%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM482+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 11:48:04 EDT 2023 % Result : Theorem 15.26s 2.76s % Output : Proof 37.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM482+3 : TPTP v8.1.2. Released v4.0.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.33 % Computer : n007.cluster.edu % 0.14/0.33 % Model : x86_64 x86_64 % 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.33 % Memory : 8042.1875MB % 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Aug 25 07:51:25 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.60/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.60/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.60/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.60/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.60/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.60/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.60/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.65/1.21 Prover 1: Preprocessing ... % 3.65/1.21 Prover 4: Preprocessing ... % 4.11/1.27 Prover 6: Preprocessing ... % 4.11/1.27 Prover 0: Preprocessing ... % 4.11/1.27 Prover 3: Preprocessing ... % 4.11/1.27 Prover 5: Preprocessing ... % 4.11/1.27 Prover 2: Preprocessing ... % 8.64/1.93 Prover 1: Constructing countermodel ... % 9.15/1.95 Prover 3: Constructing countermodel ... % 9.66/2.01 Prover 6: Proving ... % 9.66/2.02 Prover 5: Constructing countermodel ... % 9.93/2.07 Prover 3: gave up % 9.93/2.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.58/2.13 Prover 1: gave up % 10.58/2.14 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 10.58/2.15 Prover 2: Proving ... % 10.91/2.22 Prover 8: Preprocessing ... % 11.44/2.25 Prover 7: Preprocessing ... % 11.95/2.32 Prover 4: Constructing countermodel ... % 11.95/2.39 Prover 8: Warning: ignoring some quantifiers % 11.95/2.40 Prover 8: Constructing countermodel ... % 12.69/2.51 Prover 7: Constructing countermodel ... % 13.84/2.57 Prover 0: Proving ... % 14.68/2.69 Prover 8: gave up % 14.68/2.69 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.26/2.76 Prover 9: Preprocessing ... % 15.26/2.76 Prover 5: proved (2146ms) % 15.26/2.76 % 15.26/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.26/2.76 % 15.26/2.76 Prover 0: stopped % 15.26/2.76 Prover 6: stopped % 15.26/2.77 Prover 2: stopped % 15.26/2.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 15.26/2.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 15.26/2.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 15.26/2.79 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 16.19/2.87 Prover 16: Preprocessing ... % 16.19/2.87 Prover 10: Preprocessing ... % 16.19/2.87 Prover 13: Preprocessing ... % 16.19/2.89 Prover 11: Preprocessing ... % 17.00/3.00 Prover 10: Constructing countermodel ... % 17.00/3.00 Prover 16: Constructing countermodel ... % 17.00/3.05 Prover 13: Constructing countermodel ... % 20.45/3.47 Prover 9: Constructing countermodel ... % 20.45/3.47 Prover 9: stopped % 20.45/3.48 Prover 11: Constructing countermodel ... % 20.45/3.48 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 21.24/3.57 Prover 19: Preprocessing ... % 22.36/3.76 Prover 19: Warning: ignoring some quantifiers % 23.15/3.77 Prover 19: Constructing countermodel ... % 36.19/5.51 Prover 4: Found proof (size 173) % 36.19/5.51 Prover 4: proved (4896ms) % 36.19/5.51 Prover 7: stopped % 36.19/5.51 Prover 19: stopped % 36.19/5.51 Prover 13: stopped % 36.19/5.51 Prover 16: stopped % 36.19/5.51 Prover 10: stopped % 36.19/5.52 Prover 11: stopped % 36.19/5.52 % 36.19/5.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 36.19/5.52 % 36.66/5.53 % SZS output start Proof for theBenchmark % 36.66/5.53 Assumptions after simplification: % 36.66/5.53 --------------------------------- % 36.66/5.53 % 36.66/5.53 (mAddCanc) % 36.83/5.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 % 36.83/5.58 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ $i(v2) | ~ % 36.83/5.58 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: % 36.83/5.58 $i] : ? [v9: $i] : (sdtpldt0(v0, v2) = v9 & sdtpldt0(v0, v1) = v8 & % 36.83/5.58 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) % 36.83/5.58 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ % 36.83/5.58 (v9 = v8) & ~ (v4 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 36.83/5.58 : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ % 36.83/5.58 (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : % 36.83/5.58 ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (sdtpldt0(v1, v0) % 36.83/5.58 = v9 & sdtpldt0(v0, v2) = v8 & aNaturalNumber0(v2) = v7 & % 36.83/5.58 aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & $i(v8) & ( % 36.83/5.58 ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v4) & ~ (v8 = % 36.83/5.58 v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 36.83/5.58 [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) % 36.83/5.58 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: % 36.83/5.58 any] : ? [v8: $i] : ? [v9: $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v0, % 36.83/5.58 v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & % 36.83/5.58 aNaturalNumber0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | % 36.83/5.58 ~ (v5 = 0) | ( ~ (v9 = v4) & ~ (v8 = v3))))) & ! [v0: $i] : ! [v1: % 36.83/5.58 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v0, % 36.83/5.58 v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 36.83/5.58 $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: % 36.83/5.58 $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2) % 36.83/5.58 = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & % 36.83/5.58 $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4 % 36.83/5.58 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 36.83/5.58 (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ % 36.83/5.58 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : % 36.83/5.58 ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v1, v0) = v8 & sdtpldt0(v0, v2) = v7 & % 36.83/5.58 sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v2) = v5 & aNaturalNumber0(v0) = % 36.83/5.58 v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ( ~ (v8 = v3) % 36.83/5.58 & ~ (v7 = v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 36.83/5.58 $i] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | % 36.83/5.58 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: % 36.83/5.58 $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0) = v8 & sdtpldt0(v0, % 36.83/5.58 v2) = v7 & sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 & % 36.83/5.58 aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ % 36.83/5.58 (v4 = 0) | ( ~ (v8 = v3) & ~ (v7 = v6))))) & ! [v0: $i] : ! [v1: $i] % 36.83/5.58 : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ % 36.83/5.58 (aNaturalNumber0(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 36.83/5.58 : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0) % 36.83/5.58 = v8 & sdtpldt0(v1, v0) = v7 & sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v2) % 36.83/5.58 = v5 & aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) % 36.83/5.58 | ~ (v4 = 0) | ( ~ (v8 = v7) & ~ (v6 = v3))))) & ! [v0: $i] : ! [v1: % 36.83/5.58 $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (sdtpldt0(v0, v1) = v3) | ~ % 36.83/5.58 (aNaturalNumber0(v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] % 36.83/5.58 : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0) % 36.83/5.58 = v8 & sdtpldt0(v1, v0) = v7 & sdtpldt0(v0, v2) = v6 & aNaturalNumber0(v1) % 36.83/5.58 = v5 & aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) % 36.83/5.58 | ~ (v4 = 0) | ( ~ (v8 = v7) & ~ (v6 = v3))))) & ! [v0: $i] : ! [v1: % 36.83/5.58 $i] : ! [v2: $i] : (v2 = v1 | ~ (aNaturalNumber0(v2) = 0) | ~ % 36.83/5.58 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ % 36.83/5.58 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 36.83/5.58 ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 % 36.83/5.58 & sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4) % 36.83/5.58 & $i(v3))) % 36.83/5.58 % 36.83/5.58 (mDefPrime) % 36.83/5.59 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 36.83/5.59 (isPrime0(v0) = 0) | ~ (doDivides0(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | % 36.83/5.59 ? [v2: int] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & % 36.83/5.59 aNaturalNumber0(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 % 36.83/5.59 = sz10 | ~ (isPrime0(v0) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ $i(v1) | % 36.83/5.59 ~ $i(v0) | ? [v2: int] : (( ~ (v2 = 0) & doDivides0(v1, v0) = v2) | ( ~ (v2 % 36.83/5.59 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0: $i] : ! [v1: int] : (v1 % 36.83/5.59 = 0 | v0 = sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ~ $i(v0) | ? [v2: % 36.83/5.59 int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v5 = 0 & v4 % 36.83/5.59 = 0 & ~ (v3 = v0) & ~ (v3 = sz10) & doDivides0(v3, v0) = 0 & % 36.83/5.59 aNaturalNumber0(v3) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))) % 36.83/5.59 & ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 36.83/5.59 [v2: $i] : ? [v3: int] : ? [v4: int] : (isPrime0(v0) = v1 & $i(v2) & ( ~ % 36.83/5.59 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v5: $i] : (v5 = v0 | % 36.83/5.59 v5 = sz10 | ~ (doDivides0(v5, v0) = 0) | ~ $i(v5) | ? [v6: int] : % 36.83/5.59 ( ~ (v6 = 0) & aNaturalNumber0(v5) = v6)) & ! [v5: $i] : (v5 = v0 | % 36.83/5.59 v5 = sz10 | ~ (aNaturalNumber0(v5) = 0) | ~ $i(v5) | ? [v6: int] % 36.83/5.59 : ( ~ (v6 = 0) & doDivides0(v5, v0) = v6)))) & (v1 = 0 | v0 = sz10 | % 36.83/5.59 v0 = sz00 | (v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = sz10) & % 36.83/5.59 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0)))) & ( ~ % 36.83/5.59 (isPrime0(sz10) = 0) | ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(sz10) = % 36.83/5.59 v0)) & ( ~ (isPrime0(sz00) = 0) | ? [v0: int] : ( ~ (v0 = 0) & % 36.83/5.59 aNaturalNumber0(sz00) = v0)) % 36.83/5.59 % 36.83/5.59 (mMulCanc) % 36.83/5.60 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 36.83/5.60 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = % 36.83/5.60 v3) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 36.83/5.60 ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v0, v2) = % 36.83/5.60 v8 & sdtasdt0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & % 36.83/5.60 aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | % 36.83/5.60 ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 36.83/5.60 $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, % 36.83/5.60 v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | % 36.83/5.60 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] % 36.83/5.60 : ? [v8: $i] : (sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v7 & % 36.83/5.60 aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( % 36.83/5.60 ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v4) & ~ (v7 = v3))))) & ! [v0: % 36.83/5.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 % 36.83/5.60 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 36.83/5.60 (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] % 36.83/5.60 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v2, v0) = v8 & % 36.83/5.60 sdtasdt0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = % 36.83/5.60 v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v4) & ~ (v7 % 36.83/5.60 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 36.83/5.60 ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ % 36.83/5.60 (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ % 36.83/5.60 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] % 36.83/5.60 : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6 % 36.83/5.60 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) % 36.83/5.60 | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 36.83/5.60 $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ % 36.83/5.60 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ % 36.83/5.60 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 36.83/5.60 : (sdtasdt0(v1, v0) = v7 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & % 36.83/5.60 aNaturalNumber0(v2) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~ % 36.83/5.60 (v7 = v3) & ~ (v6 = v5))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 36.83/5.60 : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v3) | ~ % 36.83/5.60 (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ % 36.83/5.60 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 36.83/5.60 : (sdtasdt0(v2, v0) = v7 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & % 36.83/5.60 aNaturalNumber0(v1) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~ % 36.83/5.60 (v7 = v3) & ~ (v6 = v5))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 36.83/5.60 : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ % 36.83/5.60 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ % 36.83/5.60 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 36.83/5.60 : (sdtasdt0(v2, v0) = v7 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v1) = v5 & % 36.83/5.60 aNaturalNumber0(v2) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~ % 36.83/5.60 (v7 = v6) & ~ (v5 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 36.83/5.60 : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = v3) | ~ % 36.83/5.60 (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ % 36.83/5.60 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 36.83/5.60 : (sdtasdt0(v2, v0) = v7 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & % 36.83/5.60 aNaturalNumber0(v1) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~ % 36.83/5.60 (v7 = v6) & ~ (v5 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 36.83/5.60 : (v2 = v1 | v0 = sz00 | ~ (aNaturalNumber0(v2) = 0) | ~ % 36.83/5.60 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ % 36.83/5.60 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 36.83/5.60 ( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 % 36.83/5.60 & sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4) % 36.83/5.60 & $i(v3))) % 36.83/5.60 % 36.83/5.60 (mSortsC) % 36.83/5.60 aNaturalNumber0(sz00) = 0 & $i(sz00) % 36.83/5.60 % 36.83/5.60 (mSortsC_01) % 36.83/5.60 ~ (sz10 = sz00) & aNaturalNumber0(sz10) = 0 & $i(sz10) & $i(sz00) % 36.83/5.60 % 36.83/5.60 (m_AddZero) % 36.83/5.60 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ % 36.83/5.60 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtpldt0(sz00, v0) = v3 & % 36.83/5.60 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) % 36.83/5.60 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ? % 36.83/5.60 [v2: any] : ? [v3: $i] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) = % 36.83/5.60 v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~ % 36.83/5.60 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtpldt0(v0, sz00) = v0 & % 36.83/5.60 sdtpldt0(sz00, v0) = v0)) % 36.83/5.60 % 36.83/5.60 (m_MulUnit) % 36.83/5.60 $i(sz10) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ % 36.83/5.60 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz10, v0) = v3 & % 36.83/5.60 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) % 36.83/5.60 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ? % 36.83/5.60 [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) = % 36.83/5.60 v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~ % 36.83/5.60 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz10) = v0 & % 36.83/5.60 sdtasdt0(sz10, v0) = v0)) % 36.83/5.60 % 36.83/5.61 (m__) % 36.83/5.62 isPrime0(xk) = 0 & $i(xk) & $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: % 36.83/5.62 MultipleValueBool] : ! [v2: $i] : (v0 = xk | v0 = sz10 | ~ (doDivides0(v0, % 36.83/5.62 xk) = v1) | ~ (sdtasdt0(v0, v2) = xk) | ~ $i(v2) | ~ $i(v0) | ? [v3: % 36.83/5.62 int] : (( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & % 36.83/5.62 aNaturalNumber0(v0) = v3))) & ! [v0: $i] : ! [v1: MultipleValueBool] : % 36.83/5.62 ! [v2: $i] : (v0 = xk | v0 = sz10 | ~ (doDivides0(v0, xk) = v1) | ~ % 36.83/5.62 (aNaturalNumber0(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : (( ~ (v3 % 36.83/5.62 = xk) & sdtasdt0(v0, v2) = v3 & $i(v3)) | ( ~ (v3 = 0) & % 36.83/5.62 aNaturalNumber0(v0) = v3))) & ! [v0: $i] : ! [v1: MultipleValueBool] : % 36.83/5.62 ! [v2: $i] : ( ~ (doDivides0(v0, xk) = v1) | ~ (sdtasdt0(v0, v2) = xk) | ~ % 36.83/5.62 $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: % 36.83/5.62 int] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: % 36.83/5.62 int] : ($i(v8) & $i(v5) & (( ~ (v11 = 0) & aNaturalNumber0(v2) = v11) | % 36.83/5.62 (isPrime0(v0) = v4 & aNaturalNumber0(v0) = v3 & ( ~ (v3 = 0) | ( ~ (v4 = % 36.83/5.62 0) & (v0 = sz10 | v0 = sz00 | (v10 = v0 & v9 = 0 & v7 = 0 & v6 = % 36.83/5.62 0 & ~ (v5 = v0) & ~ (v5 = sz10) & doDivides0(v5, v0) = 0 & % 36.83/5.62 sdtasdt0(v5, v8) = v0 & aNaturalNumber0(v8) = 0 & % 36.83/5.62 aNaturalNumber0(v5) = 0)))))))) & ! [v0: $i] : ! [v1: % 36.83/5.62 MultipleValueBool] : ! [v2: $i] : ( ~ (doDivides0(v0, xk) = v1) | ~ % 36.83/5.62 (aNaturalNumber0(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: % 36.83/5.62 any] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8: $i] : ? [v9: % 36.83/5.62 int] : ? [v10: $i] : ? [v11: $i] : ($i(v8) & $i(v5) & (( ~ (v11 = xk) & % 36.83/5.62 sdtasdt0(v0, v2) = v11 & $i(v11)) | (isPrime0(v0) = v4 & % 36.83/5.62 aNaturalNumber0(v0) = v3 & ( ~ (v3 = 0) | ( ~ (v4 = 0) & (v0 = sz10 | % 36.83/5.62 v0 = sz00 | (v10 = v0 & v9 = 0 & v7 = 0 & v6 = 0 & ~ (v5 = v0) % 36.83/5.62 & ~ (v5 = sz10) & doDivides0(v5, v0) = 0 & sdtasdt0(v5, v8) = % 36.83/5.62 v0 & aNaturalNumber0(v8) = 0 & aNaturalNumber0(v5) = 0)))))))) % 36.83/5.62 & ! [v0: $i] : ! [v1: $i] : (v0 = xk | v0 = sz10 | ~ (sdtasdt0(v0, v1) = % 36.83/5.62 xk) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] % 36.83/5.62 : ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2)) & ! [v0: $i] : ! [v1: $i] : % 36.83/5.62 (v0 = xk | v0 = sz10 | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) % 36.83/5.62 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ( ~ (v2 = xk) & sdtasdt0(v0, % 36.83/5.62 v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: MultipleValueBool] : (v0 = % 36.83/5.62 sz10 | v0 = sz00 | ~ (isPrime0(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 36.83/5.62 [v3: any] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ? [v7: $i] : ? % 36.83/5.62 [v8: int] : ? [v9: $i] : ($i(v7) & $i(v4) & ((v9 = v0 & v8 = 0 & v6 = 0 & % 36.83/5.62 v5 = 0 & ~ (v4 = v0) & ~ (v4 = sz10) & doDivides0(v4, v0) = 0 & % 36.83/5.62 sdtasdt0(v4, v7) = v0 & aNaturalNumber0(v7) = 0 & aNaturalNumber0(v4) % 36.83/5.62 = 0) | (doDivides0(v0, xk) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v2 = % 36.83/5.62 0) | ( ~ (v3 = 0) & ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xk) | % 36.83/5.62 ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & aNaturalNumber0(v10) % 36.83/5.62 = v11)) & ! [v10: $i] : ( ~ (aNaturalNumber0(v10) = 0) | ~ % 36.83/5.62 $i(v10) | ? [v11: $i] : ( ~ (v11 = xk) & sdtasdt0(v0, v10) = % 36.83/5.62 v11 & $i(v11))))))))) & ! [v0: $i] : (v0 = xk | v0 = sz10 | % 36.83/5.62 ~ (doDivides0(v0, xk) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 36.83/5.62 aNaturalNumber0(v0) = v1)) & ! [v0: $i] : (v0 = xk | v0 = sz10 | ~ % 36.83/5.62 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & % 36.83/5.62 doDivides0(v0, xk) = v1)) & ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ % 36.83/5.62 $i(v0) | ? [v1: any] : ? [v2: any] : (doDivides0(v0, xk) = v2 & % 36.83/5.62 aNaturalNumber0(v0) = v1 & ( ~ (v1 = 0) | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ % 36.83/5.62 (sdtasdt0(v0, v3) = xk) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 36.83/5.62 aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 36.83/5.62 (aNaturalNumber0(v3) = 0) | ~ $i(v3) | ? [v4: $i] : ( ~ (v4 = xk) % 36.83/5.62 & sdtasdt0(v0, v3) = v4 & $i(v4))))))) & ! [v0: $i] : ( ~ % 36.83/5.62 (doDivides0(v0, xk) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: % 36.83/5.62 $i] : ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: int] : ? [v8: % 36.83/5.62 $i] : (isPrime0(v0) = v2 & aNaturalNumber0(v0) = v1 & $i(v6) & $i(v3) & ( % 36.83/5.62 ~ (v1 = 0) | ( ~ (v2 = 0) & (v0 = sz10 | v0 = sz00 | (v8 = v0 & v7 = 0 & % 36.83/5.62 v5 = 0 & v4 = 0 & ~ (v3 = v0) & ~ (v3 = sz10) & doDivides0(v3, % 36.83/5.62 v0) = 0 & sdtasdt0(v3, v6) = v0 & aNaturalNumber0(v6) = 0 & % 36.83/5.62 aNaturalNumber0(v3) = 0)))))) & ! [v0: $i] : ( ~ % 36.83/5.62 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? % 36.83/5.62 [v3: $i] : ? [v4: int] : ? [v5: int] : ? [v6: $i] : ? [v7: int] : ? % 36.83/5.62 [v8: $i] : (isPrime0(v0) = v2 & doDivides0(v0, xk) = v1 & $i(v6) & $i(v3) & % 36.83/5.62 (( ~ (v2 = 0) & (v0 = sz10 | v0 = sz00 | (v8 = v0 & v7 = 0 & v5 = 0 & v4 = % 36.83/5.62 0 & ~ (v3 = v0) & ~ (v3 = sz10) & doDivides0(v3, v0) = 0 & % 36.83/5.62 sdtasdt0(v3, v6) = v0 & aNaturalNumber0(v6) = 0 & % 36.83/5.62 aNaturalNumber0(v3) = 0))) | ( ~ (v1 = 0) & ! [v9: $i] : ( ~ % 36.83/5.62 (sdtasdt0(v0, v9) = xk) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) % 36.83/5.62 & aNaturalNumber0(v9) = v10)) & ! [v9: $i] : ( ~ % 36.83/5.62 (aNaturalNumber0(v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 = % 36.83/5.62 xk) & sdtasdt0(v0, v9) = v10 & $i(v10))))))) % 36.83/5.62 % 36.83/5.62 (m__1716) % 36.83/5.62 aNaturalNumber0(xk) = 0 & $i(xk) % 36.83/5.62 % 36.83/5.62 (m__1716_04) % 36.83/5.62 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00) % 36.83/5.62 % 36.83/5.62 (function-axioms) % 36.83/5.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.83/5.62 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: % 36.83/5.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 36.83/5.62 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & ! % 36.83/5.62 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 36.83/5.62 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! % 36.83/5.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.83/5.62 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: % 36.83/5.62 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 36.83/5.62 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! % 36.83/5.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 36.83/5.62 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 36.83/5.62 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | % 36.83/5.62 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.83/5.62 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ % 36.83/5.62 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 36.83/5.62 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) % 36.83/5.62 | ~ (aNaturalNumber0(v2) = v0)) % 36.83/5.62 % 36.83/5.62 Further assumptions not needed in the proof: % 36.83/5.62 -------------------------------------------- % 36.83/5.62 mAMDistr, mAddAsso, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefQuot, mDivAsso, % 36.83/5.62 mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, % 36.83/5.62 mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulComm, mNatSort, % 36.83/5.62 mSortsB, mSortsB_02, mZeroAdd, mZeroMul, m_MulZero, m__1700 % 36.83/5.62 % 36.83/5.62 Those formulas are unsatisfiable: % 36.83/5.62 --------------------------------- % 36.83/5.62 % 36.83/5.62 Begin of proof % 36.83/5.62 | % 36.83/5.62 | ALPHA: (mSortsC) implies: % 36.83/5.62 | (1) aNaturalNumber0(sz00) = 0 % 36.83/5.62 | % 36.83/5.62 | ALPHA: (mSortsC_01) implies: % 36.83/5.62 | (2) ~ (sz10 = sz00) % 36.83/5.63 | (3) aNaturalNumber0(sz10) = 0 % 36.83/5.63 | % 36.83/5.63 | ALPHA: (m_AddZero) implies: % 36.83/5.63 | (4) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtpldt0(v0, % 36.83/5.63 | sz00) = v0 & sdtpldt0(sz00, v0) = v0)) % 36.83/5.63 | % 36.83/5.63 | ALPHA: (m_MulUnit) implies: % 36.83/5.63 | (5) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, % 36.83/5.63 | sz10) = v0 & sdtasdt0(sz10, v0) = v0)) % 36.83/5.63 | % 36.83/5.63 | ALPHA: (mAddCanc) implies: % 36.83/5.63 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ % 36.83/5.63 | (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ % 36.83/5.63 | (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 36.83/5.63 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 36.83/5.63 | ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & % 36.83/5.63 | sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3 & $i(v6) & $i(v5) & % 36.83/5.63 | $i(v4) & $i(v3))) % 36.83/5.63 | % 36.83/5.63 | ALPHA: (mMulCanc) implies: % 36.83/5.63 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v0 = sz00 | ~ % 36.83/5.63 | (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ % 36.83/5.63 | (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 36.83/5.63 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 36.83/5.63 | ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & % 36.83/5.63 | sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3 & $i(v6) & $i(v5) & % 36.83/5.63 | $i(v4) & $i(v3))) % 36.83/5.63 | % 36.83/5.63 | ALPHA: (mDefPrime) implies: % 36.83/5.63 | (8) ~ (isPrime0(sz10) = 0) | ? [v0: int] : ( ~ (v0 = 0) & % 36.83/5.63 | aNaturalNumber0(sz10) = v0) % 36.83/5.63 | (9) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: any] % 36.83/5.63 | : ? [v2: $i] : ? [v3: int] : ? [v4: int] : (isPrime0(v0) = v1 & % 36.83/5.63 | $i(v2) & ( ~ (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v5: % 36.83/5.63 | $i] : (v5 = v0 | v5 = sz10 | ~ (doDivides0(v5, v0) = 0) | ~ % 36.83/5.63 | $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & aNaturalNumber0(v5) = % 36.83/5.63 | v6)) & ! [v5: $i] : (v5 = v0 | v5 = sz10 | ~ % 36.83/5.63 | (aNaturalNumber0(v5) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ % 36.83/5.63 | (v6 = 0) & doDivides0(v5, v0) = v6)))) & (v1 = 0 | v0 = % 36.83/5.63 | sz10 | v0 = sz00 | (v4 = 0 & v3 = 0 & ~ (v2 = v0) & ~ (v2 = % 36.83/5.63 | sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0)))) % 36.83/5.63 | % 36.83/5.63 | ALPHA: (m__1716) implies: % 36.83/5.63 | (10) aNaturalNumber0(xk) = 0 % 36.83/5.63 | % 36.83/5.63 | ALPHA: (m__1716_04) implies: % 36.83/5.63 | (11) ~ (xk = sz00) % 36.83/5.63 | (12) ~ (xk = sz10) % 36.83/5.63 | % 36.83/5.63 | ALPHA: (m__) implies: % 36.83/5.63 | (13) $i(sz00) % 36.83/5.63 | (14) $i(sz10) % 36.83/5.63 | (15) $i(xk) % 36.83/5.63 | (16) isPrime0(xk) = 0 % 37.18/5.63 | (17) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: any] % 37.18/5.63 | : ? [v2: any] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : ? [v6: % 37.18/5.63 | $i] : ? [v7: int] : ? [v8: $i] : (isPrime0(v0) = v2 & % 37.18/5.63 | doDivides0(v0, xk) = v1 & $i(v6) & $i(v3) & (( ~ (v2 = 0) & (v0 = % 37.18/5.63 | sz10 | v0 = sz00 | (v8 = v0 & v7 = 0 & v5 = 0 & v4 = 0 & ~ % 37.18/5.63 | (v3 = v0) & ~ (v3 = sz10) & doDivides0(v3, v0) = 0 & % 37.18/5.63 | sdtasdt0(v3, v6) = v0 & aNaturalNumber0(v6) = 0 & % 37.18/5.63 | aNaturalNumber0(v3) = 0))) | ( ~ (v1 = 0) & ! [v9: $i] : % 37.18/5.63 | ( ~ (sdtasdt0(v0, v9) = xk) | ~ $i(v9) | ? [v10: int] : ( ~ % 37.18/5.63 | (v10 = 0) & aNaturalNumber0(v9) = v10)) & ! [v9: $i] : ( % 37.18/5.63 | ~ (aNaturalNumber0(v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ % 37.18/5.63 | (v10 = xk) & sdtasdt0(v0, v9) = v10 & $i(v10))))))) % 37.18/5.64 | (18) ! [v0: $i] : ( ~ (isPrime0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? % 37.18/5.64 | [v2: any] : (doDivides0(v0, xk) = v2 & aNaturalNumber0(v0) = v1 & ( % 37.18/5.64 | ~ (v1 = 0) | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) % 37.18/5.64 | = xk) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & % 37.18/5.64 | aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~ % 37.18/5.64 | (aNaturalNumber0(v3) = 0) | ~ $i(v3) | ? [v4: $i] : ( ~ % 37.18/5.64 | (v4 = xk) & sdtasdt0(v0, v3) = v4 & $i(v4))))))) % 37.18/5.64 | % 37.18/5.64 | ALPHA: (function-axioms) implies: % 37.18/5.64 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 37.18/5.64 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = % 37.18/5.64 | v0)) % 37.18/5.64 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 37.18/5.64 | : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0)) % 37.18/5.64 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 37.18/5.64 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 37.18/5.64 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 37.18/5.64 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 37.18/5.64 | % 37.18/5.64 | BETA: splitting (8) gives: % 37.18/5.64 | % 37.18/5.64 | Case 1: % 37.18/5.64 | | % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (6) with sz10, sz00, sz10, simplifying with (1), % 37.18/5.64 | | (3), (13), (14) gives: % 37.18/5.64 | | (23) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 37.18/5.64 | | : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v3 & % 37.18/5.64 | | sdtpldt0(sz10, sz10) = v1 & sdtpldt0(sz10, sz00) = v0 & % 37.18/5.64 | | sdtpldt0(sz00, sz10) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (6) with sz10, sz10, sz00, simplifying with (1), % 37.18/5.64 | | (3), (13), (14) gives: % 37.18/5.64 | | (24) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 37.18/5.64 | | : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v2 & % 37.18/5.64 | | sdtpldt0(sz10, sz10) = v0 & sdtpldt0(sz10, sz00) = v1 & % 37.18/5.64 | | sdtpldt0(sz00, sz10) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (6) with sz00, sz00, sz10, simplifying with (1), % 37.18/5.64 | | (3), (13), (14) gives: % 37.18/5.64 | | (25) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 37.18/5.64 | | : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v3 & % 37.18/5.64 | | sdtpldt0(sz00, sz10) = v1 & sdtpldt0(sz00, sz00) = v2 & % 37.18/5.64 | | sdtpldt0(sz00, sz00) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (6) with sz00, sz10, sz00, simplifying with (1), % 37.18/5.64 | | (3), (13), (14) gives: % 37.18/5.64 | | (26) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 37.18/5.64 | | : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) = v2 & % 37.18/5.64 | | sdtpldt0(sz00, sz10) = v0 & sdtpldt0(sz00, sz00) = v3 & % 37.18/5.64 | | sdtpldt0(sz00, sz00) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (4) with sz10, simplifying with (3), (14) gives: % 37.18/5.64 | | (27) sdtpldt0(sz10, sz00) = sz10 & sdtpldt0(sz00, sz10) = sz10 % 37.18/5.64 | | % 37.18/5.64 | | ALPHA: (27) implies: % 37.18/5.64 | | (28) sdtpldt0(sz10, sz00) = sz10 % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (7) with xk, sz10, xk, simplifying with (3), % 37.18/5.64 | | (10), (14), (15) gives: % 37.18/5.64 | | (29) xk = sz10 | xk = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 37.18/5.64 | | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v3 & % 37.18/5.64 | | sdtasdt0(xk, xk) = v1 & sdtasdt0(xk, sz10) = v0 & sdtasdt0(sz10, % 37.18/5.64 | | xk) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (7) with xk, xk, sz10, simplifying with (3), % 37.18/5.64 | | (10), (14), (15) gives: % 37.18/5.64 | | (30) xk = sz10 | xk = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 37.18/5.64 | | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v2 & % 37.18/5.64 | | sdtasdt0(xk, xk) = v0 & sdtasdt0(xk, sz10) = v1 & sdtasdt0(sz10, % 37.18/5.64 | | xk) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.64 | | % 37.18/5.64 | | GROUND_INST: instantiating (7) with sz10, sz10, xk, simplifying with (3), % 37.18/5.65 | | (10), (14), (15) gives: % 37.18/5.65 | | (31) xk = sz10 | sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 37.18/5.65 | | ? [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v3 % 37.18/5.65 | | & sdtasdt0(sz10, xk) = v1 & sdtasdt0(sz10, sz10) = v2 & % 37.18/5.65 | | sdtasdt0(sz10, sz10) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (7) with sz10, xk, sz10, simplifying with (3), % 37.18/5.65 | | (10), (14), (15) gives: % 37.18/5.65 | | (32) xk = sz10 | sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 37.18/5.65 | | ? [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v2 % 37.18/5.65 | | & sdtasdt0(sz10, xk) = v0 & sdtasdt0(sz10, sz10) = v3 & % 37.18/5.65 | | sdtasdt0(sz10, sz10) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (7) with xk, sz10, sz00, simplifying with (1), % 37.18/5.65 | | (3), (10), (13), (14), (15) gives: % 37.18/5.65 | | (33) xk = sz00 | sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 37.18/5.65 | | ? [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, sz10) = v0 % 37.18/5.65 | | & sdtasdt0(xk, sz00) = v1 & sdtasdt0(sz10, xk) = v2 & % 37.18/5.65 | | sdtasdt0(sz00, xk) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (6) with sz10, sz00, xk, simplifying with (1), % 37.18/5.65 | | (3), (10), (13), (14), (15) gives: % 37.18/5.65 | | (34) xk = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 37.18/5.65 | | ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v3 & % 37.18/5.65 | | sdtpldt0(sz10, xk) = v1 & sdtpldt0(sz10, sz00) = v0 & % 37.18/5.65 | | sdtpldt0(sz00, sz10) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (6) with sz10, xk, sz00, simplifying with (1), % 37.18/5.65 | | (3), (10), (13), (14), (15) gives: % 37.18/5.65 | | (35) xk = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 37.18/5.65 | | ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v2 & % 37.18/5.65 | | sdtpldt0(sz10, xk) = v0 & sdtpldt0(sz10, sz00) = v1 & % 37.18/5.65 | | sdtpldt0(sz00, sz10) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (17) with xk, simplifying with (10), (15) gives: % 37.18/5.65 | | (36) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4: % 37.18/5.65 | | int] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : (isPrime0(xk) = % 37.18/5.65 | | v1 & doDivides0(xk, xk) = v0 & $i(v5) & $i(v2) & (( ~ (v1 = 0) & % 37.18/5.65 | | (xk = sz10 | xk = sz00 | (v7 = xk & v6 = 0 & v4 = 0 & v3 = 0 & % 37.18/5.65 | | ~ (v2 = xk) & ~ (v2 = sz10) & doDivides0(v2, xk) = 0 & % 37.18/5.65 | | sdtasdt0(v2, v5) = xk & aNaturalNumber0(v5) = 0 & % 37.18/5.65 | | aNaturalNumber0(v2) = 0))) | ( ~ (v0 = 0) & ! [v8: $i] : % 37.18/5.65 | | ( ~ (sdtasdt0(xk, v8) = xk) | ~ $i(v8) | ? [v9: int] : ( ~ % 37.18/5.65 | | (v9 = 0) & aNaturalNumber0(v8) = v9)) & ! [v8: $i] : ( ~ % 37.18/5.65 | | (aNaturalNumber0(v8) = 0) | ~ $i(v8) | ? [v9: $i] : ( ~ % 37.18/5.65 | | (v9 = xk) & sdtasdt0(xk, v8) = v9 & $i(v9)))))) % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (9) with xk, simplifying with (10), (15) gives: % 37.18/5.65 | | (37) ? [v0: any] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : % 37.18/5.65 | | (isPrime0(xk) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ~ (xk = sz10) & ~ % 37.18/5.65 | | (xk = sz00) & ! [v4: $i] : (v4 = xk | v4 = sz10 | ~ % 37.18/5.65 | | (doDivides0(v4, xk) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ % 37.18/5.65 | | (v5 = 0) & aNaturalNumber0(v4) = v5)) & ! [v4: $i] : (v4 % 37.18/5.65 | | = xk | v4 = sz10 | ~ (aNaturalNumber0(v4) = 0) | ~ $i(v4) % 37.18/5.65 | | | ? [v5: int] : ( ~ (v5 = 0) & doDivides0(v4, xk) = v5)))) % 37.18/5.65 | | & (v0 = 0 | xk = sz10 | xk = sz00 | (v3 = 0 & v2 = 0 & ~ (v1 = % 37.18/5.65 | | xk) & ~ (v1 = sz10) & doDivides0(v1, xk) = 0 & % 37.18/5.65 | | aNaturalNumber0(v1) = 0))) % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (5) with xk, simplifying with (10), (15) gives: % 37.18/5.65 | | (38) sdtasdt0(xk, sz10) = xk & sdtasdt0(sz10, xk) = xk % 37.18/5.65 | | % 37.18/5.65 | | ALPHA: (38) implies: % 37.18/5.65 | | (39) sdtasdt0(xk, sz10) = xk % 37.18/5.65 | | % 37.18/5.65 | | GROUND_INST: instantiating (18) with xk, simplifying with (15), (16) gives: % 37.18/5.65 | | (40) ? [v0: any] : ? [v1: any] : (doDivides0(xk, xk) = v1 & % 37.18/5.65 | | aNaturalNumber0(xk) = v0 & ( ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v2: % 37.18/5.65 | | $i] : ( ~ (sdtasdt0(xk, v2) = xk) | ~ $i(v2) | ? [v3: int] % 37.18/5.65 | | : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)) & ! [v2: $i] : % 37.18/5.65 | | ( ~ (aNaturalNumber0(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ( ~ % 37.18/5.65 | | (v3 = xk) & sdtasdt0(xk, v2) = v3 & $i(v3)))))) % 37.18/5.65 | | % 37.18/5.65 | | DELTA: instantiating (40) with fresh symbols all_165_0, all_165_1 gives: % 37.18/5.65 | | (41) doDivides0(xk, xk) = all_165_0 & aNaturalNumber0(xk) = all_165_1 & ( % 37.18/5.65 | | ~ (all_165_1 = 0) | ( ~ (all_165_0 = 0) & ! [v0: $i] : ( ~ % 37.18/5.65 | | (sdtasdt0(xk, v0) = xk) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 37.18/5.65 | | 0) & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ % 37.18/5.65 | | (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 % 37.18/5.65 | | = xk) & sdtasdt0(xk, v0) = v1 & $i(v1))))) % 37.18/5.65 | | % 37.18/5.65 | | ALPHA: (41) implies: % 37.18/5.65 | | (42) aNaturalNumber0(xk) = all_165_1 % 37.18/5.65 | | (43) ~ (all_165_1 = 0) | ( ~ (all_165_0 = 0) & ! [v0: $i] : ( ~ % 37.18/5.65 | | (sdtasdt0(xk, v0) = xk) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = % 37.18/5.65 | | 0) & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ % 37.18/5.65 | | (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = % 37.18/5.65 | | xk) & sdtasdt0(xk, v0) = v1 & $i(v1)))) % 37.18/5.65 | | % 37.18/5.65 | | DELTA: instantiating (37) with fresh symbols all_171_0, all_171_1, % 37.18/5.65 | | all_171_2, all_171_3 gives: % 37.18/5.66 | | (44) isPrime0(xk) = all_171_3 & $i(all_171_2) & ( ~ (all_171_3 = 0) | ( ~ % 37.18/5.66 | | (xk = sz10) & ~ (xk = sz00) & ! [v0: $i] : (v0 = xk | v0 = % 37.18/5.66 | | sz10 | ~ (doDivides0(v0, xk) = 0) | ~ $i(v0) | ? [v1: int] % 37.18/5.66 | | : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0: $i] : % 37.18/5.66 | | (v0 = xk | v0 = sz10 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) % 37.18/5.66 | | | ? [v1: int] : ( ~ (v1 = 0) & doDivides0(v0, xk) = v1)))) & % 37.18/5.66 | | (all_171_3 = 0 | xk = sz10 | xk = sz00 | (all_171_0 = 0 & all_171_1 % 37.18/5.66 | | = 0 & ~ (all_171_2 = xk) & ~ (all_171_2 = sz10) & % 37.18/5.66 | | doDivides0(all_171_2, xk) = 0 & aNaturalNumber0(all_171_2) = 0)) % 37.18/5.66 | | % 37.18/5.66 | | ALPHA: (44) implies: % 37.18/5.66 | | (45) isPrime0(xk) = all_171_3 % 37.18/5.66 | | (46) ~ (all_171_3 = 0) | ( ~ (xk = sz10) & ~ (xk = sz00) & ! [v0: $i] % 37.18/5.66 | | : (v0 = xk | v0 = sz10 | ~ (doDivides0(v0, xk) = 0) | ~ $i(v0) | % 37.18/5.66 | | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! % 37.18/5.66 | | [v0: $i] : (v0 = xk | v0 = sz10 | ~ (aNaturalNumber0(v0) = 0) | % 37.18/5.66 | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & doDivides0(v0, xk) = % 37.18/5.66 | | v1))) % 37.18/5.66 | | % 37.18/5.66 | | DELTA: instantiating (36) with fresh symbols all_173_0, all_173_1, % 37.18/5.66 | | all_173_2, all_173_3, all_173_4, all_173_5, all_173_6, all_173_7 % 37.18/5.66 | | gives: % 37.18/5.66 | | (47) isPrime0(xk) = all_173_6 & doDivides0(xk, xk) = all_173_7 & % 37.18/5.66 | | $i(all_173_2) & $i(all_173_5) & (( ~ (all_173_6 = 0) & (xk = sz10 | % 37.18/5.66 | | xk = sz00 | (all_173_0 = xk & all_173_1 = 0 & all_173_3 = 0 & % 37.18/5.66 | | all_173_4 = 0 & ~ (all_173_5 = xk) & ~ (all_173_5 = sz10) % 37.18/5.66 | | & doDivides0(all_173_5, xk) = 0 & sdtasdt0(all_173_5, % 37.18/5.66 | | all_173_2) = xk & aNaturalNumber0(all_173_2) = 0 & % 37.18/5.66 | | aNaturalNumber0(all_173_5) = 0))) | ( ~ (all_173_7 = 0) & ! % 37.18/5.66 | | [v0: $i] : ( ~ (sdtasdt0(xk, v0) = xk) | ~ $i(v0) | ? [v1: % 37.18/5.66 | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1)) & ! [v0: % 37.18/5.66 | | $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 37.18/5.66 | | : ( ~ (v1 = xk) & sdtasdt0(xk, v0) = v1 & $i(v1))))) % 37.18/5.66 | | % 37.18/5.66 | | ALPHA: (47) implies: % 37.18/5.66 | | (48) isPrime0(xk) = all_173_6 % 37.18/5.66 | | % 37.18/5.66 | | BETA: splitting (23) gives: % 37.18/5.66 | | % 37.18/5.66 | | Case 1: % 37.18/5.66 | | | % 37.18/5.66 | | | (49) sz10 = sz00 % 37.18/5.66 | | | % 37.18/5.66 | | | REDUCE: (2), (49) imply: % 37.18/5.66 | | | (50) $false % 37.18/5.66 | | | % 37.18/5.66 | | | CLOSE: (50) is inconsistent. % 37.18/5.66 | | | % 37.18/5.66 | | Case 2: % 37.18/5.66 | | | % 37.18/5.66 | | | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = % 37.18/5.66 | | | v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v3 & % 37.18/5.66 | | | sdtpldt0(sz10, sz10) = v1 & sdtpldt0(sz10, sz00) = v0 & % 37.18/5.66 | | | sdtpldt0(sz00, sz10) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.66 | | | % 37.18/5.66 | | | DELTA: instantiating (51) with fresh symbols all_182_0, all_182_1, % 37.18/5.66 | | | all_182_2, all_182_3 gives: % 37.18/5.66 | | | (52) ~ (all_182_0 = all_182_1) & ~ (all_182_2 = all_182_3) & % 37.18/5.66 | | | sdtpldt0(sz10, sz10) = all_182_0 & sdtpldt0(sz10, sz10) = % 37.18/5.66 | | | all_182_2 & sdtpldt0(sz10, sz00) = all_182_3 & sdtpldt0(sz00, % 37.18/5.66 | | | sz10) = all_182_1 & $i(all_182_0) & $i(all_182_1) & % 37.18/5.66 | | | $i(all_182_2) & $i(all_182_3) % 37.18/5.66 | | | % 37.18/5.66 | | | ALPHA: (52) implies: % 37.18/5.66 | | | (53) $i(all_182_3) % 37.18/5.66 | | | (54) sdtpldt0(sz10, sz00) = all_182_3 % 37.18/5.66 | | | % 37.18/5.66 | | | BETA: splitting (34) gives: % 37.18/5.66 | | | % 37.18/5.66 | | | Case 1: % 37.18/5.66 | | | | % 37.18/5.66 | | | | (55) xk = sz00 % 37.18/5.66 | | | | % 37.18/5.66 | | | | REDUCE: (11), (55) imply: % 37.18/5.66 | | | | (56) $false % 37.18/5.66 | | | | % 37.18/5.66 | | | | CLOSE: (56) is inconsistent. % 37.18/5.66 | | | | % 37.18/5.66 | | | Case 2: % 37.18/5.66 | | | | % 37.18/5.66 | | | | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 % 37.18/5.66 | | | | = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v3 & % 37.18/5.66 | | | | sdtpldt0(sz10, xk) = v1 & sdtpldt0(sz10, sz00) = v0 & % 37.18/5.66 | | | | sdtpldt0(sz00, sz10) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.66 | | | | % 37.18/5.66 | | | | DELTA: instantiating (57) with fresh symbols all_212_0, all_212_1, % 37.18/5.66 | | | | all_212_2, all_212_3 gives: % 37.18/5.66 | | | | (58) ~ (all_212_0 = all_212_1) & ~ (all_212_2 = all_212_3) & % 37.18/5.66 | | | | sdtpldt0(xk, sz10) = all_212_0 & sdtpldt0(sz10, xk) = all_212_2 % 37.18/5.66 | | | | & sdtpldt0(sz10, sz00) = all_212_3 & sdtpldt0(sz00, sz10) = % 37.18/5.66 | | | | all_212_1 & $i(all_212_0) & $i(all_212_1) & $i(all_212_2) & % 37.18/5.66 | | | | $i(all_212_3) % 37.18/5.66 | | | | % 37.18/5.66 | | | | ALPHA: (58) implies: % 37.18/5.66 | | | | (59) sdtpldt0(sz10, sz00) = all_212_3 % 37.18/5.66 | | | | % 37.18/5.66 | | | | BETA: splitting (29) gives: % 37.18/5.66 | | | | % 37.18/5.66 | | | | Case 1: % 37.18/5.66 | | | | | % 37.18/5.66 | | | | | (60) xk = sz00 % 37.18/5.66 | | | | | % 37.18/5.66 | | | | | REDUCE: (11), (60) imply: % 37.18/5.66 | | | | | (61) $false % 37.18/5.66 | | | | | % 37.18/5.66 | | | | | CLOSE: (61) is inconsistent. % 37.18/5.66 | | | | | % 37.18/5.66 | | | | Case 2: % 37.18/5.66 | | | | | % 37.18/5.66 | | | | | (62) xk = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 37.18/5.66 | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, xk) = v3 & % 37.18/5.66 | | | | | sdtasdt0(xk, xk) = v1 & sdtasdt0(xk, sz10) = v0 & % 37.18/5.66 | | | | | sdtasdt0(sz10, xk) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.18/5.66 | | | | | % 37.18/5.66 | | | | | BETA: splitting (35) gives: % 37.18/5.66 | | | | | % 37.18/5.66 | | | | | Case 1: % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | (63) xk = sz00 % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | REDUCE: (11), (63) imply: % 37.18/5.66 | | | | | | (64) $false % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | CLOSE: (64) is inconsistent. % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | Case 2: % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ % 37.18/5.66 | | | | | | (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xk, sz10) = v2 & % 37.18/5.66 | | | | | | sdtpldt0(sz10, xk) = v0 & sdtpldt0(sz10, sz00) = v1 & % 37.18/5.66 | | | | | | sdtpldt0(sz00, sz10) = v3 & $i(v3) & $i(v2) & $i(v1) & % 37.18/5.66 | | | | | | $i(v0)) % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | DELTA: instantiating (65) with fresh symbols all_231_0, all_231_1, % 37.18/5.66 | | | | | | all_231_2, all_231_3 gives: % 37.18/5.66 | | | | | | (66) ~ (all_231_0 = all_231_1) & ~ (all_231_2 = all_231_3) & % 37.18/5.66 | | | | | | sdtpldt0(xk, sz10) = all_231_1 & sdtpldt0(sz10, xk) = % 37.18/5.66 | | | | | | all_231_3 & sdtpldt0(sz10, sz00) = all_231_2 & % 37.18/5.66 | | | | | | sdtpldt0(sz00, sz10) = all_231_0 & $i(all_231_0) & % 37.18/5.66 | | | | | | $i(all_231_1) & $i(all_231_2) & $i(all_231_3) % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | ALPHA: (66) implies: % 37.18/5.66 | | | | | | (67) sdtpldt0(sz10, sz00) = all_231_2 % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | BETA: splitting (24) gives: % 37.18/5.66 | | | | | | % 37.18/5.66 | | | | | | Case 1: % 37.18/5.66 | | | | | | | % 37.18/5.66 | | | | | | | (68) sz10 = sz00 % 37.18/5.66 | | | | | | | % 37.18/5.66 | | | | | | | REDUCE: (2), (68) imply: % 37.18/5.66 | | | | | | | (69) $false % 37.18/5.66 | | | | | | | % 37.18/5.66 | | | | | | | CLOSE: (69) is inconsistent. % 37.18/5.66 | | | | | | | % 37.18/5.66 | | | | | | Case 2: % 37.18/5.66 | | | | | | | % 37.18/5.67 | | | | | | | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( % 37.18/5.67 | | | | | | | ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v2 & % 37.18/5.67 | | | | | | | sdtpldt0(sz10, sz10) = v0 & sdtpldt0(sz10, sz00) = v1 & % 37.18/5.67 | | | | | | | sdtpldt0(sz00, sz10) = v3 & $i(v3) & $i(v2) & $i(v1) & % 37.18/5.67 | | | | | | | $i(v0)) % 37.18/5.67 | | | | | | | % 37.18/5.67 | | | | | | | DELTA: instantiating (70) with fresh symbols all_267_0, all_267_1, % 37.18/5.67 | | | | | | | all_267_2, all_267_3 gives: % 37.18/5.67 | | | | | | | (71) ~ (all_267_0 = all_267_1) & ~ (all_267_2 = all_267_3) & % 37.18/5.67 | | | | | | | sdtpldt0(sz10, sz10) = all_267_1 & sdtpldt0(sz10, sz10) = % 37.18/5.67 | | | | | | | all_267_3 & sdtpldt0(sz10, sz00) = all_267_2 & % 37.18/5.67 | | | | | | | sdtpldt0(sz00, sz10) = all_267_0 & $i(all_267_0) & % 37.18/5.67 | | | | | | | $i(all_267_1) & $i(all_267_2) & $i(all_267_3) % 37.18/5.67 | | | | | | | % 37.18/5.67 | | | | | | | ALPHA: (71) implies: % 37.18/5.67 | | | | | | | (72) sdtpldt0(sz10, sz00) = all_267_2 % 37.18/5.67 | | | | | | | % 37.18/5.67 | | | | | | | BETA: splitting (30) gives: % 37.18/5.67 | | | | | | | % 37.18/5.67 | | | | | | | Case 1: % 37.18/5.67 | | | | | | | | % 37.18/5.67 | | | | | | | | (73) xk = sz00 % 37.18/5.67 | | | | | | | | % 37.18/5.67 | | | | | | | | REDUCE: (11), (73) imply: % 37.18/5.67 | | | | | | | | (74) $false % 37.18/5.67 | | | | | | | | % 37.18/5.67 | | | | | | | | CLOSE: (74) is inconsistent. % 37.18/5.67 | | | | | | | | % 37.18/5.67 | | | | | | | Case 2: % 37.18/5.67 | | | | | | | | % 37.18/5.67 | | | | | | | | (75) xk = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 37.18/5.67 | | | | | | | | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xk, % 37.18/5.67 | | | | | | | | xk) = v2 & sdtasdt0(xk, xk) = v0 & sdtasdt0(xk, % 37.18/5.67 | | | | | | | | sz10) = v1 & sdtasdt0(sz10, xk) = v3 & $i(v3) & % 37.18/5.67 | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 37.18/5.67 | | | | | | | | % 37.18/5.67 | | | | | | | | BETA: splitting (26) gives: % 37.18/5.67 | | | | | | | | % 37.18/5.67 | | | | | | | | Case 1: % 37.18/5.67 | | | | | | | | | % 37.18/5.67 | | | | | | | | | (76) sz10 = sz00 % 37.18/5.67 | | | | | | | | | % 37.18/5.67 | | | | | | | | | REDUCE: (2), (76) imply: % 37.18/5.67 | | | | | | | | | (77) $false % 37.18/5.67 | | | | | | | | | % 37.18/5.67 | | | | | | | | | CLOSE: (77) is inconsistent. % 37.18/5.67 | | | | | | | | | % 37.18/5.67 | | | | | | | | Case 2: % 37.18/5.67 | | | | | | | | | % 37.18/5.67 | | | | | | | | | (78) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] % 37.18/5.67 | | | | | | | | | : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz00) % 37.18/5.67 | | | | | | | | | = v2 & sdtpldt0(sz00, sz10) = v0 & sdtpldt0(sz00, % 37.18/5.67 | | | | | | | | | sz00) = v3 & sdtpldt0(sz00, sz00) = v1 & $i(v3) & % 37.18/5.67 | | | | | | | | | $i(v2) & $i(v1) & $i(v0)) % 37.18/5.67 | | | | | | | | | % 37.18/5.67 | | | | | | | | | DELTA: instantiating (78) with fresh symbols all_284_0, % 37.18/5.67 | | | | | | | | | all_284_1, all_284_2, all_284_3 gives: % 37.35/5.67 | | | | | | | | | (79) ~ (all_284_0 = all_284_1) & ~ (all_284_2 = % 37.35/5.67 | | | | | | | | | all_284_3) & sdtpldt0(sz10, sz00) = all_284_1 & % 37.35/5.67 | | | | | | | | | sdtpldt0(sz00, sz10) = all_284_3 & sdtpldt0(sz00, % 37.35/5.67 | | | | | | | | | sz00) = all_284_0 & sdtpldt0(sz00, sz00) = all_284_2 % 37.35/5.67 | | | | | | | | | & $i(all_284_0) & $i(all_284_1) & $i(all_284_2) & % 37.35/5.67 | | | | | | | | | $i(all_284_3) % 37.35/5.67 | | | | | | | | | % 37.35/5.67 | | | | | | | | | ALPHA: (79) implies: % 37.35/5.67 | | | | | | | | | (80) sdtpldt0(sz10, sz00) = all_284_1 % 37.35/5.67 | | | | | | | | | % 37.35/5.67 | | | | | | | | | BETA: splitting (25) gives: % 37.35/5.67 | | | | | | | | | % 37.35/5.67 | | | | | | | | | Case 1: % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | (81) sz10 = sz00 % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | REDUCE: (2), (81) imply: % 37.35/5.67 | | | | | | | | | | (82) $false % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | CLOSE: (82) is inconsistent. % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | Case 2: % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 37.35/5.67 | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & % 37.35/5.67 | | | | | | | | | | sdtpldt0(sz10, sz00) = v3 & sdtpldt0(sz00, sz10) = % 37.35/5.67 | | | | | | | | | | v1 & sdtpldt0(sz00, sz00) = v2 & sdtpldt0(sz00, % 37.35/5.67 | | | | | | | | | | sz00) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | DELTA: instantiating (83) with fresh symbols all_290_0, % 37.35/5.67 | | | | | | | | | | all_290_1, all_290_2, all_290_3 gives: % 37.35/5.67 | | | | | | | | | | (84) ~ (all_290_0 = all_290_1) & ~ (all_290_2 = % 37.35/5.67 | | | | | | | | | | all_290_3) & sdtpldt0(sz10, sz00) = all_290_0 & % 37.35/5.67 | | | | | | | | | | sdtpldt0(sz00, sz10) = all_290_2 & sdtpldt0(sz00, % 37.35/5.67 | | | | | | | | | | sz00) = all_290_1 & sdtpldt0(sz00, sz00) = % 37.35/5.67 | | | | | | | | | | all_290_3 & $i(all_290_0) & $i(all_290_1) & % 37.35/5.67 | | | | | | | | | | $i(all_290_2) & $i(all_290_3) % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | ALPHA: (84) implies: % 37.35/5.67 | | | | | | | | | | (85) sdtpldt0(sz10, sz00) = all_290_0 % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | BETA: splitting (33) gives: % 37.35/5.67 | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | Case 1: % 37.35/5.67 | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | (86) xk = sz00 % 37.35/5.67 | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | REDUCE: (11), (86) imply: % 37.35/5.67 | | | | | | | | | | | (87) $false % 37.35/5.67 | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | CLOSE: (87) is inconsistent. % 37.35/5.67 | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | Case 2: % 37.35/5.67 | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | (88) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 37.35/5.67 | | | | | | | | | | | $i] : ? [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) % 37.35/5.67 | | | | | | | | | | | & sdtasdt0(xk, sz10) = v0 & sdtasdt0(xk, sz00) = % 37.35/5.67 | | | | | | | | | | | v1 & sdtasdt0(sz10, xk) = v2 & sdtasdt0(sz00, % 37.35/5.67 | | | | | | | | | | | xk) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.35/5.67 | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | BETA: splitting (62) gives: % 37.35/5.67 | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | Case 1: % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | (89) xk = sz10 % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | REDUCE: (12), (89) imply: % 37.35/5.67 | | | | | | | | | | | | (90) $false % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | CLOSE: (90) is inconsistent. % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | Case 2: % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | (91) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 37.35/5.67 | | | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & % 37.35/5.67 | | | | | | | | | | | | sdtasdt0(xk, xk) = v3 & sdtasdt0(xk, xk) = v1 & % 37.35/5.67 | | | | | | | | | | | | sdtasdt0(xk, sz10) = v0 & sdtasdt0(sz10, xk) = % 37.35/5.67 | | | | | | | | | | | | v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | DELTA: instantiating (91) with fresh symbols all_310_0, % 37.35/5.67 | | | | | | | | | | | | all_310_1, all_310_2, all_310_3 gives: % 37.35/5.67 | | | | | | | | | | | | (92) ~ (all_310_0 = all_310_1) & ~ (all_310_2 = % 37.35/5.67 | | | | | | | | | | | | all_310_3) & sdtasdt0(xk, xk) = all_310_0 & % 37.35/5.67 | | | | | | | | | | | | sdtasdt0(xk, xk) = all_310_2 & sdtasdt0(xk, sz10) % 37.35/5.67 | | | | | | | | | | | | = all_310_3 & sdtasdt0(sz10, xk) = all_310_1 & % 37.35/5.67 | | | | | | | | | | | | $i(all_310_0) & $i(all_310_1) & $i(all_310_2) & % 37.35/5.67 | | | | | | | | | | | | $i(all_310_3) % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | ALPHA: (92) implies: % 37.35/5.67 | | | | | | | | | | | | (93) sdtasdt0(xk, sz10) = all_310_3 % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | BETA: splitting (32) gives: % 37.35/5.67 | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | Case 1: % 37.35/5.67 | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | (94) sz10 = sz00 % 37.35/5.67 | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | REDUCE: (2), (94) imply: % 37.35/5.67 | | | | | | | | | | | | | (95) $false % 37.35/5.67 | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | CLOSE: (95) is inconsistent. % 37.35/5.67 | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | Case 2: % 37.35/5.67 | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | (96) xk = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 37.35/5.67 | | | | | | | | | | | | | $i] : ? [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) % 37.35/5.67 | | | | | | | | | | | | | & sdtasdt0(xk, sz10) = v2 & sdtasdt0(sz10, xk) = % 37.35/5.67 | | | | | | | | | | | | | v0 & sdtasdt0(sz10, sz10) = v3 & sdtasdt0(sz10, % 37.35/5.67 | | | | | | | | | | | | | sz10) = v1 & $i(v3) & $i(v2) & $i(v1) & % 37.35/5.67 | | | | | | | | | | | | | $i(v0)) % 37.35/5.67 | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | BETA: splitting (31) gives: % 37.35/5.67 | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | Case 1: % 37.35/5.67 | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | (97) sz10 = sz00 % 37.35/5.67 | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | REDUCE: (2), (97) imply: % 37.35/5.67 | | | | | | | | | | | | | | (98) $false % 37.35/5.67 | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | CLOSE: (98) is inconsistent. % 37.35/5.67 | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | Case 2: % 37.35/5.67 | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | (99) xk = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: % 37.35/5.67 | | | | | | | | | | | | | | $i] : ? [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) % 37.35/5.67 | | | | | | | | | | | | | | & sdtasdt0(xk, sz10) = v3 & sdtasdt0(sz10, xk) = % 37.35/5.67 | | | | | | | | | | | | | | v1 & sdtasdt0(sz10, sz10) = v2 & sdtasdt0(sz10, % 37.35/5.67 | | | | | | | | | | | | | | sz10) = v0 & $i(v3) & $i(v2) & $i(v1) & % 37.35/5.67 | | | | | | | | | | | | | | $i(v0)) % 37.35/5.67 | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | BETA: splitting (75) gives: % 37.35/5.67 | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | Case 1: % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | (100) xk = sz10 % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | REDUCE: (12), (100) imply: % 37.35/5.67 | | | | | | | | | | | | | | | (101) $false % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | CLOSE: (101) is inconsistent. % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | Case 2: % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | (102) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 37.35/5.67 | | | | | | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & % 37.35/5.67 | | | | | | | | | | | | | | | sdtasdt0(xk, xk) = v2 & sdtasdt0(xk, xk) = v0 & % 37.35/5.67 | | | | | | | | | | | | | | | sdtasdt0(xk, sz10) = v1 & sdtasdt0(sz10, xk) = % 37.35/5.67 | | | | | | | | | | | | | | | v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_335_0, % 37.35/5.67 | | | | | | | | | | | | | | | all_335_1, all_335_2, all_335_3 gives: % 37.35/5.67 | | | | | | | | | | | | | | | (103) ~ (all_335_0 = all_335_1) & ~ (all_335_2 = % 37.35/5.67 | | | | | | | | | | | | | | | all_335_3) & sdtasdt0(xk, xk) = all_335_1 & % 37.35/5.67 | | | | | | | | | | | | | | | sdtasdt0(xk, xk) = all_335_3 & sdtasdt0(xk, sz10) % 37.35/5.67 | | | | | | | | | | | | | | | = all_335_2 & sdtasdt0(sz10, xk) = all_335_0 & % 37.35/5.67 | | | | | | | | | | | | | | | $i(all_335_0) & $i(all_335_1) & $i(all_335_2) & % 37.35/5.67 | | | | | | | | | | | | | | | $i(all_335_3) % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | ALPHA: (103) implies: % 37.35/5.67 | | | | | | | | | | | | | | | (104) sdtasdt0(xk, sz10) = all_335_2 % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | BETA: splitting (99) gives: % 37.35/5.67 | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | Case 1: % 37.35/5.67 | | | | | | | | | | | | | | | | % 37.35/5.67 | | | | | | | | | | | | | | | | (105) xk = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | REDUCE: (12), (105) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | (106) $false % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | CLOSE: (106) is inconsistent. % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | Case 2: % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | (107) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 37.35/5.68 | | | | | | | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & % 37.35/5.68 | | | | | | | | | | | | | | | | sdtasdt0(xk, sz10) = v3 & sdtasdt0(sz10, xk) = % 37.35/5.68 | | | | | | | | | | | | | | | | v1 & sdtasdt0(sz10, sz10) = v2 & sdtasdt0(sz10, % 37.35/5.68 | | | | | | | | | | | | | | | | sz10) = v0 & $i(v3) & $i(v2) & $i(v1) & % 37.35/5.68 | | | | | | | | | | | | | | | | $i(v0)) % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | DELTA: instantiating (107) with fresh symbols all_341_0, % 37.35/5.68 | | | | | | | | | | | | | | | | all_341_1, all_341_2, all_341_3 gives: % 37.35/5.68 | | | | | | | | | | | | | | | | (108) ~ (all_341_0 = all_341_1) & ~ (all_341_2 = % 37.35/5.68 | | | | | | | | | | | | | | | | all_341_3) & sdtasdt0(xk, sz10) = all_341_0 & % 37.35/5.68 | | | | | | | | | | | | | | | | sdtasdt0(sz10, xk) = all_341_2 & sdtasdt0(sz10, % 37.35/5.68 | | | | | | | | | | | | | | | | sz10) = all_341_1 & sdtasdt0(sz10, sz10) = % 37.35/5.68 | | | | | | | | | | | | | | | | all_341_3 & $i(all_341_0) & $i(all_341_1) & % 37.35/5.68 | | | | | | | | | | | | | | | | $i(all_341_2) & $i(all_341_3) % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | ALPHA: (108) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | (109) sdtasdt0(xk, sz10) = all_341_0 % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | Case 1: % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | (110) sz10 = sz00 % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | REDUCE: (2), (110) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | (111) $false % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | CLOSE: (111) is inconsistent. % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | Case 2: % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | (112) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 37.35/5.68 | | | | | | | | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & % 37.35/5.68 | | | | | | | | | | | | | | | | | sdtasdt0(xk, sz10) = v0 & sdtasdt0(xk, sz00) = % 37.35/5.68 | | | | | | | | | | | | | | | | | v1 & sdtasdt0(sz10, xk) = v2 & sdtasdt0(sz00, % 37.35/5.68 | | | | | | | | | | | | | | | | | xk) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | DELTA: instantiating (112) with fresh symbols all_347_0, % 37.35/5.68 | | | | | | | | | | | | | | | | | all_347_1, all_347_2, all_347_3 gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | (113) ~ (all_347_0 = all_347_1) & ~ (all_347_2 = % 37.35/5.68 | | | | | | | | | | | | | | | | | all_347_3) & sdtasdt0(xk, sz10) = all_347_3 & % 37.35/5.68 | | | | | | | | | | | | | | | | | sdtasdt0(xk, sz00) = all_347_2 & sdtasdt0(sz10, % 37.35/5.68 | | | | | | | | | | | | | | | | | xk) = all_347_1 & sdtasdt0(sz00, xk) = all_347_0 % 37.35/5.68 | | | | | | | | | | | | | | | | | & $i(all_347_0) & $i(all_347_1) & $i(all_347_2) & % 37.35/5.68 | | | | | | | | | | | | | | | | | $i(all_347_3) % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | ALPHA: (113) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | (114) sdtasdt0(xk, sz10) = all_347_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | Case 1: % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | (115) xk = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | REDUCE: (12), (115) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (116) $false % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | CLOSE: (116) is inconsistent. % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | Case 2: % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | (117) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 37.35/5.68 | | | | | | | | | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & % 37.35/5.68 | | | | | | | | | | | | | | | | | | sdtasdt0(xk, sz10) = v2 & sdtasdt0(sz10, xk) = % 37.35/5.68 | | | | | | | | | | | | | | | | | | v0 & sdtasdt0(sz10, sz10) = v3 & sdtasdt0(sz10, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz10) = v1 & $i(v3) & $i(v2) & $i(v1) & % 37.35/5.68 | | | | | | | | | | | | | | | | | | $i(v0)) % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | DELTA: instantiating (117) with fresh symbols all_353_0, % 37.35/5.68 | | | | | | | | | | | | | | | | | | all_353_1, all_353_2, all_353_3 gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (118) ~ (all_353_0 = all_353_1) & ~ (all_353_2 = % 37.35/5.68 | | | | | | | | | | | | | | | | | | all_353_3) & sdtasdt0(xk, sz10) = all_353_1 & % 37.35/5.68 | | | | | | | | | | | | | | | | | | sdtasdt0(sz10, xk) = all_353_3 & sdtasdt0(sz10, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz10) = all_353_0 & sdtasdt0(sz10, sz10) = % 37.35/5.68 | | | | | | | | | | | | | | | | | | all_353_2 & $i(all_353_0) & $i(all_353_1) & % 37.35/5.68 | | | | | | | | | | | | | | | | | | $i(all_353_2) & $i(all_353_3) % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | ALPHA: (118) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (119) sdtasdt0(xk, sz10) = all_353_1 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_165_1, xk, % 37.35/5.68 | | | | | | | | | | | | | | | | | | simplifying with (10), (42) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (120) all_165_1 = 0 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with sz10, all_267_2, sz00, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz10, simplifying with (28), (72) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (121) all_267_2 = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_212_3, all_284_1, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz00, sz10, simplifying with (59), (80) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (122) all_284_1 = all_212_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_182_3, all_284_1, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz00, sz10, simplifying with (54), (80) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (123) all_284_1 = all_182_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_284_1, all_290_0, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz00, sz10, simplifying with (80), (85) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (124) all_290_0 = all_284_1 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_267_2, all_290_0, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz00, sz10, simplifying with (72), (85) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (125) all_290_0 = all_267_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_231_2, all_290_0, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz00, sz10, simplifying with (67), (85) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (126) all_290_0 = all_231_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_310_3, all_335_2, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz10, xk, simplifying with (93), (104) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (127) all_335_2 = all_310_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_335_2, all_347_3, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz10, xk, simplifying with (104), (114) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (128) all_347_3 = all_335_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with xk, all_347_3, sz10, xk, % 37.35/5.68 | | | | | | | | | | | | | | | | | | simplifying with (39), (114) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (129) all_347_3 = xk % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_347_3, all_353_1, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz10, xk, simplifying with (114), (119) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (130) all_353_1 = all_347_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_341_0, all_353_1, % 37.35/5.68 | | | | | | | | | | | | | | | | | | sz10, xk, simplifying with (109), (119) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (131) all_353_1 = all_341_0 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_173_6, xk, % 37.35/5.68 | | | | | | | | | | | | | | | | | | simplifying with (16), (48) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (132) all_173_6 = 0 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (20) with all_171_3, all_173_6, xk, % 37.35/5.68 | | | | | | | | | | | | | | | | | | simplifying with (45), (48) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (133) all_173_6 = all_171_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (131) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (134) all_347_3 = all_341_0 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (134) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (135) all_347_3 = all_341_0 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (135) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (136) all_341_0 = xk % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (135) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (137) all_341_0 = all_335_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (137) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (138) all_335_2 = xk % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (138) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (139) all_335_2 = xk % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (139) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (140) all_310_3 = xk % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (140) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (141) all_310_3 = xk % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (126) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (142) all_267_2 = all_231_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (142) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (143) all_267_2 = all_231_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (126) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (144) all_284_1 = all_231_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (144) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (145) all_284_1 = all_231_2 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (123) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (146) all_212_3 = all_182_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (145) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (147) all_231_2 = all_212_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (147) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (148) all_231_2 = all_212_3 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (143) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (149) all_231_2 = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (149) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (150) all_231_2 = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (150) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (151) all_212_3 = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (151) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (152) all_212_3 = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (146), (152) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (153) all_182_3 = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | SIMP: (153) implies: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (154) all_182_3 = sz10 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (133) imply: % 37.35/5.68 | | | | | | | | | | | | | | | | | | (155) all_171_3 = 0 % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 37.35/5.68 | | | | | | | | | | | | | | | | | | % 37.35/5.68 | | | | | | | | | | | | | | | | | | Case 1: % 37.35/5.68 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | (156) ~ (all_165_1 = 0) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | REDUCE: (120), (156) imply: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | (157) $false % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent. % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | Case 2: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | (158) ~ (all_165_0 = 0) & ! [v0: $i] : ( ~ % 37.35/5.69 | | | | | | | | | | | | | | | | | | | (sdtasdt0(xk, v0) = xk) | ~ $i(v0) | ? [v1: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = % 37.35/5.69 | | | | | | | | | | | | | | | | | | | v1)) & ! [v0: $i] : ( ~ (aNaturalNumber0(v0) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xk) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | & sdtasdt0(xk, v0) = v1 & $i(v1))) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | (159) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ % 37.35/5.69 | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: $i] : ( ~ (v1 = xk) & % 37.35/5.69 | | | | | | | | | | | | | | | | | | | sdtasdt0(xk, v0) = v1 & $i(v1))) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (159) with sz10, simplifying with % 37.35/5.69 | | | | | | | | | | | | | | | | | | | (3), (14) gives: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | (160) ? [v0: $i] : ( ~ (v0 = xk) & sdtasdt0(xk, sz10) = % 37.35/5.69 | | | | | | | | | | | | | | | | | | | v0 & $i(v0)) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | Case 1: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | (161) ~ (all_171_3 = 0) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (161) imply: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | (162) $false % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | CLOSE: (162) is inconsistent. % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | Case 2: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (160) with fresh symbol all_388_0 % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | gives: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | (163) ~ (all_388_0 = xk) & sdtasdt0(xk, sz10) = % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | all_388_0 & $i(all_388_0) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | (164) ~ (all_388_0 = xk) % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | (165) sdtasdt0(xk, sz10) = all_388_0 % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (22) with xk, all_388_0, sz10, xk, % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | simplifying with (39), (165) gives: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | (166) all_388_0 = xk % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (166) imply: % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | (167) $false % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent. % 37.35/5.69 | | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | | % 37.35/5.69 | | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | | % 37.35/5.69 | | | | | | | | | End of split % 37.35/5.69 | | | | | | | | | % 37.35/5.69 | | | | | | | | End of split % 37.35/5.69 | | | | | | | | % 37.35/5.69 | | | | | | | End of split % 37.35/5.69 | | | | | | | % 37.35/5.69 | | | | | | End of split % 37.35/5.69 | | | | | | % 37.35/5.69 | | | | | End of split % 37.35/5.69 | | | | | % 37.35/5.69 | | | | End of split % 37.35/5.69 | | | | % 37.35/5.69 | | | End of split % 37.35/5.69 | | | % 37.35/5.69 | | End of split % 37.35/5.69 | | % 37.35/5.69 | Case 2: % 37.35/5.69 | | % 37.35/5.69 | | (168) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(sz10) = v0) % 37.35/5.69 | | % 37.35/5.69 | | DELTA: instantiating (168) with fresh symbol all_47_0 gives: % 37.35/5.69 | | (169) ~ (all_47_0 = 0) & aNaturalNumber0(sz10) = all_47_0 % 37.35/5.69 | | % 37.35/5.69 | | ALPHA: (169) implies: % 37.35/5.69 | | (170) ~ (all_47_0 = 0) % 37.35/5.69 | | (171) aNaturalNumber0(sz10) = all_47_0 % 37.35/5.69 | | % 37.35/5.69 | | GROUND_INST: instantiating (19) with 0, all_47_0, sz10, simplifying with % 37.35/5.69 | | (3), (171) gives: % 37.35/5.69 | | (172) all_47_0 = 0 % 37.35/5.69 | | % 37.35/5.69 | | REDUCE: (170), (172) imply: % 37.35/5.69 | | (173) $false % 37.35/5.69 | | % 37.35/5.69 | | CLOSE: (173) is inconsistent. % 37.35/5.69 | | % 37.35/5.69 | End of split % 37.35/5.69 | % 37.35/5.69 End of proof % 37.35/5.69 % SZS output end Proof for theBenchmark % 37.35/5.69 % 37.35/5.69 5099ms %------------------------------------------------------------------------------