%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM474+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:48:00 EDT 2023 % Result : Theorem 11.95s 2.31s % Output : Proof 22.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : NUM474+1 : TPTP v8.1.2. Released v4.0.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n002.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Aug 25 08:45:17 EDT 2023 % 0.18/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.13/1.15 Prover 1: Preprocessing ... % 3.13/1.15 Prover 4: Preprocessing ... % 3.52/1.18 Prover 3: Preprocessing ... % 3.52/1.18 Prover 5: Preprocessing ... % 3.52/1.18 Prover 2: Preprocessing ... % 3.52/1.19 Prover 0: Preprocessing ... % 3.52/1.19 Prover 6: Preprocessing ... % 7.60/1.74 Prover 1: Constructing countermodel ... % 7.60/1.79 Prover 3: Constructing countermodel ... % 8.26/1.80 Prover 6: Proving ... % 8.26/1.90 Prover 5: Constructing countermodel ... % 10.23/2.07 Prover 2: Proving ... % 10.85/2.16 Prover 4: Constructing countermodel ... % 11.95/2.31 Prover 6: proved (1676ms) % 11.95/2.31 % 11.95/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.95/2.31 % 11.95/2.31 Prover 3: stopped % 11.95/2.31 Prover 5: stopped % 11.95/2.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.95/2.32 Prover 2: stopped % 11.95/2.32 Prover 0: Proving ... % 11.95/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.95/2.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.95/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.95/2.32 Prover 0: stopped % 11.95/2.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.85/2.43 Prover 10: Preprocessing ... % 12.85/2.43 Prover 11: Preprocessing ... % 12.85/2.43 Prover 8: Preprocessing ... % 13.12/2.44 Prover 13: Preprocessing ... % 13.12/2.45 Prover 7: Preprocessing ... % 14.01/2.60 Prover 10: Constructing countermodel ... % 14.01/2.63 Prover 8: Warning: ignoring some quantifiers % 14.01/2.65 Prover 8: Constructing countermodel ... % 15.10/2.73 Prover 13: Constructing countermodel ... % 15.10/2.76 Prover 7: Constructing countermodel ... % 16.09/2.87 Prover 11: Constructing countermodel ... % 21.73/3.59 Prover 1: Found proof (size 360) % 21.73/3.59 Prover 1: proved (2973ms) % 21.73/3.59 Prover 11: stopped % 21.73/3.59 Prover 13: stopped % 21.73/3.59 Prover 10: stopped % 21.86/3.60 Prover 7: stopped % 21.86/3.60 Prover 8: stopped % 21.86/3.61 Prover 4: stopped % 21.86/3.61 % 21.86/3.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 21.86/3.61 % 21.94/3.67 % SZS output start Proof for theBenchmark % 21.94/3.67 Assumptions after simplification: % 21.94/3.67 --------------------------------- % 21.94/3.67 % 21.94/3.67 (mAMDistr) % 21.94/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 21.94/3.70 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 21.94/3.70 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : % 21.94/3.70 ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? % 21.94/3.70 [v12: $i] : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v9, v0) = v11 & % 21.94/3.70 sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v9) = v10 & % 21.94/3.70 sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9 & aNaturalNumber0(v2) = % 21.94/3.70 v8 & aNaturalNumber0(v1) = v7 & aNaturalNumber0(v0) = v6 & $i(v14) & % 21.94/3.70 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = % 21.94/3.70 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) % 21.94/3.70 % 21.94/3.70 (mAddComm) % 21.94/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 21.94/3.70 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 21.94/3.70 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 21.94/3.70 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 21.94/3.70 % 21.94/3.70 (mDefDiff) % 21.94/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ % 21.94/3.71 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 21.94/3.71 (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 21.94/3.71 v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | ( ! [v3: $i] : (v3 = v2 % 21.94/3.71 | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 21.94/3.71 aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ (sdtpldt0(v0, v2) = v3) % 21.94/3.71 | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = 0)))) % 21.94/3.71 % 21.94/3.71 (mDefDiv) % 21.94/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 21.94/3.71 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 21.94/3.71 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 21.94/3.71 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 21.94/3.71 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 21.94/3.71 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 21.94/3.71 % 21.94/3.71 (mDefQuot) % 21.94/3.71 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 21.94/3.71 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 21.94/3.71 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 21.94/3.71 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 21.94/3.71 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4: % 21.94/3.71 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 21.94/3.71 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = % 21.94/3.71 0)))) % 21.94/3.71 % 21.94/3.71 (mMulComm) % 21.94/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 21.94/3.71 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 21.94/3.71 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 21.94/3.71 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 21.94/3.71 % 21.94/3.71 (mSortsB) % 21.94/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 21.94/3.71 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 21.94/3.71 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 21.94/3.71 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 21.94/3.71 % 21.94/3.71 (mSortsB_02) % 21.94/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 21.94/3.71 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 21.94/3.71 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 21.94/3.71 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 21.94/3.71 % 21.94/3.71 (m__) % 21.94/3.71 $i(xr) & $i(xp) & $i(xn) & $i(xl) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 21.94/3.71 ? [v3: $i] : ( ~ (v3 = v2) & sdtasdt0(xl, xr) = v1 & sdtasdt0(xl, xp) = v0 & % 21.94/3.71 sdtpldt0(v0, v1) = v2 & sdtpldt0(v0, xn) = v3 & $i(v3) & $i(v2) & $i(v1) & % 21.94/3.71 $i(v0)) % 21.94/3.71 % 21.94/3.71 (m__1324) % 22.38/3.71 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xl) = 0 & % 22.38/3.71 $i(xn) & $i(xm) & $i(xl) % 22.38/3.71 % 22.38/3.71 (m__1324_04) % 22.38/3.71 $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : (doDivides0(xl, v0) = 0 & % 22.38/3.71 doDivides0(xl, xm) = 0 & sdtpldt0(xm, xn) = v0 & $i(v0)) % 22.38/3.71 % 22.38/3.71 (m__1347) % 22.38/3.71 ~ (xl = sz00) & $i(xl) & $i(sz00) % 22.38/3.71 % 22.38/3.71 (m__1360) % 22.38/3.71 sdtsldt0(xm, xl) = xp & $i(xp) & $i(xm) & $i(xl) % 22.38/3.71 % 22.38/3.71 (m__1379) % 22.38/3.72 $i(xq) & $i(xn) & $i(xm) & $i(xl) & ? [v0: $i] : (sdtsldt0(v0, xl) = xq & % 22.38/3.72 sdtpldt0(xm, xn) = v0 & $i(v0)) % 22.38/3.72 % 22.38/3.72 (m__1395) % 22.38/3.72 sdtlseqdt0(xp, xq) = 0 & $i(xq) & $i(xp) % 22.38/3.72 % 22.38/3.72 (m__1422) % 22.38/3.72 sdtmndt0(xq, xp) = xr & $i(xr) & $i(xq) & $i(xp) % 22.38/3.72 % 22.38/3.72 (function-axioms) % 22.38/3.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.38/3.72 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 22.38/3.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.38/3.72 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 22.38/3.72 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 22.38/3.72 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 22.38/3.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.38/3.72 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 22.38/3.72 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 22.38/3.72 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 22.38/3.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.38/3.72 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 22.38/3.72 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 22.38/3.72 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 22.38/3.72 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 22.38/3.72 | ~ (aNaturalNumber0(v2) = v0)) % 22.38/3.72 % 22.38/3.72 Further assumptions not needed in the proof: % 22.38/3.72 -------------------------------------------- % 22.38/3.72 mAddAsso, mAddCanc, mDefLE, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, % 22.38/3.72 mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc, % 22.38/3.72 mNatSort, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, % 22.38/3.72 m_MulZero % 22.38/3.72 % 22.38/3.72 Those formulas are unsatisfiable: % 22.38/3.72 --------------------------------- % 22.38/3.72 % 22.38/3.72 Begin of proof % 22.38/3.72 | % 22.38/3.72 | ALPHA: (mDefQuot) implies: % 22.38/3.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 22.38/3.72 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 22.38/3.72 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 22.38/3.72 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 22.38/3.72 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | % 22.38/3.72 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = % 22.38/3.72 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | % 22.38/3.72 | (v3 = v1 & aNaturalNumber0(v2) = 0)))) % 22.38/3.72 | % 22.38/3.72 | ALPHA: (m__1324) implies: % 22.38/3.72 | (2) aNaturalNumber0(xl) = 0 % 22.38/3.72 | (3) aNaturalNumber0(xm) = 0 % 22.38/3.72 | (4) aNaturalNumber0(xn) = 0 % 22.38/3.72 | % 22.38/3.72 | ALPHA: (m__1324_04) implies: % 22.38/3.72 | (5) ? [v0: $i] : (doDivides0(xl, v0) = 0 & doDivides0(xl, xm) = 0 & % 22.38/3.72 | sdtpldt0(xm, xn) = v0 & $i(v0)) % 22.38/3.72 | % 22.38/3.72 | ALPHA: (m__1347) implies: % 22.38/3.72 | (6) ~ (xl = sz00) % 22.38/3.72 | % 22.38/3.72 | ALPHA: (m__1360) implies: % 22.38/3.72 | (7) sdtsldt0(xm, xl) = xp % 22.38/3.72 | % 22.38/3.72 | ALPHA: (m__1379) implies: % 22.38/3.72 | (8) $i(xm) % 22.38/3.73 | (9) ? [v0: $i] : (sdtsldt0(v0, xl) = xq & sdtpldt0(xm, xn) = v0 & $i(v0)) % 22.38/3.73 | % 22.38/3.73 | ALPHA: (m__1395) implies: % 22.38/3.73 | (10) sdtlseqdt0(xp, xq) = 0 % 22.38/3.73 | % 22.38/3.73 | ALPHA: (m__1422) implies: % 22.38/3.73 | (11) $i(xq) % 22.38/3.73 | (12) sdtmndt0(xq, xp) = xr % 22.38/3.73 | % 22.38/3.73 | ALPHA: (m__) implies: % 22.38/3.73 | (13) $i(xl) % 22.38/3.73 | (14) $i(xn) % 22.38/3.73 | (15) $i(xp) % 22.38/3.73 | (16) $i(xr) % 22.38/3.73 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) % 22.38/3.73 | & sdtasdt0(xl, xr) = v1 & sdtasdt0(xl, xp) = v0 & sdtpldt0(v0, v1) = % 22.38/3.73 | v2 & sdtpldt0(v0, xn) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 22.38/3.73 | % 22.38/3.73 | ALPHA: (function-axioms) implies: % 22.38/3.73 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.38/3.73 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 22.38/3.73 | v0)) % 22.38/3.73 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.38/3.73 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 22.38/3.73 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 22.38/3.73 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 22.38/3.73 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.38/3.73 | : ! [v3: $i] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ % 22.38/3.73 | (sdtlseqdt0(v3, v2) = v0)) % 22.38/3.73 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 22.38/3.73 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 22.38/3.73 | (doDivides0(v3, v2) = v0)) % 22.38/3.73 | % 22.38/3.73 | DELTA: instantiating (9) with fresh symbol all_33_0 gives: % 22.38/3.73 | (23) sdtsldt0(all_33_0, xl) = xq & sdtpldt0(xm, xn) = all_33_0 & % 22.38/3.73 | $i(all_33_0) % 22.38/3.73 | % 22.38/3.73 | ALPHA: (23) implies: % 22.38/3.73 | (24) sdtpldt0(xm, xn) = all_33_0 % 22.38/3.73 | (25) sdtsldt0(all_33_0, xl) = xq % 22.38/3.73 | % 22.38/3.73 | DELTA: instantiating (5) with fresh symbol all_35_0 gives: % 22.38/3.73 | (26) doDivides0(xl, all_35_0) = 0 & doDivides0(xl, xm) = 0 & sdtpldt0(xm, % 22.38/3.73 | xn) = all_35_0 & $i(all_35_0) % 22.38/3.73 | % 22.38/3.73 | ALPHA: (26) implies: % 22.38/3.73 | (27) $i(all_35_0) % 22.38/3.73 | (28) sdtpldt0(xm, xn) = all_35_0 % 22.38/3.73 | (29) doDivides0(xl, xm) = 0 % 22.38/3.73 | (30) doDivides0(xl, all_35_0) = 0 % 22.38/3.73 | % 22.38/3.73 | DELTA: instantiating (17) with fresh symbols all_37_0, all_37_1, all_37_2, % 22.38/3.73 | all_37_3 gives: % 22.38/3.73 | (31) ~ (all_37_0 = all_37_1) & sdtasdt0(xl, xr) = all_37_2 & sdtasdt0(xl, % 22.38/3.73 | xp) = all_37_3 & sdtpldt0(all_37_3, all_37_2) = all_37_1 & % 22.38/3.73 | sdtpldt0(all_37_3, xn) = all_37_0 & $i(all_37_0) & $i(all_37_1) & % 22.38/3.73 | $i(all_37_2) & $i(all_37_3) % 22.38/3.73 | % 22.38/3.73 | ALPHA: (31) implies: % 22.38/3.73 | (32) ~ (all_37_0 = all_37_1) % 22.38/3.73 | (33) $i(all_37_3) % 22.38/3.73 | (34) $i(all_37_2) % 22.38/3.73 | (35) sdtpldt0(all_37_3, xn) = all_37_0 % 22.38/3.73 | (36) sdtpldt0(all_37_3, all_37_2) = all_37_1 % 22.38/3.73 | (37) sdtasdt0(xl, xp) = all_37_3 % 22.38/3.73 | (38) sdtasdt0(xl, xr) = all_37_2 % 22.38/3.73 | % 22.38/3.73 | GROUND_INST: instantiating (19) with all_33_0, all_35_0, xn, xm, simplifying % 22.38/3.73 | with (24), (28) gives: % 22.38/3.73 | (39) all_35_0 = all_33_0 % 22.38/3.73 | % 22.38/3.73 | REDUCE: (30), (39) imply: % 22.38/3.73 | (40) doDivides0(xl, all_33_0) = 0 % 22.38/3.73 | % 22.38/3.73 | REDUCE: (27), (39) imply: % 22.38/3.74 | (41) $i(all_33_0) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mAddComm) with xm, xn, all_33_0, simplifying with % 22.38/3.74 | (8), (14), (24) gives: % 22.38/3.74 | (42) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xn, xm) = v2 & % 22.38/3.74 | aNaturalNumber0(xn) = v1 & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ % 22.38/3.74 | (v1 = 0) | ~ (v0 = 0) | v2 = all_33_0)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mSortsB) with xm, xn, all_33_0, simplifying with % 22.38/3.74 | (8), (14), (24) gives: % 22.38/3.74 | (43) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.74 | (aNaturalNumber0(all_33_0) = v2 & aNaturalNumber0(xn) = v1 & % 22.38/3.74 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mAddComm) with all_37_3, xn, all_37_0, simplifying % 22.38/3.74 | with (14), (33), (35) gives: % 22.38/3.74 | (44) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xn, all_37_3) = % 22.38/3.74 | v2 & aNaturalNumber0(all_37_3) = v0 & aNaturalNumber0(xn) = v1 & % 22.38/3.74 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_37_0)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mSortsB) with all_37_3, xn, all_37_0, simplifying % 22.38/3.74 | with (14), (33), (35) gives: % 22.38/3.74 | (45) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.74 | (aNaturalNumber0(all_37_0) = v2 & aNaturalNumber0(all_37_3) = v0 & % 22.38/3.74 | aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mAddComm) with all_37_3, all_37_2, all_37_1, % 22.38/3.74 | simplifying with (33), (34), (36) gives: % 22.38/3.74 | (46) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_37_2, % 22.38/3.74 | all_37_3) = v2 & aNaturalNumber0(all_37_2) = v1 & % 22.38/3.74 | aNaturalNumber0(all_37_3) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) % 22.38/3.74 | | v2 = all_37_1)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mMulComm) with xl, xp, all_37_3, simplifying with % 22.38/3.74 | (13), (15), (37) gives: % 22.38/3.74 | (47) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xp, xl) = v2 & % 22.38/3.74 | aNaturalNumber0(xp) = v1 & aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ % 22.38/3.74 | (v1 = 0) | ~ (v0 = 0) | v2 = all_37_3)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mSortsB_02) with xl, xp, all_37_3, simplifying % 22.38/3.74 | with (13), (15), (37) gives: % 22.38/3.74 | (48) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.74 | (aNaturalNumber0(all_37_3) = v2 & aNaturalNumber0(xp) = v1 & % 22.38/3.74 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mAMDistr) with xl, xp, xr, all_37_3, all_37_2, % 22.38/3.74 | all_37_1, simplifying with (13), (15), (16), (36), (37), (38) % 22.38/3.74 | gives: % 22.38/3.74 | (49) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 22.38/3.74 | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 22.38/3.74 | (sdtasdt0(v3, xl) = v5 & sdtasdt0(xr, xl) = v7 & sdtasdt0(xp, xl) = v6 % 22.38/3.74 | & sdtasdt0(xl, v3) = v4 & sdtpldt0(v6, v7) = v8 & sdtpldt0(xp, xr) = % 22.38/3.74 | v3 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xp) = v1 & % 22.38/3.74 | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 22.38/3.74 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = % 22.38/3.74 | v5 & v4 = all_37_1))) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mMulComm) with xl, xr, all_37_2, simplifying with % 22.38/3.74 | (13), (16), (38) gives: % 22.38/3.74 | (50) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xr, xl) = v2 & % 22.38/3.74 | aNaturalNumber0(xr) = v1 & aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ % 22.38/3.74 | (v1 = 0) | ~ (v0 = 0) | v2 = all_37_2)) % 22.38/3.74 | % 22.38/3.74 | GROUND_INST: instantiating (mSortsB_02) with xl, xr, all_37_2, simplifying % 22.38/3.74 | with (13), (16), (38) gives: % 22.38/3.75 | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.75 | (aNaturalNumber0(all_37_2) = v2 & aNaturalNumber0(xr) = v1 & % 22.38/3.75 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.38/3.75 | % 22.38/3.75 | GROUND_INST: instantiating (mDefDiff) with xp, xq, xr, simplifying with (11), % 22.38/3.75 | (12), (15) gives: % 22.38/3.75 | (52) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xp, xq) = v2 % 22.38/3.75 | & aNaturalNumber0(xq) = v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) % 22.38/3.75 | | ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 = xr | ~ % 22.38/3.75 | (sdtpldt0(xp, v0) = xq) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 22.38/3.75 | & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtpldt0(xp, % 22.38/3.75 | xr) = v0) | ~ $i(xr) | (v0 = xq & aNaturalNumber0(xr) = 0))) % 22.38/3.75 | % 22.38/3.75 | GROUND_INST: instantiating (mDefDiv) with xl, xm, 0, simplifying with (8), % 22.38/3.75 | (13), (29) gives: % 22.38/3.75 | (53) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 22.38/3.75 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 22.38/3.75 | $i] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0) = 0 & $i(v0)) % 22.38/3.75 | % 22.38/3.75 | GROUND_INST: instantiating (mDefDiv) with xl, all_33_0, 0, simplifying with % 22.38/3.75 | (13), (40), (41) gives: % 22.38/3.75 | (54) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_0) = v1 & % 22.38/3.75 | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 22.38/3.75 | $i] : (sdtasdt0(xl, v0) = all_33_0 & aNaturalNumber0(v0) = 0 & % 22.38/3.75 | $i(v0)) % 22.38/3.75 | % 22.38/3.75 | GROUND_INST: instantiating (1) with xl, xm, xp, simplifying with (7), (8), % 22.38/3.75 | (13) gives: % 22.38/3.75 | (55) xl = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.75 | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & % 22.38/3.75 | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.38/3.75 | 0))) | ( ! [v0: $i] : (v0 = xp | ~ (sdtasdt0(xl, v0) = xm) | ~ % 22.38/3.75 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 22.38/3.75 | & ! [v0: $i] : ( ~ (sdtasdt0(xl, xp) = v0) | ~ $i(xp) | (v0 = xm & % 22.38/3.75 | aNaturalNumber0(xp) = 0))) % 22.38/3.75 | % 22.38/3.75 | GROUND_INST: instantiating (1) with xl, all_33_0, xq, simplifying with (13), % 22.38/3.75 | (25), (41) gives: % 22.38/3.75 | (56) xl = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.75 | (doDivides0(xl, all_33_0) = v2 & aNaturalNumber0(all_33_0) = v1 & % 22.38/3.75 | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.38/3.75 | 0))) | ( ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xl, v0) = % 22.38/3.75 | all_33_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.38/3.75 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xl, xq) % 22.38/3.75 | = v0) | ~ $i(xq) | (v0 = all_33_0 & aNaturalNumber0(xq) = 0))) % 22.38/3.75 | % 22.38/3.75 | DELTA: instantiating (51) with fresh symbols all_48_0, all_48_1, all_48_2 % 22.38/3.75 | gives: % 22.38/3.75 | (57) aNaturalNumber0(all_37_2) = all_48_0 & aNaturalNumber0(xr) = all_48_1 % 22.38/3.75 | & aNaturalNumber0(xl) = all_48_2 & ( ~ (all_48_1 = 0) | ~ (all_48_2 = % 22.38/3.75 | 0) | all_48_0 = 0) % 22.38/3.75 | % 22.38/3.75 | ALPHA: (57) implies: % 22.38/3.75 | (58) aNaturalNumber0(xl) = all_48_2 % 22.38/3.75 | (59) aNaturalNumber0(xr) = all_48_1 % 22.38/3.75 | % 22.38/3.75 | DELTA: instantiating (48) with fresh symbols all_50_0, all_50_1, all_50_2 % 22.38/3.75 | gives: % 22.38/3.75 | (60) aNaturalNumber0(all_37_3) = all_50_0 & aNaturalNumber0(xp) = all_50_1 % 22.38/3.75 | & aNaturalNumber0(xl) = all_50_2 & ( ~ (all_50_1 = 0) | ~ (all_50_2 = % 22.38/3.75 | 0) | all_50_0 = 0) % 22.38/3.75 | % 22.38/3.75 | ALPHA: (60) implies: % 22.38/3.75 | (61) aNaturalNumber0(xl) = all_50_2 % 22.38/3.75 | (62) aNaturalNumber0(xp) = all_50_1 % 22.38/3.75 | % 22.38/3.75 | DELTA: instantiating (45) with fresh symbols all_52_0, all_52_1, all_52_2 % 22.38/3.75 | gives: % 22.38/3.76 | (63) aNaturalNumber0(all_37_0) = all_52_0 & aNaturalNumber0(all_37_3) = % 22.38/3.76 | all_52_2 & aNaturalNumber0(xn) = all_52_1 & ( ~ (all_52_1 = 0) | ~ % 22.38/3.76 | (all_52_2 = 0) | all_52_0 = 0) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (63) implies: % 22.38/3.76 | (64) aNaturalNumber0(xn) = all_52_1 % 22.38/3.76 | % 22.38/3.76 | DELTA: instantiating (43) with fresh symbols all_54_0, all_54_1, all_54_2 % 22.38/3.76 | gives: % 22.38/3.76 | (65) aNaturalNumber0(all_33_0) = all_54_0 & aNaturalNumber0(xn) = all_54_1 % 22.38/3.76 | & aNaturalNumber0(xm) = all_54_2 & ( ~ (all_54_1 = 0) | ~ (all_54_2 = % 22.38/3.76 | 0) | all_54_0 = 0) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (65) implies: % 22.38/3.76 | (66) aNaturalNumber0(xm) = all_54_2 % 22.38/3.76 | (67) aNaturalNumber0(xn) = all_54_1 % 22.38/3.76 | (68) aNaturalNumber0(all_33_0) = all_54_0 % 22.38/3.76 | (69) ~ (all_54_1 = 0) | ~ (all_54_2 = 0) | all_54_0 = 0 % 22.38/3.76 | % 22.38/3.76 | DELTA: instantiating (50) with fresh symbols all_58_0, all_58_1, all_58_2 % 22.38/3.76 | gives: % 22.38/3.76 | (70) sdtasdt0(xr, xl) = all_58_0 & aNaturalNumber0(xr) = all_58_1 & % 22.38/3.76 | aNaturalNumber0(xl) = all_58_2 & $i(all_58_0) & ( ~ (all_58_1 = 0) | % 22.38/3.76 | ~ (all_58_2 = 0) | all_58_0 = all_37_2) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (70) implies: % 22.38/3.76 | (71) aNaturalNumber0(xl) = all_58_2 % 22.38/3.76 | (72) aNaturalNumber0(xr) = all_58_1 % 22.38/3.76 | (73) sdtasdt0(xr, xl) = all_58_0 % 22.38/3.76 | % 22.38/3.76 | DELTA: instantiating (47) with fresh symbols all_60_0, all_60_1, all_60_2 % 22.38/3.76 | gives: % 22.38/3.76 | (74) sdtasdt0(xp, xl) = all_60_0 & aNaturalNumber0(xp) = all_60_1 & % 22.38/3.76 | aNaturalNumber0(xl) = all_60_2 & $i(all_60_0) & ( ~ (all_60_1 = 0) | % 22.38/3.76 | ~ (all_60_2 = 0) | all_60_0 = all_37_3) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (74) implies: % 22.38/3.76 | (75) aNaturalNumber0(xl) = all_60_2 % 22.38/3.76 | (76) aNaturalNumber0(xp) = all_60_1 % 22.38/3.76 | (77) ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | all_60_0 = all_37_3 % 22.38/3.76 | % 22.38/3.76 | DELTA: instantiating (46) with fresh symbols all_62_0, all_62_1, all_62_2 % 22.38/3.76 | gives: % 22.38/3.76 | (78) sdtpldt0(all_37_2, all_37_3) = all_62_0 & aNaturalNumber0(all_37_2) = % 22.38/3.76 | all_62_1 & aNaturalNumber0(all_37_3) = all_62_2 & $i(all_62_0) & ( ~ % 22.38/3.76 | (all_62_1 = 0) | ~ (all_62_2 = 0) | all_62_0 = all_37_1) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (78) implies: % 22.38/3.76 | (79) sdtpldt0(all_37_2, all_37_3) = all_62_0 % 22.38/3.76 | % 22.38/3.76 | DELTA: instantiating (42) with fresh symbols all_64_0, all_64_1, all_64_2 % 22.38/3.76 | gives: % 22.38/3.76 | (80) sdtpldt0(xn, xm) = all_64_0 & aNaturalNumber0(xn) = all_64_1 & % 22.38/3.76 | aNaturalNumber0(xm) = all_64_2 & $i(all_64_0) & ( ~ (all_64_1 = 0) | % 22.38/3.76 | ~ (all_64_2 = 0) | all_64_0 = all_33_0) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (80) implies: % 22.38/3.76 | (81) aNaturalNumber0(xm) = all_64_2 % 22.38/3.76 | (82) aNaturalNumber0(xn) = all_64_1 % 22.38/3.76 | % 22.38/3.76 | DELTA: instantiating (44) with fresh symbols all_66_0, all_66_1, all_66_2 % 22.38/3.76 | gives: % 22.38/3.76 | (83) sdtpldt0(xn, all_37_3) = all_66_0 & aNaturalNumber0(all_37_3) = % 22.38/3.76 | all_66_2 & aNaturalNumber0(xn) = all_66_1 & $i(all_66_0) & ( ~ % 22.38/3.76 | (all_66_1 = 0) | ~ (all_66_2 = 0) | all_66_0 = all_37_0) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (83) implies: % 22.38/3.76 | (84) aNaturalNumber0(xn) = all_66_1 % 22.38/3.76 | % 22.38/3.76 | DELTA: instantiating (49) with fresh symbols all_68_0, all_68_1, all_68_2, % 22.38/3.76 | all_68_3, all_68_4, all_68_5, all_68_6, all_68_7, all_68_8 gives: % 22.38/3.76 | (85) sdtasdt0(all_68_5, xl) = all_68_3 & sdtasdt0(xr, xl) = all_68_1 & % 22.38/3.76 | sdtasdt0(xp, xl) = all_68_2 & sdtasdt0(xl, all_68_5) = all_68_4 & % 22.38/3.76 | sdtpldt0(all_68_2, all_68_1) = all_68_0 & sdtpldt0(xp, xr) = all_68_5 % 22.38/3.76 | & aNaturalNumber0(xr) = all_68_6 & aNaturalNumber0(xp) = all_68_7 & % 22.38/3.76 | aNaturalNumber0(xl) = all_68_8 & $i(all_68_0) & $i(all_68_1) & % 22.38/3.76 | $i(all_68_2) & $i(all_68_3) & $i(all_68_4) & $i(all_68_5) & ( ~ % 22.38/3.76 | (all_68_6 = 0) | ~ (all_68_7 = 0) | ~ (all_68_8 = 0) | (all_68_0 = % 22.38/3.76 | all_68_3 & all_68_4 = all_37_1)) % 22.38/3.76 | % 22.38/3.76 | ALPHA: (85) implies: % 22.38/3.76 | (86) $i(all_68_5) % 22.38/3.76 | (87) aNaturalNumber0(xl) = all_68_8 % 22.38/3.76 | (88) aNaturalNumber0(xp) = all_68_7 % 22.38/3.76 | (89) aNaturalNumber0(xr) = all_68_6 % 22.38/3.76 | (90) sdtpldt0(xp, xr) = all_68_5 % 22.38/3.76 | (91) sdtasdt0(xl, all_68_5) = all_68_4 % 22.38/3.76 | (92) sdtasdt0(xr, xl) = all_68_1 % 22.38/3.76 | (93) sdtasdt0(all_68_5, xl) = all_68_3 % 22.38/3.76 | (94) ~ (all_68_6 = 0) | ~ (all_68_7 = 0) | ~ (all_68_8 = 0) | (all_68_0 % 22.38/3.76 | = all_68_3 & all_68_4 = all_37_1) % 22.38/3.76 | % 22.38/3.76 | GROUND_INST: instantiating (18) with 0, all_60_2, xl, simplifying with (2), % 22.38/3.76 | (75) gives: % 22.38/3.76 | (95) all_60_2 = 0 % 22.38/3.76 | % 22.38/3.76 | GROUND_INST: instantiating (18) with all_58_2, all_60_2, xl, simplifying with % 22.38/3.76 | (71), (75) gives: % 22.38/3.76 | (96) all_60_2 = all_58_2 % 22.38/3.76 | % 22.38/3.76 | GROUND_INST: instantiating (18) with all_48_2, all_60_2, xl, simplifying with % 22.38/3.76 | (58), (75) gives: % 22.38/3.76 | (97) all_60_2 = all_48_2 % 22.38/3.76 | % 22.38/3.76 | GROUND_INST: instantiating (18) with all_60_2, all_68_8, xl, simplifying with % 22.38/3.76 | (75), (87) gives: % 22.38/3.76 | (98) all_68_8 = all_60_2 % 22.38/3.76 | % 22.38/3.76 | GROUND_INST: instantiating (18) with all_50_2, all_68_8, xl, simplifying with % 22.38/3.76 | (61), (87) gives: % 22.38/3.76 | (99) all_68_8 = all_50_2 % 22.38/3.76 | % 22.38/3.76 | GROUND_INST: instantiating (18) with 0, all_64_2, xm, simplifying with (3), % 22.38/3.76 | (81) gives: % 22.38/3.76 | (100) all_64_2 = 0 % 22.38/3.76 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_54_2, all_64_2, xm, simplifying with % 22.38/3.77 | (66), (81) gives: % 22.38/3.77 | (101) all_64_2 = all_54_2 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_54_1, all_64_1, xn, simplifying with % 22.38/3.77 | (67), (82) gives: % 22.38/3.77 | (102) all_64_1 = all_54_1 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_52_1, all_64_1, xn, simplifying with % 22.38/3.77 | (64), (82) gives: % 22.38/3.77 | (103) all_64_1 = all_52_1 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with 0, all_66_1, xn, simplifying with (4), % 22.38/3.77 | (84) gives: % 22.38/3.77 | (104) all_66_1 = 0 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_54_1, all_66_1, xn, simplifying with % 22.38/3.77 | (67), (84) gives: % 22.38/3.77 | (105) all_66_1 = all_54_1 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_60_1, all_68_7, xp, simplifying with % 22.38/3.77 | (76), (88) gives: % 22.38/3.77 | (106) all_68_7 = all_60_1 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_50_1, all_68_7, xp, simplifying with % 22.38/3.77 | (62), (88) gives: % 22.38/3.77 | (107) all_68_7 = all_50_1 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_58_1, all_68_6, xr, simplifying with % 22.38/3.77 | (72), (89) gives: % 22.38/3.77 | (108) all_68_6 = all_58_1 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (18) with all_48_1, all_68_6, xr, simplifying with % 22.38/3.77 | (59), (89) gives: % 22.38/3.77 | (109) all_68_6 = all_48_1 % 22.38/3.77 | % 22.38/3.77 | GROUND_INST: instantiating (20) with all_58_0, all_68_1, xl, xr, simplifying % 22.38/3.77 | with (73), (92) gives: % 22.38/3.77 | (110) all_68_1 = all_58_0 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (108), (109) imply: % 22.38/3.77 | (111) all_58_1 = all_48_1 % 22.38/3.77 | % 22.38/3.77 | SIMP: (111) implies: % 22.38/3.77 | (112) all_58_1 = all_48_1 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (106), (107) imply: % 22.38/3.77 | (113) all_60_1 = all_50_1 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (98), (99) imply: % 22.38/3.77 | (114) all_60_2 = all_50_2 % 22.38/3.77 | % 22.38/3.77 | SIMP: (114) implies: % 22.38/3.77 | (115) all_60_2 = all_50_2 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (104), (105) imply: % 22.38/3.77 | (116) all_54_1 = 0 % 22.38/3.77 | % 22.38/3.77 | SIMP: (116) implies: % 22.38/3.77 | (117) all_54_1 = 0 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (102), (103) imply: % 22.38/3.77 | (118) all_54_1 = all_52_1 % 22.38/3.77 | % 22.38/3.77 | SIMP: (118) implies: % 22.38/3.77 | (119) all_54_1 = all_52_1 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (100), (101) imply: % 22.38/3.77 | (120) all_54_2 = 0 % 22.38/3.77 | % 22.38/3.77 | SIMP: (120) implies: % 22.38/3.77 | (121) all_54_2 = 0 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (95), (96) imply: % 22.38/3.77 | (122) all_58_2 = 0 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (96), (97) imply: % 22.38/3.77 | (123) all_58_2 = all_48_2 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (96), (115) imply: % 22.38/3.77 | (124) all_58_2 = all_50_2 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (122), (124) imply: % 22.38/3.77 | (125) all_50_2 = 0 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (123), (124) imply: % 22.38/3.77 | (126) all_50_2 = all_48_2 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (117), (119) imply: % 22.38/3.77 | (127) all_52_1 = 0 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (125), (126) imply: % 22.38/3.77 | (128) all_48_2 = 0 % 22.38/3.77 | % 22.38/3.77 | SIMP: (128) implies: % 22.38/3.77 | (129) all_48_2 = 0 % 22.38/3.77 | % 22.38/3.77 | COMBINE_EQS: (99), (125) imply: % 22.38/3.77 | (130) all_68_8 = 0 % 22.38/3.77 | % 22.38/3.77 | BETA: splitting (55) gives: % 22.38/3.77 | % 22.38/3.77 | Case 1: % 22.38/3.77 | | % 22.38/3.77 | | (131) xl = sz00 % 22.38/3.77 | | % 22.38/3.77 | | REDUCE: (6), (131) imply: % 22.38/3.77 | | (132) $false % 22.38/3.77 | | % 22.38/3.77 | | CLOSE: (132) is inconsistent. % 22.38/3.77 | | % 22.38/3.77 | Case 2: % 22.38/3.77 | | % 22.38/3.77 | | (133) ? [v0: any] : ? [v1: any] : ? [v2: any] : (doDivides0(xl, xm) = % 22.38/3.77 | | v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xl) = v0 & ( ~ % 22.38/3.77 | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 = % 22.38/3.77 | | xp | ~ (sdtasdt0(xl, v0) = xm) | ~ $i(v0) | ? [v1: int] : ( % 22.38/3.77 | | ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ % 22.38/3.77 | | (sdtasdt0(xl, xp) = v0) | ~ $i(xp) | (v0 = xm & % 22.38/3.77 | | aNaturalNumber0(xp) = 0))) % 22.38/3.77 | | % 22.38/3.77 | | BETA: splitting (69) gives: % 22.38/3.77 | | % 22.38/3.77 | | Case 1: % 22.38/3.77 | | | % 22.38/3.77 | | | (134) ~ (all_54_1 = 0) % 22.38/3.77 | | | % 22.38/3.77 | | | REDUCE: (117), (134) imply: % 22.38/3.77 | | | (135) $false % 22.38/3.77 | | | % 22.38/3.77 | | | CLOSE: (135) is inconsistent. % 22.38/3.77 | | | % 22.38/3.77 | | Case 2: % 22.38/3.77 | | | % 22.38/3.77 | | | (136) ~ (all_54_2 = 0) | all_54_0 = 0 % 22.38/3.77 | | | % 22.38/3.77 | | | BETA: splitting (136) gives: % 22.38/3.77 | | | % 22.38/3.77 | | | Case 1: % 22.38/3.77 | | | | % 22.38/3.77 | | | | (137) ~ (all_54_2 = 0) % 22.38/3.77 | | | | % 22.38/3.77 | | | | REDUCE: (121), (137) imply: % 22.38/3.77 | | | | (138) $false % 22.38/3.77 | | | | % 22.38/3.77 | | | | CLOSE: (138) is inconsistent. % 22.38/3.77 | | | | % 22.38/3.77 | | | Case 2: % 22.38/3.77 | | | | % 22.38/3.77 | | | | (139) all_54_0 = 0 % 22.38/3.77 | | | | % 22.38/3.77 | | | | REDUCE: (68), (139) imply: % 22.38/3.77 | | | | (140) aNaturalNumber0(all_33_0) = 0 % 22.38/3.77 | | | | % 22.38/3.77 | | | | BETA: splitting (56) gives: % 22.38/3.77 | | | | % 22.38/3.77 | | | | Case 1: % 22.38/3.77 | | | | | % 22.38/3.77 | | | | | (141) xl = sz00 % 22.38/3.77 | | | | | % 22.38/3.77 | | | | | REDUCE: (6), (141) imply: % 22.38/3.77 | | | | | (142) $false % 22.38/3.77 | | | | | % 22.38/3.77 | | | | | CLOSE: (142) is inconsistent. % 22.38/3.77 | | | | | % 22.38/3.78 | | | | Case 2: % 22.38/3.78 | | | | | % 22.38/3.78 | | | | | (143) ? [v0: any] : ? [v1: any] : ? [v2: any] : (doDivides0(xl, % 22.38/3.78 | | | | | all_33_0) = v2 & aNaturalNumber0(all_33_0) = v1 & % 22.38/3.78 | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ % 22.38/3.78 | | | | | (v0 = 0))) | ( ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xl, % 22.38/3.78 | | | | | v0) = all_33_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 22.38/3.78 | | | | | = 0) & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ % 22.38/3.78 | | | | | (sdtasdt0(xl, xq) = v0) | ~ $i(xq) | (v0 = all_33_0 & % 22.38/3.78 | | | | | aNaturalNumber0(xq) = 0))) % 22.38/3.78 | | | | | % 22.38/3.78 | | | | | BETA: splitting (54) gives: % 22.38/3.78 | | | | | % 22.38/3.78 | | | | | Case 1: % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | (144) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_33_0) = % 22.38/3.78 | | | | | | v1 & aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 22.38/3.78 | | | | | | 0))) % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | DELTA: instantiating (144) with fresh symbols all_108_0, all_108_1 % 22.38/3.78 | | | | | | gives: % 22.38/3.78 | | | | | | (145) aNaturalNumber0(all_33_0) = all_108_0 & aNaturalNumber0(xl) % 22.38/3.78 | | | | | | = all_108_1 & ( ~ (all_108_0 = 0) | ~ (all_108_1 = 0)) % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | ALPHA: (145) implies: % 22.38/3.78 | | | | | | (146) aNaturalNumber0(xl) = all_108_1 % 22.38/3.78 | | | | | | (147) aNaturalNumber0(all_33_0) = all_108_0 % 22.38/3.78 | | | | | | (148) ~ (all_108_0 = 0) | ~ (all_108_1 = 0) % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | GROUND_INST: instantiating (18) with 0, all_108_1, xl, simplifying % 22.38/3.78 | | | | | | with (2), (146) gives: % 22.38/3.78 | | | | | | (149) all_108_1 = 0 % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | GROUND_INST: instantiating (18) with 0, all_108_0, all_33_0, % 22.38/3.78 | | | | | | simplifying with (140), (147) gives: % 22.38/3.78 | | | | | | (150) all_108_0 = 0 % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | BETA: splitting (148) gives: % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | Case 1: % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | (151) ~ (all_108_0 = 0) % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | REDUCE: (150), (151) imply: % 22.38/3.78 | | | | | | | (152) $false % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | CLOSE: (152) is inconsistent. % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | Case 2: % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | (153) ~ (all_108_1 = 0) % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | REDUCE: (149), (153) imply: % 22.38/3.78 | | | | | | | (154) $false % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | CLOSE: (154) is inconsistent. % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | End of split % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | Case 2: % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | (155) ? [v0: $i] : (sdtasdt0(xl, v0) = all_33_0 & % 22.38/3.78 | | | | | | aNaturalNumber0(v0) = 0 & $i(v0)) % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | DELTA: instantiating (155) with fresh symbol all_108_0 gives: % 22.38/3.78 | | | | | | (156) sdtasdt0(xl, all_108_0) = all_33_0 & % 22.38/3.78 | | | | | | aNaturalNumber0(all_108_0) = 0 & $i(all_108_0) % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | ALPHA: (156) implies: % 22.38/3.78 | | | | | | (157) $i(all_108_0) % 22.38/3.78 | | | | | | (158) aNaturalNumber0(all_108_0) = 0 % 22.38/3.78 | | | | | | (159) sdtasdt0(xl, all_108_0) = all_33_0 % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | BETA: splitting (53) gives: % 22.38/3.78 | | | | | | % 22.38/3.78 | | | | | | Case 1: % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | (160) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xm) = v1 & % 22.38/3.78 | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | DELTA: instantiating (160) with fresh symbols all_112_0, all_112_1 % 22.38/3.78 | | | | | | | gives: % 22.38/3.78 | | | | | | | (161) aNaturalNumber0(xm) = all_112_0 & aNaturalNumber0(xl) = % 22.38/3.78 | | | | | | | all_112_1 & ( ~ (all_112_0 = 0) | ~ (all_112_1 = 0)) % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | ALPHA: (161) implies: % 22.38/3.78 | | | | | | | (162) aNaturalNumber0(xl) = all_112_1 % 22.38/3.78 | | | | | | | (163) aNaturalNumber0(xm) = all_112_0 % 22.38/3.78 | | | | | | | (164) ~ (all_112_0 = 0) | ~ (all_112_1 = 0) % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | GROUND_INST: instantiating (18) with 0, all_112_1, xl, simplifying % 22.38/3.78 | | | | | | | with (2), (162) gives: % 22.38/3.78 | | | | | | | (165) all_112_1 = 0 % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | GROUND_INST: instantiating (18) with 0, all_112_0, xm, simplifying % 22.38/3.78 | | | | | | | with (3), (163) gives: % 22.38/3.78 | | | | | | | (166) all_112_0 = 0 % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | BETA: splitting (164) gives: % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | Case 1: % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | (167) ~ (all_112_0 = 0) % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | REDUCE: (166), (167) imply: % 22.38/3.78 | | | | | | | | (168) $false % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | CLOSE: (168) is inconsistent. % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | Case 2: % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | (169) ~ (all_112_1 = 0) % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | REDUCE: (165), (169) imply: % 22.38/3.78 | | | | | | | | (170) $false % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | CLOSE: (170) is inconsistent. % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | End of split % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | Case 2: % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | (171) ? [v0: $i] : (sdtasdt0(xl, v0) = xm & % 22.38/3.78 | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0)) % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | DELTA: instantiating (171) with fresh symbol all_112_0 gives: % 22.38/3.78 | | | | | | | (172) sdtasdt0(xl, all_112_0) = xm & aNaturalNumber0(all_112_0) % 22.38/3.78 | | | | | | | = 0 & $i(all_112_0) % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | ALPHA: (172) implies: % 22.38/3.78 | | | | | | | (173) $i(all_112_0) % 22.38/3.78 | | | | | | | (174) aNaturalNumber0(all_112_0) = 0 % 22.38/3.78 | | | | | | | (175) sdtasdt0(xl, all_112_0) = xm % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | BETA: splitting (133) gives: % 22.38/3.78 | | | | | | | % 22.38/3.78 | | | | | | | Case 1: % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | (176) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.78 | | | | | | | | (doDivides0(xl, xm) = v2 & aNaturalNumber0(xm) = v1 & % 22.38/3.78 | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) % 22.38/3.78 | | | | | | | | | ~ (v0 = 0))) % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | DELTA: instantiating (176) with fresh symbols all_119_0, % 22.38/3.78 | | | | | | | | all_119_1, all_119_2 gives: % 22.38/3.78 | | | | | | | | (177) doDivides0(xl, xm) = all_119_0 & aNaturalNumber0(xm) = % 22.38/3.78 | | | | | | | | all_119_1 & aNaturalNumber0(xl) = all_119_2 & ( ~ % 22.38/3.78 | | | | | | | | (all_119_0 = 0) | ~ (all_119_1 = 0) | ~ (all_119_2 % 22.38/3.78 | | | | | | | | = 0)) % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | ALPHA: (177) implies: % 22.38/3.78 | | | | | | | | (178) aNaturalNumber0(xl) = all_119_2 % 22.38/3.78 | | | | | | | | (179) aNaturalNumber0(xm) = all_119_1 % 22.38/3.78 | | | | | | | | (180) doDivides0(xl, xm) = all_119_0 % 22.38/3.78 | | | | | | | | (181) ~ (all_119_0 = 0) | ~ (all_119_1 = 0) | ~ (all_119_2 % 22.38/3.78 | | | | | | | | = 0) % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | GROUND_INST: instantiating (18) with 0, all_119_2, xl, % 22.38/3.78 | | | | | | | | simplifying with (2), (178) gives: % 22.38/3.78 | | | | | | | | (182) all_119_2 = 0 % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | GROUND_INST: instantiating (18) with 0, all_119_1, xm, % 22.38/3.78 | | | | | | | | simplifying with (3), (179) gives: % 22.38/3.78 | | | | | | | | (183) all_119_1 = 0 % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | GROUND_INST: instantiating (22) with 0, all_119_0, xm, xl, % 22.38/3.78 | | | | | | | | simplifying with (29), (180) gives: % 22.38/3.78 | | | | | | | | (184) all_119_0 = 0 % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | BETA: splitting (181) gives: % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | | Case 1: % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | | (185) ~ (all_119_0 = 0) % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | | REDUCE: (184), (185) imply: % 22.38/3.78 | | | | | | | | | (186) $false % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | | CLOSE: (186) is inconsistent. % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | Case 2: % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | | (187) ~ (all_119_1 = 0) | ~ (all_119_2 = 0) % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | | BETA: splitting (187) gives: % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | | Case 1: % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | | (188) ~ (all_119_1 = 0) % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | | REDUCE: (183), (188) imply: % 22.38/3.78 | | | | | | | | | | (189) $false % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | | CLOSE: (189) is inconsistent. % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | Case 2: % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | | (190) ~ (all_119_2 = 0) % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | | REDUCE: (182), (190) imply: % 22.38/3.78 | | | | | | | | | | (191) $false % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | | CLOSE: (191) is inconsistent. % 22.38/3.78 | | | | | | | | | | % 22.38/3.78 | | | | | | | | | End of split % 22.38/3.78 | | | | | | | | | % 22.38/3.78 | | | | | | | | End of split % 22.38/3.78 | | | | | | | | % 22.38/3.78 | | | | | | | Case 2: % 22.38/3.78 | | | | | | | | % 22.38/3.79 | | | | | | | | (192) ! [v0: $i] : (v0 = xp | ~ (sdtasdt0(xl, v0) = xm) | % 22.38/3.79 | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 22.38/3.79 | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ % 22.38/3.79 | | | | | | | | (sdtasdt0(xl, xp) = v0) | ~ $i(xp) | (v0 = xm & % 22.38/3.79 | | | | | | | | aNaturalNumber0(xp) = 0)) % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | ALPHA: (192) implies: % 22.38/3.79 | | | | | | | | (193) ! [v0: $i] : ( ~ (sdtasdt0(xl, xp) = v0) | ~ $i(xp) | % 22.38/3.79 | | | | | | | | (v0 = xm & aNaturalNumber0(xp) = 0)) % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | GROUND_INST: instantiating (193) with all_37_3, simplifying with % 22.38/3.79 | | | | | | | | (15), (37) gives: % 22.38/3.79 | | | | | | | | (194) all_37_3 = xm & aNaturalNumber0(xp) = 0 % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | ALPHA: (194) implies: % 22.38/3.79 | | | | | | | | (195) all_37_3 = xm % 22.38/3.79 | | | | | | | | (196) aNaturalNumber0(xp) = 0 % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | REDUCE: (37), (195) imply: % 22.38/3.79 | | | | | | | | (197) sdtasdt0(xl, xp) = xm % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | REDUCE: (79), (195) imply: % 22.38/3.79 | | | | | | | | (198) sdtpldt0(all_37_2, xm) = all_62_0 % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | REDUCE: (36), (195) imply: % 22.38/3.79 | | | | | | | | (199) sdtpldt0(xm, all_37_2) = all_37_1 % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | REDUCE: (35), (195) imply: % 22.38/3.79 | | | | | | | | (200) sdtpldt0(xm, xn) = all_37_0 % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | BETA: splitting (143) gives: % 22.38/3.79 | | | | | | | | % 22.38/3.79 | | | | | | | | Case 1: % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | (201) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.79 | | | | | | | | | (doDivides0(xl, all_33_0) = v2 & % 22.38/3.79 | | | | | | | | | aNaturalNumber0(all_33_0) = v1 & % 22.38/3.79 | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v2 = 0) | ~ (v1 = % 22.38/3.79 | | | | | | | | | 0) | ~ (v0 = 0))) % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | DELTA: instantiating (201) with fresh symbols all_121_0, % 22.38/3.79 | | | | | | | | | all_121_1, all_121_2 gives: % 22.38/3.79 | | | | | | | | | (202) doDivides0(xl, all_33_0) = all_121_0 & % 22.38/3.79 | | | | | | | | | aNaturalNumber0(all_33_0) = all_121_1 & % 22.38/3.79 | | | | | | | | | aNaturalNumber0(xl) = all_121_2 & ( ~ (all_121_0 = 0) % 22.38/3.79 | | | | | | | | | | ~ (all_121_1 = 0) | ~ (all_121_2 = 0)) % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | ALPHA: (202) implies: % 22.38/3.79 | | | | | | | | | (203) aNaturalNumber0(xl) = all_121_2 % 22.38/3.79 | | | | | | | | | (204) aNaturalNumber0(all_33_0) = all_121_1 % 22.38/3.79 | | | | | | | | | (205) doDivides0(xl, all_33_0) = all_121_0 % 22.38/3.79 | | | | | | | | | (206) ~ (all_121_0 = 0) | ~ (all_121_1 = 0) | ~ % 22.38/3.79 | | | | | | | | | (all_121_2 = 0) % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_121_2, xl, % 22.38/3.79 | | | | | | | | | simplifying with (2), (203) gives: % 22.38/3.79 | | | | | | | | | (207) all_121_2 = 0 % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_121_1, all_33_0, % 22.38/3.79 | | | | | | | | | simplifying with (140), (204) gives: % 22.38/3.79 | | | | | | | | | (208) all_121_1 = 0 % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_121_0, all_33_0, % 22.38/3.79 | | | | | | | | | xl, simplifying with (40), (205) gives: % 22.38/3.79 | | | | | | | | | (209) all_121_0 = 0 % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | BETA: splitting (206) gives: % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | Case 1: % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | (210) ~ (all_121_0 = 0) % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | REDUCE: (209), (210) imply: % 22.38/3.79 | | | | | | | | | | (211) $false % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | CLOSE: (211) is inconsistent. % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | Case 2: % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | (212) ~ (all_121_1 = 0) | ~ (all_121_2 = 0) % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | BETA: splitting (212) gives: % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | Case 1: % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | (213) ~ (all_121_1 = 0) % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | REDUCE: (208), (213) imply: % 22.38/3.79 | | | | | | | | | | | (214) $false % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | CLOSE: (214) is inconsistent. % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | Case 2: % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | (215) ~ (all_121_2 = 0) % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | REDUCE: (207), (215) imply: % 22.38/3.79 | | | | | | | | | | | (216) $false % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | CLOSE: (216) is inconsistent. % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | End of split % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | End of split % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | Case 2: % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | (217) ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xl, v0) = % 22.38/3.79 | | | | | | | | | all_33_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 22.38/3.79 | | | | | | | | | 0) & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : % 22.38/3.79 | | | | | | | | | ( ~ (sdtasdt0(xl, xq) = v0) | ~ $i(xq) | (v0 = % 22.38/3.79 | | | | | | | | | all_33_0 & aNaturalNumber0(xq) = 0)) % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | ALPHA: (217) implies: % 22.38/3.79 | | | | | | | | | (218) ! [v0: $i] : (v0 = xq | ~ (sdtasdt0(xl, v0) = % 22.38/3.79 | | | | | | | | | all_33_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 22.38/3.79 | | | | | | | | | 0) & aNaturalNumber0(v0) = v1)) % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | GROUND_INST: instantiating (18) with all_50_1, 0, xp, % 22.38/3.79 | | | | | | | | | simplifying with (62), (196) gives: % 22.38/3.79 | | | | | | | | | (219) all_50_1 = 0 % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | GROUND_INST: instantiating (19) with all_33_0, all_37_0, xn, % 22.38/3.79 | | | | | | | | | xm, simplifying with (24), (200) gives: % 22.38/3.79 | | | | | | | | | (220) all_37_0 = all_33_0 % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | COMBINE_EQS: (113), (219) imply: % 22.38/3.79 | | | | | | | | | (221) all_60_1 = 0 % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | COMBINE_EQS: (107), (219) imply: % 22.38/3.79 | | | | | | | | | (222) all_68_7 = 0 % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | REDUCE: (32), (220) imply: % 22.38/3.79 | | | | | | | | | (223) ~ (all_37_1 = all_33_0) % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | SIMP: (223) implies: % 22.38/3.79 | | | | | | | | | (224) ~ (all_37_1 = all_33_0) % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | BETA: splitting (77) gives: % 22.38/3.79 | | | | | | | | | % 22.38/3.79 | | | | | | | | | Case 1: % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | (225) ~ (all_60_1 = 0) % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | REDUCE: (221), (225) imply: % 22.38/3.79 | | | | | | | | | | (226) $false % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | CLOSE: (226) is inconsistent. % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | Case 2: % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | (227) ~ (all_60_2 = 0) | all_60_0 = all_37_3 % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | BETA: splitting (227) gives: % 22.38/3.79 | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | Case 1: % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | (228) ~ (all_60_2 = 0) % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | REDUCE: (95), (228) imply: % 22.38/3.79 | | | | | | | | | | | (229) $false % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | CLOSE: (229) is inconsistent. % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | Case 2: % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with xp, xr, all_68_5, % 22.38/3.79 | | | | | | | | | | | simplifying with (15), (16), (90) gives: % 22.38/3.79 | | | | | | | | | | | (230) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.38/3.79 | | | | | | | | | | | (sdtpldt0(xr, xp) = v2 & aNaturalNumber0(xr) = v1 % 22.38/3.79 | | | | | | | | | | | & aNaturalNumber0(xp) = v0 & $i(v2) & ( ~ (v1 = % 22.38/3.79 | | | | | | | | | | | 0) | ~ (v0 = 0) | v2 = all_68_5)) % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with xp, xr, all_68_5, % 22.38/3.79 | | | | | | | | | | | simplifying with (15), (16), (90) gives: % 22.38/3.79 | | | | | | | | | | | (231) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.79 | | | | | | | | | | | (aNaturalNumber0(all_68_5) = v2 & % 22.38/3.79 | | | | | | | | | | | aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) = % 22.38/3.79 | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.38/3.79 | | | | | | | | | | | % 22.38/3.79 | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, xr, xp, % 22.38/3.79 | | | | | | | | | | | all_37_2, xm, all_62_0, simplifying with (13), % 22.38/3.79 | | | | | | | | | | | (15), (16), (38), (197), (198) gives: % 22.38/3.80 | | | | | | | | | | | (232) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.38/3.80 | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 22.38/3.80 | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) = % 22.38/3.80 | | | | | | | | | | | v5 & sdtasdt0(xr, xl) = v6 & sdtasdt0(xp, xl) = % 22.38/3.80 | | | | | | | | | | | v7 & sdtasdt0(xl, v3) = v4 & sdtpldt0(v6, v7) = % 22.38/3.80 | | | | | | | | | | | v8 & sdtpldt0(xr, xp) = v3 & aNaturalNumber0(xr) % 22.38/3.80 | | | | | | | | | | | = v1 & aNaturalNumber0(xp) = v2 & % 22.38/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v8) & $i(v7) & % 22.38/3.80 | | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) % 22.38/3.80 | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = v5 & v4 = % 22.38/3.80 | | | | | | | | | | | all_62_0))) % 22.38/3.80 | | | | | | | | | | | % 22.38/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_68_5, % 22.38/3.80 | | | | | | | | | | | all_68_4, simplifying with (13), (86), (91) gives: % 22.38/3.80 | | | | | | | | | | | (233) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.38/3.80 | | | | | | | | | | | (sdtasdt0(all_68_5, xl) = v2 & % 22.38/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = v1 & % 22.38/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 22.38/3.80 | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_68_4)) % 22.38/3.80 | | | | | | | | | | | % 22.38/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xl, all_68_5, % 22.38/3.80 | | | | | | | | | | | all_68_4, simplifying with (13), (86), (91) gives: % 22.38/3.80 | | | | | | | | | | | (234) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.38/3.80 | | | | | | | | | | | (aNaturalNumber0(all_68_4) = v2 & % 22.38/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = v1 & % 22.38/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & ( ~ (v1 = 0) | ~ (v0 % 22.38/3.80 | | | | | | | | | | | = 0) | v2 = 0)) % 22.38/3.80 | | | | | | | | | | | % 22.38/3.80 | | | | | | | | | | | GROUND_INST: instantiating (218) with all_108_0, simplifying % 22.38/3.80 | | | | | | | | | | | with (157), (159) gives: % 22.38/3.80 | | | | | | | | | | | (235) all_108_0 = xq | ? [v0: int] : ( ~ (v0 = 0) & % 22.38/3.80 | | | | | | | | | | | aNaturalNumber0(all_108_0) = v0) % 22.38/3.80 | | | | | | | | | | | % 22.38/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_108_0, % 22.38/3.80 | | | | | | | | | | | all_33_0, simplifying with (13), (157), (159) % 22.38/3.80 | | | | | | | | | | | gives: % 22.79/3.80 | | | | | | | | | | | (236) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.79/3.80 | | | | | | | | | | | (sdtasdt0(all_108_0, xl) = v2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_108_0) = v1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 22.79/3.80 | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_33_0)) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, xr, all_112_0, % 22.79/3.80 | | | | | | | | | | | all_37_2, xm, all_62_0, simplifying with (13), % 22.79/3.80 | | | | | | | | | | | (16), (38), (173), (175), (198) gives: % 22.79/3.80 | | | | | | | | | | | (237) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.79/3.80 | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 22.79/3.80 | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) = % 22.79/3.80 | | | | | | | | | | | v5 & sdtasdt0(all_112_0, xl) = v7 & sdtasdt0(xr, % 22.79/3.80 | | | | | | | | | | | xl) = v6 & sdtasdt0(xl, v3) = v4 & % 22.79/3.80 | | | | | | | | | | | sdtpldt0(v6, v7) = v8 & sdtpldt0(xr, all_112_0) % 22.79/3.80 | | | | | | | | | | | = v3 & aNaturalNumber0(all_112_0) = v2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xr) = v1 & aNaturalNumber0(xl) = % 22.79/3.80 | | | | | | | | | | | v0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) % 22.79/3.80 | | | | | | | | | | | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.79/3.80 | | | | | | | | | | | 0) | (v8 = v5 & v4 = all_62_0))) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mAMDistr) with xl, all_112_0, xr, % 22.79/3.80 | | | | | | | | | | | xm, all_37_2, all_37_1, simplifying with (13), % 22.79/3.80 | | | | | | | | | | | (16), (38), (173), (175), (199) gives: % 22.79/3.80 | | | | | | | | | | | (238) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 22.79/3.80 | | | | | | | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 22.79/3.80 | | | | | | | | | | | : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v3, xl) = % 22.79/3.80 | | | | | | | | | | | v5 & sdtasdt0(all_112_0, xl) = v6 & sdtasdt0(xr, % 22.79/3.80 | | | | | | | | | | | xl) = v7 & sdtasdt0(xl, v3) = v4 & % 22.79/3.80 | | | | | | | | | | | sdtpldt0(v6, v7) = v8 & sdtpldt0(all_112_0, xr) % 22.79/3.80 | | | | | | | | | | | = v3 & aNaturalNumber0(all_112_0) = v1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xr) = v2 & aNaturalNumber0(xl) = % 22.79/3.80 | | | | | | | | | | | v0 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) % 22.79/3.80 | | | | | | | | | | | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 22.79/3.80 | | | | | | | | | | | 0) | (v8 = v5 & v4 = all_37_1))) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xl, all_112_0, xm, % 22.79/3.80 | | | | | | | | | | | simplifying with (13), (173), (175) gives: % 22.79/3.80 | | | | | | | | | | | (239) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.79/3.80 | | | | | | | | | | | (sdtasdt0(all_112_0, xl) = v2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_112_0) = v1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = v0 & $i(v2) & ( ~ (v1 = 0) % 22.79/3.80 | | | | | | | | | | | | ~ (v0 = 0) | v2 = xm)) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xr, xl, all_58_0, % 22.79/3.80 | | | | | | | | | | | simplifying with (13), (16), (73) gives: % 22.79/3.80 | | | | | | | | | | | (240) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.79/3.80 | | | | | | | | | | | (sdtasdt0(xl, xr) = v2 & aNaturalNumber0(xr) = v0 % 22.79/3.80 | | | | | | | | | | | & aNaturalNumber0(xl) = v1 & $i(v2) & ( ~ (v1 = % 22.79/3.80 | | | | | | | | | | | 0) | ~ (v0 = 0) | v2 = all_58_0)) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xr, xl, all_58_0, % 22.79/3.80 | | | | | | | | | | | simplifying with (13), (16), (73) gives: % 22.79/3.80 | | | | | | | | | | | (241) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.79/3.80 | | | | | | | | | | | (aNaturalNumber0(all_58_0) = v2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xr) = v0 & aNaturalNumber0(xl) = % 22.79/3.80 | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with all_68_5, xl, % 22.79/3.80 | | | | | | | | | | | all_68_3, simplifying with (13), (86), (93) gives: % 22.79/3.80 | | | | | | | | | | | (242) ? [v0: any] : ? [v1: any] : ? [v2: $i] : % 22.79/3.80 | | | | | | | | | | | (sdtasdt0(xl, all_68_5) = v2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = v0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = v1 & $i(v2) & ( ~ (v1 = 0) % 22.79/3.80 | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_68_3)) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with all_68_5, xl, % 22.79/3.80 | | | | | | | | | | | all_68_3, simplifying with (13), (86), (93) gives: % 22.79/3.80 | | | | | | | | | | | (243) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.79/3.80 | | | | | | | | | | | (aNaturalNumber0(all_68_3) = v2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = v0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = v1 & ( ~ (v1 = 0) | ~ (v0 % 22.79/3.80 | | | | | | | | | | | = 0) | v2 = 0)) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (243) with fresh symbols all_146_0, % 22.79/3.80 | | | | | | | | | | | all_146_1, all_146_2 gives: % 22.79/3.80 | | | | | | | | | | | (244) aNaturalNumber0(all_68_3) = all_146_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = all_146_2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = all_146_1 & ( ~ (all_146_1 = % 22.79/3.80 | | | | | | | | | | | 0) | ~ (all_146_2 = 0) | all_146_0 = 0) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (244) implies: % 22.79/3.80 | | | | | | | | | | | (245) aNaturalNumber0(xl) = all_146_1 % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (241) with fresh symbols all_148_0, % 22.79/3.80 | | | | | | | | | | | all_148_1, all_148_2 gives: % 22.79/3.80 | | | | | | | | | | | (246) aNaturalNumber0(all_58_0) = all_148_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xr) = all_148_2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = all_148_1 & ( ~ (all_148_1 = % 22.79/3.80 | | | | | | | | | | | 0) | ~ (all_148_2 = 0) | all_148_0 = 0) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (246) implies: % 22.79/3.80 | | | | | | | | | | | (247) aNaturalNumber0(xl) = all_148_1 % 22.79/3.80 | | | | | | | | | | | (248) aNaturalNumber0(xr) = all_148_2 % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (234) with fresh symbols all_150_0, % 22.79/3.80 | | | | | | | | | | | all_150_1, all_150_2 gives: % 22.79/3.80 | | | | | | | | | | | (249) aNaturalNumber0(all_68_4) = all_150_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = all_150_1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = all_150_2 & ( ~ (all_150_1 = % 22.79/3.80 | | | | | | | | | | | 0) | ~ (all_150_2 = 0) | all_150_0 = 0) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (249) implies: % 22.79/3.80 | | | | | | | | | | | (250) aNaturalNumber0(xl) = all_150_2 % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (231) with fresh symbols all_154_0, % 22.79/3.80 | | | | | | | | | | | all_154_1, all_154_2 gives: % 22.79/3.80 | | | | | | | | | | | (251) aNaturalNumber0(all_68_5) = all_154_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xr) = all_154_1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xp) = all_154_2 & ( ~ (all_154_1 = % 22.79/3.80 | | | | | | | | | | | 0) | ~ (all_154_2 = 0) | all_154_0 = 0) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (251) implies: % 22.79/3.80 | | | | | | | | | | | (252) aNaturalNumber0(xp) = all_154_2 % 22.79/3.80 | | | | | | | | | | | (253) aNaturalNumber0(xr) = all_154_1 % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (240) with fresh symbols all_158_0, % 22.79/3.80 | | | | | | | | | | | all_158_1, all_158_2 gives: % 22.79/3.80 | | | | | | | | | | | (254) sdtasdt0(xl, xr) = all_158_0 & aNaturalNumber0(xr) % 22.79/3.80 | | | | | | | | | | | = all_158_2 & aNaturalNumber0(xl) = all_158_1 & % 22.79/3.80 | | | | | | | | | | | $i(all_158_0) & ( ~ (all_158_1 = 0) | ~ % 22.79/3.80 | | | | | | | | | | | (all_158_2 = 0) | all_158_0 = all_58_0) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (254) implies: % 22.79/3.80 | | | | | | | | | | | (255) aNaturalNumber0(xl) = all_158_1 % 22.79/3.80 | | | | | | | | | | | (256) aNaturalNumber0(xr) = all_158_2 % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (236) with fresh symbols all_160_0, % 22.79/3.80 | | | | | | | | | | | all_160_1, all_160_2 gives: % 22.79/3.80 | | | | | | | | | | | (257) sdtasdt0(all_108_0, xl) = all_160_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_108_0) = all_160_1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = all_160_2 & $i(all_160_0) & % 22.79/3.80 | | | | | | | | | | | ( ~ (all_160_1 = 0) | ~ (all_160_2 = 0) | % 22.79/3.80 | | | | | | | | | | | all_160_0 = all_33_0) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (257) implies: % 22.79/3.80 | | | | | | | | | | | (258) aNaturalNumber0(xl) = all_160_2 % 22.79/3.80 | | | | | | | | | | | (259) aNaturalNumber0(all_108_0) = all_160_1 % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_162_0, % 22.79/3.80 | | | | | | | | | | | all_162_1, all_162_2 gives: % 22.79/3.80 | | | | | | | | | | | (260) sdtasdt0(all_68_5, xl) = all_162_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = all_162_1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = all_162_2 & $i(all_162_0) & % 22.79/3.80 | | | | | | | | | | | ( ~ (all_162_1 = 0) | ~ (all_162_2 = 0) | % 22.79/3.80 | | | | | | | | | | | all_162_0 = all_68_4) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (260) implies: % 22.79/3.80 | | | | | | | | | | | (261) aNaturalNumber0(xl) = all_162_2 % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (239) with fresh symbols all_164_0, % 22.79/3.80 | | | | | | | | | | | all_164_1, all_164_2 gives: % 22.79/3.80 | | | | | | | | | | | (262) sdtasdt0(all_112_0, xl) = all_164_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_112_0) = all_164_1 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = all_164_2 & $i(all_164_0) & % 22.79/3.80 | | | | | | | | | | | ( ~ (all_164_1 = 0) | ~ (all_164_2 = 0) | % 22.79/3.80 | | | | | | | | | | | all_164_0 = xm) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | ALPHA: (262) implies: % 22.79/3.80 | | | | | | | | | | | (263) aNaturalNumber0(xl) = all_164_2 % 22.79/3.80 | | | | | | | | | | | (264) aNaturalNumber0(all_112_0) = all_164_1 % 22.79/3.80 | | | | | | | | | | | (265) ~ (all_164_1 = 0) | ~ (all_164_2 = 0) | % 22.79/3.80 | | | | | | | | | | | all_164_0 = xm % 22.79/3.80 | | | | | | | | | | | % 22.79/3.80 | | | | | | | | | | | DELTA: instantiating (242) with fresh symbols all_170_0, % 22.79/3.80 | | | | | | | | | | | all_170_1, all_170_2 gives: % 22.79/3.80 | | | | | | | | | | | (266) sdtasdt0(xl, all_68_5) = all_170_0 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(all_68_5) = all_170_2 & % 22.79/3.80 | | | | | | | | | | | aNaturalNumber0(xl) = all_170_1 & $i(all_170_0) & % 22.79/3.80 | | | | | | | | | | | ( ~ (all_170_1 = 0) | ~ (all_170_2 = 0) | % 22.79/3.80 | | | | | | | | | | | all_170_0 = all_68_3) % 22.79/3.80 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | ALPHA: (266) implies: % 22.79/3.81 | | | | | | | | | | | (267) aNaturalNumber0(xl) = all_170_1 % 22.79/3.81 | | | | | | | | | | | (268) sdtasdt0(xl, all_68_5) = all_170_0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | DELTA: instantiating (230) with fresh symbols all_172_0, % 22.79/3.81 | | | | | | | | | | | all_172_1, all_172_2 gives: % 22.79/3.81 | | | | | | | | | | | (269) sdtpldt0(xr, xp) = all_172_0 & aNaturalNumber0(xr) % 22.79/3.81 | | | | | | | | | | | = all_172_1 & aNaturalNumber0(xp) = all_172_2 & % 22.79/3.81 | | | | | | | | | | | $i(all_172_0) & ( ~ (all_172_1 = 0) | ~ % 22.79/3.81 | | | | | | | | | | | (all_172_2 = 0) | all_172_0 = all_68_5) % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | ALPHA: (269) implies: % 22.79/3.81 | | | | | | | | | | | (270) aNaturalNumber0(xp) = all_172_2 % 22.79/3.81 | | | | | | | | | | | (271) aNaturalNumber0(xr) = all_172_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | DELTA: instantiating (232) with fresh symbols all_174_0, % 22.79/3.81 | | | | | | | | | | | all_174_1, all_174_2, all_174_3, all_174_4, % 22.79/3.81 | | | | | | | | | | | all_174_5, all_174_6, all_174_7, all_174_8 gives: % 22.79/3.81 | | | | | | | | | | | (272) sdtasdt0(all_174_5, xl) = all_174_3 & sdtasdt0(xr, % 22.79/3.81 | | | | | | | | | | | xl) = all_174_2 & sdtasdt0(xp, xl) = all_174_1 & % 22.79/3.81 | | | | | | | | | | | sdtasdt0(xl, all_174_5) = all_174_4 & % 22.79/3.81 | | | | | | | | | | | sdtpldt0(all_174_2, all_174_1) = all_174_0 & % 22.79/3.81 | | | | | | | | | | | sdtpldt0(xr, xp) = all_174_5 & aNaturalNumber0(xr) % 22.79/3.81 | | | | | | | | | | | = all_174_7 & aNaturalNumber0(xp) = all_174_6 & % 22.79/3.81 | | | | | | | | | | | aNaturalNumber0(xl) = all_174_8 & $i(all_174_0) & % 22.79/3.81 | | | | | | | | | | | $i(all_174_1) & $i(all_174_2) & $i(all_174_3) & % 22.79/3.81 | | | | | | | | | | | $i(all_174_4) & $i(all_174_5) & ( ~ (all_174_6 = % 22.79/3.81 | | | | | | | | | | | 0) | ~ (all_174_7 = 0) | ~ (all_174_8 = 0) | % 22.79/3.81 | | | | | | | | | | | (all_174_0 = all_174_3 & all_174_4 = all_62_0)) % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | ALPHA: (272) implies: % 22.79/3.81 | | | | | | | | | | | (273) aNaturalNumber0(xl) = all_174_8 % 22.79/3.81 | | | | | | | | | | | (274) aNaturalNumber0(xp) = all_174_6 % 22.79/3.81 | | | | | | | | | | | (275) aNaturalNumber0(xr) = all_174_7 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | DELTA: instantiating (238) with fresh symbols all_176_0, % 22.79/3.81 | | | | | | | | | | | all_176_1, all_176_2, all_176_3, all_176_4, % 22.79/3.81 | | | | | | | | | | | all_176_5, all_176_6, all_176_7, all_176_8 gives: % 22.79/3.81 | | | | | | | | | | | (276) sdtasdt0(all_176_5, xl) = all_176_3 & % 22.79/3.81 | | | | | | | | | | | sdtasdt0(all_112_0, xl) = all_176_2 & sdtasdt0(xr, % 22.79/3.81 | | | | | | | | | | | xl) = all_176_1 & sdtasdt0(xl, all_176_5) = % 22.79/3.81 | | | | | | | | | | | all_176_4 & sdtpldt0(all_176_2, all_176_1) = % 22.79/3.81 | | | | | | | | | | | all_176_0 & sdtpldt0(all_112_0, xr) = all_176_5 & % 22.79/3.81 | | | | | | | | | | | aNaturalNumber0(all_112_0) = all_176_7 & % 22.79/3.81 | | | | | | | | | | | aNaturalNumber0(xr) = all_176_6 & % 22.79/3.81 | | | | | | | | | | | aNaturalNumber0(xl) = all_176_8 & $i(all_176_0) & % 22.79/3.81 | | | | | | | | | | | $i(all_176_1) & $i(all_176_2) & $i(all_176_3) & % 22.79/3.81 | | | | | | | | | | | $i(all_176_4) & $i(all_176_5) & ( ~ (all_176_6 = % 22.79/3.81 | | | | | | | | | | | 0) | ~ (all_176_7 = 0) | ~ (all_176_8 = 0) | % 22.79/3.81 | | | | | | | | | | | (all_176_0 = all_176_3 & all_176_4 = all_37_1)) % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | ALPHA: (276) implies: % 22.79/3.81 | | | | | | | | | | | (277) aNaturalNumber0(xl) = all_176_8 % 22.79/3.81 | | | | | | | | | | | (278) aNaturalNumber0(xr) = all_176_6 % 22.79/3.81 | | | | | | | | | | | (279) aNaturalNumber0(all_112_0) = all_176_7 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | DELTA: instantiating (237) with fresh symbols all_178_0, % 22.79/3.81 | | | | | | | | | | | all_178_1, all_178_2, all_178_3, all_178_4, % 22.79/3.81 | | | | | | | | | | | all_178_5, all_178_6, all_178_7, all_178_8 gives: % 22.79/3.81 | | | | | | | | | | | (280) sdtasdt0(all_178_5, xl) = all_178_3 & % 22.79/3.81 | | | | | | | | | | | sdtasdt0(all_112_0, xl) = all_178_1 & sdtasdt0(xr, % 22.79/3.81 | | | | | | | | | | | xl) = all_178_2 & sdtasdt0(xl, all_178_5) = % 22.79/3.81 | | | | | | | | | | | all_178_4 & sdtpldt0(all_178_2, all_178_1) = % 22.79/3.81 | | | | | | | | | | | all_178_0 & sdtpldt0(xr, all_112_0) = all_178_5 & % 22.79/3.81 | | | | | | | | | | | aNaturalNumber0(all_112_0) = all_178_6 & % 22.79/3.81 | | | | | | | | | | | aNaturalNumber0(xr) = all_178_7 & % 22.79/3.81 | | | | | | | | | | | aNaturalNumber0(xl) = all_178_8 & $i(all_178_0) & % 22.79/3.81 | | | | | | | | | | | $i(all_178_1) & $i(all_178_2) & $i(all_178_3) & % 22.79/3.81 | | | | | | | | | | | $i(all_178_4) & $i(all_178_5) & ( ~ (all_178_6 = % 22.79/3.81 | | | | | | | | | | | 0) | ~ (all_178_7 = 0) | ~ (all_178_8 = 0) | % 22.79/3.81 | | | | | | | | | | | (all_178_0 = all_178_3 & all_178_4 = all_62_0)) % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | ALPHA: (280) implies: % 22.79/3.81 | | | | | | | | | | | (281) aNaturalNumber0(xl) = all_178_8 % 22.79/3.81 | | | | | | | | | | | (282) aNaturalNumber0(xr) = all_178_7 % 22.79/3.81 | | | | | | | | | | | (283) aNaturalNumber0(all_112_0) = all_178_6 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_150_2, all_162_2, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (250), (261) gives: % 22.79/3.81 | | | | | | | | | | | (284) all_162_2 = all_150_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_162_2, all_170_1, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (261), (267) gives: % 22.79/3.81 | | | | | | | | | | | (285) all_170_1 = all_162_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_158_1, all_170_1, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (255), (267) gives: % 22.79/3.81 | | | | | | | | | | | (286) all_170_1 = all_158_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_174_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (2), (273) gives: % 22.79/3.81 | | | | | | | | | | | (287) all_174_8 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_162_2, all_174_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (261), (273) gives: % 22.79/3.81 | | | | | | | | | | | (288) all_174_8 = all_162_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_164_2, all_176_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (263), (277) gives: % 22.79/3.81 | | | | | | | | | | | (289) all_176_8 = all_164_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_150_2, all_176_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (250), (277) gives: % 22.79/3.81 | | | | | | | | | | | (290) all_176_8 = all_150_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_148_1, all_176_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (247), (277) gives: % 22.79/3.81 | | | | | | | | | | | (291) all_176_8 = all_148_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_160_2, all_178_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (258), (281) gives: % 22.79/3.81 | | | | | | | | | | | (292) all_178_8 = all_160_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_150_2, all_178_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (250), (281) gives: % 22.79/3.81 | | | | | | | | | | | (293) all_178_8 = all_150_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_146_1, all_178_8, xl, % 22.79/3.81 | | | | | | | | | | | simplifying with (245), (281) gives: % 22.79/3.81 | | | | | | | | | | | (294) all_178_8 = all_146_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_172_2, xp, % 22.79/3.81 | | | | | | | | | | | simplifying with (196), (270) gives: % 22.79/3.81 | | | | | | | | | | | (295) all_172_2 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_172_2, all_174_6, xp, % 22.79/3.81 | | | | | | | | | | | simplifying with (270), (274) gives: % 22.79/3.81 | | | | | | | | | | | (296) all_174_6 = all_172_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_154_2, all_174_6, xp, % 22.79/3.81 | | | | | | | | | | | simplifying with (252), (274) gives: % 22.79/3.81 | | | | | | | | | | | (297) all_174_6 = all_154_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_158_2, all_172_1, xr, % 22.79/3.81 | | | | | | | | | | | simplifying with (256), (271) gives: % 22.79/3.81 | | | | | | | | | | | (298) all_172_1 = all_158_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_158_2, all_174_7, xr, % 22.79/3.81 | | | | | | | | | | | simplifying with (256), (275) gives: % 22.79/3.81 | | | | | | | | | | | (299) all_174_7 = all_158_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_154_1, all_174_7, xr, % 22.79/3.81 | | | | | | | | | | | simplifying with (253), (275) gives: % 22.79/3.81 | | | | | | | | | | | (300) all_174_7 = all_154_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_174_7, all_176_6, xr, % 22.79/3.81 | | | | | | | | | | | simplifying with (275), (278) gives: % 22.79/3.81 | | | | | | | | | | | (301) all_176_6 = all_174_7 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_148_2, all_176_6, xr, % 22.79/3.81 | | | | | | | | | | | simplifying with (248), (278) gives: % 22.79/3.81 | | | | | | | | | | | (302) all_176_6 = all_148_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_48_1, all_178_7, xr, % 22.79/3.81 | | | | | | | | | | | simplifying with (59), (282) gives: % 22.79/3.81 | | | | | | | | | | | (303) all_178_7 = all_48_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_172_1, all_178_7, xr, % 22.79/3.81 | | | | | | | | | | | simplifying with (271), (282) gives: % 22.79/3.81 | | | | | | | | | | | (304) all_178_7 = all_172_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_160_1, all_108_0, % 22.79/3.81 | | | | | | | | | | | simplifying with (158), (259) gives: % 22.79/3.81 | | | | | | | | | | | (305) all_160_1 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_178_6, all_112_0, % 22.79/3.81 | | | | | | | | | | | simplifying with (174), (283) gives: % 22.79/3.81 | | | | | | | | | | | (306) all_178_6 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_176_7, all_178_6, % 22.79/3.81 | | | | | | | | | | | all_112_0, simplifying with (279), (283) gives: % 22.79/3.81 | | | | | | | | | | | (307) all_178_6 = all_176_7 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (18) with all_164_1, all_178_6, % 22.79/3.81 | | | | | | | | | | | all_112_0, simplifying with (264), (283) gives: % 22.79/3.81 | | | | | | | | | | | (308) all_178_6 = all_164_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_68_4, all_170_0, % 22.79/3.81 | | | | | | | | | | | all_68_5, xl, simplifying with (91), (268) gives: % 22.79/3.81 | | | | | | | | | | | (309) all_170_0 = all_68_4 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (307), (308) imply: % 22.79/3.81 | | | | | | | | | | | (310) all_176_7 = all_164_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (306), (307) imply: % 22.79/3.81 | | | | | | | | | | | (311) all_176_7 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (303), (304) imply: % 22.79/3.81 | | | | | | | | | | | (312) all_172_1 = all_48_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (312) implies: % 22.79/3.81 | | | | | | | | | | | (313) all_172_1 = all_48_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (292), (294) imply: % 22.79/3.81 | | | | | | | | | | | (314) all_160_2 = all_146_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (292), (293) imply: % 22.79/3.81 | | | | | | | | | | | (315) all_160_2 = all_150_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (301), (302) imply: % 22.79/3.81 | | | | | | | | | | | (316) all_174_7 = all_148_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (316) implies: % 22.79/3.81 | | | | | | | | | | | (317) all_174_7 = all_148_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (310), (311) imply: % 22.79/3.81 | | | | | | | | | | | (318) all_164_1 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (289), (290) imply: % 22.79/3.81 | | | | | | | | | | | (319) all_164_2 = all_150_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (289), (291) imply: % 22.79/3.81 | | | | | | | | | | | (320) all_164_2 = all_148_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (296), (297) imply: % 22.79/3.81 | | | | | | | | | | | (321) all_172_2 = all_154_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (321) implies: % 22.79/3.81 | | | | | | | | | | | (322) all_172_2 = all_154_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (299), (300) imply: % 22.79/3.81 | | | | | | | | | | | (323) all_158_2 = all_154_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (323) implies: % 22.79/3.81 | | | | | | | | | | | (324) all_158_2 = all_154_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (300), (317) imply: % 22.79/3.81 | | | | | | | | | | | (325) all_154_1 = all_148_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (287), (288) imply: % 22.79/3.81 | | | | | | | | | | | (326) all_162_2 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (326) implies: % 22.79/3.81 | | | | | | | | | | | (327) all_162_2 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (298), (313) imply: % 22.79/3.81 | | | | | | | | | | | (328) all_158_2 = all_48_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (328) implies: % 22.79/3.81 | | | | | | | | | | | (329) all_158_2 = all_48_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (295), (322) imply: % 22.79/3.81 | | | | | | | | | | | (330) all_154_2 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (285), (286) imply: % 22.79/3.81 | | | | | | | | | | | (331) all_162_2 = all_158_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (331) implies: % 22.79/3.81 | | | | | | | | | | | (332) all_162_2 = all_158_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (319), (320) imply: % 22.79/3.81 | | | | | | | | | | | (333) all_150_2 = all_148_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (333) implies: % 22.79/3.81 | | | | | | | | | | | (334) all_150_2 = all_148_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (327), (332) imply: % 22.79/3.81 | | | | | | | | | | | (335) all_158_1 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (284), (332) imply: % 22.79/3.81 | | | | | | | | | | | (336) all_158_1 = all_150_2 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (314), (315) imply: % 22.79/3.81 | | | | | | | | | | | (337) all_150_2 = all_146_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (337) implies: % 22.79/3.81 | | | | | | | | | | | (338) all_150_2 = all_146_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (335), (336) imply: % 22.79/3.81 | | | | | | | | | | | (339) all_150_2 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (339) implies: % 22.79/3.81 | | | | | | | | | | | (340) all_150_2 = 0 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | COMBINE_EQS: (324), (329) imply: % 22.79/3.81 | | | | | | | | | | | (341) all_154_1 = all_48_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.81 | | | | | | | | | | | SIMP: (341) implies: % 22.79/3.81 | | | | | | | | | | | (342) all_154_1 = all_48_1 % 22.79/3.81 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | COMBINE_EQS: (325), (342) imply: % 22.79/3.82 | | | | | | | | | | | (343) all_148_2 = all_48_1 % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | SIMP: (343) implies: % 22.79/3.82 | | | | | | | | | | | (344) all_148_2 = all_48_1 % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | COMBINE_EQS: (334), (340) imply: % 22.79/3.82 | | | | | | | | | | | (345) all_148_1 = 0 % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | COMBINE_EQS: (334), (338) imply: % 22.79/3.82 | | | | | | | | | | | (346) all_148_1 = all_146_1 % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | COMBINE_EQS: (345), (346) imply: % 22.79/3.82 | | | | | | | | | | | (347) all_146_1 = 0 % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | COMBINE_EQS: (320), (345) imply: % 22.79/3.82 | | | | | | | | | | | (348) all_164_2 = 0 % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | BETA: splitting (235) gives: % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | (349) all_108_0 = xq % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | REDUCE: (159), (349) imply: % 22.79/3.82 | | | | | | | | | | | | (350) sdtasdt0(xl, xq) = all_33_0 % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | REDUCE: (158), (349) imply: % 22.79/3.82 | | | | | | | | | | | | (351) aNaturalNumber0(xq) = 0 % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | BETA: splitting (52) gives: % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | (352) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 22.79/3.82 | | | | | | | | | | | | | (sdtlseqdt0(xp, xq) = v2 & aNaturalNumber0(xq) = % 22.79/3.82 | | | | | | | | | | | | | v1 & aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | % 22.79/3.82 | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | DELTA: instantiating (352) with fresh symbols all_203_0, % 22.79/3.82 | | | | | | | | | | | | | all_203_1, all_203_2 gives: % 22.79/3.82 | | | | | | | | | | | | | (353) sdtlseqdt0(xp, xq) = all_203_0 & % 22.79/3.82 | | | | | | | | | | | | | aNaturalNumber0(xq) = all_203_1 & % 22.79/3.82 | | | | | | | | | | | | | aNaturalNumber0(xp) = all_203_2 & ( ~ (all_203_0 = % 22.79/3.82 | | | | | | | | | | | | | 0) | ~ (all_203_1 = 0) | ~ (all_203_2 = 0)) % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | ALPHA: (353) implies: % 22.79/3.82 | | | | | | | | | | | | | (354) aNaturalNumber0(xp) = all_203_2 % 22.79/3.82 | | | | | | | | | | | | | (355) aNaturalNumber0(xq) = all_203_1 % 22.79/3.82 | | | | | | | | | | | | | (356) sdtlseqdt0(xp, xq) = all_203_0 % 22.79/3.82 | | | | | | | | | | | | | (357) ~ (all_203_0 = 0) | ~ (all_203_1 = 0) | ~ % 22.79/3.82 | | | | | | | | | | | | | (all_203_2 = 0) % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_203_2, xp, % 22.79/3.82 | | | | | | | | | | | | | simplifying with (196), (354) gives: % 22.79/3.82 | | | | | | | | | | | | | (358) all_203_2 = 0 % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_203_1, xq, % 22.79/3.82 | | | | | | | | | | | | | simplifying with (351), (355) gives: % 22.79/3.82 | | | | | | | | | | | | | (359) all_203_1 = 0 % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_203_0, xq, xp, % 22.79/3.82 | | | | | | | | | | | | | simplifying with (10), (356) gives: % 22.79/3.82 | | | | | | | | | | | | | (360) all_203_0 = 0 % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | BETA: splitting (357) gives: % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | (361) ~ (all_203_0 = 0) % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | REDUCE: (360), (361) imply: % 22.79/3.82 | | | | | | | | | | | | | | (362) $false % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | CLOSE: (362) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | (363) ~ (all_203_1 = 0) | ~ (all_203_2 = 0) % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | BETA: splitting (363) gives: % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | (364) ~ (all_203_1 = 0) % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | REDUCE: (359), (364) imply: % 22.79/3.82 | | | | | | | | | | | | | | | (365) $false % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | (366) ~ (all_203_2 = 0) % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | REDUCE: (358), (366) imply: % 22.79/3.82 | | | | | | | | | | | | | | | (367) $false % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | CLOSE: (367) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | (368) ! [v0: $i] : (v0 = xr | ~ (sdtpldt0(xp, v0) = % 22.79/3.82 | | | | | | | | | | | | | xq) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) % 22.79/3.82 | | | | | | | | | | | | | & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 22.79/3.82 | | | | | | | | | | | | | ~ (sdtpldt0(xp, xr) = v0) | ~ $i(xr) | (v0 = xq % 22.79/3.82 | | | | | | | | | | | | | & aNaturalNumber0(xr) = 0)) % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | ALPHA: (368) implies: % 22.79/3.82 | | | | | | | | | | | | | (369) ! [v0: $i] : ( ~ (sdtpldt0(xp, xr) = v0) | ~ % 22.79/3.82 | | | | | | | | | | | | | $i(xr) | (v0 = xq & aNaturalNumber0(xr) = 0)) % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | GROUND_INST: instantiating (369) with all_68_5, simplifying % 22.79/3.82 | | | | | | | | | | | | | with (16), (90) gives: % 22.79/3.82 | | | | | | | | | | | | | (370) all_68_5 = xq & aNaturalNumber0(xr) = 0 % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | ALPHA: (370) implies: % 22.79/3.82 | | | | | | | | | | | | | (371) all_68_5 = xq % 22.79/3.82 | | | | | | | | | | | | | (372) aNaturalNumber0(xr) = 0 % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | REDUCE: (91), (371) imply: % 22.79/3.82 | | | | | | | | | | | | | (373) sdtasdt0(xl, xq) = all_68_4 % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | BETA: splitting (265) gives: % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | (374) ~ (all_164_1 = 0) % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | REDUCE: (318), (374) imply: % 22.79/3.82 | | | | | | | | | | | | | | (375) $false % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | CLOSE: (375) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | (376) ~ (all_164_2 = 0) | all_164_0 = xm % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | BETA: splitting (376) gives: % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | (377) ~ (all_164_2 = 0) % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | REDUCE: (348), (377) imply: % 22.79/3.82 | | | | | | | | | | | | | | | (378) $false % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | CLOSE: (378) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_48_1, 0, xr, % 22.79/3.82 | | | | | | | | | | | | | | | simplifying with (59), (372) gives: % 22.79/3.82 | | | | | | | | | | | | | | | (379) all_48_1 = 0 % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_33_0, all_68_4, xq, % 22.79/3.82 | | | | | | | | | | | | | | | xl, simplifying with (350), (373) gives: % 22.79/3.82 | | | | | | | | | | | | | | | (380) all_68_4 = all_33_0 % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | COMBINE_EQS: (109), (379) imply: % 22.79/3.82 | | | | | | | | | | | | | | | (381) all_68_6 = 0 % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | BETA: splitting (94) gives: % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | (382) ~ (all_68_6 = 0) % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | REDUCE: (381), (382) imply: % 22.79/3.82 | | | | | | | | | | | | | | | | (383) $false % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | CLOSE: (383) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | (384) ~ (all_68_7 = 0) | ~ (all_68_8 = 0) | (all_68_0 % 22.79/3.82 | | | | | | | | | | | | | | | | = all_68_3 & all_68_4 = all_37_1) % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | BETA: splitting (384) gives: % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | (385) ~ (all_68_7 = 0) % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | REDUCE: (222), (385) imply: % 22.79/3.82 | | | | | | | | | | | | | | | | | (386) $false % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | CLOSE: (386) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | (387) ~ (all_68_8 = 0) | (all_68_0 = all_68_3 & % 22.79/3.82 | | | | | | | | | | | | | | | | | all_68_4 = all_37_1) % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | BETA: splitting (387) gives: % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | Case 1: % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | (388) ~ (all_68_8 = 0) % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | REDUCE: (130), (388) imply: % 22.79/3.82 | | | | | | | | | | | | | | | | | | (389) $false % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | CLOSE: (389) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | (390) all_68_0 = all_68_3 & all_68_4 = all_37_1 % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | ALPHA: (390) implies: % 22.79/3.82 | | | | | | | | | | | | | | | | | | (391) all_68_4 = all_37_1 % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (380), (391) imply: % 22.79/3.82 | | | | | | | | | | | | | | | | | | (392) all_37_1 = all_33_0 % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | SIMP: (392) implies: % 22.79/3.82 | | | | | | | | | | | | | | | | | | (393) all_37_1 = all_33_0 % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | REDUCE: (224), (393) imply: % 22.79/3.82 | | | | | | | | | | | | | | | | | | (394) $false % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | | CLOSE: (394) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | Case 2: % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | (395) ? [v0: int] : ( ~ (v0 = 0) & % 22.79/3.82 | | | | | | | | | | | | aNaturalNumber0(all_108_0) = v0) % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | DELTA: instantiating (395) with fresh symbol all_200_0 % 22.79/3.82 | | | | | | | | | | | | gives: % 22.79/3.82 | | | | | | | | | | | | (396) ~ (all_200_0 = 0) & aNaturalNumber0(all_108_0) = % 22.79/3.82 | | | | | | | | | | | | all_200_0 % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | ALPHA: (396) implies: % 22.79/3.82 | | | | | | | | | | | | (397) ~ (all_200_0 = 0) % 22.79/3.82 | | | | | | | | | | | | (398) aNaturalNumber0(all_108_0) = all_200_0 % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_200_0, all_108_0, % 22.79/3.82 | | | | | | | | | | | | simplifying with (158), (398) gives: % 22.79/3.82 | | | | | | | | | | | | (399) all_200_0 = 0 % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | REDUCE: (397), (399) imply: % 22.79/3.82 | | | | | | | | | | | | (400) $false % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | | CLOSE: (400) is inconsistent. % 22.79/3.82 | | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | | % 22.79/3.82 | | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | | % 22.79/3.82 | | | | | | | | | End of split % 22.79/3.82 | | | | | | | | | % 22.79/3.82 | | | | | | | | End of split % 22.79/3.82 | | | | | | | | % 22.79/3.82 | | | | | | | End of split % 22.79/3.82 | | | | | | | % 22.79/3.82 | | | | | | End of split % 22.79/3.82 | | | | | | % 22.79/3.82 | | | | | End of split % 22.79/3.82 | | | | | % 22.79/3.82 | | | | End of split % 22.79/3.82 | | | | % 22.79/3.82 | | | End of split % 22.79/3.82 | | | % 22.79/3.82 | | End of split % 22.79/3.82 | | % 22.79/3.82 | End of split % 22.79/3.82 | % 22.79/3.82 End of proof % 22.79/3.83 % SZS output end Proof for theBenchmark % 22.79/3.83 % 22.79/3.83 3223ms %------------------------------------------------------------------------------