4.32 | = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: % 26.42/4.32 | int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = % 26.42/4.32 | 0 | v0 = sz10 | v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 % 26.42/4.32 | = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & % 26.42/4.32 | $i(v2))))) % 26.42/4.32 | % 26.42/4.32 | ALPHA: (mPrimDiv) implies: % 26.42/4.32 | (4) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | % 26.42/4.32 | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & % 26.42/4.32 | aNaturalNumber0(v1) = 0 & $i(v1))) % 26.42/4.32 | % 26.42/4.32 | ALPHA: (m__2987) implies: % 26.42/4.32 | (5) aNaturalNumber0(xn) = 0 % 26.42/4.32 | (6) aNaturalNumber0(xm) = 0 % 26.42/4.32 | (7) aNaturalNumber0(xp) = 0 % 26.42/4.32 | % 26.42/4.32 | ALPHA: (m__3014) implies: % 26.42/4.32 | (8) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) = % 26.42/4.32 | v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0)) % 26.42/4.32 | % 26.42/4.32 | ALPHA: (m__3025) implies: % 26.42/4.32 | (9) isPrime0(xp) = 0 % 26.42/4.32 | % 26.42/4.32 | ALPHA: (m__3046) implies: % 26.42/4.32 | (10) ? [v0: $i] : (doDivides0(xp, v0) = 0 & doDivides0(xp, xn) = 0 & % 26.42/4.32 | sdtasdt0(xn, xn) = v0 & $i(v0)) % 26.42/4.32 | % 26.42/4.32 | ALPHA: (m__3059) implies: % 26.42/4.32 | (11) $i(xn) % 26.42/4.32 | (12) sdtsldt0(xn, xp) = xq % 26.42/4.32 | % 26.42/4.32 | ALPHA: (m__) implies: % 26.42/4.32 | (13) $i(xm) % 26.42/4.32 | (14) $i(xp) % 26.42/4.32 | (15) $i(xq) % 26.42/4.32 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 26.42/4.32 | ( ~ (v4 = v1) & sdtasdt0(xq, xq) = v2 & sdtasdt0(xp, v3) = v4 & % 26.42/4.32 | sdtasdt0(xp, v2) = v3 & sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm) = % 26.42/4.32 | v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 26.42/4.32 | % 26.42/4.32 | ALPHA: (function-axioms) implies: % 26.42/4.32 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.42/4.32 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 26.42/4.32 | v0)) % 26.42/4.32 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.42/4.32 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 26.42/4.32 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.42/4.32 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 26.42/4.32 | (doDivides0(v3, v2) = v0)) % 26.42/4.32 | % 26.42/4.32 | DELTA: instantiating (10) with fresh symbol all_40_0 gives: % 26.42/4.32 | (20) doDivides0(xp, all_40_0) = 0 & doDivides0(xp, xn) = 0 & sdtasdt0(xn, % 26.42/4.32 | xn) = all_40_0 & $i(all_40_0) % 26.42/4.32 | % 26.42/4.32 | ALPHA: (20) implies: % 26.42/4.32 | (21) sdtasdt0(xn, xn) = all_40_0 % 26.42/4.33 | (22) doDivides0(xp, xn) = 0 % 26.42/4.33 | (23) doDivides0(xp, all_40_0) = 0 % 26.42/4.33 | % 26.42/4.33 | DELTA: instantiating (8) with fresh symbols all_42_0, all_42_1 gives: % 26.42/4.33 | (24) sdtasdt0(xp, all_42_1) = all_42_0 & sdtasdt0(xm, xm) = all_42_1 & % 26.42/4.33 | sdtasdt0(xn, xn) = all_42_0 & $i(all_42_0) & $i(all_42_1) % 26.42/4.33 | % 26.42/4.33 | ALPHA: (24) implies: % 26.42/4.33 | (25) sdtasdt0(xn, xn) = all_42_0 % 26.42/4.33 | (26) sdtasdt0(xm, xm) = all_42_1 % 26.42/4.33 | (27) sdtasdt0(xp, all_42_1) = all_42_0 % 26.42/4.33 | % 26.42/4.33 | DELTA: instantiating (16) with fresh symbols all_44_0, all_44_1, all_44_2, % 26.42/4.33 | all_44_3, all_44_4 gives: % 26.42/4.33 | (28) ~ (all_44_0 = all_44_3) & sdtasdt0(xq, xq) = all_44_2 & sdtasdt0(xp, % 26.42/4.33 | all_44_1) = all_44_0 & sdtasdt0(xp, all_44_2) = all_44_1 & % 26.42/4.33 | sdtasdt0(xp, all_44_4) = all_44_3 & sdtasdt0(xm, xm) = all_44_4 & % 26.42/4.33 | $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & $i(all_44_3) & % 26.42/4.33 | $i(all_44_4) % 26.42/4.33 | % 26.42/4.33 | ALPHA: (28) implies: % 26.42/4.33 | (29) ~ (all_44_0 = all_44_3) % 26.42/4.33 | (30) $i(all_44_4) % 26.42/4.33 | (31) $i(all_44_3) % 26.42/4.33 | (32) $i(all_44_2) % 26.42/4.33 | (33) $i(all_44_1) % 26.42/4.33 | (34) sdtasdt0(xm, xm) = all_44_4 % 26.42/4.33 | (35) sdtasdt0(xp, all_44_4) = all_44_3 % 26.42/4.33 | (36) sdtasdt0(xp, all_44_2) = all_44_1 % 26.42/4.33 | (37) sdtasdt0(xp, all_44_1) = all_44_0 % 26.42/4.33 | (38) sdtasdt0(xq, xq) = all_44_2 % 26.42/4.33 | % 26.42/4.33 | GROUND_INST: instantiating (18) with all_40_0, all_42_0, xn, xn, simplifying % 26.42/4.33 | with (21), (25) gives: % 26.42/4.33 | (39) all_42_0 = all_40_0 % 26.42/4.33 | % 26.42/4.33 | GROUND_INST: instantiating (18) with all_42_1, all_44_4, xm, xm, simplifying % 26.42/4.33 | with (26), (34) gives: % 26.42/4.33 | (40) all_44_4 = all_42_1 % 26.42/4.33 | % 26.42/4.33 | REDUCE: (35), (40) imply: % 26.42/4.33 | (41) sdtasdt0(xp, all_42_1) = all_44_3 % 26.42/4.33 | % 26.42/4.33 | REDUCE: (27), (39) imply: % 26.42/4.33 | (42) sdtasdt0(xp, all_42_1) = all_40_0 % 26.42/4.33 | % 26.42/4.33 | REDUCE: (30), (40) imply: % 26.42/4.33 | (43) $i(all_42_1) % 26.42/4.33 | % 26.42/4.33 | GROUND_INST: instantiating (18) with all_40_0, all_44_3, all_42_1, xp, % 26.42/4.33 | simplifying with (41), (42) gives: % 26.42/4.33 | (44) all_44_3 = all_40_0 % 26.42/4.33 | % 26.42/4.33 | REDUCE: (29), (44) imply: % 26.42/4.33 | (45) ~ (all_44_0 = all_40_0) % 26.42/4.33 | % 26.42/4.33 | REDUCE: (31), (44) imply: % 26.42/4.33 | (46) $i(all_40_0) % 26.42/4.33 | % 26.42/4.33 | GROUND_INST: instantiating (4) with xp, simplifying with (7), (14) gives: % 26.42/4.33 | (47) xp = sz10 | xp = sz00 | ? [v0: $i] : (isPrime0(v0) = 0 & % 26.42/4.33 | doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 26.42/4.33 | % 26.42/4.33 | GROUND_INST: instantiating (mSortsB_02) with xn, xn, all_40_0, simplifying % 26.42/4.33 | with (11), (21) gives: % 26.42/4.33 | (48) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.33 | (aNaturalNumber0(all_40_0) = v2 & aNaturalNumber0(xn) = v1 & % 26.42/4.33 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 26.42/4.33 | % 26.42/4.33 | GROUND_INST: instantiating (mSortsB_02) with xm, xm, all_42_1, simplifying % 26.42/4.33 | with (13), (26) gives: % 26.42/4.33 | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.34 | (aNaturalNumber0(all_42_1) = v2 & aNaturalNumber0(xm) = v1 & % 26.42/4.34 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mMulComm) with xp, all_42_1, all_40_0, simplifying % 26.42/4.34 | with (14), (42), (43) gives: % 26.42/4.34 | (50) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_42_1, xp) = % 26.42/4.34 | v2 & aNaturalNumber0(all_42_1) = v1 & aNaturalNumber0(xp) = v0 & % 26.42/4.34 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_40_0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mSortsB_02) with xp, all_42_1, all_40_0, % 26.42/4.34 | simplifying with (14), (42), (43) gives: % 26.42/4.34 | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.34 | (aNaturalNumber0(all_42_1) = v1 & aNaturalNumber0(all_40_0) = v2 & % 26.42/4.34 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mMulComm) with xp, all_44_2, all_44_1, simplifying % 26.42/4.34 | with (14), (32), (36) gives: % 26.42/4.34 | (52) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_44_2, xp) = % 26.42/4.34 | v2 & aNaturalNumber0(all_44_2) = v1 & aNaturalNumber0(xp) = v0 & % 26.42/4.34 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_44_1)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mSortsB_02) with xp, all_44_2, all_44_1, % 26.42/4.34 | simplifying with (14), (32), (36) gives: % 26.42/4.34 | (53) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.34 | (aNaturalNumber0(all_44_1) = v2 & aNaturalNumber0(all_44_2) = v1 & % 26.42/4.34 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mMulComm) with xp, all_44_1, all_44_0, simplifying % 26.42/4.34 | with (14), (33), (37) gives: % 26.42/4.34 | (54) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_44_1, xp) = % 26.42/4.34 | v2 & aNaturalNumber0(all_44_1) = v1 & aNaturalNumber0(xp) = v0 & % 26.42/4.34 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_44_0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mSortsB_02) with xp, all_44_1, all_44_0, % 26.42/4.34 | simplifying with (14), (33), (37) gives: % 26.42/4.34 | (55) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.34 | (aNaturalNumber0(all_44_0) = v2 & aNaturalNumber0(all_44_1) = v1 & % 26.42/4.34 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mMulComm) with xq, xq, all_44_2, simplifying with % 26.42/4.34 | (15), (38) gives: % 26.42/4.34 | (56) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xq, xq) = v2 & % 26.42/4.34 | aNaturalNumber0(xq) = v1 & aNaturalNumber0(xq) = v0 & $i(v2) & ( ~ % 26.42/4.34 | (v1 = 0) | ~ (v0 = 0) | v2 = all_44_2)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mSortsB_02) with xq, xq, all_44_2, simplifying % 26.42/4.34 | with (15), (38) gives: % 26.42/4.34 | (57) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.34 | (aNaturalNumber0(all_44_2) = v2 & aNaturalNumber0(xq) = v1 & % 26.42/4.34 | aNaturalNumber0(xq) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mDefDiv) with xp, xn, 0, simplifying with (11), % 26.42/4.34 | (14), (22) gives: % 26.42/4.34 | (58) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xp) = v0 & % 26.42/4.34 | aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 26.42/4.34 | $i] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 26.42/4.34 | % 26.42/4.34 | GROUND_INST: instantiating (mPDP) with xp, all_42_1, xp, all_40_0, simplifying % 26.42/4.34 | with (14), (23), (42), (43) gives: % 26.42/4.35 | (59) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 26.42/4.35 | any] : ? [v5: any] : (isPrime0(xp) = v3 & doDivides0(xp, all_42_1) % 26.42/4.35 | = v5 & doDivides0(xp, xp) = v4 & aNaturalNumber0(all_42_1) = v1 & % 26.42/4.35 | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | % 26.42/4.35 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v5 = 0 | v4 = 0)) % 26.42/4.35 | % 26.42/4.35 | GROUND_INST: instantiating (mDefDiv) with xp, all_40_0, 0, simplifying with % 26.42/4.35 | (14), (23), (46) gives: % 26.42/4.35 | (60) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_40_0) = v1 & % 26.42/4.35 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 26.42/4.35 | $i] : (sdtasdt0(xp, v0) = all_40_0 & aNaturalNumber0(v0) = 0 & % 26.42/4.35 | $i(v0)) % 26.42/4.35 | % 26.42/4.35 | GROUND_INST: instantiating (2) with xp, xn, xq, simplifying with (11), (12), % 26.42/4.35 | (14) gives: % 26.42/4.35 | (61) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.35 | (doDivides0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & % 26.42/4.35 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 26.42/4.35 | 0))) | ( ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xp, v0) = xn) | ~ % 26.42/4.35 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 26.42/4.35 | & ! [v0: $i] : ( ~ (sdtasdt0(xp, xq) = v0) | ~ $i(xq) | (v0 = xn & % 26.42/4.35 | aNaturalNumber0(xq) = 0))) % 26.42/4.35 | % 26.42/4.35 | GROUND_INST: instantiating (3) with xp, 0, simplifying with (9), (14) gives: % 26.42/4.35 | (62) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | ( ~ (xp = % 26.42/4.35 | sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~ % 26.42/4.35 | (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 26.42/4.35 | & aNaturalNumber0(v0) = v1))) % 26.42/4.35 | % 26.42/4.35 | DELTA: instantiating (57) with fresh symbols all_59_0, all_59_1, all_59_2 % 26.42/4.35 | gives: % 26.42/4.35 | (63) aNaturalNumber0(all_44_2) = all_59_0 & aNaturalNumber0(xq) = all_59_1 % 26.42/4.35 | & aNaturalNumber0(xq) = all_59_2 & ( ~ (all_59_1 = 0) | ~ (all_59_2 = % 26.42/4.35 | 0) | all_59_0 = 0) % 26.42/4.35 | % 26.42/4.35 | ALPHA: (63) implies: % 26.42/4.35 | (64) aNaturalNumber0(xq) = all_59_2 % 26.42/4.35 | (65) aNaturalNumber0(xq) = all_59_1 % 26.42/4.35 | (66) aNaturalNumber0(all_44_2) = all_59_0 % 26.42/4.35 | (67) ~ (all_59_1 = 0) | ~ (all_59_2 = 0) | all_59_0 = 0 % 26.42/4.35 | % 26.42/4.35 | DELTA: instantiating (55) with fresh symbols all_61_0, all_61_1, all_61_2 % 26.42/4.35 | gives: % 26.42/4.35 | (68) aNaturalNumber0(all_44_0) = all_61_0 & aNaturalNumber0(all_44_1) = % 26.42/4.35 | all_61_1 & aNaturalNumber0(xp) = all_61_2 & ( ~ (all_61_1 = 0) | ~ % 26.42/4.35 | (all_61_2 = 0) | all_61_0 = 0) % 26.42/4.35 | % 26.42/4.35 | ALPHA: (68) implies: % 26.42/4.35 | (69) aNaturalNumber0(xp) = all_61_2 % 26.42/4.35 | % 26.42/4.35 | DELTA: instantiating (53) with fresh symbols all_63_0, all_63_1, all_63_2 % 26.42/4.35 | gives: % 26.42/4.35 | (70) aNaturalNumber0(all_44_1) = all_63_0 & aNaturalNumber0(all_44_2) = % 26.42/4.35 | all_63_1 & aNaturalNumber0(xp) = all_63_2 & ( ~ (all_63_1 = 0) | ~ % 26.42/4.35 | (all_63_2 = 0) | all_63_0 = 0) % 26.42/4.35 | % 26.42/4.35 | ALPHA: (70) implies: % 26.42/4.35 | (71) aNaturalNumber0(xp) = all_63_2 % 26.42/4.35 | (72) aNaturalNumber0(all_44_2) = all_63_1 % 26.42/4.35 | % 26.42/4.35 | DELTA: instantiating (48) with fresh symbols all_65_0, all_65_1, all_65_2 % 26.42/4.35 | gives: % 26.42/4.35 | (73) aNaturalNumber0(all_40_0) = all_65_0 & aNaturalNumber0(xn) = all_65_1 % 26.42/4.35 | & aNaturalNumber0(xn) = all_65_2 & ( ~ (all_65_1 = 0) | ~ (all_65_2 = % 26.42/4.35 | 0) | all_65_0 = 0) % 26.42/4.35 | % 26.42/4.35 | ALPHA: (73) implies: % 26.42/4.35 | (74) aNaturalNumber0(xn) = all_65_2 % 26.42/4.35 | (75) aNaturalNumber0(xn) = all_65_1 % 26.42/4.35 | (76) aNaturalNumber0(all_40_0) = all_65_0 % 26.42/4.35 | (77) ~ (all_65_1 = 0) | ~ (all_65_2 = 0) | all_65_0 = 0 % 26.42/4.35 | % 26.42/4.35 | DELTA: instantiating (51) with fresh symbols all_67_0, all_67_1, all_67_2 % 26.42/4.35 | gives: % 26.42/4.35 | (78) aNaturalNumber0(all_42_1) = all_67_1 & aNaturalNumber0(all_40_0) = % 26.42/4.35 | all_67_0 & aNaturalNumber0(xp) = all_67_2 & ( ~ (all_67_1 = 0) | ~ % 26.42/4.35 | (all_67_2 = 0) | all_67_0 = 0) % 26.42/4.35 | % 26.42/4.35 | ALPHA: (78) implies: % 26.42/4.35 | (79) aNaturalNumber0(xp) = all_67_2 % 26.42/4.35 | (80) aNaturalNumber0(all_40_0) = all_67_0 % 26.42/4.35 | (81) aNaturalNumber0(all_42_1) = all_67_1 % 26.42/4.35 | % 26.42/4.35 | DELTA: instantiating (49) with fresh symbols all_69_0, all_69_1, all_69_2 % 26.42/4.35 | gives: % 26.42/4.35 | (82) aNaturalNumber0(all_42_1) = all_69_0 & aNaturalNumber0(xm) = all_69_1 % 26.42/4.35 | & aNaturalNumber0(xm) = all_69_2 & ( ~ (all_69_1 = 0) | ~ (all_69_2 = % 26.42/4.35 | 0) | all_69_0 = 0) % 26.42/4.35 | % 26.42/4.35 | ALPHA: (82) implies: % 26.42/4.35 | (83) aNaturalNumber0(xm) = all_69_2 % 26.42/4.35 | (84) aNaturalNumber0(xm) = all_69_1 % 26.42/4.35 | (85) aNaturalNumber0(all_42_1) = all_69_0 % 26.42/4.35 | (86) ~ (all_69_1 = 0) | ~ (all_69_2 = 0) | all_69_0 = 0 % 26.42/4.35 | % 26.42/4.36 | DELTA: instantiating (56) with fresh symbols all_71_0, all_71_1, all_71_2 % 26.42/4.36 | gives: % 26.42/4.36 | (87) sdtasdt0(xq, xq) = all_71_0 & aNaturalNumber0(xq) = all_71_1 & % 26.42/4.36 | aNaturalNumber0(xq) = all_71_2 & $i(all_71_0) & ( ~ (all_71_1 = 0) | % 26.42/4.36 | ~ (all_71_2 = 0) | all_71_0 = all_44_2) % 26.42/4.36 | % 26.42/4.36 | ALPHA: (87) implies: % 26.42/4.36 | (88) $i(all_71_0) % 26.42/4.36 | (89) aNaturalNumber0(xq) = all_71_2 % 26.42/4.36 | (90) aNaturalNumber0(xq) = all_71_1 % 26.42/4.36 | (91) sdtasdt0(xq, xq) = all_71_0 % 26.42/4.36 | % 26.42/4.36 | DELTA: instantiating (52) with fresh symbols all_73_0, all_73_1, all_73_2 % 26.42/4.36 | gives: % 26.42/4.36 | (92) sdtasdt0(all_44_2, xp) = all_73_0 & aNaturalNumber0(all_44_2) = % 26.42/4.36 | all_73_1 & aNaturalNumber0(xp) = all_73_2 & $i(all_73_0) & ( ~ % 26.42/4.36 | (all_73_1 = 0) | ~ (all_73_2 = 0) | all_73_0 = all_44_1) % 26.42/4.36 | % 26.42/4.36 | ALPHA: (92) implies: % 26.42/4.36 | (93) aNaturalNumber0(xp) = all_73_2 % 26.42/4.36 | (94) aNaturalNumber0(all_44_2) = all_73_1 % 26.42/4.36 | (95) sdtasdt0(all_44_2, xp) = all_73_0 % 26.42/4.36 | % 26.42/4.36 | DELTA: instantiating (50) with fresh symbols all_75_0, all_75_1, all_75_2 % 26.42/4.36 | gives: % 26.42/4.36 | (96) sdtasdt0(all_42_1, xp) = all_75_0 & aNaturalNumber0(all_42_1) = % 26.42/4.36 | all_75_1 & aNaturalNumber0(xp) = all_75_2 & $i(all_75_0) & ( ~ % 26.42/4.36 | (all_75_1 = 0) | ~ (all_75_2 = 0) | all_75_0 = all_40_0) % 26.42/4.36 | % 26.42/4.36 | ALPHA: (96) implies: % 26.42/4.36 | (97) aNaturalNumber0(xp) = all_75_2 % 26.42/4.36 | (98) aNaturalNumber0(all_42_1) = all_75_1 % 26.42/4.36 | (99) sdtasdt0(all_42_1, xp) = all_75_0 % 26.42/4.36 | (100) ~ (all_75_1 = 0) | ~ (all_75_2 = 0) | all_75_0 = all_40_0 % 26.42/4.36 | % 26.42/4.36 | DELTA: instantiating (54) with fresh symbols all_77_0, all_77_1, all_77_2 % 26.42/4.36 | gives: % 26.42/4.36 | (101) sdtasdt0(all_44_1, xp) = all_77_0 & aNaturalNumber0(all_44_1) = % 26.42/4.36 | all_77_1 & aNaturalNumber0(xp) = all_77_2 & $i(all_77_0) & ( ~ % 26.42/4.36 | (all_77_1 = 0) | ~ (all_77_2 = 0) | all_77_0 = all_44_0) % 26.42/4.36 | % 26.42/4.36 | ALPHA: (101) implies: % 26.42/4.36 | (102) aNaturalNumber0(xp) = all_77_2 % 26.42/4.36 | (103) sdtasdt0(all_44_1, xp) = all_77_0 % 26.42/4.36 | % 26.42/4.36 | DELTA: instantiating (59) with fresh symbols all_79_0, all_79_1, all_79_2, % 26.42/4.36 | all_79_3, all_79_4, all_79_5 gives: % 26.42/4.36 | (104) isPrime0(xp) = all_79_2 & doDivides0(xp, all_42_1) = all_79_0 & % 26.42/4.36 | doDivides0(xp, xp) = all_79_1 & aNaturalNumber0(all_42_1) = all_79_4 % 26.42/4.36 | & aNaturalNumber0(xp) = all_79_3 & aNaturalNumber0(xp) = all_79_5 & ( % 26.42/4.36 | ~ (all_79_2 = 0) | ~ (all_79_3 = 0) | ~ (all_79_4 = 0) | ~ % 26.42/4.36 | (all_79_5 = 0) | all_79_0 = 0 | all_79_1 = 0) % 26.42/4.36 | % 26.42/4.36 | ALPHA: (104) implies: % 26.42/4.36 | (105) aNaturalNumber0(xp) = all_79_5 % 26.42/4.36 | (106) aNaturalNumber0(xp) = all_79_3 % 26.42/4.36 | (107) aNaturalNumber0(all_42_1) = all_79_4 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with 0, all_65_1, xn, simplifying with (5), % 26.42/4.36 | (75) gives: % 26.42/4.36 | (108) all_65_1 = 0 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_65_2, all_65_1, xn, simplifying with % 26.42/4.36 | (74), (75) gives: % 26.42/4.36 | (109) all_65_1 = all_65_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with 0, all_69_1, xm, simplifying with (6), % 26.42/4.36 | (84) gives: % 26.42/4.36 | (110) all_69_1 = 0 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_69_2, all_69_1, xm, simplifying with % 26.42/4.36 | (83), (84) gives: % 26.42/4.36 | (111) all_69_1 = all_69_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_61_2, all_73_2, xp, simplifying with % 26.42/4.36 | (69), (93) gives: % 26.42/4.36 | (112) all_73_2 = all_61_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with 0, all_75_2, xp, simplifying with (7), % 26.42/4.36 | (97) gives: % 26.42/4.36 | (113) all_75_2 = 0 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_63_2, all_75_2, xp, simplifying with % 26.42/4.36 | (71), (97) gives: % 26.42/4.36 | (114) all_75_2 = all_63_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_75_2, all_77_2, xp, simplifying with % 26.42/4.36 | (97), (102) gives: % 26.42/4.36 | (115) all_77_2 = all_75_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_73_2, all_77_2, xp, simplifying with % 26.42/4.36 | (93), (102) gives: % 26.42/4.36 | (116) all_77_2 = all_73_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_77_2, all_79_5, xp, simplifying with % 26.42/4.36 | (102), (105) gives: % 26.42/4.36 | (117) all_79_5 = all_77_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_79_5, all_79_3, xp, simplifying with % 26.42/4.36 | (105), (106) gives: % 26.42/4.36 | (118) all_79_3 = all_79_5 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_67_2, all_79_3, xp, simplifying with % 26.42/4.36 | (79), (106) gives: % 26.42/4.36 | (119) all_79_3 = all_67_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_71_2, all_71_1, xq, simplifying with % 26.42/4.36 | (89), (90) gives: % 26.42/4.36 | (120) all_71_1 = all_71_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_59_1, all_71_1, xq, simplifying with % 26.42/4.36 | (65), (90) gives: % 26.42/4.36 | (121) all_71_1 = all_59_1 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_59_2, all_71_1, xq, simplifying with % 26.42/4.36 | (64), (90) gives: % 26.42/4.36 | (122) all_71_1 = all_59_2 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_65_0, all_67_0, all_40_0, simplifying % 26.42/4.36 | with (76), (80) gives: % 26.42/4.36 | (123) all_67_0 = all_65_0 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_75_1, all_79_4, all_42_1, simplifying % 26.42/4.36 | with (98), (107) gives: % 26.42/4.36 | (124) all_79_4 = all_75_1 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_69_0, all_79_4, all_42_1, simplifying % 26.42/4.36 | with (85), (107) gives: % 26.42/4.36 | (125) all_79_4 = all_69_0 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_67_1, all_79_4, all_42_1, simplifying % 26.42/4.36 | with (81), (107) gives: % 26.42/4.36 | (126) all_79_4 = all_67_1 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_63_1, all_73_1, all_44_2, simplifying % 26.42/4.36 | with (72), (94) gives: % 26.42/4.36 | (127) all_73_1 = all_63_1 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (17) with all_59_0, all_73_1, all_44_2, simplifying % 26.42/4.36 | with (66), (94) gives: % 26.42/4.36 | (128) all_73_1 = all_59_0 % 26.42/4.36 | % 26.42/4.36 | GROUND_INST: instantiating (18) with all_44_2, all_71_0, xq, xq, simplifying % 26.42/4.36 | with (38), (91) gives: % 26.42/4.36 | (129) all_71_0 = all_44_2 % 26.42/4.36 | % 26.42/4.37 | COMBINE_EQS: (118), (119) imply: % 26.42/4.37 | (130) all_79_5 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (130) implies: % 26.42/4.37 | (131) all_79_5 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (124), (125) imply: % 26.42/4.37 | (132) all_75_1 = all_69_0 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (124), (126) imply: % 26.42/4.37 | (133) all_75_1 = all_67_1 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (117), (131) imply: % 26.42/4.37 | (134) all_77_2 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (134) implies: % 26.42/4.37 | (135) all_77_2 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (116), (135) imply: % 26.42/4.37 | (136) all_73_2 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (136) implies: % 26.42/4.37 | (137) all_73_2 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (115), (135) imply: % 26.42/4.37 | (138) all_75_2 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (138) implies: % 26.42/4.37 | (139) all_75_2 = all_67_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (132), (133) imply: % 26.42/4.37 | (140) all_69_0 = all_67_1 % 26.42/4.37 | % 26.42/4.37 | SIMP: (140) implies: % 26.42/4.37 | (141) all_69_0 = all_67_1 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (113), (114) imply: % 26.42/4.37 | (142) all_63_2 = 0 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (114), (139) imply: % 26.42/4.37 | (143) all_67_2 = all_63_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (143) implies: % 26.42/4.37 | (144) all_67_2 = all_63_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (127), (128) imply: % 26.42/4.37 | (145) all_63_1 = all_59_0 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (112), (137) imply: % 26.42/4.37 | (146) all_67_2 = all_61_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (146) implies: % 26.42/4.37 | (147) all_67_2 = all_61_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (120), (122) imply: % 26.42/4.37 | (148) all_71_2 = all_59_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (120), (121) imply: % 26.42/4.37 | (149) all_71_2 = all_59_1 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (148), (149) imply: % 26.42/4.37 | (150) all_59_1 = all_59_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (150) implies: % 26.42/4.37 | (151) all_59_1 = all_59_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (110), (111) imply: % 26.42/4.37 | (152) all_69_2 = 0 % 26.42/4.37 | % 26.42/4.37 | SIMP: (152) implies: % 26.42/4.37 | (153) all_69_2 = 0 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (144), (147) imply: % 26.42/4.37 | (154) all_63_2 = all_61_2 % 26.42/4.37 | % 26.42/4.37 | SIMP: (154) implies: % 26.42/4.37 | (155) all_63_2 = all_61_2 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (108), (109) imply: % 26.42/4.37 | (156) all_65_2 = 0 % 26.42/4.37 | % 26.42/4.37 | COMBINE_EQS: (142), (155) imply: % 26.42/4.37 | (157) all_61_2 = 0 % 26.42/4.37 | % 26.42/4.37 | BETA: splitting (62) gives: % 26.42/4.37 | % 26.42/4.37 | Case 1: % 26.42/4.37 | | % 26.42/4.37 | | (158) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) % 26.42/4.37 | | % 26.42/4.37 | | DELTA: instantiating (158) with fresh symbol all_105_0 gives: % 26.42/4.37 | | (159) ~ (all_105_0 = 0) & aNaturalNumber0(xp) = all_105_0 % 26.42/4.37 | | % 26.42/4.37 | | ALPHA: (159) implies: % 26.42/4.37 | | (160) ~ (all_105_0 = 0) % 26.42/4.37 | | (161) aNaturalNumber0(xp) = all_105_0 % 26.42/4.37 | | % 26.42/4.37 | | GROUND_INST: instantiating (17) with 0, all_105_0, xp, simplifying with (7), % 26.42/4.37 | | (161) gives: % 26.42/4.37 | | (162) all_105_0 = 0 % 26.42/4.37 | | % 26.42/4.37 | | REDUCE: (160), (162) imply: % 26.42/4.37 | | (163) $false % 26.42/4.37 | | % 26.42/4.37 | | CLOSE: (163) is inconsistent. % 26.42/4.37 | | % 26.42/4.37 | Case 2: % 26.42/4.37 | | % 26.42/4.37 | | (164) ~ (xp = sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 = % 26.42/4.37 | | sz10 | ~ (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int] : ( % 26.42/4.37 | | ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 26.42/4.37 | | % 26.42/4.37 | | ALPHA: (164) implies: % 26.42/4.37 | | (165) ~ (xp = sz00) % 26.42/4.37 | | (166) ~ (xp = sz10) % 26.42/4.37 | | (167) ! [v0: $i] : (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = 0) | % 26.42/4.37 | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = % 26.42/4.37 | | v1)) % 26.42/4.37 | | % 26.42/4.37 | | BETA: splitting (77) gives: % 26.42/4.37 | | % 26.42/4.37 | | Case 1: % 26.42/4.37 | | | % 26.42/4.37 | | | (168) ~ (all_65_1 = 0) % 26.42/4.37 | | | % 26.42/4.37 | | | REDUCE: (108), (168) imply: % 26.42/4.37 | | | (169) $false % 26.42/4.37 | | | % 26.42/4.37 | | | CLOSE: (169) is inconsistent. % 26.42/4.37 | | | % 26.42/4.37 | | Case 2: % 26.42/4.37 | | | % 26.42/4.37 | | | (170) ~ (all_65_2 = 0) | all_65_0 = 0 % 26.42/4.37 | | | % 26.42/4.37 | | | BETA: splitting (58) gives: % 26.42/4.37 | | | % 26.42/4.37 | | | Case 1: % 26.42/4.37 | | | | % 26.42/4.37 | | | | (171) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xp) = v0 & % 26.42/4.37 | | | | aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 26.42/4.37 | | | | % 26.42/4.37 | | | | DELTA: instantiating (171) with fresh symbols all_113_0, all_113_1 % 26.42/4.37 | | | | gives: % 26.42/4.37 | | | | (172) aNaturalNumber0(xp) = all_113_1 & aNaturalNumber0(xn) = % 26.42/4.37 | | | | all_113_0 & ( ~ (all_113_0 = 0) | ~ (all_113_1 = 0)) % 26.42/4.37 | | | | % 26.42/4.37 | | | | ALPHA: (172) implies: % 26.42/4.37 | | | | (173) aNaturalNumber0(xn) = all_113_0 % 26.42/4.37 | | | | (174) aNaturalNumber0(xp) = all_113_1 % 26.42/4.37 | | | | (175) ~ (all_113_0 = 0) | ~ (all_113_1 = 0) % 26.42/4.37 | | | | % 26.42/4.38 | | | | GROUND_INST: instantiating (17) with 0, all_113_0, xn, simplifying with % 26.42/4.38 | | | | (5), (173) gives: % 26.42/4.38 | | | | (176) all_113_0 = 0 % 26.42/4.38 | | | | % 26.42/4.38 | | | | GROUND_INST: instantiating (17) with 0, all_113_1, xp, simplifying with % 26.42/4.38 | | | | (7), (174) gives: % 26.42/4.38 | | | | (177) all_113_1 = 0 % 26.42/4.38 | | | | % 26.42/4.38 | | | | BETA: splitting (175) gives: % 26.42/4.38 | | | | % 26.42/4.38 | | | | Case 1: % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | (178) ~ (all_113_0 = 0) % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | REDUCE: (176), (178) imply: % 26.42/4.38 | | | | | (179) $false % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | CLOSE: (179) is inconsistent. % 26.42/4.38 | | | | | % 26.42/4.38 | | | | Case 2: % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | (180) ~ (all_113_1 = 0) % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | REDUCE: (177), (180) imply: % 26.42/4.38 | | | | | (181) $false % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | CLOSE: (181) is inconsistent. % 26.42/4.38 | | | | | % 26.42/4.38 | | | | End of split % 26.42/4.38 | | | | % 26.42/4.38 | | | Case 2: % 26.42/4.38 | | | | % 26.42/4.38 | | | | (182) ? [v0: $i] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0) = 0 % 26.42/4.38 | | | | & $i(v0)) % 26.42/4.38 | | | | % 26.42/4.38 | | | | DELTA: instantiating (182) with fresh symbol all_113_0 gives: % 26.42/4.38 | | | | (183) sdtasdt0(xp, all_113_0) = xn & aNaturalNumber0(all_113_0) = 0 & % 26.42/4.38 | | | | $i(all_113_0) % 26.42/4.38 | | | | % 26.42/4.38 | | | | ALPHA: (183) implies: % 26.42/4.38 | | | | (184) $i(all_113_0) % 26.42/4.38 | | | | (185) aNaturalNumber0(all_113_0) = 0 % 26.42/4.38 | | | | (186) sdtasdt0(xp, all_113_0) = xn % 26.42/4.38 | | | | % 26.42/4.38 | | | | BETA: splitting (47) gives: % 26.42/4.38 | | | | % 26.42/4.38 | | | | Case 1: % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | (187) xp = sz00 % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | REDUCE: (165), (187) imply: % 26.42/4.38 | | | | | (188) $false % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | CLOSE: (188) is inconsistent. % 26.42/4.38 | | | | | % 26.42/4.38 | | | | Case 2: % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | (189) xp = sz10 | ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0, % 26.42/4.38 | | | | | xp) = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | BETA: splitting (86) gives: % 26.42/4.38 | | | | | % 26.42/4.38 | | | | | Case 1: % 26.42/4.38 | | | | | | % 26.42/4.38 | | | | | | (190) ~ (all_69_1 = 0) % 26.42/4.38 | | | | | | % 26.42/4.38 | | | | | | REDUCE: (110), (190) imply: % 26.42/4.38 | | | | | | (191) $false % 26.42/4.38 | | | | | | % 26.42/4.38 | | | | | | CLOSE: (191) is inconsistent. % 26.42/4.38 | | | | | | % 26.42/4.38 | | | | | Case 2: % 26.42/4.38 | | | | | | % 26.42/4.38 | | | | | | (192) ~ (all_69_2 = 0) | all_69_0 = 0 % 26.42/4.38 | | | | | | % 26.42/4.38 | | | | | | BETA: splitting (189) gives: % 26.42/4.38 | | | | | | % 26.42/4.38 | | | | | | Case 1: % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | (193) xp = sz10 % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | REDUCE: (166), (193) imply: % 26.42/4.38 | | | | | | | (194) $false % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | CLOSE: (194) is inconsistent. % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | Case 2: % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | (195) ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0, xp) = 0 % 26.42/4.38 | | | | | | | & aNaturalNumber0(v0) = 0 & $i(v0)) % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | DELTA: instantiating (195) with fresh symbol all_125_0 gives: % 26.42/4.38 | | | | | | | (196) isPrime0(all_125_0) = 0 & doDivides0(all_125_0, xp) = 0 & % 26.42/4.38 | | | | | | | aNaturalNumber0(all_125_0) = 0 & $i(all_125_0) % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | ALPHA: (196) implies: % 26.42/4.38 | | | | | | | (197) $i(all_125_0) % 26.42/4.38 | | | | | | | (198) aNaturalNumber0(all_125_0) = 0 % 26.42/4.38 | | | | | | | (199) doDivides0(all_125_0, xp) = 0 % 26.42/4.38 | | | | | | | (200) isPrime0(all_125_0) = 0 % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | BETA: splitting (192) gives: % 26.42/4.38 | | | | | | | % 26.42/4.38 | | | | | | | Case 1: % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | (201) ~ (all_69_2 = 0) % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | REDUCE: (153), (201) imply: % 26.42/4.38 | | | | | | | | (202) $false % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | CLOSE: (202) is inconsistent. % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | Case 2: % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | (203) all_69_0 = 0 % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | COMBINE_EQS: (141), (203) imply: % 26.42/4.38 | | | | | | | | (204) all_67_1 = 0 % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | SIMP: (204) implies: % 26.42/4.38 | | | | | | | | (205) all_67_1 = 0 % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | COMBINE_EQS: (133), (205) imply: % 26.42/4.38 | | | | | | | | (206) all_75_1 = 0 % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | BETA: splitting (61) gives: % 26.42/4.38 | | | | | | | | % 26.42/4.38 | | | | | | | | Case 1: % 26.42/4.38 | | | | | | | | | % 26.42/4.38 | | | | | | | | | (207) xp = sz00 % 26.42/4.38 | | | | | | | | | % 26.42/4.38 | | | | | | | | | REDUCE: (165), (207) imply: % 26.42/4.38 | | | | | | | | | (208) $false % 26.42/4.38 | | | | | | | | | % 26.42/4.38 | | | | | | | | | CLOSE: (208) is inconsistent. % 26.42/4.38 | | | | | | | | | % 26.42/4.38 | | | | | | | | Case 2: % 26.42/4.38 | | | | | | | | | % 26.42/4.38 | | | | | | | | | (209) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.38 | | | | | | | | | (doDivides0(xp, xn) = v2 & aNaturalNumber0(xp) = v0 & % 26.42/4.38 | | | | | | | | | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = % 26.42/4.38 | | | | | | | | | 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 = xq | % 26.42/4.38 | | | | | | | | | ~ (sdtasdt0(xp, v0) = xn) | ~ $i(v0) | ? [v1: % 26.42/4.38 | | | | | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = % 26.42/4.38 | | | | | | | | | v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xp, xq) = % 26.42/4.38 | | | | | | | | | v0) | ~ $i(xq) | (v0 = xn & % 26.42/4.38 | | | | | | | | | aNaturalNumber0(xq) = 0))) % 26.42/4.38 | | | | | | | | | % 26.42/4.38 | | | | | | | | | BETA: splitting (170) gives: % 26.42/4.38 | | | | | | | | | % 26.42/4.38 | | | | | | | | | Case 1: % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | (210) ~ (all_65_2 = 0) % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | REDUCE: (156), (210) imply: % 26.42/4.38 | | | | | | | | | | (211) $false % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | CLOSE: (211) is inconsistent. % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | Case 2: % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | (212) all_65_0 = 0 % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | REDUCE: (76), (212) imply: % 26.42/4.38 | | | | | | | | | | (213) aNaturalNumber0(all_40_0) = 0 % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | BETA: splitting (100) gives: % 26.42/4.38 | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | Case 1: % 26.42/4.38 | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | (214) ~ (all_75_1 = 0) % 26.42/4.38 | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | REDUCE: (206), (214) imply: % 26.42/4.38 | | | | | | | | | | | (215) $false % 26.42/4.38 | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | CLOSE: (215) is inconsistent. % 26.42/4.38 | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | Case 2: % 26.42/4.38 | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | (216) ~ (all_75_2 = 0) | all_75_0 = all_40_0 % 26.42/4.38 | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | BETA: splitting (209) gives: % 26.42/4.38 | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | Case 1: % 26.42/4.38 | | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | | (217) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.42/4.38 | | | | | | | | | | | | (doDivides0(xp, xn) = v2 & aNaturalNumber0(xp) = % 26.42/4.38 | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | % 26.42/4.38 | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 26.42/4.38 | | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | | DELTA: instantiating (217) with fresh symbols all_149_0, % 26.42/4.38 | | | | | | | | | | | | all_149_1, all_149_2 gives: % 26.42/4.38 | | | | | | | | | | | | (218) doDivides0(xp, xn) = all_149_0 & % 26.42/4.38 | | | | | | | | | | | | aNaturalNumber0(xp) = all_149_2 & % 26.42/4.38 | | | | | | | | | | | | aNaturalNumber0(xn) = all_149_1 & ( ~ (all_149_0 = % 26.42/4.38 | | | | | | | | | | | | 0) | ~ (all_149_1 = 0) | ~ (all_149_2 = 0)) % 26.42/4.38 | | | | | | | | | | | | % 26.42/4.38 | | | | | | | | | | | | ALPHA: (218) implies: % 26.42/4.38 | | | | | | | | | | | | (219) aNaturalNumber0(xn) = all_149_1 % 26.42/4.38 | | | | | | | | | | | | (220) aNaturalNumber0(xp) = all_149_2 % 26.42/4.38 | | | | | | | | | | | | (221) doDivides0(xp, xn) = all_149_0 % 26.42/4.38 | | | | | | | | | | | | (222) ~ (all_149_0 = 0) | ~ (all_149_1 = 0) | ~ % 26.42/4.38 | | | | | | | | | | | | (all_149_2 = 0) % 26.42/4.38 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_149_1, xn, % 26.42/4.39 | | | | | | | | | | | | simplifying with (5), (219) gives: % 26.42/4.39 | | | | | | | | | | | | (223) all_149_1 = 0 % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_149_2, xp, % 26.42/4.39 | | | | | | | | | | | | simplifying with (7), (220) gives: % 26.42/4.39 | | | | | | | | | | | | (224) all_149_2 = 0 % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_149_0, xn, xp, % 26.42/4.39 | | | | | | | | | | | | simplifying with (22), (221) gives: % 26.42/4.39 | | | | | | | | | | | | (225) all_149_0 = 0 % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | BETA: splitting (222) gives: % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | Case 1: % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | (226) ~ (all_149_0 = 0) % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | REDUCE: (225), (226) imply: % 26.42/4.39 | | | | | | | | | | | | | (227) $false % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | CLOSE: (227) is inconsistent. % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | Case 2: % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | (228) ~ (all_149_1 = 0) | ~ (all_149_2 = 0) % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | BETA: splitting (228) gives: % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | Case 1: % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | (229) ~ (all_149_1 = 0) % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | REDUCE: (223), (229) imply: % 26.42/4.39 | | | | | | | | | | | | | | (230) $false % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | CLOSE: (230) is inconsistent. % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | Case 2: % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | (231) ~ (all_149_2 = 0) % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | REDUCE: (224), (231) imply: % 26.42/4.39 | | | | | | | | | | | | | | (232) $false % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | End of split % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | End of split % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | Case 2: % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | (233) ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xp, v0) = % 26.42/4.39 | | | | | | | | | | | | xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 26.42/4.39 | | | | | | | | | | | | & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 26.42/4.39 | | | | | | | | | | | | ~ (sdtasdt0(xp, xq) = v0) | ~ $i(xq) | (v0 = xn % 26.42/4.39 | | | | | | | | | | | | & aNaturalNumber0(xq) = 0)) % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | ALPHA: (233) implies: % 26.42/4.39 | | | | | | | | | | | | (234) ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xp, v0) = % 26.42/4.39 | | | | | | | | | | | | xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 26.42/4.39 | | | | | | | | | | | | & aNaturalNumber0(v0) = v1)) % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | BETA: splitting (60) gives: % 26.42/4.39 | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | Case 1: % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | (235) ? [v0: any] : ? [v1: any] : % 26.42/4.39 | | | | | | | | | | | | | (aNaturalNumber0(all_40_0) = v1 & % 26.42/4.39 | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 % 26.42/4.39 | | | | | | | | | | | | | = 0))) % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | DELTA: instantiating (235) with fresh symbols all_151_0, % 26.42/4.39 | | | | | | | | | | | | | all_151_1 gives: % 26.42/4.39 | | | | | | | | | | | | | (236) aNaturalNumber0(all_40_0) = all_151_0 & % 26.42/4.39 | | | | | | | | | | | | | aNaturalNumber0(xp) = all_151_1 & ( ~ (all_151_0 = % 26.42/4.39 | | | | | | | | | | | | | 0) | ~ (all_151_1 = 0)) % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | ALPHA: (236) implies: % 26.42/4.39 | | | | | | | | | | | | | (237) aNaturalNumber0(xp) = all_151_1 % 26.42/4.39 | | | | | | | | | | | | | (238) aNaturalNumber0(all_40_0) = all_151_0 % 26.42/4.39 | | | | | | | | | | | | | (239) ~ (all_151_0 = 0) | ~ (all_151_1 = 0) % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_151_1, xp, % 26.42/4.39 | | | | | | | | | | | | | simplifying with (7), (237) gives: % 26.42/4.39 | | | | | | | | | | | | | (240) all_151_1 = 0 % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_151_0, all_40_0, % 26.42/4.39 | | | | | | | | | | | | | simplifying with (213), (238) gives: % 26.42/4.39 | | | | | | | | | | | | | (241) all_151_0 = 0 % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | BETA: splitting (239) gives: % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | Case 1: % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | (242) ~ (all_151_0 = 0) % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | REDUCE: (241), (242) imply: % 26.42/4.39 | | | | | | | | | | | | | | (243) $false % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | CLOSE: (243) is inconsistent. % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | Case 2: % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | (244) ~ (all_151_1 = 0) % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | REDUCE: (240), (244) imply: % 26.42/4.39 | | | | | | | | | | | | | | (245) $false % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | CLOSE: (245) is inconsistent. % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | End of split % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | Case 2: % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | (246) ? [v0: $i] : (sdtasdt0(xp, v0) = all_40_0 & % 26.42/4.39 | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0)) % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | DELTA: instantiating (246) with fresh symbol all_151_0 % 26.42/4.39 | | | | | | | | | | | | | gives: % 26.42/4.39 | | | | | | | | | | | | | (247) sdtasdt0(xp, all_151_0) = all_40_0 & % 26.42/4.39 | | | | | | | | | | | | | aNaturalNumber0(all_151_0) = 0 & $i(all_151_0) % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | ALPHA: (247) implies: % 26.42/4.39 | | | | | | | | | | | | | (248) $i(all_151_0) % 26.42/4.39 | | | | | | | | | | | | | (249) sdtasdt0(xp, all_151_0) = all_40_0 % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | BETA: splitting (216) gives: % 26.42/4.39 | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | Case 1: % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | (250) ~ (all_75_2 = 0) % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | REDUCE: (113), (250) imply: % 26.42/4.39 | | | | | | | | | | | | | | (251) $false % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | CLOSE: (251) is inconsistent. % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | Case 2: % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | (252) all_75_0 = all_40_0 % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | REDUCE: (99), (252) imply: % 26.42/4.39 | | | | | | | | | | | | | | (253) sdtasdt0(all_42_1, xp) = all_40_0 % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_125_0, simplifying with % 26.42/4.39 | | | | | | | | | | | | | | (197), (198) gives: % 26.42/4.39 | | | | | | | | | | | | | | (254) all_125_0 = sz00 | ! [v0: $i] : ! [v1: $i] : ! % 26.42/4.39 | | | | | | | | | | | | | | [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.42/4.39 | | | | | | | | | | | | | | (sdtasdt0(all_125_0, v1) = v3) | ~ % 26.42/4.39 | | | | | | | | | | | | | | (sdtasdt0(all_125_0, v0) = v2) | ~ $i(v1) | ~ % 26.42/4.39 | | | | | | | | | | | | | | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 26.42/4.39 | | | | | | | | | | | | | | $i] : ? [v7: $i] : (sdtasdt0(v1, all_125_0) = % 26.42/4.39 | | | | | | | | | | | | | | v7 & sdtasdt0(v0, all_125_0) = v6 & % 26.42/4.39 | | | | | | | | | | | | | | aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) % 26.42/4.39 | | | | | | | | | | | | | | = v4 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 % 26.42/4.39 | | | | | | | | | | | | | | = 0) | ( ~ (v7 = v6) & ~ (v3 = v2))))) % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xp, all_113_0, xn, % 26.42/4.39 | | | | | | | | | | | | | | xn, all_40_0, simplifying with (11), (14), (21), % 26.42/4.39 | | | | | | | | | | | | | | (184), (186) gives: % 26.42/4.39 | | | | | | | | | | | | | | (255) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.42/4.39 | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_113_0, xn) % 26.42/4.39 | | | | | | | | | | | | | | = v3 & sdtasdt0(xp, v3) = v4 & % 26.42/4.39 | | | | | | | | | | | | | | aNaturalNumber0(all_113_0) = v1 & % 26.42/4.39 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & aNaturalNumber0(xn) = % 26.42/4.39 | | | | | | | | | | | | | | v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 26.42/4.39 | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_40_0)) % 26.42/4.39 | | | | | | | | | | | | | | % 26.42/4.39 | | | | | | | | | | | | | | GROUND_INST: instantiating (mPDP) with xp, all_113_0, xp, xn, % 26.42/4.39 | | | | | | | | | | | | | | simplifying with (14), (22), (184), (186) gives: % 26.42/4.40 | | | | | | | | | | | | | | (256) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.42/4.40 | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : ? [v5: any] : % 26.42/4.40 | | | | | | | | | | | | | | (isPrime0(xp) = v3 & doDivides0(xp, all_113_0) = % 26.42/4.40 | | | | | | | | | | | | | | v5 & doDivides0(xp, xp) = v4 & % 26.42/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_113_0) = v1 & % 26.42/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = % 26.42/4.40 | | | | | | | | | | | | | | v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | % 26.42/4.40 | | | | | | | | | | | | | | ~ (v0 = 0) | v5 = 0 | v4 = 0)) % 26.42/4.40 | | | | | | | | | | | | | | % 26.42/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (234) with all_113_0, simplifying % 26.42/4.40 | | | | | | | | | | | | | | with (184), (186) gives: % 26.42/4.40 | | | | | | | | | | | | | | (257) all_113_0 = xq | ? [v0: int] : ( ~ (v0 = 0) & % 26.42/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_113_0) = v0) % 26.42/4.40 | | | | | | | | | | | | | | % 26.42/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_113_0, xn, % 26.42/4.40 | | | | | | | | | | | | | | simplifying with (14), (184), (186) gives: % 26.42/4.40 | | | | | | | | | | | | | | (258) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 26.42/4.40 | | | | | | | | | | | | | | (sdtasdt0(all_113_0, xp) = v2 & % 26.42/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_113_0) = v1 & % 26.42/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & $i(v2) & ( ~ (v1 = 0) % 26.42/4.40 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = xn)) % 26.42/4.40 | | | | | | | | | | | | | | % 26.42/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mPDP) with xp, all_151_0, xp, % 26.42/4.40 | | | | | | | | | | | | | | all_40_0, simplifying with (14), (23), (248), % 26.42/4.40 | | | | | | | | | | | | | | (249) gives: % 26.42/4.40 | | | | | | | | | | | | | | (259) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.42/4.40 | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : ? [v5: any] : % 26.42/4.40 | | | | | | | | | | | | | | (isPrime0(xp) = v3 & doDivides0(xp, all_151_0) = % 26.42/4.40 | | | | | | | | | | | | | | v5 & doDivides0(xp, xp) = v4 & % 26.42/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_151_0) = v1 & % 26.42/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = % 26.42/4.40 | | | | | | | | | | | | | | v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | % 26.42/4.40 | | | | | | | | | | | | | | ~ (v0 = 0) | v5 = 0 | v4 = 0)) % 26.42/4.40 | | | | | | | | | | | | | | % 26.42/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_151_0, % 26.42/4.40 | | | | | | | | | | | | | | all_40_0, simplifying with (14), (248), (249) % 26.42/4.40 | | | | | | | | | | | | | | gives: % 26.83/4.40 | | | | | | | | | | | | | | (260) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 26.83/4.40 | | | | | | | | | | | | | | (sdtasdt0(all_151_0, xp) = v2 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_151_0) = v1 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & $i(v2) & ( ~ (v1 = 0) % 26.83/4.40 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_40_0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xm, xm, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_42_1, all_40_0, simplifying with (13), (14), % 26.83/4.40 | | | | | | | | | | | | | | (26), (253) gives: % 26.83/4.40 | | | | | | | | | | | | | | (261) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.40 | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(xm, v3) = v4 & % 26.83/4.40 | | | | | | | | | | | | | | sdtasdt0(xm, xp) = v3 & aNaturalNumber0(xp) = v2 % 26.83/4.40 | | | | | | | | | | | | | | & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xm) % 26.83/4.40 | | | | | | | | | | | | | | = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 26.83/4.40 | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_40_0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mPDP) with all_42_1, xp, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_40_0, simplifying with (14), (23), (43), (253) % 26.83/4.40 | | | | | | | | | | | | | | gives: % 26.83/4.40 | | | | | | | | | | | | | | (262) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.40 | | | | | | | | | | | | | | [v3: any] : ? [v4: any] : ? [v5: any] : % 26.83/4.40 | | | | | | | | | | | | | | (isPrime0(xp) = v3 & doDivides0(xp, all_42_1) = v4 % 26.83/4.40 | | | | | | | | | | | | | | & doDivides0(xp, xp) = v5 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_42_1) = v0 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = % 26.83/4.40 | | | | | | | | | | | | | | v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | % 26.83/4.40 | | | | | | | | | | | | | | ~ (v0 = 0) | v5 = 0 | v4 = 0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xq, xq, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_44_2, all_73_0, simplifying with (14), (15), % 26.83/4.40 | | | | | | | | | | | | | | (38), (95) gives: % 26.83/4.40 | | | | | | | | | | | | | | (263) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.40 | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(xq, v3) = v4 & % 26.83/4.40 | | | | | | | | | | | | | | sdtasdt0(xq, xp) = v3 & aNaturalNumber0(xq) = v1 % 26.83/4.40 | | | | | | | | | | | | | | & aNaturalNumber0(xq) = v0 & aNaturalNumber0(xp) % 26.83/4.40 | | | | | | | | | | | | | | = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 26.83/4.40 | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_73_0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_44_2, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_73_0, simplifying with (14), (32), (95) gives: % 26.83/4.40 | | | | | | | | | | | | | | (264) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 26.83/4.40 | | | | | | | | | | | | | | (sdtasdt0(xp, all_44_2) = v2 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_44_2) = v0 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & $i(v2) & ( ~ (v1 = 0) % 26.83/4.40 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_73_0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_44_2, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_73_0, simplifying with (14), (32), (95) gives: % 26.83/4.40 | | | | | | | | | | | | | | (265) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.83/4.40 | | | | | | | | | | | | | | (aNaturalNumber0(all_73_0) = v2 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_44_2) = v0 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 % 26.83/4.40 | | | | | | | | | | | | | | = 0) | v2 = 0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xp, all_44_2, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_44_1, all_77_0, simplifying with (14), (32), % 26.83/4.40 | | | | | | | | | | | | | | (36), (103) gives: % 26.83/4.40 | | | | | | | | | | | | | | (266) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 26.83/4.40 | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_44_2, xp) = % 26.83/4.40 | | | | | | | | | | | | | | v3 & sdtasdt0(xp, v3) = v4 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_44_2) = v1 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xp) = % 26.83/4.40 | | | | | | | | | | | | | | v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 26.83/4.40 | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_77_0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_44_1, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_77_0, simplifying with (14), (33), (103) % 26.83/4.40 | | | | | | | | | | | | | | gives: % 26.83/4.40 | | | | | | | | | | | | | | (267) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 26.83/4.40 | | | | | | | | | | | | | | (sdtasdt0(xp, all_44_1) = v2 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_44_1) = v0 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & $i(v2) & ( ~ (v1 = 0) % 26.83/4.40 | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_77_0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_44_1, xp, % 26.83/4.40 | | | | | | | | | | | | | | all_77_0, simplifying with (14), (33), (103) % 26.83/4.40 | | | | | | | | | | | | | | gives: % 26.83/4.40 | | | | | | | | | | | | | | (268) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 26.83/4.40 | | | | | | | | | | | | | | (aNaturalNumber0(all_77_0) = v2 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(all_44_1) = v0 & % 26.83/4.40 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 % 26.83/4.40 | | | | | | | | | | | | | | = 0) | v2 = 0)) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_125_0, simplifying % 26.83/4.40 | | | | | | | | | | | | | | with (197), (199) gives: % 26.83/4.40 | | | | | | | | | | | | | | (269) all_125_0 = xp | all_125_0 = sz10 | ? [v0: int] : % 26.83/4.40 | | | | | | | | | | | | | | ( ~ (v0 = 0) & aNaturalNumber0(all_125_0) = v0) % 26.83/4.40 | | | | | | | | | | | | | | % 26.83/4.40 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_125_0, 0, simplifying % 26.83/4.40 | | | | | | | | | | | | | | with (197), (200) gives: % 26.83/4.41 | | | | | | | | | | | | | | (270) ? [v0: int] : ( ~ (v0 = 0) & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_125_0) = v0) | ( ~ % 26.83/4.41 | | | | | | | | | | | | | | (all_125_0 = sz10) & ~ (all_125_0 = sz00) & ! % 26.83/4.41 | | | | | | | | | | | | | | [v0: any] : (v0 = all_125_0 | v0 = sz10 | ~ % 26.83/4.41 | | | | | | | | | | | | | | (doDivides0(v0, all_125_0) = 0) | ~ $i(v0) | % 26.83/4.41 | | | | | | | | | | | | | | ? [v1: int] : ( ~ (v1 = 0) & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1))) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (268) with fresh symbols all_162_0, % 26.83/4.41 | | | | | | | | | | | | | | all_162_1, all_162_2 gives: % 26.83/4.41 | | | | | | | | | | | | | | (271) aNaturalNumber0(all_77_0) = all_162_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_44_1) = all_162_2 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_162_1 & ( ~ (all_162_1 = % 26.83/4.41 | | | | | | | | | | | | | | 0) | ~ (all_162_2 = 0) | all_162_0 = 0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (271) implies: % 26.83/4.41 | | | | | | | | | | | | | | (272) aNaturalNumber0(xp) = all_162_1 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (265) with fresh symbols all_164_0, % 26.83/4.41 | | | | | | | | | | | | | | all_164_1, all_164_2 gives: % 26.83/4.41 | | | | | | | | | | | | | | (273) aNaturalNumber0(all_73_0) = all_164_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_44_2) = all_164_2 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_164_1 & ( ~ (all_164_1 = % 26.83/4.41 | | | | | | | | | | | | | | 0) | ~ (all_164_2 = 0) | all_164_0 = 0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (273) implies: % 26.83/4.41 | | | | | | | | | | | | | | (274) aNaturalNumber0(xp) = all_164_1 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (264) with fresh symbols all_166_0, % 26.83/4.41 | | | | | | | | | | | | | | all_166_1, all_166_2 gives: % 26.83/4.41 | | | | | | | | | | | | | | (275) sdtasdt0(xp, all_44_2) = all_166_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_44_2) = all_166_2 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_166_1 & $i(all_166_0) & % 26.83/4.41 | | | | | | | | | | | | | | ( ~ (all_166_1 = 0) | ~ (all_166_2 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | all_166_0 = all_73_0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (275) implies: % 26.83/4.41 | | | | | | | | | | | | | | (276) aNaturalNumber0(xp) = all_166_1 % 26.83/4.41 | | | | | | | | | | | | | | (277) aNaturalNumber0(all_44_2) = all_166_2 % 26.83/4.41 | | | | | | | | | | | | | | (278) sdtasdt0(xp, all_44_2) = all_166_0 % 26.83/4.41 | | | | | | | | | | | | | | (279) ~ (all_166_1 = 0) | ~ (all_166_2 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | all_166_0 = all_73_0 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (260) with fresh symbols all_168_0, % 26.83/4.41 | | | | | | | | | | | | | | all_168_1, all_168_2 gives: % 26.83/4.41 | | | | | | | | | | | | | | (280) sdtasdt0(all_151_0, xp) = all_168_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_151_0) = all_168_1 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_168_2 & $i(all_168_0) & % 26.83/4.41 | | | | | | | | | | | | | | ( ~ (all_168_1 = 0) | ~ (all_168_2 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | all_168_0 = all_40_0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (280) implies: % 26.83/4.41 | | | | | | | | | | | | | | (281) aNaturalNumber0(xp) = all_168_2 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (267) with fresh symbols all_170_0, % 26.83/4.41 | | | | | | | | | | | | | | all_170_1, all_170_2 gives: % 26.83/4.41 | | | | | | | | | | | | | | (282) sdtasdt0(xp, all_44_1) = all_170_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_44_1) = all_170_2 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_170_1 & $i(all_170_0) & % 26.83/4.41 | | | | | | | | | | | | | | ( ~ (all_170_1 = 0) | ~ (all_170_2 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | all_170_0 = all_77_0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (282) implies: % 26.83/4.41 | | | | | | | | | | | | | | (283) aNaturalNumber0(xp) = all_170_1 % 26.83/4.41 | | | | | | | | | | | | | | (284) sdtasdt0(xp, all_44_1) = all_170_0 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (258) with fresh symbols all_172_0, % 26.83/4.41 | | | | | | | | | | | | | | all_172_1, all_172_2 gives: % 26.83/4.41 | | | | | | | | | | | | | | (285) sdtasdt0(all_113_0, xp) = all_172_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_113_0) = all_172_1 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_172_2 & $i(all_172_0) & % 26.83/4.41 | | | | | | | | | | | | | | ( ~ (all_172_1 = 0) | ~ (all_172_2 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | all_172_0 = xn) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (285) implies: % 26.83/4.41 | | | | | | | | | | | | | | (286) aNaturalNumber0(xp) = all_172_2 % 26.83/4.41 | | | | | | | | | | | | | | (287) aNaturalNumber0(all_113_0) = all_172_1 % 26.83/4.41 | | | | | | | | | | | | | | (288) sdtasdt0(all_113_0, xp) = all_172_0 % 26.83/4.41 | | | | | | | | | | | | | | (289) ~ (all_172_1 = 0) | ~ (all_172_2 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | all_172_0 = xn % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (263) with fresh symbols all_174_0, % 26.83/4.41 | | | | | | | | | | | | | | all_174_1, all_174_2, all_174_3, all_174_4 gives: % 26.83/4.41 | | | | | | | | | | | | | | (290) sdtasdt0(xq, all_174_1) = all_174_0 & sdtasdt0(xq, % 26.83/4.41 | | | | | | | | | | | | | | xp) = all_174_1 & aNaturalNumber0(xq) = % 26.83/4.41 | | | | | | | | | | | | | | all_174_3 & aNaturalNumber0(xq) = all_174_4 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_174_2 & $i(all_174_0) & % 26.83/4.41 | | | | | | | | | | | | | | $i(all_174_1) & ( ~ (all_174_2 = 0) | ~ % 26.83/4.41 | | | | | | | | | | | | | | (all_174_3 = 0) | ~ (all_174_4 = 0) | all_174_0 % 26.83/4.41 | | | | | | | | | | | | | | = all_73_0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (290) implies: % 26.83/4.41 | | | | | | | | | | | | | | (291) aNaturalNumber0(xp) = all_174_2 % 26.83/4.41 | | | | | | | | | | | | | | (292) aNaturalNumber0(xq) = all_174_4 % 26.83/4.41 | | | | | | | | | | | | | | (293) aNaturalNumber0(xq) = all_174_3 % 26.83/4.41 | | | | | | | | | | | | | | (294) sdtasdt0(xq, xp) = all_174_1 % 26.83/4.41 | | | | | | | | | | | | | | (295) sdtasdt0(xq, all_174_1) = all_174_0 % 26.83/4.41 | | | | | | | | | | | | | | (296) ~ (all_174_2 = 0) | ~ (all_174_3 = 0) | ~ % 26.83/4.41 | | | | | | | | | | | | | | (all_174_4 = 0) | all_174_0 = all_73_0 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (255) with fresh symbols all_176_0, % 26.83/4.41 | | | | | | | | | | | | | | all_176_1, all_176_2, all_176_3, all_176_4 gives: % 26.83/4.41 | | | | | | | | | | | | | | (297) sdtasdt0(all_113_0, xn) = all_176_1 & sdtasdt0(xp, % 26.83/4.41 | | | | | | | | | | | | | | all_176_1) = all_176_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_113_0) = all_176_3 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_176_4 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_176_2 & $i(all_176_0) & % 26.83/4.41 | | | | | | | | | | | | | | $i(all_176_1) & ( ~ (all_176_2 = 0) | ~ % 26.83/4.41 | | | | | | | | | | | | | | (all_176_3 = 0) | ~ (all_176_4 = 0) | all_176_0 % 26.83/4.41 | | | | | | | | | | | | | | = all_40_0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (297) implies: % 26.83/4.41 | | | | | | | | | | | | | | (298) aNaturalNumber0(xn) = all_176_2 % 26.83/4.41 | | | | | | | | | | | | | | (299) aNaturalNumber0(xp) = all_176_4 % 26.83/4.41 | | | | | | | | | | | | | | (300) aNaturalNumber0(all_113_0) = all_176_3 % 26.83/4.41 | | | | | | | | | | | | | | (301) sdtasdt0(xp, all_176_1) = all_176_0 % 26.83/4.41 | | | | | | | | | | | | | | (302) sdtasdt0(all_113_0, xn) = all_176_1 % 26.83/4.41 | | | | | | | | | | | | | | (303) ~ (all_176_2 = 0) | ~ (all_176_3 = 0) | ~ % 26.83/4.41 | | | | | | | | | | | | | | (all_176_4 = 0) | all_176_0 = all_40_0 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (266) with fresh symbols all_178_0, % 26.83/4.41 | | | | | | | | | | | | | | all_178_1, all_178_2, all_178_3, all_178_4 gives: % 26.83/4.41 | | | | | | | | | | | | | | (304) sdtasdt0(all_44_2, xp) = all_178_1 & sdtasdt0(xp, % 26.83/4.41 | | | | | | | | | | | | | | all_178_1) = all_178_0 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(all_44_2) = all_178_3 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_178_2 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_178_4 & $i(all_178_0) & % 26.83/4.41 | | | | | | | | | | | | | | $i(all_178_1) & ( ~ (all_178_2 = 0) | ~ % 26.83/4.41 | | | | | | | | | | | | | | (all_178_3 = 0) | ~ (all_178_4 = 0) | all_178_0 % 26.83/4.41 | | | | | | | | | | | | | | = all_77_0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (304) implies: % 26.83/4.41 | | | | | | | | | | | | | | (305) aNaturalNumber0(xp) = all_178_4 % 26.83/4.41 | | | | | | | | | | | | | | (306) aNaturalNumber0(xp) = all_178_2 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (261) with fresh symbols all_180_0, % 26.83/4.41 | | | | | | | | | | | | | | all_180_1, all_180_2, all_180_3, all_180_4 gives: % 26.83/4.41 | | | | | | | | | | | | | | (307) sdtasdt0(xm, all_180_1) = all_180_0 & sdtasdt0(xm, % 26.83/4.41 | | | | | | | | | | | | | | xp) = all_180_1 & aNaturalNumber0(xp) = % 26.83/4.41 | | | | | | | | | | | | | | all_180_2 & aNaturalNumber0(xm) = all_180_3 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_180_4 & $i(all_180_0) & % 26.83/4.41 | | | | | | | | | | | | | | $i(all_180_1) & ( ~ (all_180_2 = 0) | ~ % 26.83/4.41 | | | | | | | | | | | | | | (all_180_3 = 0) | ~ (all_180_4 = 0) | all_180_0 % 26.83/4.41 | | | | | | | | | | | | | | = all_40_0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (307) implies: % 26.83/4.41 | | | | | | | | | | | | | | (308) aNaturalNumber0(xp) = all_180_2 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (256) with fresh symbols all_182_0, % 26.83/4.41 | | | | | | | | | | | | | | all_182_1, all_182_2, all_182_3, all_182_4, % 26.83/4.41 | | | | | | | | | | | | | | all_182_5 gives: % 26.83/4.41 | | | | | | | | | | | | | | (309) isPrime0(xp) = all_182_2 & doDivides0(xp, % 26.83/4.41 | | | | | | | | | | | | | | all_113_0) = all_182_0 & doDivides0(xp, xp) = % 26.83/4.41 | | | | | | | | | | | | | | all_182_1 & aNaturalNumber0(all_113_0) = all_182_4 % 26.83/4.41 | | | | | | | | | | | | | | & aNaturalNumber0(xp) = all_182_3 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_182_5 & ( ~ (all_182_2 = % 26.83/4.41 | | | | | | | | | | | | | | 0) | ~ (all_182_3 = 0) | ~ (all_182_4 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | ~ (all_182_5 = 0) | all_182_0 = 0 | all_182_1 = % 26.83/4.41 | | | | | | | | | | | | | | 0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (309) implies: % 26.83/4.41 | | | | | | | | | | | | | | (310) aNaturalNumber0(xp) = all_182_5 % 26.83/4.41 | | | | | | | | | | | | | | (311) aNaturalNumber0(xp) = all_182_3 % 26.83/4.41 | | | | | | | | | | | | | | (312) aNaturalNumber0(all_113_0) = all_182_4 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (262) with fresh symbols all_184_0, % 26.83/4.41 | | | | | | | | | | | | | | all_184_1, all_184_2, all_184_3, all_184_4, % 26.83/4.41 | | | | | | | | | | | | | | all_184_5 gives: % 26.83/4.41 | | | | | | | | | | | | | | (313) isPrime0(xp) = all_184_2 & doDivides0(xp, % 26.83/4.41 | | | | | | | | | | | | | | all_42_1) = all_184_1 & doDivides0(xp, xp) = % 26.83/4.41 | | | | | | | | | | | | | | all_184_0 & aNaturalNumber0(all_42_1) = all_184_5 % 26.83/4.41 | | | | | | | | | | | | | | & aNaturalNumber0(xp) = all_184_3 & % 26.83/4.41 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_184_4 & ( ~ (all_184_2 = % 26.83/4.41 | | | | | | | | | | | | | | 0) | ~ (all_184_3 = 0) | ~ (all_184_4 = 0) | % 26.83/4.41 | | | | | | | | | | | | | | ~ (all_184_5 = 0) | all_184_0 = 0 | all_184_1 = % 26.83/4.41 | | | | | | | | | | | | | | 0) % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | ALPHA: (313) implies: % 26.83/4.41 | | | | | | | | | | | | | | (314) aNaturalNumber0(xp) = all_184_4 % 26.83/4.41 | | | | | | | | | | | | | | (315) aNaturalNumber0(xp) = all_184_3 % 26.83/4.41 | | | | | | | | | | | | | | % 26.83/4.41 | | | | | | | | | | | | | | DELTA: instantiating (259) with fresh symbols all_186_0, % 26.83/4.41 | | | | | | | | | | | | | | all_186_1, all_186_2, all_186_3, all_186_4, % 26.83/4.41 | | | | | | | | | | | | | | all_186_5 gives: % 26.83/4.42 | | | | | | | | | | | | | | (316) isPrime0(xp) = all_186_2 & doDivides0(xp, % 26.83/4.42 | | | | | | | | | | | | | | all_151_0) = all_186_0 & doDivides0(xp, xp) = % 26.83/4.42 | | | | | | | | | | | | | | all_186_1 & aNaturalNumber0(all_151_0) = all_186_4 % 26.83/4.42 | | | | | | | | | | | | | | & aNaturalNumber0(xp) = all_186_3 & % 26.83/4.42 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_186_5 & ( ~ (all_186_2 = % 26.83/4.42 | | | | | | | | | | | | | | 0) | ~ (all_186_3 = 0) | ~ (all_186_4 = 0) | % 26.83/4.42 | | | | | | | | | | | | | | ~ (all_186_5 = 0) | all_186_0 = 0 | all_186_1 = % 26.83/4.42 | | | | | | | | | | | | | | 0) % 26.83/4.42 | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | ALPHA: (316) implies: % 26.83/4.42 | | | | | | | | | | | | | | (317) aNaturalNumber0(xp) = all_186_5 % 26.83/4.42 | | | | | | | | | | | | | | (318) aNaturalNumber0(xp) = all_186_3 % 26.83/4.42 | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | BETA: splitting (270) gives: % 26.83/4.42 | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | Case 1: % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | (319) ? [v0: int] : ( ~ (v0 = 0) & % 26.83/4.42 | | | | | | | | | | | | | | | aNaturalNumber0(all_125_0) = v0) % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | DELTA: instantiating (319) with fresh symbol all_191_0 % 26.83/4.42 | | | | | | | | | | | | | | | gives: % 26.83/4.42 | | | | | | | | | | | | | | | (320) ~ (all_191_0 = 0) & aNaturalNumber0(all_125_0) = % 26.83/4.42 | | | | | | | | | | | | | | | all_191_0 % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | REF_CLOSE: (17), (198), (320) are inconsistent by sub-proof % 26.83/4.42 | | | | | | | | | | | | | | | #1. % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | Case 2: % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | (321) ~ (all_125_0 = sz10) & ~ (all_125_0 = sz00) & ! % 26.83/4.42 | | | | | | | | | | | | | | | [v0: any] : (v0 = all_125_0 | v0 = sz10 | ~ % 26.83/4.42 | | | | | | | | | | | | | | | (doDivides0(v0, all_125_0) = 0) | ~ $i(v0) | ? % 26.83/4.42 | | | | | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = % 26.83/4.42 | | | | | | | | | | | | | | | v1)) % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | ALPHA: (321) implies: % 26.83/4.42 | | | | | | | | | | | | | | | (322) ~ (all_125_0 = sz00) % 26.83/4.42 | | | | | | | | | | | | | | | (323) ~ (all_125_0 = sz10) % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 26.83/4.42 | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | Case 1: % 26.83/4.42 | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | (324) all_125_0 = xp % 26.83/4.42 | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | Case 1: % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | (325) all_125_0 = sz00 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (325) imply: % 26.83/4.42 | | | | | | | | | | | | | | | | | (326) xp = sz00 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | REDUCE: (165), (326) imply: % 26.83/4.42 | | | | | | | | | | | | | | | | | (327) $false % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent. % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | Case 2: % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_176_2, xn, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (5), (298) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (328) all_176_2 = 0 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_172_2, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (7), (286) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (329) all_172_2 = 0 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_168_2, all_172_2, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (281), (286) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (330) all_172_2 = all_168_2 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_164_1, all_172_2, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (274), (286) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (331) all_172_2 = all_164_1 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_172_2, all_176_4, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (286), (299) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (332) all_176_4 = all_172_2 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_174_2, all_178_4, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (291), (305) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (333) all_178_4 = all_174_2 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_164_1, all_178_4, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (274), (305) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (334) all_178_4 = all_164_1 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_162_1, all_178_4, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (272), (305) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (335) all_178_4 = all_162_1 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_176_4, all_178_2, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (299), (306) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (336) all_178_2 = all_176_4 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_178_2, all_182_3, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (306), (311) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (337) all_182_3 = all_178_2 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_180_2, all_184_4, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (308), (314) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (338) all_184_4 = all_180_2 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_184_4, all_186_5, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (314), (317) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (339) all_186_5 = all_184_4 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_182_5, all_186_5, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (310), (317) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (340) all_186_5 = all_182_5 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_172_2, all_186_5, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (286), (317) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (341) all_186_5 = all_172_2 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_166_1, all_186_5, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (276), (317) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (342) all_186_5 = all_166_1 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_184_3, all_186_3, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (315), (318) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (343) all_186_3 = all_184_3 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_182_3, all_186_3, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (311), (318) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (344) all_186_3 = all_182_3 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.42 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_170_1, all_186_3, xp, % 26.83/4.42 | | | | | | | | | | | | | | | | | simplifying with (283), (318) gives: % 26.83/4.42 | | | | | | | | | | | | | | | | | (345) all_186_3 = all_170_1 % 26.83/4.42 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_59_2, all_174_3, xq, % 26.83/4.43 | | | | | | | | | | | | | | | | | simplifying with (64), (293) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (346) all_174_3 = all_59_2 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_174_4, all_174_3, xq, % 26.83/4.43 | | | | | | | | | | | | | | | | | simplifying with (292), (293) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (347) all_174_3 = all_174_4 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_59_0, all_166_2, % 26.83/4.43 | | | | | | | | | | | | | | | | | all_44_2, simplifying with (66), (277) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (348) all_166_2 = all_59_0 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_182_4, all_113_0, % 26.83/4.43 | | | | | | | | | | | | | | | | | simplifying with (185), (312) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (349) all_182_4 = 0 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_176_3, all_182_4, % 26.83/4.43 | | | | | | | | | | | | | | | | | all_113_0, simplifying with (300), (312) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (350) all_182_4 = all_176_3 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_172_1, all_182_4, % 26.83/4.43 | | | | | | | | | | | | | | | | | all_113_0, simplifying with (287), (312) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (351) all_182_4 = all_172_1 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_44_1, all_166_0, % 26.83/4.43 | | | | | | | | | | | | | | | | | all_44_2, xp, simplifying with (36), (278) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (352) all_166_0 = all_44_1 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_44_0, all_170_0, % 26.83/4.43 | | | | | | | | | | | | | | | | | all_44_1, xp, simplifying with (37), (284) gives: % 26.83/4.43 | | | | | | | | | | | | | | | | | (353) all_170_0 = all_44_0 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (344) imply: % 26.83/4.43 | | | | | | | | | | | | | | | | | (354) all_184_3 = all_182_3 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (343), (345) imply: % 26.83/4.43 | | | | | | | | | | | | | | | | | (355) all_184_3 = all_170_1 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (339), (340) imply: % 26.83/4.43 | | | | | | | | | | | | | | | | | (356) all_184_4 = all_182_5 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | SIMP: (356) implies: % 26.83/4.43 | | | | | | | | | | | | | | | | | (357) all_184_4 = all_182_5 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (340), (342) imply: % 26.83/4.43 | | | | | | | | | | | | | | | | | (358) all_182_5 = all_166_1 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (340), (341) imply: % 26.83/4.43 | | | | | | | | | | | | | | | | | (359) all_182_5 = all_172_2 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (355) imply: % 26.83/4.43 | | | | | | | | | | | | | | | | | (360) all_182_3 = all_170_1 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | SIMP: (360) implies: % 26.83/4.43 | | | | | | | | | | | | | | | | | (361) all_182_3 = all_170_1 % 26.83/4.43 | | | | | | | | | | | | | | | | | % 26.83/4.43 | | | | | | | | | | | | | | | | | COMBINE_EQS: (338), (357) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (362) all_182_5 = all_180_2 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | SIMP: (362) implies: % 26.83/4.44 | | | | | | | | | | | | | | | | | (363) all_182_5 = all_180_2 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (337), (361) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (364) all_178_2 = all_170_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | SIMP: (364) implies: % 26.83/4.44 | | | | | | | | | | | | | | | | | (365) all_178_2 = all_170_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (350) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (366) all_176_3 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (351) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (367) all_176_3 = all_172_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (358), (363) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (368) all_180_2 = all_166_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (363) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (369) all_180_2 = all_172_2 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (368), (369) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (370) all_172_2 = all_166_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | SIMP: (370) implies: % 26.83/4.44 | | | | | | | | | | | | | | | | | (371) all_172_2 = all_166_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (365) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (372) all_176_4 = all_170_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | SIMP: (372) implies: % 26.83/4.44 | | | | | | | | | | | | | | | | | (373) all_176_4 = all_170_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (333), (334) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (374) all_174_2 = all_164_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (333), (335) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (375) all_174_2 = all_162_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (366), (367) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (376) all_172_1 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (373) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (377) all_172_2 = all_170_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | SIMP: (377) implies: % 26.83/4.44 | | | | | | | | | | | | | | | | | (378) all_172_2 = all_170_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (375) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (379) all_164_1 = all_162_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | SIMP: (379) implies: % 26.83/4.44 | | | | | | | | | | | | | | | | | (380) all_164_1 = all_162_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (347) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (381) all_174_4 = all_59_2 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (329), (378) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (382) all_170_1 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (378) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (383) all_170_1 = all_166_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (331), (378) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (384) all_170_1 = all_164_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (378) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (385) all_170_1 = all_168_2 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (385) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (386) all_168_2 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (384), (385) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (387) all_168_2 = all_164_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (383), (385) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (388) all_168_2 = all_166_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (388) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (389) all_166_1 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (387), (388) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (390) all_166_1 = all_164_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (389), (390) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (391) all_164_1 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | SIMP: (391) implies: % 26.83/4.44 | | | | | | | | | | | | | | | | | (392) all_164_1 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (392) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (393) all_162_1 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (393) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (394) all_174_2 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (382) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | (395) all_176_4 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | BETA: splitting (303) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | (396) ~ (all_176_2 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | REDUCE: (328), (396) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | (397) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | CLOSE: (397) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | (398) ~ (all_176_3 = 0) | ~ (all_176_4 = 0) | % 26.83/4.44 | | | | | | | | | | | | | | | | | | all_176_0 = all_40_0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | BETA: splitting (398) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | (399) ~ (all_176_3 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | REDUCE: (366), (399) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | (400) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | CLOSE: (400) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | (401) ~ (all_176_4 = 0) | all_176_0 = all_40_0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | (402) ~ (all_176_4 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (402) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | (403) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | CLOSE: (403) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | (404) all_176_0 = all_40_0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (404) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | (405) sdtasdt0(xp, all_176_1) = all_40_0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | (406) all_113_0 = xq % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (288), (406) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | (407) sdtasdt0(xq, xp) = all_172_0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (406) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | (408) sdtasdt0(xq, xn) = all_176_1 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (406) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | (409) aNaturalNumber0(xq) = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | (410) ~ (all_172_1 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (410) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | (411) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (411) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | (412) ~ (all_172_2 = 0) | all_172_0 = xn % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (412) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (413) ~ (all_172_2 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (329), (413) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (414) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (414) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (415) all_172_0 = xn % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (407), (415) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (416) sdtasdt0(xq, xp) = xn % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_59_2, 0, xq, % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (64), (409) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (417) all_59_2 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_174_1, xn, xp, xq, % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (294), (416) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (418) all_174_1 = xn % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (417) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (419) all_59_1 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (381), (417) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (420) all_174_4 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (417) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (421) all_174_3 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (295), (418) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | (422) sdtasdt0(xq, xn) = all_174_0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | (423) ~ (all_59_1 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (423) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | (424) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (424) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | (425) ~ (all_59_2 = 0) | all_59_0 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (425) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | (426) ~ (all_59_2 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (417), (426) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | (427) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (427) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_59_0 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (428) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_166_2 = 0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (430) ~ (all_166_1 = 0) % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (430) imply: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (431) $false % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (431) is inconsistent. % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (432) ~ (all_166_2 = 0) | all_166_0 = all_73_0 % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) ~ (all_166_2 = 0) % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (429), (433) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) $false % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (434) is inconsistent. % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_166_0 = all_73_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (352), (435) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_73_0 = all_44_1 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) ~ (all_174_2 = 0) % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (437) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) $false % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (438) is inconsistent. % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) ~ (all_174_3 = 0) | ~ (all_174_4 = 0) | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_174_0 = all_73_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (439) gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) ~ (all_174_3 = 0) % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (440) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) $false % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (441) is inconsistent. % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) ~ (all_174_4 = 0) | all_174_0 = all_73_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (442) gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) ~ (all_174_4 = 0) % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (420), (443) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) $false % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (444) is inconsistent. % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_174_0 = all_73_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (436), (445) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) all_174_0 = all_44_1 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (422), (446) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) sdtasdt0(xq, xn) = all_44_1 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_176_1, all_44_1, xn, % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | xq, simplifying with (408), (447) gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_176_1 = all_44_1 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (448) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) sdtasdt0(xp, all_44_1) = all_40_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_44_0, all_40_0, % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_1, xp, simplifying with (37), (449) gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_44_0 = all_40_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (450) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) $false % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (451) is inconsistent. % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | Case 2: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | (452) ? [v0: int] : ( ~ (v0 = 0) & % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_113_0) = v0) % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (452) with fresh symbol all_252_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | (453) ~ (all_252_0 = 0) & aNaturalNumber0(all_113_0) = % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | all_252_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | ALPHA: (453) implies: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | (454) ~ (all_252_0 = 0) % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | (455) aNaturalNumber0(all_113_0) = all_252_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_252_0, all_113_0, % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | simplifying with (185), (455) gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | (456) all_252_0 = 0 % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | REDUCE: (454), (456) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | (457) $false % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | CLOSE: (457) is inconsistent. % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | Case 2: % 26.83/4.45 | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | (458) all_125_0 = sz10 | ? [v0: int] : ( ~ (v0 = 0) & % 26.83/4.45 | | | | | | | | | | | | | | | | aNaturalNumber0(all_125_0) = v0) % 26.83/4.45 | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 26.83/4.45 | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | Case 1: % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | (459) all_125_0 = sz10 % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | REDUCE: (323), (459) imply: % 26.83/4.45 | | | | | | | | | | | | | | | | | (460) $false % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | CLOSE: (460) is inconsistent. % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | Case 2: % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | (461) ? [v0: int] : ( ~ (v0 = 0) & % 26.83/4.45 | | | | | | | | | | | | | | | | | aNaturalNumber0(all_125_0) = v0) % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | DELTA: instantiating (461) with fresh symbol all_191_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | gives: % 26.83/4.45 | | | | | | | | | | | | | | | | | (462) ~ (all_191_0 = 0) & aNaturalNumber0(all_125_0) = % 26.83/4.45 | | | | | | | | | | | | | | | | | all_191_0 % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (198), (462) are inconsistent by sub-proof % 26.83/4.45 | | | | | | | | | | | | | | | | | #1. % 26.83/4.45 | | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | | % 26.83/4.45 | | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | | % 26.83/4.45 | | | | | | | | | End of split % 26.83/4.45 | | | | | | | | | % 26.83/4.45 | | | | | | | | End of split % 26.83/4.45 | | | | | | | | % 26.83/4.45 | | | | | | | End of split % 26.83/4.45 | | | | | | | % 26.83/4.45 | | | | | | End of split % 26.83/4.45 | | | | | | % 26.83/4.45 | | | | | End of split % 26.83/4.45 | | | | | % 26.83/4.45 | | | | End of split % 26.83/4.45 | | | | % 26.83/4.45 | | | End of split % 26.83/4.45 | | | % 26.83/4.45 | | End of split % 26.83/4.45 | | % 26.83/4.45 | End of split % 26.83/4.45 | % 26.83/4.45 End of proof % 26.83/4.45 % 26.83/4.45 Sub-proof #1 shows that the following formulas are inconsistent: % 26.83/4.45 ---------------------------------------------------------------- % 26.83/4.45 (1) ~ (all_191_0 = 0) & aNaturalNumber0(all_125_0) = all_191_0 % 26.83/4.45 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.83/4.45 (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) % 26.83/4.45 (3) aNaturalNumber0(all_125_0) = 0 % 26.83/4.45 % 26.83/4.45 Begin of proof % 26.83/4.45 | % 26.83/4.45 | ALPHA: (1) implies: % 26.83/4.45 | (4) ~ (all_191_0 = 0) % 26.83/4.45 | (5) aNaturalNumber0(all_125_0) = all_191_0 % 26.83/4.45 | % 26.83/4.45 | GROUND_INST: instantiating (2) with 0, all_191_0, all_125_0, simplifying with % 26.83/4.45 | (3), (5) gives: % 26.83/4.45 | (6) all_191_0 = 0 % 26.83/4.45 | % 26.83/4.45 | REDUCE: (4), (6) imply: % 26.83/4.45 | (7) $false % 26.83/4.45 | % 26.83/4.45 | CLOSE: (7) is inconsistent. % 26.83/4.45 | % 26.83/4.45 End of proof % 26.83/4.45 % SZS output end Proof for theBenchmark % 26.83/4.45 % 26.83/4.45 3865ms %------------------------------------------------------------------------------