TSTP Solution File: NUM482+3 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------