%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM514+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 : n028.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 11:48:17 EDT 2023 % Result : Theorem 17.25s 3.09s % Output : Proof 65.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM514+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n028.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 13:42:21 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.62/1.21 Prover 4: Preprocessing ... % 3.62/1.21 Prover 1: Preprocessing ... % 3.62/1.26 Prover 3: Preprocessing ... % 3.62/1.26 Prover 2: Preprocessing ... % 3.62/1.26 Prover 0: Preprocessing ... % 3.62/1.26 Prover 6: Preprocessing ... % 3.62/1.28 Prover 5: Preprocessing ... % 8.61/1.92 Prover 1: Constructing countermodel ... % 9.19/1.99 Prover 3: Constructing countermodel ... % 9.19/2.01 Prover 6: Proving ... % 9.19/2.05 Prover 5: Constructing countermodel ... % 11.13/2.29 Prover 2: Proving ... % 11.13/2.30 Prover 4: Constructing countermodel ... % 12.21/2.44 Prover 0: Proving ... % 17.25/3.09 Prover 3: proved (2480ms) % 17.25/3.09 % 17.25/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.25/3.09 % 17.25/3.09 Prover 5: stopped % 17.25/3.09 Prover 0: stopped % 17.25/3.09 Prover 2: stopped % 17.25/3.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.25/3.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 17.25/3.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.25/3.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 17.25/3.11 Prover 6: stopped % 17.25/3.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.36/3.27 Prover 7: Preprocessing ... % 18.36/3.27 Prover 10: Preprocessing ... % 18.36/3.27 Prover 13: Preprocessing ... % 18.36/3.27 Prover 8: Preprocessing ... % 18.36/3.29 Prover 11: Preprocessing ... % 19.50/3.45 Prover 10: Constructing countermodel ... % 20.12/3.46 Prover 8: Warning: ignoring some quantifiers % 20.12/3.47 Prover 8: Constructing countermodel ... % 20.12/3.50 Prover 13: Constructing countermodel ... % 20.12/3.58 Prover 7: Constructing countermodel ... % 22.55/3.84 Prover 11: Constructing countermodel ... % 62.33/9.03 Prover 13: stopped % 62.33/9.05 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 62.33/9.13 Prover 16: Preprocessing ... % 62.71/9.23 Prover 8: Found proof (size 702) % 62.71/9.23 Prover 8: proved (6081ms) % 62.71/9.23 Prover 10: stopped % 62.71/9.24 Prover 7: stopped % 62.71/9.24 Prover 1: stopped % 62.71/9.24 Prover 16: Constructing countermodel ... % 62.71/9.24 Prover 11: stopped % 62.71/9.24 Prover 4: stopped % 62.71/9.24 Prover 16: stopped % 62.71/9.24 % 62.71/9.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 62.71/9.25 % 64.35/9.36 % SZS output start Proof for theBenchmark % 64.35/9.37 Assumptions after simplification: % 64.35/9.37 --------------------------------- % 64.35/9.37 % 64.35/9.37 (mAddAsso) % 64.35/9.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 64.35/9.39 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 64.35/9.39 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 64.35/9.39 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 & % 64.35/9.39 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 64.35/9.39 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 64.35/9.39 v4))) % 64.35/9.39 % 64.35/9.40 (mAddCanc) % 64.35/9.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 % 64.35/9.40 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ % 64.35/9.40 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 64.35/9.40 $i] : ? [v9: $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & % 64.35/9.40 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 64.35/9.40 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ % 64.35/9.40 (v9 = v8) & ~ (v4 = v3))))) % 64.35/9.40 % 64.35/9.40 (mAddComm) % 64.35/9.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 64.35/9.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 64.35/9.40 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 64.35/9.40 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 64.35/9.40 % 64.35/9.40 (mDefDiv) % 64.35/9.40 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~ % 64.35/9.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4 % 64.35/9.40 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0) % 64.35/9.40 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 & % 64.35/9.40 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~ % 64.35/9.40 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4))))) % 64.35/9.40 % 64.35/9.40 (mDefPrime) % 64.35/9.41 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | % 64.35/9.41 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ % 64.35/9.41 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | % 64.35/9.41 v2 = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] : % 64.35/9.41 ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = 0 | v0 = sz10 | % 64.35/9.41 v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) & % 64.35/9.41 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & $i(v2))))) % 64.35/9.41 % 64.35/9.41 (mDefQuot) % 64.35/9.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 64.35/9.41 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 64.35/9.41 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 64.35/9.41 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 64.35/9.41 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4: % 64.35/9.41 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 64.35/9.41 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) = % 64.35/9.41 0)))) % 64.35/9.41 % 64.35/9.41 (mDivAsso) % 64.35/9.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ % 64.35/9.41 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 64.35/9.41 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 % 64.35/9.41 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) | % 64.35/9.41 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtsldt0(v4, v0) = v5) | ~ % 64.35/9.41 (sdtasdt0(v3, v1) = v4) | ~ $i(v3) | ? [v6: any] : ? [v7: $i] : % 64.35/9.41 (sdtasdt0(v3, v2) = v7 & aNaturalNumber0(v3) = v6 & $i(v7) & ( ~ (v6 = 0) % 64.35/9.41 | v7 = v5)))) % 64.35/9.41 % 64.35/9.41 (mDivTrans) % 64.35/9.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 64.35/9.41 (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ~ $i(v2) | ~ % 64.35/9.41 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: % 64.35/9.41 any] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & % 64.35/9.41 aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ % 64.35/9.41 (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 64.35/9.41 % 64.35/9.41 (mLEAsym) % 64.35/9.41 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1) % 64.35/9.41 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (sdtlseqdt0(v1, % 64.35/9.41 v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4 % 64.35/9.41 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) % 64.35/9.41 % 64.35/9.41 (mLETran) % 64.35/9.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 64.35/9.41 (sdtlseqdt0(v0, v2) = v3) | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v2) | ~ % 64.35/9.41 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: % 64.35/9.41 any] : (sdtlseqdt0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 & % 64.35/9.41 aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~ % 64.35/9.41 (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)))) % 64.35/9.41 % 64.35/9.41 (mMonAdd) % 64.35/9.42 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1) % 64.35/9.42 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 & % 64.35/9.42 aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))) | ! [v2: $i] : ! % 64.35/9.42 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (sdtlseqdt0(v3, v4) = v5) | ~ % 64.35/9.42 (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ? [v6: % 64.35/9.42 any] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : (sdtlseqdt0(v7, v8) = % 64.35/9.42 v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2) % 64.35/9.42 = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7) % 64.35/9.42 & ~ (v4 = v3)))))) % 64.35/9.42 % 64.35/9.42 (mMulAsso) % 64.35/9.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 64.35/9.42 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 64.35/9.42 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 64.35/9.42 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & % 64.35/9.42 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 64.35/9.42 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = % 64.35/9.42 v4))) % 64.35/9.42 % 64.35/9.42 (mMulCanc) % 64.35/9.42 $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) % 64.35/9.42 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ % 64.35/9.42 (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ % 64.35/9.42 $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : % 64.35/9.42 (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 % 64.35/9.42 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 64.35/9.42 0) | ( ~ (v8 = v7) & ~ (v4 = v3)))))) % 64.35/9.42 % 64.35/9.42 (mMulComm) % 64.35/9.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 64.35/9.42 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : % 64.35/9.42 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3 % 64.35/9.42 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 64.35/9.42 % 64.35/9.42 (mPrimDiv) % 64.35/9.42 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ % 64.35/9.42 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & % 64.35/9.42 doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0 & $i(v1))) % 64.35/9.42 % 64.35/9.42 (mSortsB) % 64.35/9.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 64.35/9.42 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 64.35/9.42 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 64.35/9.42 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 64.35/9.42 % 64.35/9.42 (mSortsB_02) % 64.35/9.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 64.35/9.42 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 64.35/9.42 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = % 64.35/9.42 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 64.35/9.42 % 64.35/9.42 (m__) % 64.35/9.42 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 64.35/9.42 ( ~ (v2 = 0) & sdtsldt0(xn, xr) = v0 & doDivides0(xp, v1) = v2 & sdtasdt0(v0, % 64.35/9.42 xm) = v1 & $i(v1) & $i(v0)) % 64.35/9.42 % 64.35/9.42 (m__1799) % 64.35/9.42 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 % 64.35/9.42 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! % 64.35/9.42 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ % 64.35/9.42 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v7: any] % 64.35/9.42 : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: $i] : ? [v12: % 64.35/9.42 any] : ? [v13: any] : ? [v14: any] : ? [v15: any] : (isPrime0(v4) = % 64.35/9.42 v10 & doDivides0(v4, v11) = v12 & doDivides0(v4, v3) = v15 & % 64.35/9.42 doDivides0(v4, v2) = v14 & iLess0(v6, v1) = v13 & sdtasdt0(v2, v3) = v11 % 64.35/9.42 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 & % 64.35/9.42 aNaturalNumber0(v2) = v7 & $i(v11) & ( ~ (v13 = 0) | ~ (v12 = 0) | ~ % 64.35/9.42 (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = % 64.35/9.42 0)))) % 64.35/9.42 % 64.35/9.42 (m__1837) % 64.35/9.43 aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 & % 64.35/9.43 $i(xp) & $i(xm) & $i(xn) % 64.35/9.43 % 64.35/9.43 (m__1860) % 64.35/9.43 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp, % 64.35/9.43 v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0)) % 64.35/9.43 % 64.35/9.43 (m__2287) % 64.35/9.43 ~ (xp = xm) & ~ (xp = xn) & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0 % 64.35/9.43 & $i(xp) & $i(xm) & $i(xn) % 64.35/9.43 % 64.35/9.43 (m__2306) % 64.35/9.43 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk & % 64.35/9.43 sdtasdt0(xn, xm) = v0 & $i(v0)) % 64.35/9.43 % 64.35/9.43 (m__2315) % 64.35/9.43 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00) % 64.35/9.43 % 64.35/9.43 (m__2327) % 64.35/9.43 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00) % 64.35/9.43 % 64.35/9.43 (m__2342) % 64.35/9.43 isPrime0(xr) = 0 & doDivides0(xr, xk) = 0 & aNaturalNumber0(xr) = 0 & $i(xr) & % 64.35/9.43 $i(xk) % 64.35/9.43 % 64.35/9.43 (m__2362) % 64.35/9.43 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : (doDivides0(xr, v0) = 0 & % 64.35/9.43 sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0)) % 64.35/9.43 % 64.35/9.43 (m__2377) % 64.35/9.43 ~ (xk = xp) & sdtlseqdt0(xk, xp) = 0 & $i(xk) & $i(xp) % 64.35/9.43 % 64.35/9.43 (m__2449) % 64.35/9.43 $i(xr) & $i(xm) & $i(xn) & ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = % 64.35/9.43 v1 & doDivides0(xr, xn) = v0 & (v1 = 0 | v0 = 0)) % 64.35/9.43 % 64.35/9.43 (m__2487) % 64.35/9.43 doDivides0(xr, xn) = 0 & $i(xr) & $i(xn) % 64.35/9.43 % 64.35/9.43 (m__2504) % 64.35/9.43 $i(xr) & $i(xn) & ? [v0: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 & % 64.35/9.43 sdtlseqdt0(v0, xn) = 0 & $i(v0)) % 64.35/9.43 % 64.35/9.43 (m__2576) % 64.35/9.43 $i(xr) & $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? % 64.35/9.43 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtsldt0(v3, xr) = v4 & sdtsldt0(xn, % 64.35/9.43 xr) = v0 & sdtasdt0(v4, xr) = v2 & sdtasdt0(v1, xr) = v2 & sdtasdt0(v0, % 64.35/9.43 xm) = v1 & sdtasdt0(xp, xk) = v3 & sdtasdt0(xn, xm) = v2 & $i(v4) & $i(v3) % 64.35/9.43 & $i(v2) & $i(v1) & $i(v0)) % 64.35/9.43 % 64.35/9.43 (m__2613) % 64.35/9.43 $i(xr) & $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? % 64.35/9.43 [v2: $i] : (sdtsldt0(xk, xr) = v0 & sdtsldt0(xn, xr) = v2 & sdtasdt0(v2, xm) = % 64.35/9.43 v1 & sdtasdt0(xp, v0) = v1 & $i(v2) & $i(v1) & $i(v0)) % 64.35/9.43 % 64.35/9.43 (function-axioms) % 64.35/9.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.35/9.43 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 64.35/9.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 64.35/9.43 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 64.35/9.43 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 64.35/9.43 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 64.35/9.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.35/9.43 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 64.35/9.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 64.35/9.43 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 64.35/9.43 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.35/9.43 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 64.35/9.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 64.35/9.43 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 64.35/9.43 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 64.35/9.44 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 64.35/9.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 64.35/9.44 | ~ (aNaturalNumber0(v2) = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 64.35/9.44 MultipleValueBool] : (doDivides0(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : % 64.35/9.44 ? [v2: MultipleValueBool] : (iLess0(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] % 64.35/9.44 : ? [v2: MultipleValueBool] : (sdtlseqdt0(v1, v0) = v2) & ? [v0: $i] : ? % 64.35/9.44 [v1: $i] : ? [v2: $i] : (sdtsldt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? % 64.35/9.44 [v1: $i] : ? [v2: $i] : (sdtmndt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? % 64.35/9.44 [v1: $i] : ? [v2: $i] : (sdtasdt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? % 64.35/9.44 [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? % 64.35/9.44 [v1: MultipleValueBool] : (isPrime0(v0) = v1) & ? [v0: $i] : ? [v1: % 64.35/9.44 MultipleValueBool] : (aNaturalNumber0(v0) = v1) % 64.35/9.44 % 64.35/9.44 Further assumptions not needed in the proof: % 64.35/9.44 -------------------------------------------- % 64.35/9.44 mAMDistr, mDefDiff, mDefLE, mDivLE, mDivMin, mDivSum, mIH, mIH_03, mLENTr, % 64.35/9.44 mLERefl, mLETotal, mMonMul, mMonMul2, mNatSort, mSortsC, mSortsC_01, mZeroAdd, % 64.35/9.44 mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1870, m__2075 % 64.35/9.44 % 64.35/9.44 Those formulas are unsatisfiable: % 64.35/9.44 --------------------------------- % 64.35/9.44 % 64.35/9.44 Begin of proof % 64.35/9.44 | % 64.35/9.44 | ALPHA: (mMulCanc) implies: % 64.35/9.44 | (1) ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | % 64.35/9.44 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ % 64.35/9.44 | (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | % 64.35/9.44 | ~ $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] % 64.35/9.44 | : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & % 64.35/9.44 | aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & $i(v8) & % 64.35/9.44 | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 = % 64.35/9.44 | v3)))))) % 64.35/9.44 | % 64.35/9.44 | ALPHA: (mDefQuot) implies: % 64.35/9.44 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 64.35/9.44 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 64.35/9.44 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 64.35/9.44 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 64.35/9.44 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | % 64.35/9.44 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = % 64.35/9.44 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | % 64.35/9.44 | (v3 = v1 & aNaturalNumber0(v2) = 0)))) % 64.35/9.44 | % 64.35/9.44 | ALPHA: (mDivAsso) implies: % 64.35/9.44 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1, % 64.35/9.44 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 64.35/9.44 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 & % 64.35/9.44 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = % 64.35/9.44 | 0))) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 64.35/9.44 | (sdtsldt0(v4, v0) = v5) | ~ (sdtasdt0(v3, v1) = v4) | ~ $i(v3) | % 64.35/9.44 | ? [v6: any] : ? [v7: $i] : (sdtasdt0(v3, v2) = v7 & % 64.35/9.44 | aNaturalNumber0(v3) = v6 & $i(v7) & ( ~ (v6 = 0) | v7 = v5)))) % 64.35/9.44 | % 64.35/9.44 | ALPHA: (mDefPrime) implies: % 64.35/9.44 | (4) ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | ~ $i(v0) | ? % 64.35/9.44 | [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ (v1 = 0) % 64.35/9.44 | | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | v2 % 64.35/9.44 | = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: % 64.35/9.44 | int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = % 64.35/9.44 | 0 | v0 = sz10 | v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 % 64.35/9.44 | = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & % 64.35/9.44 | $i(v2))))) % 64.35/9.44 | % 64.35/9.44 | ALPHA: (mPrimDiv) implies: % 64.35/9.44 | (5) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | % 64.35/9.44 | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 & % 64.35/9.44 | aNaturalNumber0(v1) = 0 & $i(v1))) % 64.35/9.44 | % 64.35/9.44 | ALPHA: (m__1837) implies: % 64.35/9.45 | (6) aNaturalNumber0(xn) = 0 % 64.35/9.45 | (7) aNaturalNumber0(xm) = 0 % 64.35/9.45 | (8) aNaturalNumber0(xp) = 0 % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__1799) implies: % 64.35/9.45 | (9) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = % 64.35/9.45 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 64.35/9.45 | [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~ % 64.35/9.45 | (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? % 64.35/9.45 | [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11: % 64.35/9.45 | $i] : ? [v12: any] : ? [v13: any] : ? [v14: any] : ? [v15: % 64.35/9.45 | any] : (isPrime0(v4) = v10 & doDivides0(v4, v11) = v12 & % 64.35/9.45 | doDivides0(v4, v3) = v15 & doDivides0(v4, v2) = v14 & iLess0(v6, % 64.35/9.45 | v1) = v13 & sdtasdt0(v2, v3) = v11 & aNaturalNumber0(v4) = v9 & % 64.35/9.45 | aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & $i(v11) & ( % 64.35/9.45 | ~ (v13 = 0) | ~ (v12 = 0) | ~ (v10 = 0) | ~ (v9 = 0) | ~ % 64.35/9.45 | (v8 = 0) | ~ (v7 = 0) | v15 = 0 | v14 = 0)))) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__1860) implies: % 64.35/9.45 | (10) ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp, v0) = 0 & % 64.35/9.45 | sdtasdt0(xn, xm) = v0 & $i(v0)) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2287) implies: % 64.35/9.45 | (11) ~ (xp = xn) % 64.35/9.45 | (12) sdtlseqdt0(xn, xp) = 0 % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2306) implies: % 64.35/9.45 | (13) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xn, xm) = v0 & $i(v0)) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2327) implies: % 64.35/9.45 | (14) ~ (xk = sz00) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2342) implies: % 64.35/9.45 | (15) aNaturalNumber0(xr) = 0 % 64.35/9.45 | (16) doDivides0(xr, xk) = 0 % 64.35/9.45 | (17) isPrime0(xr) = 0 % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2362) implies: % 64.35/9.45 | (18) ? [v0: $i] : (doDivides0(xr, v0) = 0 & sdtlseqdt0(xr, xk) = 0 & % 64.35/9.45 | sdtasdt0(xn, xm) = v0 & $i(v0)) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2377) implies: % 64.35/9.45 | (19) ~ (xk = xp) % 64.35/9.45 | (20) sdtlseqdt0(xk, xp) = 0 % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2449) implies: % 64.35/9.45 | (21) ? [v0: any] : ? [v1: any] : (doDivides0(xr, xm) = v1 & % 64.35/9.45 | doDivides0(xr, xn) = v0 & (v1 = 0 | v0 = 0)) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2487) implies: % 64.35/9.45 | (22) doDivides0(xr, xn) = 0 % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2504) implies: % 64.35/9.45 | (23) ? [v0: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 & sdtlseqdt0(v0, % 64.35/9.45 | xn) = 0 & $i(v0)) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2576) implies: % 64.35/9.45 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 64.35/9.45 | (sdtsldt0(v3, xr) = v4 & sdtsldt0(xn, xr) = v0 & sdtasdt0(v4, xr) = v2 % 64.35/9.45 | & sdtasdt0(v1, xr) = v2 & sdtasdt0(v0, xm) = v1 & sdtasdt0(xp, xk) = % 64.35/9.45 | v3 & sdtasdt0(xn, xm) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 64.35/9.45 | $i(v0)) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__2613) implies: % 64.35/9.45 | (25) $i(xk) % 64.35/9.45 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtsldt0(xk, xr) = v0 & % 64.35/9.45 | sdtsldt0(xn, xr) = v2 & sdtasdt0(v2, xm) = v1 & sdtasdt0(xp, v0) = % 64.35/9.45 | v1 & $i(v2) & $i(v1) & $i(v0)) % 64.35/9.45 | % 64.35/9.45 | ALPHA: (m__) implies: % 64.35/9.45 | (27) $i(xn) % 64.35/9.45 | (28) $i(xm) % 64.35/9.45 | (29) $i(xp) % 64.35/9.45 | (30) $i(xr) % 64.82/9.45 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & sdtsldt0(xn, % 64.82/9.45 | xr) = v0 & doDivides0(xp, v1) = v2 & sdtasdt0(v0, xm) = v1 & % 64.82/9.45 | $i(v1) & $i(v0)) % 64.82/9.45 | % 64.82/9.45 | ALPHA: (function-axioms) implies: % 64.82/9.46 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 64.82/9.46 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 64.82/9.46 | v0)) % 64.82/9.46 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.82/9.46 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 64.82/9.46 | (34) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 64.82/9.46 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ % 64.82/9.46 | (doDivides0(v3, v2) = v0)) % 64.82/9.46 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 64.82/9.46 | (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (13) with fresh symbol all_60_0 gives: % 64.82/9.46 | (36) sdtsldt0(all_60_0, xp) = xk & sdtasdt0(xn, xm) = all_60_0 & % 64.82/9.46 | $i(all_60_0) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (36) implies: % 64.82/9.46 | (37) sdtasdt0(xn, xm) = all_60_0 % 64.82/9.46 | (38) sdtsldt0(all_60_0, xp) = xk % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (21) with fresh symbols all_62_0, all_62_1 gives: % 64.82/9.46 | (39) doDivides0(xr, xm) = all_62_0 & doDivides0(xr, xn) = all_62_1 & % 64.82/9.46 | (all_62_0 = 0 | all_62_1 = 0) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (39) implies: % 64.82/9.46 | (40) doDivides0(xr, xn) = all_62_1 % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (23) with fresh symbol all_64_0 gives: % 64.82/9.46 | (41) ~ (all_64_0 = xn) & sdtsldt0(xn, xr) = all_64_0 & % 64.82/9.46 | sdtlseqdt0(all_64_0, xn) = 0 & $i(all_64_0) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (41) implies: % 64.82/9.46 | (42) ~ (all_64_0 = xn) % 64.82/9.46 | (43) sdtlseqdt0(all_64_0, xn) = 0 % 64.82/9.46 | (44) sdtsldt0(xn, xr) = all_64_0 % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (10) with fresh symbol all_66_0 gives: % 64.82/9.46 | (45) isPrime0(xp) = 0 & doDivides0(xp, all_66_0) = 0 & sdtasdt0(xn, xm) = % 64.82/9.46 | all_66_0 & $i(all_66_0) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (45) implies: % 64.82/9.46 | (46) $i(all_66_0) % 64.82/9.46 | (47) sdtasdt0(xn, xm) = all_66_0 % 64.82/9.46 | (48) doDivides0(xp, all_66_0) = 0 % 64.82/9.46 | (49) isPrime0(xp) = 0 % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (18) with fresh symbol all_68_0 gives: % 64.82/9.46 | (50) doDivides0(xr, all_68_0) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn, % 64.82/9.46 | xm) = all_68_0 & $i(all_68_0) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (50) implies: % 64.82/9.46 | (51) sdtasdt0(xn, xm) = all_68_0 % 64.82/9.46 | (52) doDivides0(xr, all_68_0) = 0 % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (31) with fresh symbols all_70_0, all_70_1, all_70_2 % 64.82/9.46 | gives: % 64.82/9.46 | (53) ~ (all_70_0 = 0) & sdtsldt0(xn, xr) = all_70_2 & doDivides0(xp, % 64.82/9.46 | all_70_1) = all_70_0 & sdtasdt0(all_70_2, xm) = all_70_1 & % 64.82/9.46 | $i(all_70_1) & $i(all_70_2) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (53) implies: % 64.82/9.46 | (54) ~ (all_70_0 = 0) % 64.82/9.46 | (55) $i(all_70_2) % 64.82/9.46 | (56) sdtasdt0(all_70_2, xm) = all_70_1 % 64.82/9.46 | (57) doDivides0(xp, all_70_1) = all_70_0 % 64.82/9.46 | (58) sdtsldt0(xn, xr) = all_70_2 % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (26) with fresh symbols all_72_0, all_72_1, all_72_2 % 64.82/9.46 | gives: % 64.82/9.46 | (59) sdtsldt0(xk, xr) = all_72_2 & sdtsldt0(xn, xr) = all_72_0 & % 64.82/9.46 | sdtasdt0(all_72_0, xm) = all_72_1 & sdtasdt0(xp, all_72_2) = all_72_1 % 64.82/9.46 | & $i(all_72_0) & $i(all_72_1) & $i(all_72_2) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (59) implies: % 64.82/9.46 | (60) $i(all_72_2) % 64.82/9.46 | (61) $i(all_72_1) % 64.82/9.46 | (62) sdtasdt0(xp, all_72_2) = all_72_1 % 64.82/9.46 | (63) sdtasdt0(all_72_0, xm) = all_72_1 % 64.82/9.46 | (64) sdtsldt0(xn, xr) = all_72_0 % 64.82/9.46 | (65) sdtsldt0(xk, xr) = all_72_2 % 64.82/9.46 | % 64.82/9.46 | DELTA: instantiating (24) with fresh symbols all_74_0, all_74_1, all_74_2, % 64.82/9.46 | all_74_3, all_74_4 gives: % 64.82/9.46 | (66) sdtsldt0(all_74_1, xr) = all_74_0 & sdtsldt0(xn, xr) = all_74_4 & % 64.82/9.46 | sdtasdt0(all_74_0, xr) = all_74_2 & sdtasdt0(all_74_3, xr) = all_74_2 % 64.82/9.46 | & sdtasdt0(all_74_4, xm) = all_74_3 & sdtasdt0(xp, xk) = all_74_1 & % 64.82/9.46 | sdtasdt0(xn, xm) = all_74_2 & $i(all_74_0) & $i(all_74_1) & % 64.82/9.46 | $i(all_74_2) & $i(all_74_3) & $i(all_74_4) % 64.82/9.46 | % 64.82/9.46 | ALPHA: (66) implies: % 64.82/9.46 | (67) $i(all_74_1) % 64.82/9.46 | (68) $i(all_74_0) % 64.82/9.46 | (69) sdtasdt0(xn, xm) = all_74_2 % 64.82/9.46 | (70) sdtasdt0(xp, xk) = all_74_1 % 64.82/9.46 | (71) sdtasdt0(all_74_4, xm) = all_74_3 % 64.82/9.46 | (72) sdtasdt0(all_74_3, xr) = all_74_2 % 64.82/9.46 | (73) sdtasdt0(all_74_0, xr) = all_74_2 % 64.82/9.46 | (74) sdtsldt0(xn, xr) = all_74_4 % 64.82/9.47 | (75) sdtsldt0(all_74_1, xr) = all_74_0 % 64.82/9.47 | % 64.82/9.47 | DELTA: instantiating (9) with fresh symbols all_76_0, all_76_1 gives: % 64.82/9.47 | (76) sdtpldt0(all_76_1, xp) = all_76_0 & sdtpldt0(xn, xm) = all_76_1 & % 64.82/9.47 | $i(all_76_0) & $i(all_76_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 64.82/9.47 | : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ % 64.82/9.47 | (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 64.82/9.47 | [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] % 64.82/9.47 | : ? [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: any] : % 64.82/9.47 | (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) = % 64.82/9.47 | v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_76_0) = v11 & % 64.82/9.47 | sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 & % 64.82/9.47 | aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & ( ~ % 64.82/9.47 | (v11 = 0) | ~ (v10 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 64.82/9.47 | 0) | ~ (v5 = 0) | v13 = 0 | v12 = 0))) % 64.82/9.47 | % 64.82/9.47 | ALPHA: (76) implies: % 64.82/9.47 | (77) $i(all_76_1) % 64.82/9.47 | (78) sdtpldt0(xn, xm) = all_76_1 % 64.82/9.47 | (79) sdtpldt0(all_76_1, xp) = all_76_0 % 64.82/9.47 | (80) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 64.82/9.47 | ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | % 64.82/9.47 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : % 64.82/9.47 | ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: any] : ? % 64.82/9.47 | [v12: any] : ? [v13: any] : (isPrime0(v2) = v8 & doDivides0(v2, v9) % 64.82/9.47 | = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 & % 64.82/9.47 | iLess0(v4, all_76_0) = v11 & sdtasdt0(v0, v1) = v9 & % 64.82/9.47 | aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & % 64.82/9.47 | aNaturalNumber0(v0) = v5 & $i(v9) & ( ~ (v11 = 0) | ~ (v10 = 0) | % 64.82/9.47 | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v13 = 0 % 64.82/9.47 | | v12 = 0))) % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (33) with all_66_0, all_68_0, xm, xn, simplifying % 64.82/9.47 | with (47), (51) gives: % 64.82/9.47 | (81) all_68_0 = all_66_0 % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (33) with all_68_0, all_74_2, xm, xn, simplifying % 64.82/9.47 | with (51), (69) gives: % 64.82/9.47 | (82) all_74_2 = all_68_0 % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (33) with all_60_0, all_74_2, xm, xn, simplifying % 64.82/9.47 | with (37), (69) gives: % 64.82/9.47 | (83) all_74_2 = all_60_0 % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (34) with 0, all_62_1, xn, xr, simplifying with % 64.82/9.47 | (22), (40) gives: % 64.82/9.47 | (84) all_62_1 = 0 % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (35) with all_64_0, all_72_0, xr, xn, simplifying % 64.82/9.47 | with (44), (64) gives: % 64.82/9.47 | (85) all_72_0 = all_64_0 % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (35) with all_72_0, all_74_4, xr, xn, simplifying % 64.82/9.47 | with (64), (74) gives: % 64.82/9.47 | (86) all_74_4 = all_72_0 % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (35) with all_70_2, all_74_4, xr, xn, simplifying % 64.82/9.47 | with (58), (74) gives: % 64.82/9.47 | (87) all_74_4 = all_70_2 % 64.82/9.47 | % 64.82/9.47 | COMBINE_EQS: (82), (83) imply: % 64.82/9.47 | (88) all_68_0 = all_60_0 % 64.82/9.47 | % 64.82/9.47 | SIMP: (88) implies: % 64.82/9.47 | (89) all_68_0 = all_60_0 % 64.82/9.47 | % 64.82/9.47 | COMBINE_EQS: (86), (87) imply: % 64.82/9.47 | (90) all_72_0 = all_70_2 % 64.82/9.47 | % 64.82/9.47 | SIMP: (90) implies: % 64.82/9.47 | (91) all_72_0 = all_70_2 % 64.82/9.47 | % 64.82/9.47 | COMBINE_EQS: (85), (91) imply: % 64.82/9.47 | (92) all_70_2 = all_64_0 % 64.82/9.47 | % 64.82/9.47 | COMBINE_EQS: (81), (89) imply: % 64.82/9.47 | (93) all_66_0 = all_60_0 % 64.82/9.47 | % 64.82/9.47 | SIMP: (93) implies: % 64.82/9.47 | (94) all_66_0 = all_60_0 % 64.82/9.47 | % 64.82/9.47 | COMBINE_EQS: (87), (92) imply: % 64.82/9.47 | (95) all_74_4 = all_64_0 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (52), (89) imply: % 64.82/9.47 | (96) doDivides0(xr, all_60_0) = 0 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (48), (94) imply: % 64.82/9.47 | (97) doDivides0(xp, all_60_0) = 0 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (73), (83) imply: % 64.82/9.47 | (98) sdtasdt0(all_74_0, xr) = all_60_0 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (72), (83) imply: % 64.82/9.47 | (99) sdtasdt0(all_74_3, xr) = all_60_0 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (71), (95) imply: % 64.82/9.47 | (100) sdtasdt0(all_64_0, xm) = all_74_3 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (63), (85) imply: % 64.82/9.47 | (101) sdtasdt0(all_64_0, xm) = all_72_1 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (56), (92) imply: % 64.82/9.47 | (102) sdtasdt0(all_64_0, xm) = all_70_1 % 64.82/9.47 | % 64.82/9.47 | REDUCE: (55), (92) imply: % 64.82/9.47 | (103) $i(all_64_0) % 64.82/9.47 | % 64.82/9.47 | REDUCE: (46), (94) imply: % 64.82/9.47 | (104) $i(all_60_0) % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (33) with all_72_1, all_74_3, xm, all_64_0, % 64.82/9.47 | simplifying with (100), (101) gives: % 64.82/9.47 | (105) all_74_3 = all_72_1 % 64.82/9.47 | % 64.82/9.47 | GROUND_INST: instantiating (33) with all_70_1, all_74_3, xm, all_64_0, % 64.82/9.47 | simplifying with (100), (102) gives: % 64.82/9.48 | (106) all_74_3 = all_70_1 % 64.82/9.48 | % 64.82/9.48 | COMBINE_EQS: (105), (106) imply: % 64.82/9.48 | (107) all_72_1 = all_70_1 % 64.82/9.48 | % 64.82/9.48 | SIMP: (107) implies: % 64.82/9.48 | (108) all_72_1 = all_70_1 % 64.82/9.48 | % 64.82/9.48 | REDUCE: (99), (106) imply: % 64.82/9.48 | (109) sdtasdt0(all_70_1, xr) = all_60_0 % 64.82/9.48 | % 64.82/9.48 | REDUCE: (62), (108) imply: % 64.82/9.48 | (110) sdtasdt0(xp, all_72_2) = all_70_1 % 64.82/9.48 | % 64.82/9.48 | REDUCE: (61), (108) imply: % 64.82/9.48 | (111) $i(all_70_1) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (5) with xp, simplifying with (8), (29) gives: % 64.82/9.48 | (112) xp = sz10 | xp = sz00 | ? [v0: $i] : (isPrime0(v0) = 0 & % 64.82/9.48 | doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_76_1, simplifying with % 64.82/9.48 | (27), (28), (78) gives: % 64.82/9.48 | (113) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xm, xn) = v2 & % 64.82/9.48 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ % 64.82/9.48 | (v1 = 0) | ~ (v0 = 0) | v2 = all_76_1)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_76_1, simplifying with % 64.82/9.48 | (27), (28), (78) gives: % 64.82/9.48 | (114) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.48 | (aNaturalNumber0(all_76_1) = v2 & aNaturalNumber0(xm) = v1 & % 64.82/9.48 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (80) with xn, xm, xp, all_76_1, all_76_0, % 64.82/9.48 | simplifying with (27), (28), (29), (78), (79) gives: % 64.82/9.48 | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4: % 64.82/9.48 | $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : % 64.82/9.48 | (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 & doDivides0(xp, xm) = % 64.82/9.48 | v8 & doDivides0(xp, xn) = v7 & iLess0(all_76_0, all_76_0) = v6 & % 64.82/9.48 | sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 & % 64.82/9.48 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4) & ( ~ % 64.82/9.48 | (v6 = 0) | ~ (v5 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) % 64.82/9.48 | | ~ (v0 = 0) | v8 = 0 | v7 = 0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xp, all_76_1, all_76_0, % 64.82/9.48 | simplifying with (27), (28), (29), (78), (79) gives: % 64.82/9.48 | (116) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 64.82/9.48 | $i] : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & % 64.82/9.48 | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 & % 64.82/9.48 | aNaturalNumber0(xn) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 64.82/9.48 | = 0) | ~ (v0 = 0) | v4 = all_76_0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mAddComm) with all_76_1, xp, all_76_0, simplifying % 64.82/9.48 | with (29), (77), (79) gives: % 64.82/9.48 | (117) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xp, all_76_1) = % 64.82/9.48 | v2 & aNaturalNumber0(all_76_1) = v0 & aNaturalNumber0(xp) = v1 & % 64.82/9.48 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_76_0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mSortsB) with all_76_1, xp, all_76_0, simplifying % 64.82/9.48 | with (29), (77), (79) gives: % 64.82/9.48 | (118) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.48 | (aNaturalNumber0(all_76_0) = v2 & aNaturalNumber0(all_76_1) = v0 & % 64.82/9.48 | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_60_0, simplifying with % 64.82/9.48 | (27), (28), (37) gives: % 64.82/9.48 | (119) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 & % 64.82/9.48 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~ % 64.82/9.48 | (v1 = 0) | ~ (v0 = 0) | v2 = all_60_0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_60_0, simplifying % 64.82/9.48 | with (27), (28), (37) gives: % 64.82/9.48 | (120) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.48 | (aNaturalNumber0(all_60_0) = v2 & aNaturalNumber0(xm) = v1 & % 64.82/9.48 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mMulComm) with xp, xk, all_74_1, simplifying with % 64.82/9.48 | (25), (29), (70) gives: % 64.82/9.48 | (121) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xk, xp) = v2 & % 64.82/9.48 | aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & $i(v2) & ( ~ % 64.82/9.48 | (v1 = 0) | ~ (v0 = 0) | v2 = all_74_1)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mSortsB_02) with xp, xk, all_74_1, simplifying % 64.82/9.48 | with (25), (29), (70) gives: % 64.82/9.48 | (122) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.48 | (aNaturalNumber0(all_74_1) = v2 & aNaturalNumber0(xk) = v1 & % 64.82/9.48 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mMulComm) with xp, all_72_2, all_70_1, simplifying % 64.82/9.48 | with (29), (60), (110) gives: % 64.82/9.48 | (123) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_72_2, xp) = % 64.82/9.48 | v2 & aNaturalNumber0(all_72_2) = v1 & aNaturalNumber0(xp) = v0 & % 64.82/9.48 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_70_1)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mSortsB_02) with xp, all_72_2, all_70_1, % 64.82/9.48 | simplifying with (29), (60), (110) gives: % 64.82/9.48 | (124) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.48 | (aNaturalNumber0(all_72_2) = v1 & aNaturalNumber0(all_70_1) = v2 & % 64.82/9.48 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mMulComm) with all_64_0, xm, all_70_1, simplifying % 64.82/9.48 | with (28), (102), (103) gives: % 64.82/9.48 | (125) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, all_64_0) = % 64.82/9.48 | v2 & aNaturalNumber0(all_64_0) = v0 & aNaturalNumber0(xm) = v1 & % 64.82/9.48 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_70_1)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mSortsB_02) with all_64_0, xm, all_70_1, % 64.82/9.48 | simplifying with (28), (102), (103) gives: % 64.82/9.48 | (126) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.48 | (aNaturalNumber0(all_70_1) = v2 & aNaturalNumber0(all_64_0) = v0 & % 64.82/9.48 | aNaturalNumber0(xm) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.48 | % 64.82/9.48 | GROUND_INST: instantiating (mMulAsso) with all_64_0, xm, xr, all_70_1, % 64.82/9.48 | all_60_0, simplifying with (28), (30), (102), (103), (109) gives: % 64.82/9.49 | (127) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 64.82/9.49 | $i] : (sdtasdt0(all_64_0, v3) = v4 & sdtasdt0(xm, xr) = v3 & % 64.82/9.49 | aNaturalNumber0(all_64_0) = v0 & aNaturalNumber0(xr) = v2 & % 64.82/9.49 | aNaturalNumber0(xm) = v1 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 64.82/9.49 | = 0) | ~ (v0 = 0) | v4 = all_60_0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mMulAsso) with xp, all_72_2, xr, all_70_1, % 64.82/9.49 | all_60_0, simplifying with (29), (30), (60), (109), (110) gives: % 64.82/9.49 | (128) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: % 64.82/9.49 | $i] : (sdtasdt0(all_72_2, xr) = v3 & sdtasdt0(xp, v3) = v4 & % 64.82/9.49 | aNaturalNumber0(all_72_2) = v1 & aNaturalNumber0(xr) = v2 & % 64.82/9.49 | aNaturalNumber0(xp) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 % 64.82/9.49 | = 0) | ~ (v0 = 0) | v4 = all_60_0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mMulComm) with all_70_1, xr, all_60_0, simplifying % 64.82/9.49 | with (30), (109), (111) gives: % 64.82/9.49 | (129) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xr, all_70_1) = % 64.82/9.49 | v2 & aNaturalNumber0(all_70_1) = v0 & aNaturalNumber0(xr) = v1 & % 64.82/9.49 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_60_0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mSortsB_02) with all_70_1, xr, all_60_0, % 64.82/9.49 | simplifying with (30), (109), (111) gives: % 64.82/9.49 | (130) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (aNaturalNumber0(all_70_1) = v0 & aNaturalNumber0(all_60_0) = v2 & % 64.82/9.49 | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mMulComm) with all_74_0, xr, all_60_0, simplifying % 64.82/9.49 | with (30), (68), (98) gives: % 64.82/9.49 | (131) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xr, all_74_0) = % 64.82/9.49 | v2 & aNaturalNumber0(all_74_0) = v0 & aNaturalNumber0(xr) = v1 & % 64.82/9.49 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_60_0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mSortsB_02) with all_74_0, xr, all_60_0, % 64.82/9.49 | simplifying with (30), (68), (98) gives: % 64.82/9.49 | (132) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (aNaturalNumber0(all_74_0) = v0 & aNaturalNumber0(all_60_0) = v2 & % 64.82/9.49 | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mLEAsym) with xk, xp, simplifying with (20), (25), % 64.82/9.49 | (29) gives: % 64.82/9.49 | (133) xk = xp | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (sdtlseqdt0(xp, xk) = v2 & aNaturalNumber0(xk) = v0 & % 64.82/9.49 | aNaturalNumber0(xp) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 64.82/9.49 | 0))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mLEAsym) with all_64_0, xn, simplifying with (27), % 64.82/9.49 | (43), (103) gives: % 64.82/9.49 | (134) all_64_0 = xn | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (sdtlseqdt0(xn, all_64_0) = v2 & aNaturalNumber0(all_64_0) = v0 & % 64.82/9.49 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 64.82/9.49 | 0))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mMonAdd) with all_64_0, xn, simplifying with (27), % 64.82/9.49 | (43), (103) gives: % 64.82/9.49 | (135) all_64_0 = xn | ? [v0: any] : ? [v1: any] : % 64.82/9.49 | (aNaturalNumber0(all_64_0) = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 % 64.82/9.49 | = 0) | ~ (v0 = 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 64.82/9.49 | : ! [v3: any] : ( ~ (sdtlseqdt0(v1, v2) = v3) | ~ % 64.82/9.49 | (sdtpldt0(all_64_0, v0) = v1) | ~ (sdtpldt0(xn, v0) = v2) | ~ % 64.82/9.49 | $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] : % 64.82/9.49 | (sdtlseqdt0(v5, v6) = v7 & sdtpldt0(v0, all_64_0) = v5 & % 64.82/9.49 | sdtpldt0(v0, xn) = v6 & aNaturalNumber0(v0) = v4 & $i(v6) & % 64.82/9.49 | $i(v5) & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0 & ~ (v6 = v5) & ~ (v2 % 64.82/9.49 | = v1))))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mDivTrans) with xp, all_60_0, all_70_1, all_70_0, % 64.82/9.49 | simplifying with (29), (57), (97), (104), (111) gives: % 64.82/9.49 | (136) all_70_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: % 64.82/9.49 | any] : (doDivides0(all_60_0, all_70_1) = v3 & % 64.82/9.49 | aNaturalNumber0(all_70_1) = v2 & aNaturalNumber0(all_60_0) = v1 & % 64.82/9.49 | aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) % 64.82/9.49 | | ~ (v0 = 0))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mDefDiv) with xp, all_70_1, all_70_0, simplifying % 64.82/9.49 | with (29), (57), (111) gives: % 64.82/9.49 | (137) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_70_1) = v1 & % 64.82/9.49 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (( ~ % 64.82/9.49 | (all_70_0 = 0) | ? [v0: $i] : (sdtasdt0(xp, v0) = all_70_1 & % 64.82/9.49 | aNaturalNumber0(v0) = 0 & $i(v0))) & (all_70_0 = 0 | ! [v0: % 64.82/9.49 | $i] : ( ~ (sdtasdt0(xp, v0) = all_70_1) | ~ $i(v0) | ? [v1: % 64.82/9.49 | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mDefDiv) with xr, xn, 0, simplifying with (22), % 64.82/9.49 | (27), (30) gives: % 64.82/9.49 | (138) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xr) = v0 & % 64.82/9.49 | aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 64.82/9.49 | $i] : (sdtasdt0(xr, v0) = xn & aNaturalNumber0(v0) = 0 & $i(v0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (mDefDiv) with xr, xk, 0, simplifying with (16), % 64.82/9.49 | (25), (30) gives: % 64.82/9.49 | (139) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xr) = v0 & % 64.82/9.49 | aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0: % 64.82/9.49 | $i] : (sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0 & $i(v0)) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (3) with xr, xn, all_64_0, simplifying with (27), % 64.82/9.49 | (30), (44) gives: % 64.82/9.49 | (140) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & % 64.82/9.49 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 64.82/9.49 | 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 64.82/9.49 | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xn) = v1) | ~ $i(v0) | % 64.82/9.49 | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, all_64_0) = v4 & % 64.82/9.49 | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (2) with xr, xn, all_64_0, simplifying with (27), % 64.82/9.49 | (30), (44) gives: % 64.82/9.49 | (141) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & % 64.82/9.49 | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 64.82/9.49 | 0))) | ( ! [v0: any] : (v0 = all_64_0 | ~ (sdtasdt0(xr, v0) = % 64.82/9.49 | xn) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 64.82/9.49 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xr, % 64.82/9.49 | all_64_0) = v0) | ~ $i(all_64_0) | (v0 = xn & % 64.82/9.49 | aNaturalNumber0(all_64_0) = 0))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (3) with xr, xk, all_72_2, simplifying with (25), % 64.82/9.49 | (30), (65) gives: % 64.82/9.49 | (142) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & % 64.82/9.49 | aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 64.82/9.49 | 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 64.82/9.49 | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) | % 64.82/9.49 | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, all_72_2) = v4 & % 64.82/9.49 | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (2) with xr, xk, all_72_2, simplifying with (25), % 64.82/9.49 | (30), (65) gives: % 64.82/9.49 | (143) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.49 | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 & % 64.82/9.49 | aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 64.82/9.49 | 0))) | ( ! [v0: any] : (v0 = all_72_2 | ~ (sdtasdt0(xr, v0) = % 64.82/9.49 | xk) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 64.82/9.49 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xr, % 64.82/9.49 | all_72_2) = v0) | ~ $i(all_72_2) | (v0 = xk & % 64.82/9.49 | aNaturalNumber0(all_72_2) = 0))) % 64.82/9.49 | % 64.82/9.49 | GROUND_INST: instantiating (2) with xp, all_60_0, xk, simplifying with (29), % 64.82/9.50 | (38), (104) gives: % 64.82/9.50 | (144) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 64.82/9.50 | (doDivides0(xp, all_60_0) = v2 & aNaturalNumber0(all_60_0) = v1 & % 64.82/9.50 | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 64.82/9.50 | 0))) | ( ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) = % 64.82/9.50 | all_60_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.02/9.50 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xp, % 65.02/9.50 | xk) = v0) | ~ $i(xk) | (v0 = all_60_0 & aNaturalNumber0(xk) % 65.02/9.50 | = 0))) % 65.02/9.50 | % 65.02/9.50 | GROUND_INST: instantiating (3) with xr, all_74_1, all_74_0, simplifying with % 65.02/9.50 | (30), (67), (75) gives: % 65.02/9.50 | (145) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.02/9.50 | (doDivides0(xr, all_74_1) = v2 & aNaturalNumber0(all_74_1) = v1 & % 65.02/9.50 | aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 65.02/9.50 | 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 65.02/9.50 | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, all_74_1) = v1) | ~ % 65.02/9.50 | $i(v0) | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, all_74_0) = v4 % 65.02/9.50 | & aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 65.02/9.50 | % 65.02/9.50 | GROUND_INST: instantiating (2) with xr, all_74_1, all_74_0, simplifying with % 65.02/9.50 | (30), (67), (75) gives: % 65.02/9.50 | (146) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.02/9.50 | (doDivides0(xr, all_74_1) = v2 & aNaturalNumber0(all_74_1) = v1 & % 65.02/9.50 | aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = % 65.02/9.50 | 0))) | ( ! [v0: any] : (v0 = all_74_0 | ~ (sdtasdt0(xr, v0) = % 65.02/9.50 | all_74_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.02/9.50 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xr, % 65.02/9.50 | all_74_0) = v0) | ~ $i(all_74_0) | (v0 = all_74_1 & % 65.02/9.50 | aNaturalNumber0(all_74_0) = 0))) % 65.02/9.50 | % 65.02/9.50 | GROUND_INST: instantiating (4) with xp, 0, simplifying with (29), (49) gives: % 65.02/9.50 | (147) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | ( ~ (xp = % 65.02/9.50 | sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~ % 65.02/9.50 | (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 65.02/9.50 | 0) & aNaturalNumber0(v0) = v1))) % 65.02/9.50 | % 65.02/9.50 | GROUND_INST: instantiating (4) with xr, 0, simplifying with (17), (30) gives: % 65.02/9.50 | (148) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0) | ( ~ (xr = % 65.02/9.50 | sz10) & ~ (xr = sz00) & ! [v0: $i] : (v0 = xr | v0 = sz10 | ~ % 65.02/9.50 | (doDivides0(v0, xr) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 65.02/9.50 | 0) & aNaturalNumber0(v0) = v1))) % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (132) with fresh symbols all_92_0, all_92_1, all_92_2 % 65.02/9.50 | gives: % 65.02/9.50 | (149) aNaturalNumber0(all_74_0) = all_92_2 & aNaturalNumber0(all_60_0) = % 65.02/9.50 | all_92_0 & aNaturalNumber0(xr) = all_92_1 & ( ~ (all_92_1 = 0) | ~ % 65.02/9.50 | (all_92_2 = 0) | all_92_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (149) implies: % 65.02/9.50 | (150) aNaturalNumber0(xr) = all_92_1 % 65.02/9.50 | (151) aNaturalNumber0(all_60_0) = all_92_0 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (130) with fresh symbols all_94_0, all_94_1, all_94_2 % 65.02/9.50 | gives: % 65.02/9.50 | (152) aNaturalNumber0(all_70_1) = all_94_2 & aNaturalNumber0(all_60_0) = % 65.02/9.50 | all_94_0 & aNaturalNumber0(xr) = all_94_1 & ( ~ (all_94_1 = 0) | ~ % 65.02/9.50 | (all_94_2 = 0) | all_94_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (152) implies: % 65.02/9.50 | (153) aNaturalNumber0(xr) = all_94_1 % 65.02/9.50 | (154) aNaturalNumber0(all_60_0) = all_94_0 % 65.02/9.50 | (155) aNaturalNumber0(all_70_1) = all_94_2 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (124) with fresh symbols all_96_0, all_96_1, all_96_2 % 65.02/9.50 | gives: % 65.02/9.50 | (156) aNaturalNumber0(all_72_2) = all_96_1 & aNaturalNumber0(all_70_1) = % 65.02/9.50 | all_96_0 & aNaturalNumber0(xp) = all_96_2 & ( ~ (all_96_1 = 0) | ~ % 65.02/9.50 | (all_96_2 = 0) | all_96_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (156) implies: % 65.02/9.50 | (157) aNaturalNumber0(xp) = all_96_2 % 65.02/9.50 | (158) aNaturalNumber0(all_70_1) = all_96_0 % 65.02/9.50 | (159) aNaturalNumber0(all_72_2) = all_96_1 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (120) with fresh symbols all_98_0, all_98_1, all_98_2 % 65.02/9.50 | gives: % 65.02/9.50 | (160) aNaturalNumber0(all_60_0) = all_98_0 & aNaturalNumber0(xm) = all_98_1 % 65.02/9.50 | & aNaturalNumber0(xn) = all_98_2 & ( ~ (all_98_1 = 0) | ~ (all_98_2 % 65.02/9.50 | = 0) | all_98_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (160) implies: % 65.02/9.50 | (161) aNaturalNumber0(xn) = all_98_2 % 65.02/9.50 | (162) aNaturalNumber0(xm) = all_98_1 % 65.02/9.50 | (163) aNaturalNumber0(all_60_0) = all_98_0 % 65.02/9.50 | (164) ~ (all_98_1 = 0) | ~ (all_98_2 = 0) | all_98_0 = 0 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (126) with fresh symbols all_100_0, all_100_1, all_100_2 % 65.02/9.50 | gives: % 65.02/9.50 | (165) aNaturalNumber0(all_70_1) = all_100_0 & aNaturalNumber0(all_64_0) = % 65.02/9.50 | all_100_2 & aNaturalNumber0(xm) = all_100_1 & ( ~ (all_100_1 = 0) | % 65.02/9.50 | ~ (all_100_2 = 0) | all_100_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (165) implies: % 65.02/9.50 | (166) aNaturalNumber0(xm) = all_100_1 % 65.02/9.50 | (167) aNaturalNumber0(all_64_0) = all_100_2 % 65.02/9.50 | (168) aNaturalNumber0(all_70_1) = all_100_0 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (118) with fresh symbols all_102_0, all_102_1, all_102_2 % 65.02/9.50 | gives: % 65.02/9.50 | (169) aNaturalNumber0(all_76_0) = all_102_0 & aNaturalNumber0(all_76_1) = % 65.02/9.50 | all_102_2 & aNaturalNumber0(xp) = all_102_1 & ( ~ (all_102_1 = 0) | % 65.02/9.50 | ~ (all_102_2 = 0) | all_102_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (169) implies: % 65.02/9.50 | (170) aNaturalNumber0(xp) = all_102_1 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (122) with fresh symbols all_104_0, all_104_1, all_104_2 % 65.02/9.50 | gives: % 65.02/9.50 | (171) aNaturalNumber0(all_74_1) = all_104_0 & aNaturalNumber0(xk) = % 65.02/9.50 | all_104_1 & aNaturalNumber0(xp) = all_104_2 & ( ~ (all_104_1 = 0) | % 65.02/9.50 | ~ (all_104_2 = 0) | all_104_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (171) implies: % 65.02/9.50 | (172) aNaturalNumber0(xp) = all_104_2 % 65.02/9.50 | (173) aNaturalNumber0(xk) = all_104_1 % 65.02/9.50 | (174) aNaturalNumber0(all_74_1) = all_104_0 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (114) with fresh symbols all_106_0, all_106_1, all_106_2 % 65.02/9.50 | gives: % 65.02/9.50 | (175) aNaturalNumber0(all_76_1) = all_106_0 & aNaturalNumber0(xm) = % 65.02/9.50 | all_106_1 & aNaturalNumber0(xn) = all_106_2 & ( ~ (all_106_1 = 0) | % 65.02/9.50 | ~ (all_106_2 = 0) | all_106_0 = 0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (175) implies: % 65.02/9.50 | (176) aNaturalNumber0(xn) = all_106_2 % 65.02/9.50 | (177) aNaturalNumber0(xm) = all_106_1 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (129) with fresh symbols all_108_0, all_108_1, all_108_2 % 65.02/9.50 | gives: % 65.02/9.50 | (178) sdtasdt0(xr, all_70_1) = all_108_0 & aNaturalNumber0(all_70_1) = % 65.02/9.50 | all_108_2 & aNaturalNumber0(xr) = all_108_1 & $i(all_108_0) & ( ~ % 65.02/9.50 | (all_108_1 = 0) | ~ (all_108_2 = 0) | all_108_0 = all_60_0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (178) implies: % 65.02/9.50 | (179) aNaturalNumber0(xr) = all_108_1 % 65.02/9.50 | (180) aNaturalNumber0(all_70_1) = all_108_2 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (121) with fresh symbols all_110_0, all_110_1, all_110_2 % 65.02/9.50 | gives: % 65.02/9.50 | (181) sdtasdt0(xk, xp) = all_110_0 & aNaturalNumber0(xk) = all_110_1 & % 65.02/9.50 | aNaturalNumber0(xp) = all_110_2 & $i(all_110_0) & ( ~ (all_110_1 = 0) % 65.02/9.50 | | ~ (all_110_2 = 0) | all_110_0 = all_74_1) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (181) implies: % 65.02/9.50 | (182) aNaturalNumber0(xp) = all_110_2 % 65.02/9.50 | (183) aNaturalNumber0(xk) = all_110_1 % 65.02/9.50 | (184) sdtasdt0(xk, xp) = all_110_0 % 65.02/9.50 | (185) ~ (all_110_1 = 0) | ~ (all_110_2 = 0) | all_110_0 = all_74_1 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (131) with fresh symbols all_112_0, all_112_1, all_112_2 % 65.02/9.50 | gives: % 65.02/9.50 | (186) sdtasdt0(xr, all_74_0) = all_112_0 & aNaturalNumber0(all_74_0) = % 65.02/9.50 | all_112_2 & aNaturalNumber0(xr) = all_112_1 & $i(all_112_0) & ( ~ % 65.02/9.50 | (all_112_1 = 0) | ~ (all_112_2 = 0) | all_112_0 = all_60_0) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (186) implies: % 65.02/9.50 | (187) aNaturalNumber0(xr) = all_112_1 % 65.02/9.50 | (188) sdtasdt0(xr, all_74_0) = all_112_0 % 65.02/9.50 | % 65.02/9.50 | DELTA: instantiating (113) with fresh symbols all_114_0, all_114_1, all_114_2 % 65.02/9.50 | gives: % 65.02/9.50 | (189) sdtpldt0(xm, xn) = all_114_0 & aNaturalNumber0(xm) = all_114_1 & % 65.02/9.50 | aNaturalNumber0(xn) = all_114_2 & $i(all_114_0) & ( ~ (all_114_1 = 0) % 65.02/9.50 | | ~ (all_114_2 = 0) | all_114_0 = all_76_1) % 65.02/9.50 | % 65.02/9.50 | ALPHA: (189) implies: % 65.02/9.50 | (190) aNaturalNumber0(xn) = all_114_2 % 65.02/9.50 | (191) aNaturalNumber0(xm) = all_114_1 % 65.02/9.51 | (192) sdtpldt0(xm, xn) = all_114_0 % 65.02/9.51 | (193) ~ (all_114_1 = 0) | ~ (all_114_2 = 0) | all_114_0 = all_76_1 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (119) with fresh symbols all_116_0, all_116_1, all_116_2 % 65.02/9.51 | gives: % 65.02/9.51 | (194) sdtasdt0(xm, xn) = all_116_0 & aNaturalNumber0(xm) = all_116_1 & % 65.02/9.51 | aNaturalNumber0(xn) = all_116_2 & $i(all_116_0) & ( ~ (all_116_1 = 0) % 65.02/9.51 | | ~ (all_116_2 = 0) | all_116_0 = all_60_0) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (194) implies: % 65.02/9.51 | (195) aNaturalNumber0(xn) = all_116_2 % 65.02/9.51 | (196) aNaturalNumber0(xm) = all_116_1 % 65.02/9.51 | (197) sdtasdt0(xm, xn) = all_116_0 % 65.02/9.51 | (198) ~ (all_116_1 = 0) | ~ (all_116_2 = 0) | all_116_0 = all_60_0 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (123) with fresh symbols all_118_0, all_118_1, all_118_2 % 65.02/9.51 | gives: % 65.02/9.51 | (199) sdtasdt0(all_72_2, xp) = all_118_0 & aNaturalNumber0(all_72_2) = % 65.02/9.51 | all_118_1 & aNaturalNumber0(xp) = all_118_2 & $i(all_118_0) & ( ~ % 65.02/9.51 | (all_118_1 = 0) | ~ (all_118_2 = 0) | all_118_0 = all_70_1) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (199) implies: % 65.02/9.51 | (200) aNaturalNumber0(xp) = all_118_2 % 65.02/9.51 | (201) aNaturalNumber0(all_72_2) = all_118_1 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (125) with fresh symbols all_120_0, all_120_1, all_120_2 % 65.02/9.51 | gives: % 65.02/9.51 | (202) sdtasdt0(xm, all_64_0) = all_120_0 & aNaturalNumber0(all_64_0) = % 65.02/9.51 | all_120_2 & aNaturalNumber0(xm) = all_120_1 & $i(all_120_0) & ( ~ % 65.02/9.51 | (all_120_1 = 0) | ~ (all_120_2 = 0) | all_120_0 = all_70_1) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (202) implies: % 65.02/9.51 | (203) aNaturalNumber0(xm) = all_120_1 % 65.02/9.51 | (204) aNaturalNumber0(all_64_0) = all_120_2 % 65.02/9.51 | (205) sdtasdt0(xm, all_64_0) = all_120_0 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (117) with fresh symbols all_122_0, all_122_1, all_122_2 % 65.02/9.51 | gives: % 65.02/9.51 | (206) sdtpldt0(xp, all_76_1) = all_122_0 & aNaturalNumber0(all_76_1) = % 65.02/9.51 | all_122_2 & aNaturalNumber0(xp) = all_122_1 & $i(all_122_0) & ( ~ % 65.02/9.51 | (all_122_1 = 0) | ~ (all_122_2 = 0) | all_122_0 = all_76_0) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (206) implies: % 65.02/9.51 | (207) aNaturalNumber0(xp) = all_122_1 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (127) with fresh symbols all_124_0, all_124_1, all_124_2, % 65.02/9.51 | all_124_3, all_124_4 gives: % 65.02/9.51 | (208) sdtasdt0(all_64_0, all_124_1) = all_124_0 & sdtasdt0(xm, xr) = % 65.02/9.51 | all_124_1 & aNaturalNumber0(all_64_0) = all_124_4 & % 65.02/9.51 | aNaturalNumber0(xr) = all_124_2 & aNaturalNumber0(xm) = all_124_3 & % 65.02/9.51 | $i(all_124_0) & $i(all_124_1) & ( ~ (all_124_2 = 0) | ~ (all_124_3 = % 65.02/9.51 | 0) | ~ (all_124_4 = 0) | all_124_0 = all_60_0) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (208) implies: % 65.02/9.51 | (209) aNaturalNumber0(xm) = all_124_3 % 65.02/9.51 | (210) aNaturalNumber0(xr) = all_124_2 % 65.02/9.51 | (211) aNaturalNumber0(all_64_0) = all_124_4 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (128) with fresh symbols all_126_0, all_126_1, all_126_2, % 65.02/9.51 | all_126_3, all_126_4 gives: % 65.02/9.51 | (212) sdtasdt0(all_72_2, xr) = all_126_1 & sdtasdt0(xp, all_126_1) = % 65.02/9.51 | all_126_0 & aNaturalNumber0(all_72_2) = all_126_3 & % 65.02/9.51 | aNaturalNumber0(xr) = all_126_2 & aNaturalNumber0(xp) = all_126_4 & % 65.02/9.51 | $i(all_126_0) & $i(all_126_1) & ( ~ (all_126_2 = 0) | ~ (all_126_3 = % 65.02/9.51 | 0) | ~ (all_126_4 = 0) | all_126_0 = all_60_0) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (212) implies: % 65.02/9.51 | (213) aNaturalNumber0(xp) = all_126_4 % 65.02/9.51 | (214) aNaturalNumber0(xr) = all_126_2 % 65.02/9.51 | (215) aNaturalNumber0(all_72_2) = all_126_3 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (116) with fresh symbols all_128_0, all_128_1, all_128_2, % 65.02/9.51 | all_128_3, all_128_4 gives: % 65.02/9.51 | (216) sdtpldt0(xm, xp) = all_128_1 & sdtpldt0(xn, all_128_1) = all_128_0 & % 65.02/9.51 | aNaturalNumber0(xp) = all_128_2 & aNaturalNumber0(xm) = all_128_3 & % 65.02/9.51 | aNaturalNumber0(xn) = all_128_4 & $i(all_128_0) & $i(all_128_1) & ( ~ % 65.02/9.51 | (all_128_2 = 0) | ~ (all_128_3 = 0) | ~ (all_128_4 = 0) | % 65.02/9.51 | all_128_0 = all_76_0) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (216) implies: % 65.02/9.51 | (217) aNaturalNumber0(xn) = all_128_4 % 65.02/9.51 | (218) aNaturalNumber0(xm) = all_128_3 % 65.02/9.51 | (219) aNaturalNumber0(xp) = all_128_2 % 65.02/9.51 | (220) sdtpldt0(xm, xp) = all_128_1 % 65.02/9.51 | % 65.02/9.51 | DELTA: instantiating (115) with fresh symbols all_130_0, all_130_1, all_130_2, % 65.02/9.51 | all_130_3, all_130_4, all_130_5, all_130_6, all_130_7, all_130_8 gives: % 65.02/9.51 | (221) isPrime0(xp) = all_130_5 & doDivides0(xp, all_130_4) = all_130_3 & % 65.02/9.51 | doDivides0(xp, xm) = all_130_0 & doDivides0(xp, xn) = all_130_1 & % 65.02/9.51 | iLess0(all_76_0, all_76_0) = all_130_2 & sdtasdt0(xn, xm) = all_130_4 % 65.02/9.51 | & aNaturalNumber0(xp) = all_130_6 & aNaturalNumber0(xm) = all_130_7 & % 65.02/9.51 | aNaturalNumber0(xn) = all_130_8 & $i(all_130_4) & ( ~ (all_130_2 = 0) % 65.02/9.51 | | ~ (all_130_3 = 0) | ~ (all_130_5 = 0) | ~ (all_130_6 = 0) | ~ % 65.02/9.51 | (all_130_7 = 0) | ~ (all_130_8 = 0) | all_130_0 = 0 | all_130_1 = % 65.02/9.51 | 0) % 65.02/9.51 | % 65.02/9.51 | ALPHA: (221) implies: % 65.02/9.51 | (222) aNaturalNumber0(xn) = all_130_8 % 65.02/9.51 | (223) aNaturalNumber0(xm) = all_130_7 % 65.02/9.51 | (224) aNaturalNumber0(xp) = all_130_6 % 65.02/9.51 | (225) sdtasdt0(xn, xm) = all_130_4 % 65.02/9.51 | (226) doDivides0(xp, all_130_4) = all_130_3 % 65.02/9.51 | % 65.02/9.51 | BETA: splitting (133) gives: % 65.02/9.51 | % 65.02/9.51 | Case 1: % 65.02/9.51 | | % 65.02/9.51 | | (227) xk = xp % 65.02/9.51 | | % 65.02/9.51 | | REDUCE: (19), (227) imply: % 65.02/9.51 | | (228) $false % 65.02/9.51 | | % 65.02/9.51 | | CLOSE: (228) is inconsistent. % 65.02/9.51 | | % 65.02/9.51 | Case 2: % 65.02/9.51 | | % 65.02/9.51 | | (229) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xp, xk) = % 65.02/9.51 | | v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & ( ~ % 65.02/9.51 | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 65.02/9.51 | | % 65.02/9.51 | | DELTA: instantiating (229) with fresh symbols all_140_0, all_140_1, % 65.02/9.51 | | all_140_2 gives: % 65.02/9.51 | | (230) sdtlseqdt0(xp, xk) = all_140_0 & aNaturalNumber0(xk) = all_140_2 & % 65.02/9.51 | | aNaturalNumber0(xp) = all_140_1 & ( ~ (all_140_0 = 0) | ~ % 65.02/9.51 | | (all_140_1 = 0) | ~ (all_140_2 = 0)) % 65.02/9.51 | | % 65.02/9.51 | | ALPHA: (230) implies: % 65.02/9.51 | | (231) aNaturalNumber0(xp) = all_140_1 % 65.02/9.51 | | (232) aNaturalNumber0(xk) = all_140_2 % 65.02/9.51 | | % 65.02/9.51 | | BETA: splitting (134) gives: % 65.02/9.51 | | % 65.02/9.51 | | Case 1: % 65.02/9.51 | | | % 65.02/9.51 | | | (233) all_64_0 = xn % 65.02/9.51 | | | % 65.02/9.51 | | | REDUCE: (42), (233) imply: % 65.02/9.51 | | | (234) $false % 65.02/9.51 | | | % 65.02/9.51 | | | CLOSE: (234) is inconsistent. % 65.02/9.51 | | | % 65.02/9.51 | | Case 2: % 65.02/9.51 | | | % 65.02/9.51 | | | (235) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xn, % 65.02/9.51 | | | all_64_0) = v2 & aNaturalNumber0(all_64_0) = v0 & % 65.02/9.51 | | | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 65.02/9.51 | | | = 0))) % 65.02/9.51 | | | % 65.02/9.51 | | | DELTA: instantiating (235) with fresh symbols all_145_0, all_145_1, % 65.02/9.51 | | | all_145_2 gives: % 65.02/9.51 | | | (236) sdtlseqdt0(xn, all_64_0) = all_145_0 & aNaturalNumber0(all_64_0) % 65.02/9.51 | | | = all_145_2 & aNaturalNumber0(xn) = all_145_1 & ( ~ (all_145_0 = % 65.02/9.51 | | | 0) | ~ (all_145_1 = 0) | ~ (all_145_2 = 0)) % 65.02/9.51 | | | % 65.02/9.51 | | | ALPHA: (236) implies: % 65.02/9.51 | | | (237) aNaturalNumber0(xn) = all_145_1 % 65.02/9.51 | | | (238) aNaturalNumber0(all_64_0) = all_145_2 % 65.02/9.51 | | | (239) sdtlseqdt0(xn, all_64_0) = all_145_0 % 65.02/9.51 | | | (240) ~ (all_145_0 = 0) | ~ (all_145_1 = 0) | ~ (all_145_2 = 0) % 65.02/9.51 | | | % 65.02/9.51 | | | BETA: splitting (136) gives: % 65.02/9.51 | | | % 65.02/9.51 | | | Case 1: % 65.02/9.51 | | | | % 65.02/9.51 | | | | (241) all_70_0 = 0 % 65.02/9.51 | | | | % 65.02/9.51 | | | | REDUCE: (54), (241) imply: % 65.02/9.51 | | | | (242) $false % 65.02/9.51 | | | | % 65.02/9.51 | | | | CLOSE: (242) is inconsistent. % 65.02/9.51 | | | | % 65.02/9.51 | | | Case 2: % 65.02/9.51 | | | | % 65.02/9.51 | | | | (243) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : % 65.02/9.51 | | | | (doDivides0(all_60_0, all_70_1) = v3 & % 65.02/9.51 | | | | aNaturalNumber0(all_70_1) = v2 & aNaturalNumber0(all_60_0) = % 65.02/9.51 | | | | v1 & aNaturalNumber0(xp) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | % 65.02/9.51 | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 65.02/9.51 | | | | % 65.02/9.51 | | | | DELTA: instantiating (243) with fresh symbols all_150_0, all_150_1, % 65.02/9.51 | | | | all_150_2, all_150_3 gives: % 65.02/9.51 | | | | (244) doDivides0(all_60_0, all_70_1) = all_150_0 & % 65.02/9.51 | | | | aNaturalNumber0(all_70_1) = all_150_1 & % 65.02/9.51 | | | | aNaturalNumber0(all_60_0) = all_150_2 & aNaturalNumber0(xp) = % 65.02/9.51 | | | | all_150_3 & ( ~ (all_150_0 = 0) | ~ (all_150_1 = 0) | ~ % 65.02/9.51 | | | | (all_150_2 = 0) | ~ (all_150_3 = 0)) % 65.02/9.51 | | | | % 65.02/9.51 | | | | ALPHA: (244) implies: % 65.02/9.52 | | | | (245) aNaturalNumber0(xp) = all_150_3 % 65.02/9.52 | | | | (246) aNaturalNumber0(all_60_0) = all_150_2 % 65.02/9.52 | | | | (247) aNaturalNumber0(all_70_1) = all_150_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with 0, all_114_2, xn, simplifying with % 65.02/9.52 | | | | (6), (190) gives: % 65.02/9.52 | | | | (248) all_114_2 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_106_2, all_114_2, xn, % 65.02/9.52 | | | | simplifying with (176), (190) gives: % 65.02/9.52 | | | | (249) all_114_2 = all_106_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_106_2, all_116_2, xn, % 65.02/9.52 | | | | simplifying with (176), (195) gives: % 65.02/9.52 | | | | (250) all_116_2 = all_106_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_116_2, all_128_4, xn, % 65.02/9.52 | | | | simplifying with (195), (217) gives: % 65.02/9.52 | | | | (251) all_128_4 = all_116_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_128_4, all_130_8, xn, % 65.02/9.52 | | | | simplifying with (217), (222) gives: % 65.02/9.52 | | | | (252) all_130_8 = all_128_4 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_130_8, all_145_1, xn, % 65.02/9.52 | | | | simplifying with (222), (237) gives: % 65.02/9.52 | | | | (253) all_145_1 = all_130_8 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_98_2, all_145_1, xn, % 65.02/9.52 | | | | simplifying with (161), (237) gives: % 65.02/9.52 | | | | (254) all_145_1 = all_98_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with 0, all_100_1, xm, simplifying with % 65.02/9.52 | | | | (7), (166) gives: % 65.02/9.52 | | | | (255) all_100_1 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_100_1, all_106_1, xm, % 65.02/9.52 | | | | simplifying with (166), (177) gives: % 65.02/9.52 | | | | (256) all_106_1 = all_100_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_106_1, all_114_1, xm, % 65.02/9.52 | | | | simplifying with (177), (191) gives: % 65.02/9.52 | | | | (257) all_114_1 = all_106_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_114_1, all_116_1, xm, % 65.02/9.52 | | | | simplifying with (191), (196) gives: % 65.02/9.52 | | | | (258) all_116_1 = all_114_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_116_1, all_120_1, xm, % 65.02/9.52 | | | | simplifying with (196), (203) gives: % 65.02/9.52 | | | | (259) all_120_1 = all_116_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_120_1, all_124_3, xm, % 65.02/9.52 | | | | simplifying with (203), (209) gives: % 65.02/9.52 | | | | (260) all_124_3 = all_120_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_124_3, all_128_3, xm, % 65.02/9.52 | | | | simplifying with (209), (218) gives: % 65.02/9.52 | | | | (261) all_128_3 = all_124_3 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_128_3, all_130_7, xm, % 65.02/9.52 | | | | simplifying with (218), (223) gives: % 65.02/9.52 | | | | (262) all_130_7 = all_128_3 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_98_1, all_130_7, xm, % 65.02/9.52 | | | | simplifying with (162), (223) gives: % 65.02/9.52 | | | | (263) all_130_7 = all_98_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_104_2, all_110_2, xp, % 65.02/9.52 | | | | simplifying with (172), (182) gives: % 65.02/9.52 | | | | (264) all_110_2 = all_104_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_118_2, all_122_1, xp, % 65.02/9.52 | | | | simplifying with (200), (207) gives: % 65.02/9.52 | | | | (265) all_122_1 = all_118_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_104_2, all_122_1, xp, % 65.02/9.52 | | | | simplifying with (172), (207) gives: % 65.02/9.52 | | | | (266) all_122_1 = all_104_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_96_2, all_122_1, xp, % 65.02/9.52 | | | | simplifying with (157), (207) gives: % 65.02/9.52 | | | | (267) all_122_1 = all_96_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_122_1, all_128_2, xp, % 65.02/9.52 | | | | simplifying with (207), (219) gives: % 65.02/9.52 | | | | (268) all_128_2 = all_122_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_102_1, all_128_2, xp, % 65.02/9.52 | | | | simplifying with (170), (219) gives: % 65.02/9.52 | | | | (269) all_128_2 = all_102_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_126_4, all_130_6, xp, % 65.02/9.52 | | | | simplifying with (213), (224) gives: % 65.02/9.52 | | | | (270) all_130_6 = all_126_4 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_110_2, all_130_6, xp, % 65.02/9.52 | | | | simplifying with (182), (224) gives: % 65.02/9.52 | | | | (271) all_130_6 = all_110_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_130_6, all_140_1, xp, % 65.02/9.52 | | | | simplifying with (224), (231) gives: % 65.02/9.52 | | | | (272) all_140_1 = all_130_6 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with 0, all_150_3, xp, simplifying with % 65.02/9.52 | | | | (8), (245) gives: % 65.02/9.52 | | | | (273) all_150_3 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_140_1, all_150_3, xp, % 65.02/9.52 | | | | simplifying with (231), (245) gives: % 65.02/9.52 | | | | (274) all_150_3 = all_140_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_110_1, all_140_2, xk, % 65.02/9.52 | | | | simplifying with (183), (232) gives: % 65.02/9.52 | | | | (275) all_140_2 = all_110_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_104_1, all_140_2, xk, % 65.02/9.52 | | | | simplifying with (173), (232) gives: % 65.02/9.52 | | | | (276) all_140_2 = all_104_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_92_1, all_108_1, xr, % 65.02/9.52 | | | | simplifying with (150), (179) gives: % 65.02/9.52 | | | | (277) all_108_1 = all_92_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_108_1, all_112_1, xr, % 65.02/9.52 | | | | simplifying with (179), (187) gives: % 65.02/9.52 | | | | (278) all_112_1 = all_108_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_112_1, all_124_2, xr, % 65.02/9.52 | | | | simplifying with (187), (210) gives: % 65.02/9.52 | | | | (279) all_124_2 = all_112_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_94_1, all_124_2, xr, % 65.02/9.52 | | | | simplifying with (153), (210) gives: % 65.02/9.52 | | | | (280) all_124_2 = all_94_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with 0, all_126_2, xr, simplifying with % 65.02/9.52 | | | | (15), (214) gives: % 65.02/9.52 | | | | (281) all_126_2 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_108_1, all_126_2, xr, % 65.02/9.52 | | | | simplifying with (179), (214) gives: % 65.02/9.52 | | | | (282) all_126_2 = all_108_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_92_0, all_98_0, all_60_0, % 65.02/9.52 | | | | simplifying with (151), (163) gives: % 65.02/9.52 | | | | (283) all_98_0 = all_92_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_98_0, all_150_2, all_60_0, % 65.02/9.52 | | | | simplifying with (163), (246) gives: % 65.02/9.52 | | | | (284) all_150_2 = all_98_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_94_0, all_150_2, all_60_0, % 65.02/9.52 | | | | simplifying with (154), (246) gives: % 65.02/9.52 | | | | (285) all_150_2 = all_94_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_120_2, all_124_4, all_64_0, % 65.02/9.52 | | | | simplifying with (204), (211) gives: % 65.02/9.52 | | | | (286) all_124_4 = all_120_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_124_4, all_145_2, all_64_0, % 65.02/9.52 | | | | simplifying with (211), (238) gives: % 65.02/9.52 | | | | (287) all_145_2 = all_124_4 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_100_2, all_145_2, all_64_0, % 65.02/9.52 | | | | simplifying with (167), (238) gives: % 65.02/9.52 | | | | (288) all_145_2 = all_100_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_100_0, all_108_2, all_70_1, % 65.02/9.52 | | | | simplifying with (168), (180) gives: % 65.02/9.52 | | | | (289) all_108_2 = all_100_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_94_2, all_108_2, all_70_1, % 65.02/9.52 | | | | simplifying with (155), (180) gives: % 65.02/9.52 | | | | (290) all_108_2 = all_94_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_100_0, all_150_1, all_70_1, % 65.02/9.52 | | | | simplifying with (168), (247) gives: % 65.02/9.52 | | | | (291) all_150_1 = all_100_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_96_0, all_150_1, all_70_1, % 65.02/9.52 | | | | simplifying with (158), (247) gives: % 65.02/9.52 | | | | (292) all_150_1 = all_96_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_118_1, all_126_3, all_72_2, % 65.02/9.52 | | | | simplifying with (201), (215) gives: % 65.02/9.52 | | | | (293) all_126_3 = all_118_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (32) with all_96_1, all_126_3, all_72_2, % 65.02/9.52 | | | | simplifying with (159), (215) gives: % 65.02/9.52 | | | | (294) all_126_3 = all_96_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | GROUND_INST: instantiating (33) with all_60_0, all_130_4, xm, xn, % 65.02/9.52 | | | | simplifying with (37), (225) gives: % 65.02/9.52 | | | | (295) all_130_4 = all_60_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (291), (292) imply: % 65.02/9.52 | | | | (296) all_100_0 = all_96_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (296) implies: % 65.02/9.52 | | | | (297) all_100_0 = all_96_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (284), (285) imply: % 65.02/9.52 | | | | (298) all_98_0 = all_94_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (298) implies: % 65.02/9.52 | | | | (299) all_98_0 = all_94_0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (273), (274) imply: % 65.02/9.52 | | | | (300) all_140_1 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (300) implies: % 65.02/9.52 | | | | (301) all_140_1 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (253), (254) imply: % 65.02/9.52 | | | | (302) all_130_8 = all_98_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (302) implies: % 65.02/9.52 | | | | (303) all_130_8 = all_98_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (287), (288) imply: % 65.02/9.52 | | | | (304) all_124_4 = all_100_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (304) implies: % 65.02/9.52 | | | | (305) all_124_4 = all_100_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (272), (301) imply: % 65.02/9.52 | | | | (306) all_130_6 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (306) implies: % 65.02/9.52 | | | | (307) all_130_6 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (275), (276) imply: % 65.02/9.52 | | | | (308) all_110_1 = all_104_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (308) implies: % 65.02/9.52 | | | | (309) all_110_1 = all_104_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (270), (271) imply: % 65.02/9.52 | | | | (310) all_126_4 = all_110_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (270), (307) imply: % 65.02/9.52 | | | | (311) all_126_4 = 0 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (262), (263) imply: % 65.02/9.52 | | | | (312) all_128_3 = all_98_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (312) implies: % 65.02/9.52 | | | | (313) all_128_3 = all_98_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (252), (303) imply: % 65.02/9.52 | | | | (314) all_128_4 = all_98_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (314) implies: % 65.02/9.52 | | | | (315) all_128_4 = all_98_2 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (268), (269) imply: % 65.02/9.52 | | | | (316) all_122_1 = all_102_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (316) implies: % 65.02/9.52 | | | | (317) all_122_1 = all_102_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | COMBINE_EQS: (261), (313) imply: % 65.02/9.52 | | | | (318) all_124_3 = all_98_1 % 65.02/9.52 | | | | % 65.02/9.52 | | | | SIMP: (318) implies: % 65.02/9.53 | | | | (319) all_124_3 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (251), (315) imply: % 65.02/9.53 | | | | (320) all_116_2 = all_98_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (320) implies: % 65.02/9.53 | | | | (321) all_116_2 = all_98_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (281), (282) imply: % 65.02/9.53 | | | | (322) all_108_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (322) implies: % 65.02/9.53 | | | | (323) all_108_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (293), (294) imply: % 65.02/9.53 | | | | (324) all_118_1 = all_96_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (310), (311) imply: % 65.02/9.53 | | | | (325) all_110_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (325) implies: % 65.02/9.53 | | | | (326) all_110_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (279), (280) imply: % 65.02/9.53 | | | | (327) all_112_1 = all_94_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (327) implies: % 65.02/9.53 | | | | (328) all_112_1 = all_94_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (260), (319) imply: % 65.02/9.53 | | | | (329) all_120_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (329) implies: % 65.02/9.53 | | | | (330) all_120_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (286), (305) imply: % 65.02/9.53 | | | | (331) all_120_2 = all_100_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (331) implies: % 65.02/9.53 | | | | (332) all_120_2 = all_100_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (265), (267) imply: % 65.02/9.53 | | | | (333) all_118_2 = all_96_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (265), (266) imply: % 65.02/9.53 | | | | (334) all_118_2 = all_104_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (265), (317) imply: % 65.02/9.53 | | | | (335) all_118_2 = all_102_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (259), (330) imply: % 65.02/9.53 | | | | (336) all_116_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (336) implies: % 65.02/9.53 | | | | (337) all_116_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (333), (335) imply: % 65.02/9.53 | | | | (338) all_102_1 = all_96_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (334), (335) imply: % 65.02/9.53 | | | | (339) all_104_2 = all_102_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (339) implies: % 65.02/9.53 | | | | (340) all_104_2 = all_102_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (258), (337) imply: % 65.02/9.53 | | | | (341) all_114_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (341) implies: % 65.02/9.53 | | | | (342) all_114_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (250), (321) imply: % 65.02/9.53 | | | | (343) all_106_2 = all_98_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (343) implies: % 65.02/9.53 | | | | (344) all_106_2 = all_98_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (257), (342) imply: % 65.02/9.53 | | | | (345) all_106_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (345) implies: % 65.02/9.53 | | | | (346) all_106_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (248), (249) imply: % 65.02/9.53 | | | | (347) all_106_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (347) implies: % 65.02/9.53 | | | | (348) all_106_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (278), (328) imply: % 65.02/9.53 | | | | (349) all_108_1 = all_94_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (349) implies: % 65.02/9.53 | | | | (350) all_108_1 = all_94_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (264), (326) imply: % 65.02/9.53 | | | | (351) all_104_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (351) implies: % 65.02/9.53 | | | | (352) all_104_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (277), (350) imply: % 65.02/9.53 | | | | (353) all_94_1 = all_92_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (323), (350) imply: % 65.02/9.53 | | | | (354) all_94_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (289), (290) imply: % 65.02/9.53 | | | | (355) all_100_0 = all_94_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (355) implies: % 65.02/9.53 | | | | (356) all_100_0 = all_94_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (256), (346) imply: % 65.02/9.53 | | | | (357) all_100_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (357) implies: % 65.02/9.53 | | | | (358) all_100_1 = all_98_1 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (344), (348) imply: % 65.02/9.53 | | | | (359) all_98_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (340), (352) imply: % 65.02/9.53 | | | | (360) all_102_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (360) implies: % 65.02/9.53 | | | | (361) all_102_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (338), (361) imply: % 65.02/9.53 | | | | (362) all_96_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (362) implies: % 65.02/9.53 | | | | (363) all_96_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (297), (356) imply: % 65.02/9.53 | | | | (364) all_96_0 = all_94_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | SIMP: (364) implies: % 65.02/9.53 | | | | (365) all_96_0 = all_94_2 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (255), (358) imply: % 65.02/9.53 | | | | (366) all_98_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (283), (299) imply: % 65.02/9.53 | | | | (367) all_94_0 = all_92_0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (353), (354) imply: % 65.02/9.53 | | | | (368) all_92_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (342), (366) imply: % 65.02/9.53 | | | | (369) all_114_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (321), (359) imply: % 65.02/9.53 | | | | (370) all_116_2 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (337), (366) imply: % 65.02/9.53 | | | | (371) all_116_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | COMBINE_EQS: (254), (359) imply: % 65.02/9.53 | | | | (372) all_145_1 = 0 % 65.02/9.53 | | | | % 65.02/9.53 | | | | REDUCE: (226), (295) imply: % 65.02/9.53 | | | | (373) doDivides0(xp, all_60_0) = all_130_3 % 65.02/9.53 | | | | % 65.02/9.53 | | | | BETA: splitting (148) gives: % 65.02/9.53 | | | | % 65.02/9.53 | | | | Case 1: % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | (374) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0) % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | DELTA: instantiating (374) with fresh symbol all_159_0 gives: % 65.02/9.53 | | | | | (375) ~ (all_159_0 = 0) & aNaturalNumber0(xr) = all_159_0 % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | ALPHA: (375) implies: % 65.02/9.53 | | | | | (376) ~ (all_159_0 = 0) % 65.02/9.53 | | | | | (377) aNaturalNumber0(xr) = all_159_0 % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | GROUND_INST: instantiating (32) with 0, all_159_0, xr, simplifying % 65.02/9.53 | | | | | with (15), (377) gives: % 65.02/9.53 | | | | | (378) all_159_0 = 0 % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | REDUCE: (376), (378) imply: % 65.02/9.53 | | | | | (379) $false % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | CLOSE: (379) is inconsistent. % 65.02/9.53 | | | | | % 65.02/9.53 | | | | Case 2: % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | (380) ~ (xr = sz10) & ~ (xr = sz00) & ! [v0: $i] : (v0 = xr | v0 % 65.02/9.53 | | | | | = sz10 | ~ (doDivides0(v0, xr) = 0) | ~ $i(v0) | ? [v1: % 65.02/9.53 | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | ALPHA: (380) implies: % 65.02/9.53 | | | | | (381) ~ (xr = sz00) % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | BETA: splitting (198) gives: % 65.02/9.53 | | | | | % 65.02/9.53 | | | | | Case 1: % 65.02/9.53 | | | | | | % 65.02/9.53 | | | | | | (382) ~ (all_116_1 = 0) % 65.02/9.53 | | | | | | % 65.02/9.53 | | | | | | REDUCE: (371), (382) imply: % 65.02/9.53 | | | | | | (383) $false % 65.02/9.53 | | | | | | % 65.02/9.53 | | | | | | CLOSE: (383) is inconsistent. % 65.02/9.53 | | | | | | % 65.02/9.53 | | | | | Case 2: % 65.02/9.53 | | | | | | % 65.02/9.53 | | | | | | (384) ~ (all_116_2 = 0) | all_116_0 = all_60_0 % 65.02/9.53 | | | | | | % 65.02/9.53 | | | | | | BETA: splitting (140) gives: % 65.02/9.53 | | | | | | % 65.02/9.53 | | | | | | Case 1: % 65.02/9.53 | | | | | | | % 65.02/9.53 | | | | | | | (385) xr = sz00 % 65.02/9.53 | | | | | | | % 65.02/9.53 | | | | | | | REDUCE: (381), (385) imply: % 65.02/9.53 | | | | | | | (386) $false % 65.02/9.53 | | | | | | | % 65.02/9.53 | | | | | | | CLOSE: (386) is inconsistent. % 65.02/9.53 | | | | | | | % 65.02/9.53 | | | | | | Case 2: % 65.02/9.53 | | | | | | | % 65.02/9.53 | | | | | | | (387) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.02/9.53 | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & % 65.02/9.53 | | | | | | | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | % 65.02/9.53 | | | | | | | ~ (v0 = 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: % 65.02/9.53 | | | | | | | $i] : ( ~ (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, % 65.02/9.53 | | | | | | | xn) = v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] % 65.02/9.53 | | | | | | | : (sdtasdt0(v0, all_64_0) = v4 & aNaturalNumber0(v0) = % 65.02/9.53 | | | | | | | v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 65.02/9.53 | | | | | | | % 65.02/9.53 | | | | | | | BETA: splitting (141) gives: % 65.02/9.53 | | | | | | | % 65.02/9.53 | | | | | | | Case 1: % 65.02/9.53 | | | | | | | | % 65.02/9.53 | | | | | | | | (388) xr = sz00 % 65.02/9.53 | | | | | | | | % 65.02/9.53 | | | | | | | | REDUCE: (381), (388) imply: % 65.02/9.53 | | | | | | | | (389) $false % 65.02/9.53 | | | | | | | | % 65.02/9.53 | | | | | | | | CLOSE: (389) is inconsistent. % 65.02/9.53 | | | | | | | | % 65.02/9.53 | | | | | | | Case 2: % 65.02/9.53 | | | | | | | | % 65.02/9.53 | | | | | | | | (390) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.02/9.53 | | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = v0 & % 65.02/9.53 | | | | | | | | aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) % 65.02/9.53 | | | | | | | | | ~ (v0 = 0))) | ( ! [v0: any] : (v0 = all_64_0 | % 65.02/9.53 | | | | | | | | ~ (sdtasdt0(xr, v0) = xn) | ~ $i(v0) | ? [v1: % 65.02/9.53 | | | | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) % 65.02/9.53 | | | | | | | | & ! [v0: $i] : ( ~ (sdtasdt0(xr, all_64_0) = v0) | % 65.02/9.53 | | | | | | | | ~ $i(all_64_0) | (v0 = xn & % 65.02/9.53 | | | | | | | | aNaturalNumber0(all_64_0) = 0))) % 65.02/9.53 | | | | | | | | % 65.02/9.53 | | | | | | | | BETA: splitting (164) gives: % 65.02/9.53 | | | | | | | | % 65.02/9.53 | | | | | | | | Case 1: % 65.02/9.53 | | | | | | | | | % 65.02/9.53 | | | | | | | | | (391) ~ (all_98_1 = 0) % 65.02/9.53 | | | | | | | | | % 65.02/9.53 | | | | | | | | | REDUCE: (366), (391) imply: % 65.02/9.53 | | | | | | | | | (392) $false % 65.02/9.53 | | | | | | | | | % 65.02/9.53 | | | | | | | | | CLOSE: (392) is inconsistent. % 65.02/9.53 | | | | | | | | | % 65.02/9.53 | | | | | | | | Case 2: % 65.02/9.53 | | | | | | | | | % 65.02/9.53 | | | | | | | | | (393) ~ (all_98_2 = 0) | all_98_0 = 0 % 65.02/9.53 | | | | | | | | | % 65.02/9.53 | | | | | | | | | BETA: splitting (193) gives: % 65.02/9.53 | | | | | | | | | % 65.02/9.53 | | | | | | | | | Case 1: % 65.02/9.53 | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | (394) ~ (all_114_1 = 0) % 65.02/9.53 | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | REDUCE: (369), (394) imply: % 65.02/9.53 | | | | | | | | | | (395) $false % 65.02/9.53 | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | CLOSE: (395) is inconsistent. % 65.02/9.53 | | | | | | | | | | % 65.02/9.53 | | | | | | | | | Case 2: % 65.02/9.53 | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | (396) ~ (all_114_2 = 0) | all_114_0 = all_76_1 % 65.02/9.53 | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | BETA: splitting (396) gives: % 65.02/9.53 | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | Case 1: % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | (397) ~ (all_114_2 = 0) % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | REDUCE: (248), (397) imply: % 65.02/9.53 | | | | | | | | | | | (398) $false % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | CLOSE: (398) is inconsistent. % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | Case 2: % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | (399) all_114_0 = all_76_1 % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | REDUCE: (192), (399) imply: % 65.02/9.53 | | | | | | | | | | | (400) sdtpldt0(xm, xn) = all_76_1 % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | BETA: splitting (138) gives: % 65.02/9.53 | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | Case 1: % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | (401) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xr) % 65.02/9.53 | | | | | | | | | | | | = v0 & aNaturalNumber0(xn) = v1 & ( ~ (v1 = 0) | % 65.02/9.53 | | | | | | | | | | | | ~ (v0 = 0))) % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | DELTA: instantiating (401) with fresh symbols all_201_0, % 65.02/9.53 | | | | | | | | | | | | all_201_1 gives: % 65.02/9.53 | | | | | | | | | | | | (402) aNaturalNumber0(xr) = all_201_1 & % 65.02/9.53 | | | | | | | | | | | | aNaturalNumber0(xn) = all_201_0 & ( ~ (all_201_0 = % 65.02/9.53 | | | | | | | | | | | | 0) | ~ (all_201_1 = 0)) % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | ALPHA: (402) implies: % 65.02/9.53 | | | | | | | | | | | | (403) aNaturalNumber0(xn) = all_201_0 % 65.02/9.53 | | | | | | | | | | | | (404) aNaturalNumber0(xr) = all_201_1 % 65.02/9.53 | | | | | | | | | | | | (405) ~ (all_201_0 = 0) | ~ (all_201_1 = 0) % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_201_0, xn, % 65.02/9.53 | | | | | | | | | | | | simplifying with (6), (403) gives: % 65.02/9.53 | | | | | | | | | | | | (406) all_201_0 = 0 % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_201_1, xr, % 65.02/9.53 | | | | | | | | | | | | simplifying with (15), (404) gives: % 65.02/9.53 | | | | | | | | | | | | (407) all_201_1 = 0 % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | BETA: splitting (405) gives: % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | Case 1: % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | | (408) ~ (all_201_0 = 0) % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | | REDUCE: (406), (408) imply: % 65.02/9.53 | | | | | | | | | | | | | (409) $false % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | | CLOSE: (409) is inconsistent. % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | Case 2: % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | | (410) ~ (all_201_1 = 0) % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | | REDUCE: (407), (410) imply: % 65.02/9.53 | | | | | | | | | | | | | (411) $false % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | | CLOSE: (411) is inconsistent. % 65.02/9.53 | | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | | End of split % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.53 | | | | | | | | | | | Case 2: % 65.02/9.53 | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | (412) ? [v0: $i] : (sdtasdt0(xr, v0) = xn & % 65.02/9.54 | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0)) % 65.02/9.54 | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | DELTA: instantiating (412) with fresh symbol all_201_0 % 65.02/9.54 | | | | | | | | | | | | gives: % 65.02/9.54 | | | | | | | | | | | | (413) sdtasdt0(xr, all_201_0) = xn & % 65.02/9.54 | | | | | | | | | | | | aNaturalNumber0(all_201_0) = 0 & $i(all_201_0) % 65.02/9.54 | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | ALPHA: (413) implies: % 65.02/9.54 | | | | | | | | | | | | (414) $i(all_201_0) % 65.02/9.54 | | | | | | | | | | | | (415) aNaturalNumber0(all_201_0) = 0 % 65.02/9.54 | | | | | | | | | | | | (416) sdtasdt0(xr, all_201_0) = xn % 65.02/9.54 | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | BETA: splitting (384) gives: % 65.02/9.54 | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | Case 1: % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | (417) ~ (all_116_2 = 0) % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | REDUCE: (370), (417) imply: % 65.02/9.54 | | | | | | | | | | | | | (418) $false % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | CLOSE: (418) is inconsistent. % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | Case 2: % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | (419) all_116_0 = all_60_0 % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | REDUCE: (197), (419) imply: % 65.02/9.54 | | | | | | | | | | | | | (420) sdtasdt0(xm, xn) = all_60_0 % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | BETA: splitting (147) gives: % 65.02/9.54 | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | Case 1: % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | (421) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) % 65.02/9.54 | | | | | | | | | | | | | | = v0) % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | DELTA: instantiating (421) with fresh symbol all_214_0 % 65.02/9.54 | | | | | | | | | | | | | | gives: % 65.02/9.54 | | | | | | | | | | | | | | (422) ~ (all_214_0 = 0) & aNaturalNumber0(xp) = % 65.02/9.54 | | | | | | | | | | | | | | all_214_0 % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | ALPHA: (422) implies: % 65.02/9.54 | | | | | | | | | | | | | | (423) ~ (all_214_0 = 0) % 65.02/9.54 | | | | | | | | | | | | | | (424) aNaturalNumber0(xp) = all_214_0 % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_214_0, xp, % 65.02/9.54 | | | | | | | | | | | | | | simplifying with (8), (424) gives: % 65.02/9.54 | | | | | | | | | | | | | | (425) all_214_0 = 0 % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | REDUCE: (423), (425) imply: % 65.02/9.54 | | | | | | | | | | | | | | (426) $false % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | CLOSE: (426) is inconsistent. % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | Case 2: % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | (427) ~ (xp = sz10) & ~ (xp = sz00) & ! [v0: $i] : % 65.02/9.54 | | | | | | | | | | | | | | (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = 0) % 65.02/9.54 | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.02/9.54 | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | ALPHA: (427) implies: % 65.02/9.54 | | | | | | | | | | | | | | (428) ~ (xp = sz00) % 65.02/9.54 | | | | | | | | | | | | | | (429) ~ (xp = sz10) % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | BETA: splitting (112) gives: % 65.02/9.54 | | | | | | | | | | | | | | % 65.02/9.54 | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | (430) xp = sz00 % 65.22/9.54 | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | REDUCE: (428), (430) imply: % 65.22/9.54 | | | | | | | | | | | | | | | (431) $false % 65.22/9.54 | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | CLOSE: (431) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | (432) xp = sz10 | ? [v0: $i] : (isPrime0(v0) = 0 & % 65.22/9.54 | | | | | | | | | | | | | | | doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 % 65.22/9.54 | | | | | | | | | | | | | | | & $i(v0)) % 65.22/9.54 | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | BETA: splitting (432) gives: % 65.22/9.54 | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | (433) xp = sz10 % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | REDUCE: (429), (433) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | (434) $false % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | CLOSE: (434) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | (435) ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0, % 65.22/9.54 | | | | | | | | | | | | | | | | xp) = 0 & aNaturalNumber0(v0) = 0 & $i(v0)) % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | DELTA: instantiating (435) with fresh symbol all_247_0 % 65.22/9.54 | | | | | | | | | | | | | | | | gives: % 65.22/9.54 | | | | | | | | | | | | | | | | (436) isPrime0(all_247_0) = 0 & doDivides0(all_247_0, % 65.22/9.54 | | | | | | | | | | | | | | | | xp) = 0 & aNaturalNumber0(all_247_0) = 0 & % 65.22/9.54 | | | | | | | | | | | | | | | | $i(all_247_0) % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | ALPHA: (436) implies: % 65.22/9.54 | | | | | | | | | | | | | | | | (437) $i(all_247_0) % 65.22/9.54 | | | | | | | | | | | | | | | | (438) aNaturalNumber0(all_247_0) = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | (439) isPrime0(all_247_0) = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | (440) ~ (all_98_2 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | REDUCE: (359), (440) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | (441) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | CLOSE: (441) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | (442) all_98_0 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (442) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | (443) all_92_0 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | REDUCE: (151), (443) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | (444) aNaturalNumber0(all_60_0) = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | BETA: splitting (387) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | (445) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.54 | | | | | | | | | | | | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = % 65.22/9.54 | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | % 65.22/9.54 | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | DELTA: instantiating (445) with fresh symbols all_256_0, % 65.22/9.54 | | | | | | | | | | | | | | | | | | all_256_1, all_256_2 gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | (446) doDivides0(xr, xn) = all_256_0 & % 65.22/9.54 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_256_2 & % 65.22/9.54 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_256_1 & ( ~ (all_256_0 = % 65.22/9.54 | | | | | | | | | | | | | | | | | | 0) | ~ (all_256_1 = 0) | ~ (all_256_2 = 0)) % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | ALPHA: (446) implies: % 65.22/9.54 | | | | | | | | | | | | | | | | | | (447) aNaturalNumber0(xn) = all_256_1 % 65.22/9.54 | | | | | | | | | | | | | | | | | | (448) aNaturalNumber0(xr) = all_256_2 % 65.22/9.54 | | | | | | | | | | | | | | | | | | (449) doDivides0(xr, xn) = all_256_0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | (450) ~ (all_256_0 = 0) | ~ (all_256_1 = 0) | ~ % 65.22/9.54 | | | | | | | | | | | | | | | | | | (all_256_2 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_256_1, xn, % 65.22/9.54 | | | | | | | | | | | | | | | | | | simplifying with (6), (447) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | (451) all_256_1 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_256_2, xr, % 65.22/9.54 | | | | | | | | | | | | | | | | | | simplifying with (15), (448) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | (452) all_256_2 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with 0, all_256_0, xn, xr, % 65.22/9.54 | | | | | | | | | | | | | | | | | | simplifying with (22), (449) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | (453) all_256_0 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | (454) ~ (all_256_0 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | REDUCE: (453), (454) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | (455) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | CLOSE: (455) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | (456) ~ (all_256_1 = 0) | ~ (all_256_2 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (456) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (457) ~ (all_256_1 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (451), (457) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (458) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | CLOSE: (458) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (459) ~ (all_256_2 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (452), (459) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (460) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | CLOSE: (460) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | End of split % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | (461) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 65.22/9.54 | | | | | | | | | | | | | | | | | | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xn) = % 65.22/9.54 | | | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 65.22/9.54 | | | | | | | | | | | | | | | | | | (sdtasdt0(v0, all_64_0) = v4 & % 65.22/9.54 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = % 65.22/9.54 | | | | | | | | | | | | | | | | | | 0) | v4 = v2))) % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | (462) xp = sz00 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | REDUCE: (428), (462) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | (463) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | CLOSE: (463) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | (464) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.54 | | | | | | | | | | | | | | | | | | | (doDivides0(xp, all_60_0) = v2 & % 65.22/9.54 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_60_0) = v1 & % 65.22/9.54 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 = % 65.22/9.54 | | | | | | | | | | | | | | | | | | | xk | ~ (sdtasdt0(xp, v0) = all_60_0) | ~ % 65.22/9.54 | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.22/9.54 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 65.22/9.54 | | | | | | | | | | | | | | | | | | | ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | (v0 = % 65.22/9.54 | | | | | | | | | | | | | | | | | | | all_60_0 & aNaturalNumber0(xk) = 0))) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (465) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xn) = v2 & aNaturalNumber0(xr) = % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & ( ~ (v2 = 0) | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (465) with fresh symbols all_298_0, % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | all_298_1, all_298_2 gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (466) doDivides0(xr, xn) = all_298_0 & % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_298_2 & % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_298_1 & ( ~ (all_298_0 = % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_298_1 = 0) | ~ (all_298_2 = 0)) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (466) implies: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (467) aNaturalNumber0(xn) = all_298_1 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (468) aNaturalNumber0(xr) = all_298_2 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (469) doDivides0(xr, xn) = all_298_0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (470) ~ (all_298_0 = 0) | ~ (all_298_1 = 0) | ~ % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (all_298_2 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_298_1, xn, % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | simplifying with (6), (467) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (471) all_298_1 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_298_2, xr, % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | simplifying with (15), (468) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (472) all_298_2 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with 0, all_298_0, xn, xr, % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | simplifying with (22), (469) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | (473) all_298_0 = 0 % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (470) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | (474) ~ (all_298_0 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | REDUCE: (473), (474) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | (475) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | CLOSE: (475) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | (476) ~ (all_298_1 = 0) | ~ (all_298_2 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (476) gives: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | (477) ~ (all_298_1 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (471), (477) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | (478) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | (479) ~ (all_298_2 = 0) % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (472), (479) imply: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | (480) $false % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (480) is inconsistent. % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.54 | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.54 | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | (481) ! [v0: any] : (v0 = all_64_0 | ~ (sdtasdt0(xr, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | [v0: $i] : ( ~ (sdtasdt0(xr, all_64_0) = v0) | ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | $i(all_64_0) | (v0 = xn & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_64_0) = 0)) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (481) implies: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | (482) ! [v0: any] : (v0 = all_64_0 | ~ (sdtasdt0(xr, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | v0) = xn) | ~ $i(v0) | ? [v1: int] : ( ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | (v1 = 0) & aNaturalNumber0(v0) = v1)) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with 0, all_130_3, all_60_0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | xp, simplifying with (97), (373) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | (483) all_130_3 = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (464) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (484) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (doDivides0(xp, all_60_0) = v2 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_60_0) = v1 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (484) with fresh symbols all_315_0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | all_315_1, all_315_2 gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (485) doDivides0(xp, all_60_0) = all_315_0 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_60_0) = all_315_1 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_315_2 & ( ~ (all_315_0 = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_315_1 = 0) | ~ (all_315_2 = 0)) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (486) aNaturalNumber0(xp) = all_315_2 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (487) aNaturalNumber0(all_60_0) = all_315_1 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (488) doDivides0(xp, all_60_0) = all_315_0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (489) ~ (all_315_0 = 0) | ~ (all_315_1 = 0) | ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (all_315_2 = 0) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_315_2, xp, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | simplifying with (8), (486) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (490) all_315_2 = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_315_1, all_60_0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | simplifying with (444), (487) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (491) all_315_1 = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (34) with 0, all_315_0, all_60_0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | xp, simplifying with (97), (488) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (492) all_315_0 = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (489) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | (493) ~ (all_315_0 = 0) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (492), (493) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | (494) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (494) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | (495) ~ (all_315_1 = 0) | ~ (all_315_2 = 0) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (496) ~ (all_315_1 = 0) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (491), (496) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (497) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (497) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (498) ~ (all_315_2 = 0) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (490), (498) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (499) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (499) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (500) ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | all_60_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1)) & ! [v0: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (v0 = all_60_0 & aNaturalNumber0(xk) = 0)) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (500) implies: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (501) ! [v0: $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | $i(xk) | (v0 = all_60_0 & aNaturalNumber0(xk) = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | 0)) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (501) with all_74_1, simplifying % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | with (25), (70) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (502) all_74_1 = all_60_0 & aNaturalNumber0(xk) = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (502) implies: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (503) all_74_1 = all_60_0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (504) aNaturalNumber0(xk) = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (75), (503) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (505) sdtsldt0(all_60_0, xr) = all_74_0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (503) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (506) sdtasdt0(xp, xk) = all_60_0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (503) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (507) aNaturalNumber0(all_60_0) = all_104_0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_104_1, 0, xk, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | simplifying with (173), (504) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (508) all_104_1 = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_104_0, all_60_0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | simplifying with (444), (507) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (509) all_104_0 = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (309), (508) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | (510) all_110_1 = 0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | (511) ~ (all_110_1 = 0) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (510), (511) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | (512) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (512) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | (513) ~ (all_110_2 = 0) | all_110_0 = all_74_1 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (514) xr = sz00 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (514) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (515) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (515) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (516) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, all_74_1) = v2 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_1) = v1 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: any] : (v0 = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | all_74_0 | ~ (sdtasdt0(xr, v0) = all_74_1) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | ~ (sdtasdt0(xr, all_74_0) = v0) | ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_0) | (v0 = all_74_1 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_0) = 0))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | (517) xr = sz00 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (517) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | (518) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (518) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | (519) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | ( ! [v0: any] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = all_72_2 | ~ (sdtasdt0(xr, v0) = xk) | ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | ~ (sdtasdt0(xr, all_72_2) = v0) | ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_72_2) | (v0 = xk & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_72_2) = 0))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | (520) xr = sz00 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (520) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | (521) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (521) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | (522) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | ! [v0: $i] : ! % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | [v1: $i] : ! [v2: $i] : ( ~ (sdtsldt0(v1, xr) = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | v2) | ~ (sdtasdt0(v0, xk) = v1) | ~ $i(v0) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_72_2) = v4 & aNaturalNumber0(v0) = v3 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (523) xr = sz00 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (523) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (524) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (524) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (525) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, all_74_1) = v2 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_1) = v1 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ! [v0: $i] : ! [v1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ! [v2: $i] : ( ~ (sdtsldt0(v1, xr) = v2) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (sdtasdt0(v0, all_74_1) = v1) | ~ $i(v0) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ? [v3: any] : ? [v4: $i] : (sdtasdt0(v0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_74_0) = v4 & aNaturalNumber0(v0) = v3 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v4) & ( ~ (v3 = 0) | v4 = v2))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (513) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) ~ (all_110_2 = 0) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (326), (526) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) $false % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (527) is inconsistent. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_110_0 = all_74_1 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (503), (528) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_110_0 = all_60_0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (529) imply: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) sdtasdt0(xk, xp) = all_60_0 % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (32), (34), (504), (531) are % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #2. % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (sdtsldt0(v1, xr) = v2) | ~ (sdtasdt0(v0, xk) = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (sdtasdt0(v0, all_72_2) = v4 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v3 & $i(v4) & ( ~ (v3 = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | v4 = v2))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xr) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0))) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (533) with fresh symbols all_364_0, % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_364_1 gives: % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) aNaturalNumber0(xr) = all_364_1 & % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xk) = all_364_0 & ( ~ (all_364_0 = % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_364_1 = 0)) % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) aNaturalNumber0(xk) = all_364_0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) aNaturalNumber0(xr) = all_364_1 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) ~ (all_364_0 = 0) | ~ (all_364_1 = 0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_364_0, xk, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (504), (535) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_364_0 = 0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_364_1, xr, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (536) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_364_1 = 0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (537) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) ~ (all_364_0 = 0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (540) imply: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) $false % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (541) is inconsistent. % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) ~ (all_364_1 = 0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (542) imply: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) $false % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (543) is inconsistent. % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) ? [v0: $i] : (sdtasdt0(xr, v0) = xk & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (544) with fresh symbol all_364_0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) sdtasdt0(xr, all_364_0) = xk & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_364_0) = 0 & $i(all_364_0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (545) implies: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) $i(all_364_0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) aNaturalNumber0(all_364_0) = 0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) sdtasdt0(xr, all_364_0) = xk % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (516) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, all_74_1) = v2 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_1) = v1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (549) with fresh symbols all_376_0, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, all_376_2 gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) doDivides0(xr, all_74_1) = all_376_0 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_1) = all_376_1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_376_2 & ( ~ (all_376_0 = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_376_1 = 0) | ~ (all_376_2 = 0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (34), (96), (444), (503), (550) are % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) ! [v0: any] : (v0 = all_74_0 | ~ (sdtasdt0(xr, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) = all_74_1) | ~ $i(v0) | ? [v1: int] : % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v0: $i] : ( ~ (sdtasdt0(xr, all_74_0) = v0) | ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_74_0) | (v0 = all_74_1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_0) = 0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (551) implies: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) ! [v0: $i] : ( ~ (sdtasdt0(xr, all_74_0) = v0) | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ $i(all_74_0) | (v0 = all_74_1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_0) = 0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (519) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, xk) = v2 & aNaturalNumber0(xr) = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (32), (34), (504), (553) are % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #2. % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) ! [v0: any] : (v0 = all_72_2 | ~ (sdtasdt0(xr, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) = xk) | ~ $i(v0) | ? [v1: int] : ( ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v0: $i] : ( ~ (sdtasdt0(xr, all_72_2) = v0) | ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_72_2) | (v0 = xk & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_72_2) = 0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (554) implies: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) ! [v0: any] : (v0 = all_72_2 | ~ (sdtasdt0(xr, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) = xk) | ~ $i(v0) | ? [v1: int] : ( ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) & aNaturalNumber0(v0) = v1)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (525) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(xr, all_74_1) = v2 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_1) = v1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v0 & ( ~ (v2 = 0) | ~ (v1 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (556) with fresh symbols all_376_0, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, all_376_2 gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) doDivides0(xr, all_74_1) = all_376_0 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_74_1) = all_376_1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_376_2 & ( ~ (all_376_0 = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_376_1 = 0) | ~ (all_376_2 = 0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (34), (96), (444), (503), (557) are % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with xk, simplifying with (25), % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) xk = sz00 | ! [v0: $i] : ! [v1: $i] : ! [v2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(xk, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1) = v3) | ~ (sdtasdt0(xk, v0) = v2) | ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | : ? [v6: $i] : ? [v7: $i] : (sdtasdt0(v1, xk) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v7 & sdtasdt0(v0, xk) = v6 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v4 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ( ~ (v7 = v6) & ~ (v3 = v2))))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_247_0, simplifying with % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437), (438) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_247_0 = sz00 | ! [v0: $i] : ! [v1: $i] : ! % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (sdtasdt0(all_247_0, v1) = v3) | ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (sdtasdt0(all_247_0, v0) = v2) | ~ $i(v1) | ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ? [v7: $i] : (sdtasdt0(v1, all_247_0) = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v7 & sdtasdt0(v0, all_247_0) = v6 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v4 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ( ~ (v7 = v6) & ~ (v3 = v2))))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddCanc) with xm, xn, xp, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_76_1, all_128_1, simplifying with (27), (28), % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (29), (220), (400) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) xp = xn | ? [v0: any] : ? [v1: any] : ? [v2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(xp, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | xm) = v4 & sdtpldt0(xn, xm) = v3 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v1 & $i(v4) & $i(v3) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v4 = v3) & ~ (all_128_1 = all_76_1)))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddCanc) with xm, xp, xn, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_128_1, all_76_1, simplifying with (27), (28), % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (29), (220), (400) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) xp = xn | ? [v0: any] : ? [v1: any] : ? [v2: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(xp, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | xm) = v3 & sdtpldt0(xn, xm) = v4 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & aNaturalNumber0(xn) = v2 & $i(v4) & $i(v3) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | ( ~ % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v4 = v3) & ~ (all_128_1 = all_76_1)))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB_02) with xm, all_64_0, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_120_0, simplifying with (28), (103), (205) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_120_0) = v2 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_64_0) = v1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | v2 = 0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (552) with all_112_0, simplifying % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (68), (188) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_112_0 = all_74_1 & aNaturalNumber0(all_74_0) = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) aNaturalNumber0(all_74_0) = 0 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (482) with all_201_0, simplifying % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (414), (416) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_201_0 = all_64_0 | ? [v0: int] : ( ~ (v0 = 0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & aNaturalNumber0(all_201_0) = v0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xr, all_364_0, xp, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | xk, all_60_0, simplifying with (29), (30), (530), % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546), (548) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_364_0, xp) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v3 & sdtasdt0(xr, v3) = v4 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_364_0) = v1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_60_0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (555) with all_364_0, simplifying % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (546), (548) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_364_0 = all_72_2 | ? [v0: int] : ( ~ (v0 = 0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & aNaturalNumber0(all_364_0) = v0) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mLETran) with xn, xp, all_64_0, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_145_0, simplifying with (12), (27), (29), % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (103), (239) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_145_0 = 0 | ? [v0: any] : ? [v1: any] : ? % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v2: any] : ? [v3: any] : (sdtlseqdt0(xp, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_64_0) = v3 & aNaturalNumber0(all_64_0) = % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 & aNaturalNumber0(xp) = v1 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = v0 & ( ~ (v3 = 0) | ~ (v2 % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (532) with xp, all_60_0, all_74_0, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (29), (505), (506) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) ? [v0: any] : ? [v1: $i] : (sdtasdt0(xp, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_72_2) = v1 & aNaturalNumber0(xp) = v0 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) & ( ~ (v0 = 0) | v1 = all_74_0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (461) with xm, all_60_0, all_74_0, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (28), (420), (505) gives: % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) ? [v0: any] : ? [v1: $i] : (sdtasdt0(xm, % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_64_0) = v1 & aNaturalNumber0(xm) = v0 & % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) & ( ~ (v0 = 0) | v1 = all_74_0)) % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_247_0, 0, simplifying % 65.22/9.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (437), (439) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) ? [v0: int] : ( ~ (v0 = 0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_247_0) = v0) | ( ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_247_0 = sz10) & ~ (all_247_0 = sz00) & ! % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v0: any] : (v0 = all_247_0 | v0 = sz10 | ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(v0, all_247_0) = 0) | ~ $i(v0) | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ? [v1: int] : ( ~ (v1 = 0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1))) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (570) with fresh symbols all_382_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1 gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) sdtasdt0(xm, all_64_0) = all_382_0 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_382_1 & $i(all_382_0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_382_1 = 0) | all_382_0 = all_74_0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (572) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) aNaturalNumber0(xm) = all_382_1 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) sdtasdt0(xm, all_64_0) = all_382_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) ~ (all_382_1 = 0) | all_382_0 = all_74_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (569) with fresh symbols all_384_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_384_1 gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) sdtasdt0(xp, all_72_2) = all_384_0 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_384_1 & $i(all_384_0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ( ~ (all_384_1 = 0) | all_384_0 = all_74_0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (576) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) aNaturalNumber0(xp) = all_384_1 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) sdtasdt0(xp, all_72_2) = all_384_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) ~ (all_384_1 = 0) | all_384_0 = all_74_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (562) with fresh symbols all_390_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_390_1, all_390_2 gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) aNaturalNumber0(all_120_0) = all_390_0 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_64_0) = all_390_1 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_390_2 & ( ~ (all_390_1 = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_390_2 = 0) | all_390_0 = 0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) aNaturalNumber0(all_120_0) = all_390_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (566) with fresh symbols all_452_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_452_1, all_452_2, all_452_3, all_452_4 gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) sdtasdt0(all_364_0, xp) = all_452_1 & sdtasdt0(xr, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_452_1) = all_452_0 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_364_0) = all_452_3 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_452_4 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_452_2 & $i(all_452_0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_452_1) & ( ~ (all_452_2 = 0) | ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_452_3 = 0) | ~ (all_452_4 = 0) | all_452_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_60_0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (582) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) aNaturalNumber0(xp) = all_452_2 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) aNaturalNumber0(xr) = all_452_4 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) aNaturalNumber0(all_364_0) = all_452_3 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) ~ (all_452_2 = 0) | ~ (all_452_3 = 0) | ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_452_4 = 0) | all_452_0 = all_60_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (558) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) xk = sz00 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (587) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (588) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_382_1, xm, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (7), (573) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_382_1 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_384_1, xp, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (8), (577) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_384_1 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_452_2, xp, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (8), (583) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_452_2 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_452_4, xr, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (584) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_452_4 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_452_3, all_364_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (547), (585) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_452_3 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_120_0, all_382_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_64_0, xm, simplifying with (205), (574) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) all_382_0 = all_120_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with all_70_1, all_384_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_72_2, xp, simplifying with (110), (578) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) all_384_0 = all_70_1 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (571) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) ? [v0: int] : ( ~ (v0 = 0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_247_0) = v0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (596) with fresh symbol all_530_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) ~ (all_530_0 = 0) & aNaturalNumber0(all_247_0) = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_530_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (597) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) ~ (all_530_0 = 0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) aNaturalNumber0(all_247_0) = all_530_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_530_0, all_247_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (438), (599) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_530_0 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (600) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (601) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) ~ (all_247_0 = sz10) & ~ (all_247_0 = sz00) & ! % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v0: any] : (v0 = all_247_0 | v0 = sz10 | ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (doDivides0(v0, all_247_0) = 0) | ~ $i(v0) | ? % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1)) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (602) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) ~ (all_247_0 = sz00) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (560) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) xp = xn % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (604) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (605) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtpldt0(xp, xm) = v4 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sdtpldt0(xn, xm) = v3 & aNaturalNumber0(xp) = v2 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v1 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_128_1 = all_76_1)))) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (606) with fresh symbols all_540_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_540_1, all_540_2, all_540_3, all_540_4 gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) sdtpldt0(xp, xm) = all_540_0 & sdtpldt0(xn, xm) = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_540_1 & aNaturalNumber0(xp) = all_540_2 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_540_4 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_540_3 & $i(all_540_0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_540_1) & ( ~ (all_540_2 = 0) | ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_540_3 = 0) | ~ (all_540_4 = 0) | ( ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_540_0 = all_540_1) & ~ (all_128_1 = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_76_1))) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) aNaturalNumber0(xp) = all_540_2 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (567) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_364_0 = all_72_2 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (547), (609) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) aNaturalNumber0(all_72_2) = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (575) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) ~ (all_382_1 = 0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (611) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (612) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_382_0 = all_74_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (594), (613) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_120_0 = all_74_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (614) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) all_120_0 = all_74_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (615) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) aNaturalNumber0(all_74_0) = all_390_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (561) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) xp = xn % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (617) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (618) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtpldt0(xp, xm) = v3 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sdtpldt0(xn, xm) = v4 & aNaturalNumber0(xp) = v1 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | ( ~ (v4 = v3) & ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_128_1 = all_76_1)))) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (619) with fresh symbols all_639_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_639_1, all_639_2, all_639_3, all_639_4 gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) sdtpldt0(xp, xm) = all_639_1 & sdtpldt0(xn, xm) = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_639_0 & aNaturalNumber0(xp) = all_639_3 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_639_4 & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_639_2 & $i(all_639_0) & % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_639_1) & ( ~ (all_639_2 = 0) | ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_639_3 = 0) | ~ (all_639_4 = 0) | ( ~ % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_639_0 = all_639_1) & ~ (all_128_1 = % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_76_1))) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (620) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) aNaturalNumber0(xp) = all_639_3 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (579) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) ~ (all_384_1 = 0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (622) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (623) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_384_0 = all_74_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (595), (624) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) all_74_0 = all_70_1 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (625) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_74_0 = all_70_1 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (616), (626) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) aNaturalNumber0(all_70_1) = all_390_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (626) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) aNaturalNumber0(all_70_1) = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_201_0 = all_64_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (629) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) aNaturalNumber0(all_64_0) = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) ~ (all_452_2 = 0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (631) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (632) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) ~ (all_452_3 = 0) | ~ (all_452_4 = 0) | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_452_0 = all_60_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) ~ (all_452_3 = 0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (634) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (635) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) ~ (all_452_4 = 0) | all_452_0 = all_60_0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (636) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) ~ (all_452_4 = 0) % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (592), (637) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) $false % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (638) is inconsistent. % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_639_3, xp, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (8), (621) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_639_3 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_540_2, all_639_3, xp, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (608), (621) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) all_639_3 = all_540_2 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_100_2, 0, all_64_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (167), (630) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) all_100_2 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_94_2, all_390_0, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_70_1, simplifying with (155), (627) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_390_0 = all_94_2 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_390_0, all_70_1, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (627), (628) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_390_0 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_96_1, 0, all_72_2, % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (159), (610) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_96_1 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (639), (640) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_540_2 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (645) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_540_2 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (642), (643) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_94_2 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (647) implies: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_94_2 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (641) imply: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_145_2 = 0 % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 65.22/9.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) ? [v0: any] : ? [v1: any] : % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_70_1) = v1 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0))) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_64_0 = xn % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (651) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (652) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (650) with fresh symbols all_857_0, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_857_1 gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) aNaturalNumber0(all_70_1) = all_857_0 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_857_1 & ( ~ (all_857_0 = % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_857_1 = 0)) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (653) implies: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) aNaturalNumber0(xp) = all_857_1 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) aNaturalNumber0(all_70_1) = all_857_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) ~ (all_857_0 = 0) | ~ (all_857_1 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) ~ (all_145_0 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (568) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) all_145_0 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (657), (658) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (659) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: any] : (sdtlseqdt0(xp, all_64_0) = v3 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_64_0) = v2 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & aNaturalNumber0(xn) = % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v0 = 0))) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (660) with fresh symbols all_927_0, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_927_1, all_927_2, all_927_3 gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) sdtlseqdt0(xp, all_64_0) = all_927_0 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_64_0) = all_927_1 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_927_2 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_927_3 & ( ~ (all_927_0 = % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_927_1 = 0) | ~ (all_927_2 = 0) | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_927_3 = 0)) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (661) implies: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) aNaturalNumber0(xp) = all_927_2 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_927_2, xp, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (8), (662) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_927_2 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_857_1, all_927_2, xp, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (654), (662) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_927_2 = all_857_1 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_857_0, all_70_1, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (628), (655) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_857_0 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (663), (664) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_857_1 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (656) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) ~ (all_857_0 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (665), (667) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (668) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) ~ (all_857_1 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (666), (669) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (670) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) ~ (all_145_1 = 0) | ~ (all_145_2 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (671) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) ~ (all_145_1 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (672) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (673) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) ~ (all_145_2 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (649), (674) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (675) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) ( ~ (all_70_0 = 0) | ? [v0: $i] : (sdtasdt0(xp, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) = all_70_1 & aNaturalNumber0(v0) = 0 & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0))) & (all_70_0 = 0 | ! [v0: $i] : ( ~ % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (sdtasdt0(xp, v0) = all_70_1) | ~ $i(v0) | ? % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v1))) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (676) implies: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_70_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_70_1) | ~ $i(v0) | ? [v1: int] : ( ~ % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) & aNaturalNumber0(v0) = v1)) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (677) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_70_0 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (678) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (679) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = all_70_1) | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (680) with all_72_2, simplifying % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (60), (110) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) ? [v0: int] : ( ~ (v0 = 0) & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_72_2) = v0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (681) with fresh symbol all_897_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) ~ (all_897_0 = 0) & aNaturalNumber0(all_72_2) = % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_897_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (682) implies: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) ~ (all_897_0 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) aNaturalNumber0(all_72_2) = all_897_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_897_0, all_72_2, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (610), (684) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) all_897_0 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (683), (685) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (686) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) ? [v0: int] : ( ~ (v0 = 0) & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_201_0) = v0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (687) with fresh symbol all_761_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) ~ (all_761_0 = 0) & aNaturalNumber0(all_201_0) = % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_761_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (688) implies: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) ~ (all_761_0 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) aNaturalNumber0(all_201_0) = all_761_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_761_0, all_201_0, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (415), (690) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_761_0 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (689), (691) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (692) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) ? [v0: int] : ( ~ (v0 = 0) & % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_364_0) = v0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (559) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_247_0 = sz00 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (603), (694) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (695) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (693) with fresh symbol all_557_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) ~ (all_557_0 = 0) & aNaturalNumber0(all_364_0) = % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_557_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (696) implies: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) ~ (all_557_0 = 0) % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) aNaturalNumber0(all_364_0) = all_557_0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_557_0, all_364_0, % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (547), (698) gives: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) all_557_0 = 0 % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (697), (699) imply: % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) $false % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (700) is inconsistent. % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | | % 65.22/9.58 | | | | | | | | | | End of split % 65.22/9.58 | | | | | | | | | | % 65.22/9.59 | | | | | | | | | End of split % 65.22/9.59 | | | | | | | | | % 65.22/9.59 | | | | | | | | End of split % 65.22/9.59 | | | | | | | | % 65.22/9.59 | | | | | | | End of split % 65.22/9.59 | | | | | | | % 65.22/9.59 | | | | | | End of split % 65.22/9.59 | | | | | | % 65.22/9.59 | | | | | End of split % 65.22/9.59 | | | | | % 65.22/9.59 | | | | End of split % 65.22/9.59 | | | | % 65.22/9.59 | | | End of split % 65.22/9.59 | | | % 65.22/9.59 | | End of split % 65.22/9.59 | | % 65.22/9.59 | End of split % 65.22/9.59 | % 65.22/9.59 End of proof % 65.22/9.59 % 65.22/9.59 Sub-proof #1 shows that the following formulas are inconsistent: % 65.22/9.59 ---------------------------------------------------------------- % 65.22/9.59 (1) doDivides0(xr, all_60_0) = 0 % 65.22/9.59 (2) aNaturalNumber0(all_60_0) = 0 % 65.22/9.59 (3) aNaturalNumber0(xr) = 0 % 65.22/9.59 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 65.22/9.59 (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) % 65.22/9.59 (5) doDivides0(xr, all_74_1) = all_376_0 & aNaturalNumber0(all_74_1) = % 65.22/9.59 all_376_1 & aNaturalNumber0(xr) = all_376_2 & ( ~ (all_376_0 = 0) | ~ % 65.22/9.59 (all_376_1 = 0) | ~ (all_376_2 = 0)) % 65.22/9.59 (6) all_74_1 = all_60_0 % 65.22/9.59 (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 65.22/9.59 ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, % 65.22/9.59 v2) = v0)) % 65.22/9.59 % 65.22/9.59 Begin of proof % 65.22/9.59 | % 65.22/9.59 | ALPHA: (5) implies: % 65.22/9.59 | (8) aNaturalNumber0(xr) = all_376_2 % 65.22/9.59 | (9) aNaturalNumber0(all_74_1) = all_376_1 % 65.22/9.59 | (10) doDivides0(xr, all_74_1) = all_376_0 % 65.22/9.59 | (11) ~ (all_376_0 = 0) | ~ (all_376_1 = 0) | ~ (all_376_2 = 0) % 65.22/9.59 | % 65.22/9.59 | REDUCE: (6), (10) imply: % 65.22/9.59 | (12) doDivides0(xr, all_60_0) = all_376_0 % 65.22/9.59 | % 65.22/9.59 | REDUCE: (6), (9) imply: % 65.22/9.59 | (13) aNaturalNumber0(all_60_0) = all_376_1 % 65.22/9.59 | % 65.22/9.59 | GROUND_INST: instantiating (4) with 0, all_376_2, xr, simplifying with (3), % 65.22/9.59 | (8) gives: % 65.22/9.59 | (14) all_376_2 = 0 % 65.22/9.59 | % 65.22/9.59 | GROUND_INST: instantiating (4) with 0, all_376_1, all_60_0, simplifying with % 65.22/9.59 | (2), (13) gives: % 65.22/9.59 | (15) all_376_1 = 0 % 65.22/9.59 | % 65.22/9.59 | GROUND_INST: instantiating (7) with 0, all_376_0, all_60_0, xr, simplifying % 65.22/9.59 | with (1), (12) gives: % 65.22/9.59 | (16) all_376_0 = 0 % 65.22/9.59 | % 65.22/9.59 | BETA: splitting (11) gives: % 65.22/9.59 | % 65.22/9.59 | Case 1: % 65.22/9.59 | | % 65.22/9.59 | | (17) ~ (all_376_0 = 0) % 65.22/9.59 | | % 65.22/9.59 | | REDUCE: (16), (17) imply: % 65.22/9.59 | | (18) $false % 65.22/9.59 | | % 65.22/9.59 | | CLOSE: (18) is inconsistent. % 65.22/9.59 | | % 65.22/9.59 | Case 2: % 65.22/9.59 | | % 65.22/9.59 | | (19) ~ (all_376_1 = 0) | ~ (all_376_2 = 0) % 65.22/9.59 | | % 65.22/9.59 | | BETA: splitting (19) gives: % 65.22/9.59 | | % 65.22/9.59 | | Case 1: % 65.22/9.59 | | | % 65.22/9.59 | | | (20) ~ (all_376_1 = 0) % 65.22/9.59 | | | % 65.22/9.59 | | | REDUCE: (15), (20) imply: % 65.22/9.59 | | | (21) $false % 65.22/9.59 | | | % 65.22/9.59 | | | CLOSE: (21) is inconsistent. % 65.22/9.59 | | | % 65.22/9.59 | | Case 2: % 65.22/9.59 | | | % 65.22/9.59 | | | (22) ~ (all_376_2 = 0) % 65.22/9.59 | | | % 65.22/9.59 | | | REDUCE: (14), (22) imply: % 65.22/9.59 | | | (23) $false % 65.22/9.59 | | | % 65.22/9.59 | | | CLOSE: (23) is inconsistent. % 65.22/9.59 | | | % 65.22/9.59 | | End of split % 65.22/9.59 | | % 65.22/9.59 | End of split % 65.22/9.59 | % 65.22/9.59 End of proof % 65.22/9.59 % 65.22/9.59 Sub-proof #2 shows that the following formulas are inconsistent: % 65.22/9.59 ---------------------------------------------------------------- % 65.22/9.59 (1) aNaturalNumber0(xk) = 0 % 65.22/9.59 (2) doDivides0(xr, xk) = 0 % 65.22/9.59 (3) aNaturalNumber0(xr) = 0 % 65.22/9.59 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 65.22/9.59 (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) % 65.22/9.59 (5) ? [v0: any] : ? [v1: any] : ? [v2: any] : (doDivides0(xr, xk) = v2 & % 65.22/9.59 aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v2 = 0) | ~ % 65.22/9.59 (v1 = 0) | ~ (v0 = 0))) % 65.22/9.59 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 65.22/9.59 ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, % 65.22/9.59 v2) = v0)) % 65.22/9.59 % 65.22/9.59 Begin of proof % 65.22/9.59 | % 65.22/9.59 | DELTA: instantiating (5) with fresh symbols all_373_0, all_373_1, all_373_2 % 65.22/9.59 | gives: % 65.22/9.59 | (7) doDivides0(xr, xk) = all_373_0 & aNaturalNumber0(xr) = all_373_2 & % 65.22/9.59 | aNaturalNumber0(xk) = all_373_1 & ( ~ (all_373_0 = 0) | ~ (all_373_1 = % 65.22/9.59 | 0) | ~ (all_373_2 = 0)) % 65.22/9.59 | % 65.22/9.59 | ALPHA: (7) implies: % 65.22/9.59 | (8) aNaturalNumber0(xk) = all_373_1 % 65.22/9.59 | (9) aNaturalNumber0(xr) = all_373_2 % 65.22/9.59 | (10) doDivides0(xr, xk) = all_373_0 % 65.22/9.59 | (11) ~ (all_373_0 = 0) | ~ (all_373_1 = 0) | ~ (all_373_2 = 0) % 65.22/9.59 | % 65.22/9.59 | GROUND_INST: instantiating (4) with 0, all_373_1, xk, simplifying with (1), % 65.22/9.59 | (8) gives: % 65.22/9.59 | (12) all_373_1 = 0 % 65.22/9.59 | % 65.22/9.59 | GROUND_INST: instantiating (4) with 0, all_373_2, xr, simplifying with (3), % 65.22/9.59 | (9) gives: % 65.22/9.59 | (13) all_373_2 = 0 % 65.22/9.59 | % 65.22/9.59 | GROUND_INST: instantiating (6) with 0, all_373_0, xk, xr, simplifying with % 65.22/9.59 | (2), (10) gives: % 65.22/9.59 | (14) all_373_0 = 0 % 65.22/9.59 | % 65.22/9.59 | BETA: splitting (11) gives: % 65.22/9.59 | % 65.22/9.59 | Case 1: % 65.22/9.59 | | % 65.22/9.59 | | (15) ~ (all_373_0 = 0) % 65.22/9.59 | | % 65.22/9.59 | | REDUCE: (14), (15) imply: % 65.22/9.59 | | (16) $false % 65.22/9.59 | | % 65.22/9.59 | | CLOSE: (16) is inconsistent. % 65.22/9.59 | | % 65.22/9.59 | Case 2: % 65.22/9.59 | | % 65.22/9.59 | | (17) ~ (all_373_1 = 0) | ~ (all_373_2 = 0) % 65.22/9.59 | | % 65.22/9.59 | | BETA: splitting (17) gives: % 65.22/9.59 | | % 65.22/9.59 | | Case 1: % 65.22/9.59 | | | % 65.22/9.59 | | | (18) ~ (all_373_1 = 0) % 65.22/9.59 | | | % 65.22/9.59 | | | REDUCE: (12), (18) imply: % 65.22/9.59 | | | (19) $false % 65.22/9.59 | | | % 65.22/9.59 | | | CLOSE: (19) is inconsistent. % 65.22/9.59 | | | % 65.22/9.59 | | Case 2: % 65.22/9.59 | | | % 65.22/9.59 | | | (20) ~ (all_373_2 = 0) % 65.22/9.59 | | | % 65.22/9.59 | | | REDUCE: (13), (20) imply: % 65.22/9.59 | | | (21) $false % 65.22/9.59 | | | % 65.22/9.59 | | | CLOSE: (21) is inconsistent. % 65.22/9.59 | | | % 65.22/9.59 | | End of split % 65.22/9.59 | | % 65.22/9.59 | End of split % 65.22/9.59 | % 65.22/9.59 End of proof % 65.22/9.59 % SZS output end Proof for theBenchmark % 65.22/9.59 % 65.22/9.59 9002ms %------------------------------------------------------------------------------