TSTP Solution File: RNG119+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG119+4 : 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 13:57:59 EDT 2023
% Result : Theorem 30.96s 4.90s
% Output : Proof 163.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG119+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 01:57:57 EDT 2023
% 0.13/0.33 % 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
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.87/1.28 Prover 4: Preprocessing ...
% 3.87/1.28 Prover 1: Preprocessing ...
% 3.87/1.33 Prover 6: Preprocessing ...
% 3.87/1.33 Prover 0: Preprocessing ...
% 3.87/1.33 Prover 2: Preprocessing ...
% 3.87/1.34 Prover 3: Preprocessing ...
% 3.87/1.34 Prover 5: Preprocessing ...
% 11.21/2.31 Prover 1: Constructing countermodel ...
% 11.92/2.37 Prover 6: Proving ...
% 12.14/2.42 Prover 5: Proving ...
% 12.14/2.42 Prover 3: Constructing countermodel ...
% 13.10/2.54 Prover 2: Proving ...
% 13.10/2.61 Prover 4: Constructing countermodel ...
% 13.74/2.71 Prover 0: Proving ...
% 30.96/4.90 Prover 0: proved (4275ms)
% 30.96/4.90
% 30.96/4.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.96/4.90
% 30.96/4.90 Prover 3: stopped
% 30.96/4.90 Prover 5: stopped
% 30.96/4.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 30.96/4.91 Prover 6: stopped
% 30.96/4.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 31.14/4.92 Prover 2: stopped
% 31.19/4.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 31.19/4.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 31.19/4.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 31.19/5.08 Prover 10: Preprocessing ...
% 31.94/5.10 Prover 7: Preprocessing ...
% 31.94/5.10 Prover 11: Preprocessing ...
% 31.94/5.11 Prover 13: Preprocessing ...
% 31.94/5.13 Prover 8: Preprocessing ...
% 34.25/5.34 Prover 7: Constructing countermodel ...
% 34.25/5.36 Prover 10: Constructing countermodel ...
% 34.25/5.40 Prover 8: Warning: ignoring some quantifiers
% 34.80/5.44 Prover 8: Constructing countermodel ...
% 34.80/5.44 Prover 13: Warning: ignoring some quantifiers
% 34.80/5.46 Prover 13: Constructing countermodel ...
% 35.26/5.55 Prover 11: Constructing countermodel ...
% 70.35/10.02 Prover 13: stopped
% 70.35/10.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 70.35/10.07 Prover 16: Preprocessing ...
% 70.98/10.26 Prover 16: Warning: ignoring some quantifiers
% 71.81/10.27 Prover 16: Constructing countermodel ...
% 114.33/15.74 Prover 16: stopped
% 114.33/15.74 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 115.15/15.82 Prover 19: Preprocessing ...
% 116.27/15.96 Prover 1: stopped
% 117.46/16.14 Prover 19: Warning: ignoring some quantifiers
% 117.88/16.17 Prover 19: Constructing countermodel ...
% 141.25/19.47 Prover 19: stopped
% 161.64/22.31 Prover 4: Found proof (size 307)
% 161.64/22.31 Prover 4: proved (21690ms)
% 161.64/22.31 Prover 8: stopped
% 161.64/22.31 Prover 7: stopped
% 161.64/22.31 Prover 10: stopped
% 161.64/22.32 Prover 11: stopped
% 161.64/22.32
% 161.64/22.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 161.64/22.32
% 161.64/22.35 % SZS output start Proof for theBenchmark
% 162.19/22.35 Assumptions after simplification:
% 162.19/22.35 ---------------------------------
% 162.19/22.35
% 162.19/22.35 (mAMDistr)
% 162.19/22.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 162.19/22.40 $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~
% 162.19/22.40 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] :
% 162.19/22.40 ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 162.19/22.40 [v12: $i] : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v9, v0) = v14 &
% 162.19/22.40 sdtasdt0(v0, v9) = v10 & sdtasdt0(v0, v2) = v12 & sdtasdt0(v0, v1) = v11 &
% 162.19/22.40 sdtpldt0(v11, v12) = v13 & sdtpldt0(v1, v2) = v9 & aElement0(v2) = v8 &
% 162.19/22.40 aElement0(v1) = v7 & aElement0(v0) = v6 & $i(v14) & $i(v13) & $i(v12) &
% 162.19/22.40 $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) |
% 162.19/22.40 (v14 = v5 & v13 = v10)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 162.19/22.40 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~
% 162.19/22.40 (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1)
% 162.19/22.40 | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ?
% 162.19/22.40 [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 162.19/22.40 (sdtasdt0(v9, v0) = v11 & sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 &
% 162.19/22.40 sdtasdt0(v0, v9) = v10 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v1, v2) = v9
% 162.19/22.40 & aElement0(v2) = v8 & aElement0(v1) = v7 & aElement0(v0) = v6 & $i(v14) &
% 162.19/22.40 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & ( ~ (v8 = 0) | ~ (v7 =
% 162.19/22.40 0) | ~ (v6 = 0) | (v14 = v11 & v10 = v5)))) & ! [v0: $i] : ! [v1:
% 162.19/22.40 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v0) = v4)
% 162.19/22.40 | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 162.19/22.40 any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 162.19/22.40 $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 162.19/22.40 (sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v3) = v8 &
% 162.19/22.40 sdtasdt0(v0, v2) = v10 & sdtasdt0(v0, v1) = v9 & sdtpldt0(v12, v13) = v14
% 162.19/22.40 & sdtpldt0(v9, v10) = v11 & aElement0(v2) = v7 & aElement0(v1) = v6 &
% 162.19/22.40 aElement0(v0) = v5 & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) &
% 162.19/22.40 $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | (v14 = v4 &
% 162.19/22.40 v11 = v8)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 162.19/22.40 ! [v4: $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~
% 162.19/22.40 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 162.19/22.40 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] :
% 162.19/22.40 ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v3, v0) = v11 & sdtasdt0(v2, v0) =
% 162.19/22.40 v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) =
% 162.19/22.40 v8 & sdtpldt0(v12, v13) = v14 & sdtpldt0(v8, v9) = v10 & aElement0(v2) =
% 162.19/22.40 v7 & aElement0(v1) = v6 & aElement0(v0) = v5 & $i(v14) & $i(v13) & $i(v12)
% 162.19/22.40 & $i(v11) & $i(v10) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~
% 162.19/22.40 (v5 = 0) | (v14 = v11 & v10 = v4))))
% 162.19/22.40
% 162.19/22.40 (mAddComm)
% 162.19/22.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~
% 162.19/22.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 162.19/22.40 (sdtpldt0(v0, v1) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) &
% 162.19/22.40 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0: $i] : ! [v1: $i] : !
% 162.19/22.40 [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any]
% 162.19/22.40 : ? [v4: any] : ? [v5: $i] : (sdtpldt0(v1, v0) = v5 & aElement0(v1) = v4 &
% 162.19/22.40 aElement0(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 162.19/22.40
% 162.19/22.40 (mAddZero)
% 162.19/22.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~
% 162.19/22.41 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtpldt0(sz00, v0) = v3 &
% 162.19/22.41 aElement0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & !
% 162.19/22.41 [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ? [v2:
% 162.19/22.41 any] : ? [v3: $i] : (sdtpldt0(v0, sz00) = v3 & aElement0(v0) = v2 &
% 162.19/22.41 $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~
% 162.19/22.41 (aElement0(v0) = 0) | ~ $i(v0) | (sdtpldt0(v0, sz00) = v0 & sdtpldt0(sz00,
% 162.19/22.41 v0) = v0))
% 162.19/22.41
% 162.19/22.41 (mDefDvs)
% 162.19/22.41 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aDivisorOf0(v1, v0) =
% 162.19/22.41 v2) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ?
% 162.19/22.41 [v4: any] : (doDivides0(v1, v0) = v4 & aElement0(v1) = v3 & ( ~ (v4 = 0) |
% 162.19/22.41 ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 162.19/22.41 (doDivides0(v1, v0) = v2) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 162.19/22.41 ? [v3: any] : ? [v4: any] : (aDivisorOf0(v1, v0) = v3 & aElement0(v1) = v4
% 162.19/22.41 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 162.19/22.41 [v2: any] : ( ~ (aElement0(v1) = v2) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~
% 162.19/22.41 $i(v0) | ? [v3: any] : ? [v4: any] : (aDivisorOf0(v1, v0) = v3 &
% 162.19/22.41 doDivides0(v1, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0:
% 162.19/22.41 $i] : ! [v1: $i] : ( ~ (aDivisorOf0(v1, v0) = 0) | ~ (aElement0(v0) = 0) |
% 162.19/22.41 ~ $i(v1) | ~ $i(v0) | (doDivides0(v1, v0) = 0 & aElement0(v1) = 0)) & !
% 162.19/22.41 [v0: $i] : ! [v1: $i] : ( ~ (doDivides0(v1, v0) = 0) | ~ (aElement0(v0) = 0)
% 162.19/22.41 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v1, v0)
% 162.19/22.41 = v3 & aElement0(v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : !
% 162.19/22.41 [v1: $i] : ( ~ (aElement0(v1) = 0) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~
% 162.19/22.41 $i(v0) | ? [v2: any] : ? [v3: any] : (aDivisorOf0(v1, v0) = v3 &
% 162.19/22.41 doDivides0(v1, v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 162.19/22.41
% 162.19/22.41 (mDefIdeal)
% 162.53/22.43 ! [v0: $i] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 162.53/22.43 $i] : ( ~ (aSet0(v0) = v1) | ~ (aElementOf0(v2, v0) = 0) | ~ (sdtasdt0(v3,
% 162.53/22.43 v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: int] : ? [v6:
% 162.53/22.43 any] : (( ~ (v5 = 0) & aIdeal0(v0) = v5) | (aElementOf0(v4, v0) = v6 &
% 162.53/22.43 aElement0(v3) = v5 & ( ~ (v5 = 0) | v6 = 0)))) & ! [v0: $i] : ! [v1:
% 162.53/22.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 162.53/22.43 (aSet0(v0) = v1) | ~ (aElementOf0(v2, v0) = 0) | ~ (sdtpldt0(v2, v3) = v4)
% 162.53/22.43 | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v5: int] : ? [v6: any] : (( ~ (v5
% 162.53/22.43 = 0) & aIdeal0(v0) = v5) | (aElementOf0(v4, v0) = v6 & aElementOf0(v3,
% 162.53/22.43 v0) = v5 & ( ~ (v5 = 0) | v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 162.53/22.43 [v2: $i] : ! [v3: $i] : ( ~ (aIdeal0(v0) = 0) | ~ (aElementOf0(v1, v0) = 0)
% 162.53/22.43 | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 162.53/22.43 any] : ? [v5: any] : (aElementOf0(v3, v0) = v5 & aElement0(v2) = v4 & ( ~
% 162.53/22.43 (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 162.53/22.43 $i] : ( ~ (aIdeal0(v0) = 0) | ~ (aElementOf0(v1, v0) = 0) | ~
% 162.53/22.43 (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] :
% 162.53/22.43 ? [v5: any] : (aElementOf0(v3, v0) = v5 & aElementOf0(v2, v0) = v4 & ( ~
% 162.53/22.43 (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: MultipleValueBool] : !
% 162.53/22.43 [v2: $i] : ! [v3: $i] : ( ~ (aSet0(v0) = v1) | ~ (aElementOf0(v3, v0) = 0) |
% 162.53/22.43 ~ (aElementOf0(v2, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4:
% 162.53/22.43 any] : ? [v5: int] : ((v5 = 0 & aElementOf0(v4, v0) = 0 & sdtpldt0(v2,
% 162.53/22.43 v3) = v4 & $i(v4)) | ( ~ (v4 = 0) & aIdeal0(v0) = v4))) & ! [v0: $i]
% 162.53/22.43 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ( ~ (aSet0(v0) =
% 162.53/22.43 v1) | ~ (aElementOf0(v2, v0) = 0) | ~ (aElement0(v3) = 0) | ~ $i(v3) |
% 162.53/22.43 ~ $i(v2) | ~ $i(v0) | ? [v4: any] : ? [v5: int] : ((v5 = 0 &
% 162.53/22.43 aElementOf0(v4, v0) = 0 & sdtasdt0(v3, v2) = v4 & $i(v4)) | ( ~ (v4 = 0)
% 162.53/22.43 & aIdeal0(v0) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 162.53/22.43 (aIdeal0(v0) = 0) | ~ (aElementOf0(v2, v0) = 0) | ~ (aElementOf0(v1, v0) =
% 162.53/22.43 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (aElementOf0(v3,
% 162.53/22.43 v0) = 0 & sdtpldt0(v1, v2) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] :
% 162.53/22.43 ! [v2: $i] : ( ~ (aIdeal0(v0) = 0) | ~ (aElementOf0(v1, v0) = 0) | ~
% 162.53/22.43 (aElement0(v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 162.53/22.43 (aElementOf0(v3, v0) = 0 & sdtasdt0(v2, v1) = v3 & $i(v3))) & ! [v0: $i] :
% 162.53/22.43 ! [v1: int] : (v1 = 0 | ~ (aIdeal0(v0) = v1) | ~ $i(v0) | ? [v2: int] : ?
% 162.53/22.43 [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] : ? [v8:
% 162.53/22.43 int] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ? [v12: int] :
% 162.53/22.43 ($i(v9) & $i(v5) & $i(v3) & ((v4 = 0 & aElementOf0(v3, v0) = 0 & ((v10 = 0 &
% 162.53/22.43 ~ (v12 = 0) & aElementOf0(v11, v0) = v12 & aElementOf0(v9, v0) =
% 162.53/22.43 0 & sdtpldt0(v3, v9) = v11 & $i(v11)) | (v6 = 0 & ~ (v8 = 0) &
% 162.53/22.43 aElementOf0(v7, v0) = v8 & sdtasdt0(v5, v3) = v7 & aElement0(v5) =
% 162.53/22.43 0 & $i(v7)))) | ( ~ (v2 = 0) & aSet0(v0) = v2)))) & ! [v0: $i] :
% 162.53/22.43 ! [v1: int] : (v1 = 0 | ~ (aSet0(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 162.53/22.43 (v2 = 0) & aIdeal0(v0) = v2)) & ! [v0: $i] : ( ~ (aIdeal0(v0) = 0) | ~
% 162.53/22.43 $i(v0) | aSet0(v0) = 0) & ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ?
% 162.53/22.43 [v1: int] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? [v5: int] : ?
% 162.53/22.43 [v6: $i] : ? [v7: int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ?
% 162.53/22.43 [v11: int] : ($i(v8) & $i(v4) & $i(v2) & ((v3 = 0 & aElementOf0(v2, v0) = 0
% 162.53/22.43 & ((v9 = 0 & ~ (v11 = 0) & aElementOf0(v10, v0) = v11 &
% 162.53/22.43 aElementOf0(v8, v0) = 0 & sdtpldt0(v2, v8) = v10 & $i(v10)) | (v5
% 162.53/22.43 = 0 & ~ (v7 = 0) & aElementOf0(v6, v0) = v7 & sdtasdt0(v4, v2) =
% 162.53/22.43 v6 & aElement0(v4) = 0 & $i(v6)))) | (v1 = 0 & aIdeal0(v0) = 0))))
% 162.53/22.43
% 162.53/22.43 (mDefRel)
% 162.53/22.43 $i(sz10) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 162.53/22.43 (misRelativelyPrime0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] :
% 162.53/22.43 ? [v4: any] : ? [v5: any] : (aGcdOfAnd0(sz10, v0, v1) = v5 & aElement0(v1)
% 162.53/22.43 = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = 0) |
% 162.53/22.43 v2 = 0) & ( ~ (v2 = 0) | v5 = 0))))) & ! [v0: $i] : ! [v1: $i] :
% 162.53/22.43 ! [v2: any] : ( ~ (aGcdOfAnd0(sz10, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 162.53/22.43 [v3: any] : ? [v4: any] : ? [v5: any] : (misRelativelyPrime0(v0, v1) = v5
% 162.53/22.43 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 162.53/22.43 (( ~ (v5 = 0) | v2 = 0) & ( ~ (v2 = 0) | v5 = 0)))))
% 162.53/22.43
% 162.53/22.43 (mDivision)
% 162.53/22.43 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 162.53/22.43 (sbrdtbr0(v1) = v2) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 162.53/22.43 [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ?
% 162.53/22.43 [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: any] : ($i(v5) & $i(v4) &
% 162.53/22.43 ((v9 = v0 & v7 = 0 & v6 = 0 & iLess0(v10, v2) = v11 & sbrdtbr0(v5) = v10 &
% 162.53/22.43 sdtasdt0(v4, v1) = v8 & sdtpldt0(v8, v5) = v0 & aElement0(v5) = 0 &
% 162.53/22.43 aElement0(v4) = 0 & $i(v10) & $i(v8) & (v11 = 0 | v5 = sz00)) | ( ~
% 162.53/22.43 (v3 = 0) & aElement0(v1) = v3)))) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 162.53/22.43 sz00 | ~ (aElement0(v1) = 0) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~
% 162.53/22.43 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 162.53/22.43 : ? [v7: any] : (iLess0(v6, v2) = v7 & sbrdtbr0(v4) = v6 & sbrdtbr0(v1) =
% 162.53/22.43 v2 & sdtasdt0(v3, v1) = v5 & sdtpldt0(v5, v4) = v0 & aElement0(v4) = 0 &
% 162.53/22.43 aElement0(v3) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & (v7 = 0 |
% 162.53/22.43 v4 = sz00)))
% 162.53/22.43
% 162.53/22.43 (mEOfElem)
% 162.53/22.44 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aSet0(v0) = 0) | ~
% 162.53/22.44 (aElement0(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 162.53/22.44 aElementOf0(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (aSet0(v0) =
% 162.53/22.44 0) | ~ (aElementOf0(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | aElement0(v1)
% 162.53/22.44 = 0)
% 162.53/22.44
% 162.53/22.44 (mEucSort)
% 162.53/22.44 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) |
% 162.53/22.44 ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 &
% 162.53/22.44 aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] : (v0 = sz00 |
% 162.53/22.44 ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (sbrdtbr0(v0) = v1 &
% 162.53/22.44 aNaturalNumber0(v1) = 0 & $i(v1)))
% 162.53/22.44
% 162.53/22.44 (mMulAsso)
% 162.53/22.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 162.53/22.44 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 162.53/22.44 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 162.53/22.44 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 & aElement0(v2) =
% 162.53/22.44 v7 & aElement0(v1) = v6 & aElement0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 =
% 162.53/22.44 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4))) & ! [v0: $i] : ! [v1:
% 162.53/22.44 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v1, v2) = v3)
% 162.53/22.44 | ~ (sdtasdt0(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 162.53/22.44 any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] :
% 162.53/22.44 (sdtasdt0(v8, v2) = v9 & sdtasdt0(v0, v1) = v8 & aElement0(v2) = v7 &
% 162.53/22.44 aElement0(v1) = v6 & aElement0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) |
% 162.53/22.44 ~ (v6 = 0) | ~ (v5 = 0) | v9 = v4)))
% 162.53/22.44
% 162.53/22.44 (mMulComm)
% 162.53/22.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~
% 162.53/22.44 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 162.53/22.44 (sdtasdt0(v0, v1) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & $i(v5) &
% 162.53/22.44 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0: $i] : ! [v1: $i] : !
% 162.53/22.44 [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any]
% 162.53/22.44 : ? [v4: any] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 &
% 162.53/22.44 aElement0(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 162.53/22.44
% 162.53/22.44 (mSortsB)
% 162.53/22.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 162.53/22.44 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 162.53/22.44 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0)
% 162.53/22.44 | ~ (v3 = 0) | v5 = 0)))
% 162.53/22.44
% 162.53/22.44 (mSortsB_02)
% 162.53/22.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 162.53/22.45 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 162.53/22.45 (aElement0(v2) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 & ( ~ (v4 = 0)
% 162.53/22.45 | ~ (v3 = 0) | v5 = 0)))
% 162.53/22.45
% 162.53/22.45 (mSortsC_01)
% 162.53/22.45 aElement0(sz10) = 0 & $i(sz10)
% 162.53/22.45
% 162.53/22.45 (mUnNeZr)
% 162.53/22.45 ~ (sz10 = sz00) & $i(sz10) & $i(sz00)
% 162.53/22.45
% 162.53/22.45 (m__)
% 162.53/22.45 xr = sz00 & $i(sz00)
% 162.53/22.45
% 162.53/22.45 (m__2091)
% 162.53/22.45 aElement0(xb) = 0 & aElement0(xa) = 0 & $i(xb) & $i(xa)
% 162.53/22.45
% 162.53/22.45 (m__2129)
% 162.53/22.47 $i(xc) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (aGcdOfAnd0(xc, xa, xb)
% 162.53/22.47 = 0 & aDivisorOf0(xc, xb) = 0 & aDivisorOf0(xc, xa) = 0 & doDivides0(xc, xb)
% 162.53/22.47 = 0 & doDivides0(xc, xa) = 0 & sdtasdt0(xc, v1) = xa & sdtasdt0(xc, v0) = xb
% 162.53/22.47 & aElement0(v1) = 0 & aElement0(v0) = 0 & aElement0(xc) = 0 & $i(v1) &
% 162.53/22.47 $i(v0) & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (doDivides0(v2, xc) = v3)
% 162.53/22.47 | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 162.53/22.47 ? [v8: any] : (aDivisorOf0(v2, xb) = v8 & aDivisorOf0(v2, xa) = v6 &
% 162.53/22.47 doDivides0(v2, xb) = v7 & doDivides0(v2, xa) = v5 & aElement0(v2) = v4 &
% 162.53/22.47 (( ~ (v8 = 0) & ~ (v7 = 0) & ! [v9: $i] : ( ~ (sdtasdt0(v2, v9) = xb)
% 162.53/22.47 | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & aElement0(v9) =
% 162.53/22.47 v10)) & ! [v9: $i] : ( ~ (aElement0(v9) = 0) | ~ $i(v9) | ?
% 162.53/22.47 [v10: $i] : ( ~ (v10 = xb) & sdtasdt0(v2, v9) = v10 & $i(v10)))) |
% 162.53/22.47 ( ~ (v6 = 0) & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~
% 162.53/22.47 (sdtasdt0(v2, v9) = xa) | ~ $i(v9) | ? [v10: int] : ( ~ (v10
% 162.53/22.47 = 0) & aElement0(v9) = v10)) & ! [v9: $i] : ( ~
% 162.53/22.47 (aElement0(v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10 =
% 162.53/22.47 xa) & sdtasdt0(v2, v9) = v10 & $i(v10))))))))) & ! [v2:
% 162.53/22.47 $i] : ! [v3: any] : ( ~ (aDivisorOf0(v2, xb) = v3) | ~ $i(v2) | ? [v4:
% 162.53/22.47 any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 162.53/22.47 [v9: $i] : ? [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xa) = v6 &
% 162.53/22.47 doDivides0(v2, xc) = v8 & doDivides0(v2, xb) = v7 & doDivides0(v2, xa) =
% 162.53/22.47 v5 & aElement0(v2) = v4 & $i(v9) & ((v11 = xc & v10 = 0 & v8 = 0 &
% 162.53/22.47 sdtasdt0(v2, v9) = xc & aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v3 =
% 162.53/22.47 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ?
% 162.53/22.47 [v13: int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12: $i]
% 162.53/22.47 : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 =
% 162.53/22.47 xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) | ( ~ (v6 = 0) & (
% 162.53/22.47 ~ (v4 = 0) | ( ~ (v5 = 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12)
% 162.53/22.47 = xa) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) &
% 162.53/22.47 aElement0(v12) = v13)) & ! [v12: $i] : ( ~ (aElement0(v12)
% 162.53/22.47 = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 = xa) &
% 162.53/22.47 sdtasdt0(v2, v12) = v13 & $i(v13))))))))) & ! [v2: $i] : !
% 162.53/22.47 [v3: any] : ( ~ (aDivisorOf0(v2, xa) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 162.53/22.47 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ?
% 162.53/22.47 [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xb) = v7 & doDivides0(v2, xc)
% 162.53/22.47 = v8 & doDivides0(v2, xb) = v6 & doDivides0(v2, xa) = v5 & aElement0(v2)
% 162.53/22.47 = v4 & $i(v9) & ((v11 = xc & v10 = 0 & v8 = 0 & sdtasdt0(v2, v9) = xc &
% 162.53/22.47 aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v6 = 0) & ! [v12: $i] : ( ~
% 162.53/22.47 (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 =
% 162.53/22.47 0) & aElement0(v12) = v13)) & ! [v12: $i] : ( ~
% 162.53/22.47 (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 = xb)
% 162.53/22.47 & sdtasdt0(v2, v12) = v13 & $i(v13)))) | ( ~ (v3 = 0) & ( ~ (v4
% 162.53/22.47 = 0) | ( ~ (v5 = 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12) =
% 162.53/22.47 xa) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) &
% 162.53/22.47 aElement0(v12) = v13)) & ! [v12: $i] : ( ~ (aElement0(v12)
% 162.53/22.47 = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 = xa) &
% 162.53/22.47 sdtasdt0(v2, v12) = v13 & $i(v13))))))))) & ! [v2: $i] : !
% 162.53/22.47 [v3: MultipleValueBool] : ( ~ (doDivides0(v2, xc) = v3) | ~ $i(v2) | ?
% 162.75/22.47 [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ?
% 162.75/22.47 [v9: $i] : ? [v10: int] : ? [v11: $i] : ($i(v9) & ((v11 = xc & v10 = 0 &
% 162.75/22.47 sdtasdt0(v2, v9) = xc & aElement0(v9) = 0) | (aDivisorOf0(v2, xb) =
% 162.75/22.47 v8 & aDivisorOf0(v2, xa) = v6 & doDivides0(v2, xb) = v7 &
% 162.75/22.47 doDivides0(v2, xa) = v5 & aElement0(v2) = v4 & (( ~ (v8 = 0) & ~
% 162.75/22.47 (v7 = 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~
% 162.75/22.47 $i(v12) | ? [v13: int] : ( ~ (v13 = 0) & aElement0(v12) =
% 162.75/22.47 v13)) & ! [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12)
% 162.75/22.47 | ? [v13: $i] : ( ~ (v13 = xb) & sdtasdt0(v2, v12) = v13 &
% 162.75/22.47 $i(v13)))) | ( ~ (v6 = 0) & ( ~ (v4 = 0) | ( ~ (v5 = 0) & !
% 162.75/22.47 [v12: $i] : ( ~ (sdtasdt0(v2, v12) = xa) | ~ $i(v12) | ?
% 162.75/22.47 [v13: int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & !
% 162.75/22.47 [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13:
% 162.75/22.47 $i] : ( ~ (v13 = xa) & sdtasdt0(v2, v12) = v13 &
% 162.75/22.47 $i(v13))))))))))) & ! [v2: $i] : ! [v3: any] : ( ~
% 162.75/22.47 (doDivides0(v2, xb) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ?
% 162.75/22.47 [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10: int] : ?
% 162.75/22.47 [v11: $i] : (aDivisorOf0(v2, xb) = v7 & aDivisorOf0(v2, xa) = v6 &
% 162.75/22.47 doDivides0(v2, xc) = v8 & doDivides0(v2, xa) = v5 & aElement0(v2) = v4 &
% 162.75/22.47 $i(v9) & ((v11 = xc & v10 = 0 & v8 = 0 & sdtasdt0(v2, v9) = xc &
% 162.75/22.47 aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v3 = 0) & ! [v12: $i] : ( ~
% 162.75/22.47 (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 =
% 162.75/22.47 0) & aElement0(v12) = v13)) & ! [v12: $i] : ( ~
% 162.75/22.47 (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 = xb)
% 162.75/22.47 & sdtasdt0(v2, v12) = v13 & $i(v13)))) | ( ~ (v6 = 0) & ( ~ (v4
% 162.75/22.47 = 0) | ( ~ (v5 = 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12) =
% 162.75/22.47 xa) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) &
% 162.75/22.47 aElement0(v12) = v13)) & ! [v12: $i] : ( ~ (aElement0(v12)
% 162.75/22.47 = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 = xa) &
% 162.75/22.47 sdtasdt0(v2, v12) = v13 & $i(v13))))))))) & ! [v2: $i] : !
% 162.75/22.47 [v3: any] : ( ~ (doDivides0(v2, xa) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 162.75/22.47 [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ?
% 162.75/22.47 [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xb) = v7 & aDivisorOf0(v2,
% 162.75/22.47 xa) = v5 & doDivides0(v2, xc) = v8 & doDivides0(v2, xb) = v6 &
% 162.75/22.47 aElement0(v2) = v4 & $i(v9) & ((v11 = xc & v10 = 0 & v8 = 0 &
% 162.75/22.47 sdtasdt0(v2, v9) = xc & aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v6 =
% 162.75/22.47 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ?
% 162.75/22.47 [v13: int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12: $i]
% 162.75/22.47 : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 =
% 162.75/22.47 xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) | ( ~ (v5 = 0) & (
% 162.75/22.47 ~ (v4 = 0) | ( ~ (v3 = 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12)
% 162.75/22.47 = xa) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) &
% 162.75/22.47 aElement0(v12) = v13)) & ! [v12: $i] : ( ~ (aElement0(v12)
% 162.75/22.47 = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 = xa) &
% 162.75/22.47 sdtasdt0(v2, v12) = v13 & $i(v13))))))))) & ! [v2: $i] : !
% 162.75/22.47 [v3: any] : ( ~ (aElement0(v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 162.75/22.47 any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ?
% 162.75/22.47 [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xb) = v7 & aDivisorOf0(v2,
% 162.75/22.47 xa) = v5 & doDivides0(v2, xc) = v8 & doDivides0(v2, xb) = v6 &
% 162.75/22.47 doDivides0(v2, xa) = v4 & $i(v9) & ((v11 = xc & v10 = 0 & v8 = 0 &
% 162.75/22.47 sdtasdt0(v2, v9) = xc & aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v6 =
% 162.75/22.47 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ?
% 162.75/22.47 [v13: int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12: $i]
% 162.75/22.47 : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 =
% 162.75/22.47 xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) | ( ~ (v5 = 0) & (
% 162.75/22.47 ~ (v3 = 0) | ( ~ (v4 = 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12)
% 162.75/22.47 = xa) | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) &
% 162.75/22.47 aElement0(v12) = v13)) & ! [v12: $i] : ( ~ (aElement0(v12)
% 162.75/22.47 = 0) | ~ $i(v12) | ? [v13: $i] : ( ~ (v13 = xa) &
% 162.75/22.47 sdtasdt0(v2, v12) = v13 & $i(v13))))))))))
% 162.75/22.47
% 162.75/22.47 (m__2174)
% 162.75/22.48 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 162.75/22.48 slsdtgt0(xa) = v0 & aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & aSet0(xI) = 0
% 162.75/22.48 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] :
% 162.75/22.48 (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~ (sdtpldt0(v4, v5) = v2) | ~
% 162.75/22.48 $i(v5) | ~ $i(v4) | ~ $i(v2) | ? [v6: any] : ? [v7: any] :
% 162.75/22.48 (aElementOf0(v5, v1) = v7 & aElementOf0(v4, v0) = v6 & ( ~ (v7 = 0) | ~
% 162.75/22.48 (v6 = 0)))) & ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~
% 162.75/22.48 (aElementOf0(v2, v1) = v3) | ~ (sdtasdt0(xb, v4) = v2) | ~ $i(v4) | ~
% 162.75/22.48 $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) = v5)) & ! [v2: $i]
% 162.75/22.48 : ! [v3: int] : ! [v4: $i] : (v3 = 0 | ~ (aElementOf0(v2, v1) = v3) | ~
% 162.75/22.48 (aElement0(v4) = 0) | ~ $i(v4) | ~ $i(v2) | ? [v5: $i] : ( ~ (v5 = v2)
% 162.75/22.48 & sdtasdt0(xb, v4) = v5 & $i(v5))) & ! [v2: $i] : ! [v3: int] : !
% 162.75/22.48 [v4: $i] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~ (sdtasdt0(xa, v4) =
% 162.75/22.48 v2) | ~ $i(v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) &
% 162.75/22.48 aElement0(v4) = v5)) & ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 =
% 162.75/22.48 0 | ~ (aElementOf0(v2, v0) = v3) | ~ (aElement0(v4) = 0) | ~ $i(v4) |
% 162.75/22.48 ~ $i(v2) | ? [v5: $i] : ( ~ (v5 = v2) & sdtasdt0(xa, v4) = v5 & $i(v5)))
% 162.75/22.48 & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (aElementOf0(v2, xI) = 0) |
% 162.75/22.48 ~ (sdtasdt0(v3, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6:
% 162.75/22.48 any] : (aElementOf0(v4, xI) = v6 & aElement0(v3) = v5 & ( ~ (v5 = 0) |
% 162.75/22.48 v6 = 0))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 162.75/22.48 (aElementOf0(v2, xI) = 0) | ~ (sdtpldt0(v2, v3) = v4) | ~ $i(v3) | ~
% 162.75/22.48 $i(v2) | ? [v5: any] : ? [v6: any] : (aElementOf0(v4, xI) = v6 &
% 162.75/22.48 aElementOf0(v3, xI) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v2: $i] : !
% 162.75/22.48 [v3: $i] : ( ~ (aElementOf0(v3, xI) = 0) | ~ (aElementOf0(v2, xI) = 0) | ~
% 162.75/22.48 $i(v3) | ~ $i(v2) | ? [v4: $i] : (aElementOf0(v4, xI) = 0 & sdtpldt0(v2,
% 162.75/22.48 v3) = v4 & $i(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ (aElementOf0(v2,
% 162.75/22.48 xI) = 0) | ~ (aElement0(v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4:
% 162.75/22.48 $i] : (aElementOf0(v4, xI) = 0 & sdtasdt0(v3, v2) = v4 & $i(v4))) & !
% 162.75/22.48 [v2: $i] : ( ~ (aElementOf0(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] :
% 162.75/22.48 (sdtasdt0(xb, v3) = v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~
% 162.75/22.48 (aElementOf0(v2, v0) = 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xa, v3) =
% 162.75/22.48 v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~ (aElementOf0(v2,
% 162.75/22.48 xI) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (aElementOf0(v4,
% 162.75/22.48 v1) = 0 & aElementOf0(v3, v0) = 0 & sdtpldt0(v3, v4) = v2 & $i(v4) &
% 162.75/22.48 $i(v3))))
% 162.75/22.48
% 162.75/22.48 (m__2203)
% 162.75/22.48 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 162.75/22.48 $i] : ? [v4: $i] : ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 162.75/22.48 aElementOf0(xb, v1) = 0 & aElementOf0(xa, v0) = 0 & aElementOf0(sz00, v1) =
% 162.75/22.48 0 & aElementOf0(sz00, v0) = 0 & sdtasdt0(xb, v3) = sz00 & sdtasdt0(xb, v2) =
% 162.75/22.48 xb & sdtasdt0(xa, v5) = sz00 & sdtasdt0(xa, v4) = xa & aElement0(v5) = 0 &
% 162.75/22.48 aElement0(v4) = 0 & aElement0(v3) = 0 & aElement0(v2) = 0 & $i(v5) & $i(v4)
% 162.75/22.48 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 162.75/22.48
% 162.75/22.48 (m__2228)
% 162.75/22.49 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 162.75/22.49 $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 &
% 162.75/22.49 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & aElementOf0(v5, v1) = 0 &
% 162.75/22.49 aElementOf0(v4, v0) = 0 & aElementOf0(v3, v2) = 0 & sdtpldt0(v4, v5) = v3 &
% 162.75/22.49 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7:
% 162.75/22.49 int] : ! [v8: $i] : (v7 = 0 | ~ (aElementOf0(v6, v1) = v7) | ~
% 162.75/22.49 (sdtasdt0(xb, v8) = v6) | ~ $i(v8) | ~ $i(v6) | ? [v9: int] : ( ~ (v9 =
% 162.75/22.49 0) & aElement0(v8) = v9)) & ! [v6: $i] : ! [v7: int] : ! [v8: $i] :
% 162.75/22.49 (v7 = 0 | ~ (aElementOf0(v6, v1) = v7) | ~ (aElement0(v8) = 0) | ~ $i(v8)
% 162.75/22.49 | ~ $i(v6) | ? [v9: $i] : ( ~ (v9 = v6) & sdtasdt0(xb, v8) = v9 &
% 162.75/22.49 $i(v9))) & ! [v6: $i] : ! [v7: int] : ! [v8: $i] : (v7 = 0 | ~
% 162.75/22.49 (aElementOf0(v6, v0) = v7) | ~ (sdtasdt0(xa, v8) = v6) | ~ $i(v8) | ~
% 162.75/22.49 $i(v6) | ? [v9: int] : ( ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v6: $i]
% 162.75/22.49 : ! [v7: int] : ! [v8: $i] : (v7 = 0 | ~ (aElementOf0(v6, v0) = v7) | ~
% 162.75/22.49 (aElement0(v8) = 0) | ~ $i(v8) | ~ $i(v6) | ? [v9: $i] : ( ~ (v9 = v6)
% 162.75/22.49 & sdtasdt0(xa, v8) = v9 & $i(v9))) & ! [v6: $i] : ( ~ (aElementOf0(v6,
% 162.75/22.49 v1) = 0) | ~ $i(v6) | ? [v7: $i] : (sdtasdt0(xb, v7) = v6 &
% 162.75/22.49 aElement0(v7) = 0 & $i(v7))) & ! [v6: $i] : ( ~ (aElementOf0(v6, v0) =
% 162.75/22.49 0) | ~ $i(v6) | ? [v7: $i] : (sdtasdt0(xa, v7) = v6 & aElement0(v7) =
% 162.75/22.49 0 & $i(v7))))
% 162.75/22.49
% 162.75/22.49 (m__2273)
% 162.75/22.49 $i(xu) & $i(xI) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ?
% 162.75/22.49 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (xu = sz00) & slsdtgt0(xb) = v1 &
% 162.75/22.49 slsdtgt0(xa) = v0 & sbrdtbr0(xu) = v2 & aElementOf0(v4, v1) = 0 &
% 162.75/22.49 aElementOf0(v3, v0) = 0 & aElementOf0(xu, xI) = 0 & sdtpldt0(v3, v4) = xu &
% 162.75/22.49 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6:
% 162.75/22.49 MultipleValueBool] : ! [v7: $i] : ! [v8: $i] : (v5 = sz00 | ~
% 162.75/22.49 (aElementOf0(v5, xI) = v6) | ~ (sdtpldt0(v7, v8) = v5) | ~ $i(v8) | ~
% 162.75/22.49 $i(v7) | ~ $i(v5) | ? [v9: any] : ? [v10: int] : (( ~ (v10 = 0) &
% 162.75/22.49 iLess0(v9, v2) = v10 & sbrdtbr0(v5) = v9 & $i(v9)) | (aElementOf0(v8,
% 162.75/22.49 v1) = v10 & aElementOf0(v7, v0) = v9 & ( ~ (v10 = 0) | ~ (v9 =
% 162.75/22.49 0))))) & ! [v5: $i] : ! [v6: $i] : (v5 = sz00 | ~ (sbrdtbr0(v5)
% 162.75/22.49 = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (iLess0(v6, v2) = v8 &
% 162.75/22.49 aElementOf0(v5, xI) = v7 & ( ~ (v8 = 0) | ( ~ (v7 = 0) & ! [v9: $i] :
% 162.75/22.49 ! [v10: $i] : ( ~ (sdtpldt0(v9, v10) = v5) | ~ $i(v10) | ~ $i(v9)
% 162.75/22.49 | ? [v11: any] : ? [v12: any] : (aElementOf0(v10, v1) = v12 &
% 162.75/22.49 aElementOf0(v9, v0) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))))))
% 162.75/22.49 & ! [v5: $i] : (v5 = sz00 | ~ (aElementOf0(v5, xI) = 0) | ~ $i(v5) | ?
% 162.75/22.49 [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & iLess0(v6, v2) = v7 &
% 162.75/22.49 sbrdtbr0(v5) = v6 & $i(v6))))
% 162.75/22.49
% 162.75/22.49 (m__2383)
% 162.75/22.50 $i(xu) & $i(xb) & $i(xa) & ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 162.75/22.50 [v3: any] : (aDivisorOf0(xu, xb) = v3 & aDivisorOf0(xu, xa) = v1 &
% 162.75/22.50 doDivides0(xu, xb) = v2 & doDivides0(xu, xa) = v0 & (( ~ (v3 = 0) & ~ (v2 =
% 162.75/22.50 0) & ! [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xb) | ~ $i(v4) | ? [v5:
% 162.75/22.50 int] : ( ~ (v5 = 0) & aElement0(v4) = v5)) & ! [v4: $i] : ( ~
% 162.75/22.50 (aElement0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ( ~ (v5 = xb) &
% 162.75/22.50 sdtasdt0(xu, v4) = v5 & $i(v5)))) | ( ~ (v1 = 0) & ~ (v0 = 0) & !
% 162.75/22.50 [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xa) | ~ $i(v4) | ? [v5: int] : ( ~
% 162.75/22.50 (v5 = 0) & aElement0(v4) = v5)) & ! [v4: $i] : ( ~ (aElement0(v4) =
% 162.75/22.50 0) | ~ $i(v4) | ? [v5: $i] : ( ~ (v5 = xa) & sdtasdt0(xu, v4) = v5
% 162.75/22.50 & $i(v5))))))
% 162.75/22.50
% 162.75/22.50 (m__2416)
% 162.75/22.50 $i(xu) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 162.75/22.50 $i] : (sdtasdt0(xb, v1) = v3 & sdtasdt0(xa, v0) = v2 & sdtpldt0(v2, v3) = xu
% 162.75/22.50 & aElement0(v1) = 0 & aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 162.75/22.50
% 162.75/22.50 (m__2479)
% 162.75/22.50 $i(xu) & $i(xa) & ? [v0: $i] : (doDivides0(xu, xa) = 0 & sdtasdt0(xu, v0) =
% 162.75/22.50 xa & aElement0(v0) = 0 & $i(v0))
% 162.75/22.50
% 162.75/22.50 (m__2612)
% 162.75/22.50 $i(xu) & $i(xb) & ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xu, xb) = v0 & !
% 162.75/22.50 [v1: $i] : ( ~ (sdtasdt0(xu, v1) = xb) | ~ $i(v1) | ? [v2: int] : ( ~ (v2
% 162.75/22.50 = 0) & aElement0(v1) = v2)) & ! [v1: $i] : ( ~ (aElement0(v1) = 0) |
% 162.75/22.50 ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = xb) & sdtasdt0(xu, v1) = v2 & $i(v2))))
% 162.75/22.50
% 162.75/22.50 (m__2666)
% 162.75/22.50 $i(xr) & $i(xq) & $i(xu) & $i(xb) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ?
% 162.75/22.50 [v2: $i] : ? [v3: any] : (iLess0(v1, v2) = v3 & sbrdtbr0(xr) = v1 &
% 162.75/22.50 sbrdtbr0(xu) = v2 & sdtasdt0(xq, xu) = v0 & sdtpldt0(v0, xr) = xb &
% 162.75/22.50 aElement0(xr) = 0 & aElement0(xq) = 0 & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 |
% 162.75/22.50 xr = sz00))
% 162.75/22.50
% 162.75/22.50 (function-axioms)
% 162.75/22.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 162.75/22.51 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (aGcdOfAnd0(v4, v3, v2) = v1) | ~
% 162.75/22.51 (aGcdOfAnd0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 162.75/22.51 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 162.75/22.51 (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1) | ~ (sdteqdtlpzmzozddtrp0(v4, v3,
% 162.75/22.51 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 162.75/22.51 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (misRelativelyPrime0(v3, v2) = v1) |
% 162.75/22.51 ~ (misRelativelyPrime0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 162.75/22.51 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 162.75/22.51 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0:
% 162.75/22.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 162.75/22.51 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 162.75/22.51 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 162.75/22.51 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 162.75/22.51 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 162.75/22.51 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 162.75/22.51 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 162.75/22.51 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 162.75/22.51 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 162.75/22.51 (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) & ! [v0: $i] :
% 162.75/22.51 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 162.75/22.51 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 162.75/22.51 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 162.75/22.51 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1)
% 162.75/22.51 | ~ (slsdtgt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 162.75/22.51 v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0:
% 162.75/22.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 162.75/22.51 ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0:
% 162.75/22.51 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 162.75/22.51 ~ (aIdeal0(v2) = v1) | ~ (aIdeal0(v2) = v0)) & ! [v0: MultipleValueBool] :
% 162.75/22.51 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 162.75/22.51 (aSet0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 162.75/22.51 (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 162.75/22.51 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 162.75/22.51 ~ (aElement0(v2) = v0))
% 162.75/22.51
% 162.75/22.51 Further assumptions not needed in the proof:
% 162.75/22.51 --------------------------------------------
% 162.75/22.51 mAddAsso, mAddInvr, mCancel, mChineseRemainder, mDefDiv, mDefGCD, mDefMod,
% 162.75/22.51 mDefPrIdeal, mDefSInt, mDefSSum, mElmSort, mIdeInt, mIdeSum, mMulMnOne,
% 162.75/22.51 mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort, mSortsC,
% 162.75/22.51 mSortsU, m__2110
% 162.75/22.51
% 162.75/22.51 Those formulas are unsatisfiable:
% 162.75/22.51 ---------------------------------
% 162.75/22.51
% 162.75/22.51 Begin of proof
% 162.75/22.51 |
% 162.75/22.51 | ALPHA: (mSortsC_01) implies:
% 162.75/22.51 | (1) aElement0(sz10) = 0
% 162.75/22.51 |
% 162.75/22.51 | ALPHA: (mAddComm) implies:
% 162.75/22.52 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 162.75/22.52 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 162.75/22.52 | (sdtpldt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 &
% 162.75/22.52 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 162.75/22.52 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) |
% 162.75/22.52 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 162.75/22.52 | (sdtpldt0(v0, v1) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 &
% 162.75/22.52 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 162.75/22.52 |
% 162.75/22.52 | ALPHA: (mAddZero) implies:
% 162.75/22.52 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ $i(v0) |
% 162.75/22.52 | ? [v2: any] : ? [v3: $i] : (sdtpldt0(sz00, v0) = v3 & aElement0(v0)
% 162.75/22.52 | = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 162.75/22.52 |
% 162.75/22.52 | ALPHA: (mMulComm) implies:
% 162.75/22.52 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) |
% 162.75/22.52 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 162.75/22.52 | (sdtasdt0(v1, v0) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 &
% 162.75/22.52 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 162.75/22.52 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) |
% 162.75/22.52 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 162.75/22.52 | (sdtasdt0(v0, v1) = v5 & aElement0(v1) = v4 & aElement0(v0) = v3 &
% 162.75/22.52 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 162.75/22.52 |
% 162.75/22.52 | ALPHA: (mMulAsso) implies:
% 162.75/22.52 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 162.75/22.52 | ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) |
% 162.75/22.52 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 162.75/22.52 | ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8)
% 162.75/22.52 | = v9 & aElement0(v2) = v7 & aElement0(v1) = v6 & aElement0(v0) = v5
% 162.75/22.52 | & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 162.75/22.52 | v4)))
% 162.75/22.52 |
% 162.75/22.52 | ALPHA: (mAMDistr) implies:
% 162.75/22.52 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 162.75/22.52 | ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 162.75/22.52 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 162.75/22.52 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i]
% 162.75/22.52 | : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v3, v0) = v11 &
% 162.75/22.52 | sdtasdt0(v2, v0) = v13 & sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v2)
% 162.75/22.52 | = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v12, v13) = v14 &
% 162.75/22.52 | sdtpldt0(v8, v9) = v10 & aElement0(v2) = v7 & aElement0(v1) = v6 &
% 162.75/22.52 | aElement0(v0) = v5 & $i(v14) & $i(v13) & $i(v12) & $i(v11) &
% 162.75/22.52 | $i(v10) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 =
% 162.75/22.52 | 0) | (v14 = v11 & v10 = v4))))
% 162.75/22.53 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 162.75/22.53 | ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 162.75/22.53 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 162.75/22.53 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i]
% 162.75/22.53 | : ? [v13: $i] : ? [v14: $i] : (sdtasdt0(v2, v0) = v13 &
% 162.75/22.53 | sdtasdt0(v1, v0) = v12 & sdtasdt0(v0, v3) = v8 & sdtasdt0(v0, v2) =
% 162.75/22.53 | v10 & sdtasdt0(v0, v1) = v9 & sdtpldt0(v12, v13) = v14 &
% 162.75/22.53 | sdtpldt0(v9, v10) = v11 & aElement0(v2) = v7 & aElement0(v1) = v6 &
% 162.75/22.53 | aElement0(v0) = v5 & $i(v14) & $i(v13) & $i(v12) & $i(v11) &
% 162.75/22.53 | $i(v10) & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 =
% 162.75/22.53 | 0) | (v14 = v4 & v11 = v8))))
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (mUnNeZr) implies:
% 162.75/22.53 | (10) ~ (sz10 = sz00)
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (mEOfElem) implies:
% 162.75/22.53 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (aSet0(v0) = 0) | ~ (aElementOf0(v1,
% 162.75/22.53 | v0) = 0) | ~ $i(v1) | ~ $i(v0) | aElement0(v1) = 0)
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (mDefIdeal) implies:
% 162.75/22.53 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 162.75/22.53 | (aIdeal0(v0) = 0) | ~ (aElementOf0(v1, v0) = 0) | ~ (sdtasdt0(v2,
% 162.75/22.53 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] :
% 162.75/22.53 | ? [v5: any] : (aElementOf0(v3, v0) = v5 & aElement0(v2) = v4 & ( ~
% 162.75/22.53 | (v4 = 0) | v5 = 0)))
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (mEucSort) implies:
% 162.75/22.53 | (13) ! [v0: $i] : ! [v1: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~
% 162.75/22.53 | $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 &
% 162.75/22.53 | aElement0(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (mDivision) implies:
% 162.75/22.53 | (14) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (aElement0(v1) = 0) | ~
% 162.75/22.53 | (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 162.75/22.53 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] :
% 162.75/22.53 | (iLess0(v6, v2) = v7 & sbrdtbr0(v4) = v6 & sbrdtbr0(v1) = v2 &
% 162.75/22.53 | sdtasdt0(v3, v1) = v5 & sdtpldt0(v5, v4) = v0 & aElement0(v4) = 0
% 162.75/22.53 | & aElement0(v3) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 162.75/22.53 | (v7 = 0 | v4 = sz00)))
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (mDefDvs) implies:
% 162.75/22.53 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (doDivides0(v1, v0) = 0) | ~
% 162.75/22.53 | (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 162.75/22.53 | any] : (aDivisorOf0(v1, v0) = v3 & aElement0(v1) = v2 & ( ~ (v2 =
% 162.75/22.53 | 0) | v3 = 0)))
% 162.75/22.53 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v1, v0) =
% 162.75/22.53 | v2) | ~ (aElement0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 162.75/22.53 | any] : ? [v4: any] : (aDivisorOf0(v1, v0) = v3 & aElement0(v1) =
% 162.75/22.53 | v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0))))
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (mDefRel) implies:
% 162.75/22.53 | (17) $i(sz10)
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (m__2091) implies:
% 162.75/22.53 | (18) aElement0(xa) = 0
% 162.75/22.53 | (19) aElement0(xb) = 0
% 162.75/22.53 |
% 162.75/22.53 | ALPHA: (m__2129) implies:
% 163.10/22.55 | (20) ? [v0: $i] : ? [v1: $i] : (aGcdOfAnd0(xc, xa, xb) = 0 &
% 163.10/22.55 | aDivisorOf0(xc, xb) = 0 & aDivisorOf0(xc, xa) = 0 & doDivides0(xc,
% 163.10/22.55 | xb) = 0 & doDivides0(xc, xa) = 0 & sdtasdt0(xc, v1) = xa &
% 163.10/22.55 | sdtasdt0(xc, v0) = xb & aElement0(v1) = 0 & aElement0(v0) = 0 &
% 163.10/22.55 | aElement0(xc) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: int] :
% 163.10/22.55 | (v3 = 0 | ~ (doDivides0(v2, xc) = v3) | ~ $i(v2) | ? [v4: any] :
% 163.10/22.55 | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 163.10/22.55 | (aDivisorOf0(v2, xb) = v8 & aDivisorOf0(v2, xa) = v6 &
% 163.10/22.55 | doDivides0(v2, xb) = v7 & doDivides0(v2, xa) = v5 &
% 163.10/22.55 | aElement0(v2) = v4 & (( ~ (v8 = 0) & ~ (v7 = 0) & ! [v9: $i] :
% 163.10/22.55 | ( ~ (sdtasdt0(v2, v9) = xb) | ~ $i(v9) | ? [v10: int] : (
% 163.10/22.55 | ~ (v10 = 0) & aElement0(v9) = v10)) & ! [v9: $i] : ( ~
% 163.10/22.55 | (aElement0(v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~ (v10
% 163.10/22.55 | = xb) & sdtasdt0(v2, v9) = v10 & $i(v10)))) | ( ~ (v6
% 163.10/22.55 | = 0) & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ! [v9: $i] : ( ~
% 163.10/22.55 | (sdtasdt0(v2, v9) = xa) | ~ $i(v9) | ? [v10: int] :
% 163.10/22.55 | ( ~ (v10 = 0) & aElement0(v9) = v10)) & ! [v9: $i] :
% 163.10/22.55 | ( ~ (aElement0(v9) = 0) | ~ $i(v9) | ? [v10: $i] : ( ~
% 163.10/22.55 | (v10 = xa) & sdtasdt0(v2, v9) = v10 &
% 163.10/22.55 | $i(v10))))))))) & ! [v2: $i] : ! [v3: any] : ( ~
% 163.10/22.55 | (aDivisorOf0(v2, xb) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 163.10/22.55 | any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i]
% 163.10/22.55 | : ? [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xa) = v6 &
% 163.10/22.55 | doDivides0(v2, xc) = v8 & doDivides0(v2, xb) = v7 &
% 163.10/22.55 | doDivides0(v2, xa) = v5 & aElement0(v2) = v4 & $i(v9) & ((v11 =
% 163.10/22.55 | xc & v10 = 0 & v8 = 0 & sdtasdt0(v2, v9) = xc &
% 163.10/22.55 | aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v3 = 0) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i]
% 163.10/22.55 | : ( ~ (v13 = xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) |
% 163.10/22.55 | ( ~ (v6 = 0) & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ! [v12: $i] : (
% 163.10/22.55 | ~ (sdtasdt0(v2, v12) = xa) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & !
% 163.10/22.55 | [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ?
% 163.10/22.55 | [v13: $i] : ( ~ (v13 = xa) & sdtasdt0(v2, v12) = v13 &
% 163.10/22.55 | $i(v13))))))))) & ! [v2: $i] : ! [v3: any] : ( ~
% 163.10/22.55 | (aDivisorOf0(v2, xa) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 163.10/22.55 | any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i]
% 163.10/22.55 | : ? [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xb) = v7 &
% 163.10/22.55 | doDivides0(v2, xc) = v8 & doDivides0(v2, xb) = v6 &
% 163.10/22.55 | doDivides0(v2, xa) = v5 & aElement0(v2) = v4 & $i(v9) & ((v11 =
% 163.10/22.55 | xc & v10 = 0 & v8 = 0 & sdtasdt0(v2, v9) = xc &
% 163.10/22.55 | aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v6 = 0) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i]
% 163.10/22.55 | : ( ~ (v13 = xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) |
% 163.10/22.55 | ( ~ (v3 = 0) & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ! [v12: $i] : (
% 163.10/22.55 | ~ (sdtasdt0(v2, v12) = xa) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & !
% 163.10/22.55 | [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ?
% 163.10/22.55 | [v13: $i] : ( ~ (v13 = xa) & sdtasdt0(v2, v12) = v13 &
% 163.10/22.55 | $i(v13))))))))) & ! [v2: $i] : ! [v3:
% 163.10/22.55 | MultipleValueBool] : ( ~ (doDivides0(v2, xc) = v3) | ~ $i(v2) |
% 163.10/22.55 | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8:
% 163.10/22.55 | any] : ? [v9: $i] : ? [v10: int] : ? [v11: $i] : ($i(v9) &
% 163.10/22.55 | ((v11 = xc & v10 = 0 & sdtasdt0(v2, v9) = xc & aElement0(v9) =
% 163.10/22.55 | 0) | (aDivisorOf0(v2, xb) = v8 & aDivisorOf0(v2, xa) = v6 &
% 163.10/22.55 | doDivides0(v2, xb) = v7 & doDivides0(v2, xa) = v5 &
% 163.10/22.55 | aElement0(v2) = v4 & (( ~ (v8 = 0) & ~ (v7 = 0) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ?
% 163.10/22.55 | [v13: int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) &
% 163.10/22.55 | ! [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ?
% 163.10/22.55 | [v13: $i] : ( ~ (v13 = xb) & sdtasdt0(v2, v12) = v13 &
% 163.10/22.55 | $i(v13)))) | ( ~ (v6 = 0) & ( ~ (v4 = 0) | ( ~ (v5 =
% 163.10/22.55 | 0) & ! [v12: $i] : ( ~ (sdtasdt0(v2, v12) = xa) |
% 163.10/22.55 | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) &
% 163.10/22.55 | aElement0(v12) = v13)) & ! [v12: $i] : ( ~
% 163.10/22.55 | (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i] :
% 163.10/22.55 | ( ~ (v13 = xa) & sdtasdt0(v2, v12) = v13 &
% 163.10/22.55 | $i(v13))))))))))) & ! [v2: $i] : ! [v3: any] :
% 163.10/22.55 | ( ~ (doDivides0(v2, xb) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 163.10/22.55 | any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i]
% 163.10/22.55 | : ? [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xb) = v7 &
% 163.10/22.55 | aDivisorOf0(v2, xa) = v6 & doDivides0(v2, xc) = v8 &
% 163.10/22.55 | doDivides0(v2, xa) = v5 & aElement0(v2) = v4 & $i(v9) & ((v11 =
% 163.10/22.55 | xc & v10 = 0 & v8 = 0 & sdtasdt0(v2, v9) = xc &
% 163.10/22.55 | aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v3 = 0) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i]
% 163.10/22.55 | : ( ~ (v13 = xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) |
% 163.10/22.55 | ( ~ (v6 = 0) & ( ~ (v4 = 0) | ( ~ (v5 = 0) & ! [v12: $i] : (
% 163.10/22.55 | ~ (sdtasdt0(v2, v12) = xa) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & !
% 163.10/22.55 | [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ?
% 163.10/22.55 | [v13: $i] : ( ~ (v13 = xa) & sdtasdt0(v2, v12) = v13 &
% 163.10/22.55 | $i(v13))))))))) & ! [v2: $i] : ! [v3: any] : ( ~
% 163.10/22.55 | (doDivides0(v2, xa) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 163.10/22.55 | any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i]
% 163.10/22.55 | : ? [v10: int] : ? [v11: $i] : (aDivisorOf0(v2, xb) = v7 &
% 163.10/22.55 | aDivisorOf0(v2, xa) = v5 & doDivides0(v2, xc) = v8 &
% 163.10/22.55 | doDivides0(v2, xb) = v6 & aElement0(v2) = v4 & $i(v9) & ((v11 =
% 163.10/22.55 | xc & v10 = 0 & v8 = 0 & sdtasdt0(v2, v9) = xc &
% 163.10/22.55 | aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v6 = 0) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i]
% 163.10/22.55 | : ( ~ (v13 = xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) |
% 163.10/22.55 | ( ~ (v5 = 0) & ( ~ (v4 = 0) | ( ~ (v3 = 0) & ! [v12: $i] : (
% 163.10/22.55 | ~ (sdtasdt0(v2, v12) = xa) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & !
% 163.10/22.55 | [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ?
% 163.10/22.55 | [v13: $i] : ( ~ (v13 = xa) & sdtasdt0(v2, v12) = v13 &
% 163.10/22.55 | $i(v13))))))))) & ! [v2: $i] : ! [v3: any] : ( ~
% 163.10/22.55 | (aElement0(v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any] :
% 163.10/22.55 | ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i] : ? [v10:
% 163.10/22.55 | int] : ? [v11: $i] : (aDivisorOf0(v2, xb) = v7 &
% 163.10/22.55 | aDivisorOf0(v2, xa) = v5 & doDivides0(v2, xc) = v8 &
% 163.10/22.55 | doDivides0(v2, xb) = v6 & doDivides0(v2, xa) = v4 & $i(v9) &
% 163.10/22.55 | ((v11 = xc & v10 = 0 & v8 = 0 & sdtasdt0(v2, v9) = xc &
% 163.10/22.55 | aElement0(v9) = 0) | ( ~ (v7 = 0) & ~ (v6 = 0) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (sdtasdt0(v2, v12) = xb) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & ! [v12:
% 163.10/22.55 | $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ? [v13: $i]
% 163.10/22.55 | : ( ~ (v13 = xb) & sdtasdt0(v2, v12) = v13 & $i(v13)))) |
% 163.10/22.55 | ( ~ (v5 = 0) & ( ~ (v3 = 0) | ( ~ (v4 = 0) & ! [v12: $i] : (
% 163.10/22.55 | ~ (sdtasdt0(v2, v12) = xa) | ~ $i(v12) | ? [v13:
% 163.10/22.55 | int] : ( ~ (v13 = 0) & aElement0(v12) = v13)) & !
% 163.10/22.55 | [v12: $i] : ( ~ (aElement0(v12) = 0) | ~ $i(v12) | ?
% 163.10/22.55 | [v13: $i] : ( ~ (v13 = xa) & sdtasdt0(v2, v12) = v13 &
% 163.10/22.55 | $i(v13))))))))))
% 163.10/22.55 |
% 163.10/22.55 | ALPHA: (m__2174) implies:
% 163.10/22.56 | (21) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 163.10/22.56 | aIdeal0(xI) = 0 & sdtpldt1(v0, v1) = xI & aSet0(xI) = 0 & $i(v1) &
% 163.10/22.56 | $i(v0) & ! [v2: $i] : ! [v3: int] : ! [v4: $i] : ! [v5: $i] :
% 163.10/22.56 | (v3 = 0 | ~ (aElementOf0(v2, xI) = v3) | ~ (sdtpldt0(v4, v5) = v2)
% 163.10/22.56 | | ~ $i(v5) | ~ $i(v4) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 163.10/22.56 | : (aElementOf0(v5, v1) = v7 & aElementOf0(v4, v0) = v6 & ( ~ (v7 =
% 163.10/22.56 | 0) | ~ (v6 = 0)))) & ! [v2: $i] : ! [v3: int] : ! [v4:
% 163.10/22.56 | $i] : (v3 = 0 | ~ (aElementOf0(v2, v1) = v3) | ~ (sdtasdt0(xb,
% 163.10/22.56 | v4) = v2) | ~ $i(v4) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 =
% 163.10/22.56 | 0) & aElement0(v4) = v5)) & ! [v2: $i] : ! [v3: int] : !
% 163.10/22.56 | [v4: $i] : (v3 = 0 | ~ (aElementOf0(v2, v1) = v3) | ~
% 163.10/22.56 | (aElement0(v4) = 0) | ~ $i(v4) | ~ $i(v2) | ? [v5: $i] : ( ~
% 163.10/22.56 | (v5 = v2) & sdtasdt0(xb, v4) = v5 & $i(v5))) & ! [v2: $i] : !
% 163.10/22.56 | [v3: int] : ! [v4: $i] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) |
% 163.10/22.56 | ~ (sdtasdt0(xa, v4) = v2) | ~ $i(v4) | ~ $i(v2) | ? [v5: int] :
% 163.10/22.56 | ( ~ (v5 = 0) & aElement0(v4) = v5)) & ! [v2: $i] : ! [v3: int] :
% 163.10/22.56 | ! [v4: $i] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~
% 163.10/22.56 | (aElement0(v4) = 0) | ~ $i(v4) | ~ $i(v2) | ? [v5: $i] : ( ~
% 163.10/22.56 | (v5 = v2) & sdtasdt0(xa, v4) = v5 & $i(v5))) & ! [v2: $i] : !
% 163.10/22.56 | [v3: $i] : ! [v4: $i] : ( ~ (aElementOf0(v2, xI) = 0) | ~
% 163.10/22.56 | (sdtasdt0(v3, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: any] :
% 163.10/22.56 | ? [v6: any] : (aElementOf0(v4, xI) = v6 & aElement0(v3) = v5 & ( ~
% 163.10/22.56 | (v5 = 0) | v6 = 0))) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 163.10/22.56 | : ( ~ (aElementOf0(v2, xI) = 0) | ~ (sdtpldt0(v2, v3) = v4) | ~
% 163.10/22.56 | $i(v3) | ~ $i(v2) | ? [v5: any] : ? [v6: any] :
% 163.10/22.56 | (aElementOf0(v4, xI) = v6 & aElementOf0(v3, xI) = v5 & ( ~ (v5 =
% 163.10/22.56 | 0) | v6 = 0))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 163.10/22.56 | (aElementOf0(v3, xI) = 0) | ~ (aElementOf0(v2, xI) = 0) | ~
% 163.10/22.56 | $i(v3) | ~ $i(v2) | ? [v4: $i] : (aElementOf0(v4, xI) = 0 &
% 163.10/22.56 | sdtpldt0(v2, v3) = v4 & $i(v4))) & ! [v2: $i] : ! [v3: $i] : (
% 163.10/22.56 | ~ (aElementOf0(v2, xI) = 0) | ~ (aElement0(v3) = 0) | ~ $i(v3) |
% 163.10/22.56 | ~ $i(v2) | ? [v4: $i] : (aElementOf0(v4, xI) = 0 & sdtasdt0(v3,
% 163.10/22.56 | v2) = v4 & $i(v4))) & ! [v2: $i] : ( ~ (aElementOf0(v2, v1) =
% 163.10/22.56 | 0) | ~ $i(v2) | ? [v3: $i] : (sdtasdt0(xb, v3) = v2 &
% 163.10/22.56 | aElement0(v3) = 0 & $i(v3))) & ! [v2: $i] : ( ~
% 163.10/22.56 | (aElementOf0(v2, v0) = 0) | ~ $i(v2) | ? [v3: $i] :
% 163.10/22.56 | (sdtasdt0(xa, v3) = v2 & aElement0(v3) = 0 & $i(v3))) & ! [v2:
% 163.10/22.56 | $i] : ( ~ (aElementOf0(v2, xI) = 0) | ~ $i(v2) | ? [v3: $i] : ?
% 163.10/22.56 | [v4: $i] : (aElementOf0(v4, v1) = 0 & aElementOf0(v3, v0) = 0 &
% 163.10/22.56 | sdtpldt0(v3, v4) = v2 & $i(v4) & $i(v3))))
% 163.10/22.56 |
% 163.10/22.56 | ALPHA: (m__2203) implies:
% 163.10/22.56 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 163.10/22.56 | ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & aElementOf0(xb,
% 163.10/22.56 | v1) = 0 & aElementOf0(xa, v0) = 0 & aElementOf0(sz00, v1) = 0 &
% 163.10/22.56 | aElementOf0(sz00, v0) = 0 & sdtasdt0(xb, v3) = sz00 & sdtasdt0(xb,
% 163.10/22.56 | v2) = xb & sdtasdt0(xa, v5) = sz00 & sdtasdt0(xa, v4) = xa &
% 163.10/22.56 | aElement0(v5) = 0 & aElement0(v4) = 0 & aElement0(v3) = 0 &
% 163.10/22.56 | aElement0(v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 163.10/22.56 | $i(v0))
% 163.10/22.56 |
% 163.10/22.56 | ALPHA: (m__2228) implies:
% 163.10/22.56 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 163.10/22.56 | ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 163.10/22.56 | sdtpldt1(v0, v1) = v2 & aElementOf0(v5, v1) = 0 & aElementOf0(v4,
% 163.10/22.56 | v0) = 0 & aElementOf0(v3, v2) = 0 & sdtpldt0(v4, v5) = v3 & $i(v5)
% 163.10/22.56 | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v6: $i] : ! [v7:
% 163.10/22.56 | int] : ! [v8: $i] : (v7 = 0 | ~ (aElementOf0(v6, v1) = v7) | ~
% 163.10/22.56 | (sdtasdt0(xb, v8) = v6) | ~ $i(v8) | ~ $i(v6) | ? [v9: int] : (
% 163.10/22.56 | ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v6: $i] : ! [v7: int] :
% 163.10/22.56 | ! [v8: $i] : (v7 = 0 | ~ (aElementOf0(v6, v1) = v7) | ~
% 163.10/22.56 | (aElement0(v8) = 0) | ~ $i(v8) | ~ $i(v6) | ? [v9: $i] : ( ~
% 163.10/22.56 | (v9 = v6) & sdtasdt0(xb, v8) = v9 & $i(v9))) & ! [v6: $i] : !
% 163.10/22.56 | [v7: int] : ! [v8: $i] : (v7 = 0 | ~ (aElementOf0(v6, v0) = v7) |
% 163.10/22.56 | ~ (sdtasdt0(xa, v8) = v6) | ~ $i(v8) | ~ $i(v6) | ? [v9: int] :
% 163.10/22.56 | ( ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v6: $i] : ! [v7: int] :
% 163.10/22.56 | ! [v8: $i] : (v7 = 0 | ~ (aElementOf0(v6, v0) = v7) | ~
% 163.10/22.56 | (aElement0(v8) = 0) | ~ $i(v8) | ~ $i(v6) | ? [v9: $i] : ( ~
% 163.10/22.56 | (v9 = v6) & sdtasdt0(xa, v8) = v9 & $i(v9))) & ! [v6: $i] : ( ~
% 163.10/22.56 | (aElementOf0(v6, v1) = 0) | ~ $i(v6) | ? [v7: $i] :
% 163.10/22.56 | (sdtasdt0(xb, v7) = v6 & aElement0(v7) = 0 & $i(v7))) & ! [v6:
% 163.10/22.56 | $i] : ( ~ (aElementOf0(v6, v0) = 0) | ~ $i(v6) | ? [v7: $i] :
% 163.10/22.56 | (sdtasdt0(xa, v7) = v6 & aElement0(v7) = 0 & $i(v7))))
% 163.10/22.56 |
% 163.10/22.56 | ALPHA: (m__2273) implies:
% 163.10/22.57 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 163.10/22.57 | ( ~ (xu = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sbrdtbr0(xu)
% 163.10/22.57 | = v2 & aElementOf0(v4, v1) = 0 & aElementOf0(v3, v0) = 0 &
% 163.10/22.57 | aElementOf0(xu, xI) = 0 & sdtpldt0(v3, v4) = xu & $i(v4) & $i(v3) &
% 163.10/22.57 | $i(v2) & $i(v1) & $i(v0) & ! [v5: $i] : ! [v6: MultipleValueBool]
% 163.10/22.57 | : ! [v7: $i] : ! [v8: $i] : (v5 = sz00 | ~ (aElementOf0(v5, xI) =
% 163.10/22.57 | v6) | ~ (sdtpldt0(v7, v8) = v5) | ~ $i(v8) | ~ $i(v7) | ~
% 163.10/22.57 | $i(v5) | ? [v9: any] : ? [v10: int] : (( ~ (v10 = 0) &
% 163.10/22.57 | iLess0(v9, v2) = v10 & sbrdtbr0(v5) = v9 & $i(v9)) |
% 163.10/22.57 | (aElementOf0(v8, v1) = v10 & aElementOf0(v7, v0) = v9 & ( ~ (v10
% 163.10/22.57 | = 0) | ~ (v9 = 0))))) & ! [v5: $i] : ! [v6: $i] : (v5 =
% 163.10/22.57 | sz00 | ~ (sbrdtbr0(v5) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8:
% 163.10/22.57 | any] : (iLess0(v6, v2) = v8 & aElementOf0(v5, xI) = v7 & ( ~ (v8
% 163.10/22.57 | = 0) | ( ~ (v7 = 0) & ! [v9: $i] : ! [v10: $i] : ( ~
% 163.10/22.57 | (sdtpldt0(v9, v10) = v5) | ~ $i(v10) | ~ $i(v9) | ?
% 163.10/22.57 | [v11: any] : ? [v12: any] : (aElementOf0(v10, v1) = v12 &
% 163.10/22.57 | aElementOf0(v9, v0) = v11 & ( ~ (v12 = 0) | ~ (v11 =
% 163.10/22.57 | 0)))))))) & ! [v5: $i] : (v5 = sz00 | ~
% 163.10/22.57 | (aElementOf0(v5, xI) = 0) | ~ $i(v5) | ? [v6: $i] : ? [v7: int]
% 163.10/22.57 | : ( ~ (v7 = 0) & iLess0(v6, v2) = v7 & sbrdtbr0(v5) = v6 &
% 163.10/22.57 | $i(v6))))
% 163.10/22.57 |
% 163.10/22.57 | ALPHA: (m__2383) implies:
% 163.10/22.57 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 163.10/22.57 | (aDivisorOf0(xu, xb) = v3 & aDivisorOf0(xu, xa) = v1 & doDivides0(xu,
% 163.10/22.57 | xb) = v2 & doDivides0(xu, xa) = v0 & (( ~ (v3 = 0) & ~ (v2 = 0) &
% 163.10/22.57 | ! [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xb) | ~ $i(v4) | ? [v5:
% 163.10/22.57 | int] : ( ~ (v5 = 0) & aElement0(v4) = v5)) & ! [v4: $i] : (
% 163.10/22.57 | ~ (aElement0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ( ~ (v5 =
% 163.10/22.57 | xb) & sdtasdt0(xu, v4) = v5 & $i(v5)))) | ( ~ (v1 = 0) &
% 163.10/22.57 | ~ (v0 = 0) & ! [v4: $i] : ( ~ (sdtasdt0(xu, v4) = xa) | ~
% 163.10/22.57 | $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aElement0(v4) = v5)) &
% 163.10/22.57 | ! [v4: $i] : ( ~ (aElement0(v4) = 0) | ~ $i(v4) | ? [v5: $i] :
% 163.10/22.57 | ( ~ (v5 = xa) & sdtasdt0(xu, v4) = v5 & $i(v5))))))
% 163.10/22.57 |
% 163.10/22.57 | ALPHA: (m__2416) implies:
% 163.21/22.57 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(xb,
% 163.21/22.57 | v1) = v3 & sdtasdt0(xa, v0) = v2 & sdtpldt0(v2, v3) = xu &
% 163.21/22.57 | aElement0(v1) = 0 & aElement0(v0) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 163.21/22.57 | $i(v0))
% 163.21/22.57 |
% 163.21/22.57 | ALPHA: (m__2479) implies:
% 163.21/22.57 | (27) $i(xa)
% 163.21/22.57 | (28) ? [v0: $i] : (doDivides0(xu, xa) = 0 & sdtasdt0(xu, v0) = xa &
% 163.21/22.57 | aElement0(v0) = 0 & $i(v0))
% 163.21/22.57 |
% 163.21/22.57 | ALPHA: (m__2612) implies:
% 163.21/22.57 | (29) ? [v0: int] : ( ~ (v0 = 0) & doDivides0(xu, xb) = v0 & ! [v1: $i] :
% 163.21/22.57 | ( ~ (sdtasdt0(xu, v1) = xb) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 =
% 163.21/22.57 | 0) & aElement0(v1) = v2)) & ! [v1: $i] : ( ~ (aElement0(v1) =
% 163.21/22.57 | 0) | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = xb) & sdtasdt0(xu, v1)
% 163.21/22.57 | = v2 & $i(v2))))
% 163.21/22.57 |
% 163.21/22.57 | ALPHA: (m__2666) implies:
% 163.21/22.57 | (30) $i(xb)
% 163.21/22.57 | (31) $i(xu)
% 163.21/22.57 | (32) $i(xq)
% 163.21/22.57 | (33) $i(xr)
% 163.21/22.57 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (iLess0(v1,
% 163.21/22.57 | v2) = v3 & sbrdtbr0(xr) = v1 & sbrdtbr0(xu) = v2 & sdtasdt0(xq,
% 163.21/22.57 | xu) = v0 & sdtpldt0(v0, xr) = xb & aElement0(xr) = 0 &
% 163.21/22.57 | aElement0(xq) = 0 & $i(v2) & $i(v1) & $i(v0) & (v3 = 0 | xr = sz00))
% 163.21/22.57 |
% 163.21/22.57 | ALPHA: (m__) implies:
% 163.21/22.57 | (35) xr = sz00
% 163.21/22.57 |
% 163.21/22.57 | ALPHA: (function-axioms) implies:
% 163.21/22.57 | (36) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 163.21/22.57 | : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 163.21/22.57 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2)
% 163.21/22.57 | = v1) | ~ (sbrdtbr0(v2) = v0))
% 163.21/22.57 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2)
% 163.21/22.57 | = v1) | ~ (slsdtgt0(v2) = v0))
% 163.21/22.57 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 163.21/22.57 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 163.21/22.57 | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 163.21/22.57 | (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0))
% 163.21/22.57 | (41) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 163.21/22.57 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~
% 163.21/22.57 | (doDivides0(v3, v2) = v0))
% 163.21/22.57 |
% 163.21/22.57 | DELTA: instantiating (28) with fresh symbol all_34_0 gives:
% 163.21/22.57 | (42) doDivides0(xu, xa) = 0 & sdtasdt0(xu, all_34_0) = xa &
% 163.21/22.57 | aElement0(all_34_0) = 0 & $i(all_34_0)
% 163.21/22.57 |
% 163.21/22.57 | ALPHA: (42) implies:
% 163.21/22.57 | (43) $i(all_34_0)
% 163.21/22.57 | (44) sdtasdt0(xu, all_34_0) = xa
% 163.21/22.57 | (45) doDivides0(xu, xa) = 0
% 163.21/22.57 |
% 163.21/22.57 | DELTA: instantiating (26) with fresh symbols all_36_0, all_36_1, all_36_2,
% 163.21/22.57 | all_36_3 gives:
% 163.21/22.58 | (46) sdtasdt0(xb, all_36_2) = all_36_0 & sdtasdt0(xa, all_36_3) = all_36_1
% 163.21/22.58 | & sdtpldt0(all_36_1, all_36_0) = xu & aElement0(all_36_2) = 0 &
% 163.21/22.58 | aElement0(all_36_3) = 0 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) &
% 163.21/22.58 | $i(all_36_3)
% 163.21/22.58 |
% 163.21/22.58 | ALPHA: (46) implies:
% 163.21/22.58 | (47) $i(all_36_3)
% 163.21/22.58 | (48) $i(all_36_2)
% 163.21/22.58 | (49) $i(all_36_1)
% 163.21/22.58 | (50) $i(all_36_0)
% 163.21/22.58 | (51) sdtpldt0(all_36_1, all_36_0) = xu
% 163.21/22.58 | (52) sdtasdt0(xa, all_36_3) = all_36_1
% 163.21/22.58 | (53) sdtasdt0(xb, all_36_2) = all_36_0
% 163.21/22.58 |
% 163.21/22.58 | DELTA: instantiating (29) with fresh symbol all_38_0 gives:
% 163.21/22.58 | (54) ~ (all_38_0 = 0) & doDivides0(xu, xb) = all_38_0 & ! [v0: $i] : ( ~
% 163.21/22.58 | (sdtasdt0(xu, v0) = xb) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 163.21/22.58 | aElement0(v0) = v1)) & ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~
% 163.21/22.58 | $i(v0) | ? [v1: $i] : ( ~ (v1 = xb) & sdtasdt0(xu, v0) = v1 &
% 163.21/22.58 | $i(v1)))
% 163.21/22.58 |
% 163.21/22.58 | ALPHA: (54) implies:
% 163.21/22.58 | (55) doDivides0(xu, xb) = all_38_0
% 163.21/22.58 |
% 163.21/22.58 | DELTA: instantiating (34) with fresh symbols all_41_0, all_41_1, all_41_2,
% 163.21/22.58 | all_41_3 gives:
% 163.21/22.58 | (56) iLess0(all_41_2, all_41_1) = all_41_0 & sbrdtbr0(xr) = all_41_2 &
% 163.21/22.58 | sbrdtbr0(xu) = all_41_1 & sdtasdt0(xq, xu) = all_41_3 &
% 163.21/22.58 | sdtpldt0(all_41_3, xr) = xb & aElement0(xr) = 0 & aElement0(xq) = 0 &
% 163.21/22.58 | $i(all_41_1) & $i(all_41_2) & $i(all_41_3) & (all_41_0 = 0 | xr =
% 163.21/22.58 | sz00)
% 163.21/22.58 |
% 163.21/22.58 | ALPHA: (56) implies:
% 163.21/22.58 | (57) $i(all_41_3)
% 163.21/22.58 | (58) aElement0(xq) = 0
% 163.21/22.58 | (59) sdtpldt0(all_41_3, xr) = xb
% 163.21/22.58 | (60) sdtasdt0(xq, xu) = all_41_3
% 163.21/22.58 | (61) sbrdtbr0(xu) = all_41_1
% 163.21/22.58 |
% 163.21/22.58 | DELTA: instantiating (22) with fresh symbols all_43_0, all_43_1, all_43_2,
% 163.21/22.58 | all_43_3, all_43_4, all_43_5 gives:
% 163.21/22.58 | (62) slsdtgt0(xb) = all_43_4 & slsdtgt0(xa) = all_43_5 & aElementOf0(xb,
% 163.21/22.58 | all_43_4) = 0 & aElementOf0(xa, all_43_5) = 0 & aElementOf0(sz00,
% 163.21/22.58 | all_43_4) = 0 & aElementOf0(sz00, all_43_5) = 0 & sdtasdt0(xb,
% 163.21/22.58 | all_43_2) = sz00 & sdtasdt0(xb, all_43_3) = xb & sdtasdt0(xa,
% 163.21/22.58 | all_43_0) = sz00 & sdtasdt0(xa, all_43_1) = xa & aElement0(all_43_0)
% 163.21/22.58 | = 0 & aElement0(all_43_1) = 0 & aElement0(all_43_2) = 0 &
% 163.21/22.58 | aElement0(all_43_3) = 0 & $i(all_43_0) & $i(all_43_1) & $i(all_43_2) &
% 163.21/22.58 | $i(all_43_3) & $i(all_43_4) & $i(all_43_5)
% 163.21/22.58 |
% 163.21/22.58 | ALPHA: (62) implies:
% 163.21/22.58 | (63) $i(all_43_3)
% 163.21/22.58 | (64) $i(all_43_2)
% 163.21/22.58 | (65) $i(all_43_1)
% 163.21/22.58 | (66) $i(all_43_0)
% 163.21/22.58 | (67) sdtasdt0(xa, all_43_1) = xa
% 163.21/22.58 | (68) sdtasdt0(xa, all_43_0) = sz00
% 163.21/22.58 | (69) sdtasdt0(xb, all_43_3) = xb
% 163.21/22.58 | (70) sdtasdt0(xb, all_43_2) = sz00
% 163.21/22.58 | (71) slsdtgt0(xa) = all_43_5
% 163.21/22.58 | (72) slsdtgt0(xb) = all_43_4
% 163.21/22.58 |
% 163.21/22.58 | DELTA: instantiating (25) with fresh symbols all_45_0, all_45_1, all_45_2,
% 163.21/22.58 | all_45_3 gives:
% 163.21/22.58 | (73) aDivisorOf0(xu, xb) = all_45_0 & aDivisorOf0(xu, xa) = all_45_2 &
% 163.21/22.58 | doDivides0(xu, xb) = all_45_1 & doDivides0(xu, xa) = all_45_3 & (( ~
% 163.21/22.58 | (all_45_0 = 0) & ~ (all_45_1 = 0) & ! [v0: $i] : ( ~
% 163.21/22.58 | (sdtasdt0(xu, v0) = xb) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 163.21/22.58 | 0) & aElement0(v0) = v1)) & ! [v0: $i] : ( ~ (aElement0(v0)
% 163.21/22.58 | = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xb) & sdtasdt0(xu,
% 163.21/22.58 | v0) = v1 & $i(v1)))) | ( ~ (all_45_2 = 0) & ~ (all_45_3 =
% 163.21/22.58 | 0) & ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xa) | ~ $i(v0) | ?
% 163.21/22.58 | [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = v1)) & ! [v0: $i] :
% 163.21/22.58 | ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xa)
% 163.21/22.58 | & sdtasdt0(xu, v0) = v1 & $i(v1)))))
% 163.21/22.58 |
% 163.21/22.58 | ALPHA: (73) implies:
% 163.21/22.58 | (74) doDivides0(xu, xa) = all_45_3
% 163.21/22.58 | (75) doDivides0(xu, xb) = all_45_1
% 163.21/22.58 | (76) aDivisorOf0(xu, xb) = all_45_0
% 163.21/22.58 | (77) ( ~ (all_45_0 = 0) & ~ (all_45_1 = 0) & ! [v0: $i] : ( ~
% 163.21/22.58 | (sdtasdt0(xu, v0) = xb) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 163.21/22.58 | & aElement0(v0) = v1)) & ! [v0: $i] : ( ~ (aElement0(v0) = 0) |
% 163.21/22.58 | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xb) & sdtasdt0(xu, v0) = v1 &
% 163.21/22.58 | $i(v1)))) | ( ~ (all_45_2 = 0) & ~ (all_45_3 = 0) & ! [v0: $i]
% 163.21/22.58 | : ( ~ (sdtasdt0(xu, v0) = xa) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 163.21/22.58 | 0) & aElement0(v0) = v1)) & ! [v0: $i] : ( ~ (aElement0(v0) =
% 163.21/22.58 | 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xa) & sdtasdt0(xu, v0)
% 163.21/22.58 | = v1 & $i(v1))))
% 163.21/22.58 |
% 163.21/22.58 | DELTA: instantiating (24) with fresh symbols all_50_0, all_50_1, all_50_2,
% 163.21/22.58 | all_50_3, all_50_4 gives:
% 163.21/22.59 | (78) ~ (xu = sz00) & slsdtgt0(xb) = all_50_3 & slsdtgt0(xa) = all_50_4 &
% 163.21/22.59 | sbrdtbr0(xu) = all_50_2 & aElementOf0(all_50_0, all_50_3) = 0 &
% 163.21/22.59 | aElementOf0(all_50_1, all_50_4) = 0 & aElementOf0(xu, xI) = 0 &
% 163.21/22.59 | sdtpldt0(all_50_1, all_50_0) = xu & $i(all_50_0) & $i(all_50_1) &
% 163.21/22.59 | $i(all_50_2) & $i(all_50_3) & $i(all_50_4) & ! [v0: $i] : ! [v1:
% 163.21/22.59 | MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~
% 163.21/22.59 | (aElementOf0(v0, xI) = v1) | ~ (sdtpldt0(v2, v3) = v0) | ~ $i(v3)
% 163.21/22.59 | | ~ $i(v2) | ~ $i(v0) | ? [v4: any] : ? [v5: int] : (( ~ (v5 =
% 163.21/22.59 | 0) & iLess0(v4, all_50_2) = v5 & sbrdtbr0(v0) = v4 & $i(v4)) |
% 163.21/22.59 | (aElementOf0(v3, all_50_3) = v5 & aElementOf0(v2, all_50_4) = v4 &
% 163.21/22.59 | ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : (v0
% 163.21/22.59 | = sz00 | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 163.21/22.59 | any] : (iLess0(v1, all_50_2) = v3 & aElementOf0(v0, xI) = v2 & ( ~
% 163.21/22.59 | (v3 = 0) | ( ~ (v2 = 0) & ! [v4: $i] : ! [v5: $i] : ( ~
% 163.21/22.59 | (sdtpldt0(v4, v5) = v0) | ~ $i(v5) | ~ $i(v4) | ? [v6:
% 163.21/22.59 | any] : ? [v7: any] : (aElementOf0(v5, all_50_3) = v7 &
% 163.21/22.59 | aElementOf0(v4, all_50_4) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 163.21/22.59 | 0)))))))) & ! [v0: $i] : (v0 = sz00 | ~
% 163.21/22.59 | (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: int] :
% 163.21/22.59 | ( ~ (v2 = 0) & iLess0(v1, all_50_2) = v2 & sbrdtbr0(v0) = v1 &
% 163.21/22.59 | $i(v1)))
% 163.21/22.59 |
% 163.21/22.59 | ALPHA: (78) implies:
% 163.21/22.59 | (79) ~ (xu = sz00)
% 163.21/22.59 | (80) $i(all_50_1)
% 163.21/22.59 | (81) $i(all_50_0)
% 163.21/22.59 | (82) sdtpldt0(all_50_1, all_50_0) = xu
% 163.21/22.59 | (83) aElementOf0(xu, xI) = 0
% 163.21/22.59 | (84) sbrdtbr0(xu) = all_50_2
% 163.21/22.59 | (85) slsdtgt0(xa) = all_50_4
% 163.21/22.59 | (86) slsdtgt0(xb) = all_50_3
% 163.21/22.59 |
% 163.21/22.59 | DELTA: instantiating (23) with fresh symbols all_53_0, all_53_1, all_53_2,
% 163.21/22.59 | all_53_3, all_53_4, all_53_5 gives:
% 163.21/22.59 | (87) ~ (all_53_2 = sz00) & slsdtgt0(xb) = all_53_4 & slsdtgt0(xa) =
% 163.21/22.59 | all_53_5 & sdtpldt1(all_53_5, all_53_4) = all_53_3 &
% 163.21/22.59 | aElementOf0(all_53_0, all_53_4) = 0 & aElementOf0(all_53_1, all_53_5)
% 163.21/22.59 | = 0 & aElementOf0(all_53_2, all_53_3) = 0 & sdtpldt0(all_53_1,
% 163.21/22.59 | all_53_0) = all_53_2 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) &
% 163.21/22.59 | $i(all_53_3) & $i(all_53_4) & $i(all_53_5) & ! [v0: $i] : ! [v1:
% 163.21/22.59 | int] : ! [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_53_4) = v1) |
% 163.21/22.59 | ~ (sdtasdt0(xb, v2) = v0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] :
% 163.21/22.59 | ( ~ (v3 = 0) & aElement0(v2) = v3)) & ! [v0: $i] : ! [v1: int] :
% 163.21/22.59 | ! [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_53_4) = v1) | ~
% 163.21/22.59 | (aElement0(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3
% 163.21/22.59 | = v0) & sdtasdt0(xb, v2) = v3 & $i(v3))) & ! [v0: $i] : ! [v1:
% 163.21/22.59 | int] : ! [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_53_5) = v1) |
% 163.21/22.59 | ~ (sdtasdt0(xa, v2) = v0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] :
% 163.21/22.59 | ( ~ (v3 = 0) & aElement0(v2) = v3)) & ! [v0: $i] : ! [v1: int] :
% 163.21/22.59 | ! [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_53_5) = v1) | ~
% 163.21/22.59 | (aElement0(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3
% 163.21/22.59 | = v0) & sdtasdt0(xa, v2) = v3 & $i(v3))) & ! [v0: $i] : ( ~
% 163.21/22.59 | (aElementOf0(v0, all_53_4) = 0) | ~ $i(v0) | ? [v1: $i] :
% 163.21/22.59 | (sdtasdt0(xb, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & ! [v0: $i]
% 163.21/22.59 | : ( ~ (aElementOf0(v0, all_53_5) = 0) | ~ $i(v0) | ? [v1: $i] :
% 163.21/22.59 | (sdtasdt0(xa, v1) = v0 & aElement0(v1) = 0 & $i(v1)))
% 163.21/22.59 |
% 163.21/22.59 | ALPHA: (87) implies:
% 163.21/22.59 | (88) $i(all_53_3)
% 163.21/22.59 | (89) sdtpldt1(all_53_5, all_53_4) = all_53_3
% 163.21/22.59 | (90) slsdtgt0(xa) = all_53_5
% 163.21/22.59 | (91) slsdtgt0(xb) = all_53_4
% 163.21/22.59 |
% 163.21/22.59 | DELTA: instantiating (21) with fresh symbols all_56_0, all_56_1 gives:
% 163.21/22.60 | (92) slsdtgt0(xb) = all_56_0 & slsdtgt0(xa) = all_56_1 & aIdeal0(xI) = 0 &
% 163.21/22.60 | sdtpldt1(all_56_1, all_56_0) = xI & aSet0(xI) = 0 & $i(all_56_0) &
% 163.21/22.60 | $i(all_56_1) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : ! [v3: $i]
% 163.21/22.60 | : (v1 = 0 | ~ (aElementOf0(v0, xI) = v1) | ~ (sdtpldt0(v2, v3) = v0)
% 163.21/22.60 | | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 163.21/22.60 | (aElementOf0(v3, all_56_0) = v5 & aElementOf0(v2, all_56_1) = v4 & (
% 163.21/22.60 | ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : !
% 163.21/22.60 | [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_56_0) = v1) | ~
% 163.21/22.60 | (sdtasdt0(xb, v2) = v0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ( ~
% 163.21/22.60 | (v3 = 0) & aElement0(v2) = v3)) & ! [v0: $i] : ! [v1: int] : !
% 163.21/22.60 | [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_56_0) = v1) | ~
% 163.21/22.60 | (aElement0(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3
% 163.21/22.60 | = v0) & sdtasdt0(xb, v2) = v3 & $i(v3))) & ! [v0: $i] : ! [v1:
% 163.21/22.60 | int] : ! [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_56_1) = v1) |
% 163.21/22.60 | ~ (sdtasdt0(xa, v2) = v0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] :
% 163.21/22.60 | ( ~ (v3 = 0) & aElement0(v2) = v3)) & ! [v0: $i] : ! [v1: int] :
% 163.21/22.60 | ! [v2: $i] : (v1 = 0 | ~ (aElementOf0(v0, all_56_1) = v1) | ~
% 163.21/22.60 | (aElement0(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3
% 163.21/22.60 | = v0) & sdtasdt0(xa, v2) = v3 & $i(v3))) & ! [v0: $i] : ! [v1:
% 163.21/22.60 | $i] : ! [v2: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ (sdtasdt0(v1,
% 163.21/22.60 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any]
% 163.21/22.60 | : (aElementOf0(v2, xI) = v4 & aElement0(v1) = v3 & ( ~ (v3 = 0) | v4
% 163.21/22.60 | = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 163.21/22.60 | (aElementOf0(v0, xI) = 0) | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) |
% 163.21/22.60 | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aElementOf0(v2, xI) = v4
% 163.21/22.60 | & aElementOf0(v1, xI) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0:
% 163.21/22.60 | $i] : ! [v1: $i] : ( ~ (aElementOf0(v1, xI) = 0) | ~
% 163.21/22.60 | (aElementOf0(v0, xI) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 163.21/22.60 | (aElementOf0(v2, xI) = 0 & sdtpldt0(v0, v1) = v2 & $i(v2))) & !
% 163.21/22.60 | [v0: $i] : ! [v1: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~
% 163.21/22.60 | (aElement0(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 163.21/22.60 | (aElementOf0(v2, xI) = 0 & sdtasdt0(v1, v0) = v2 & $i(v2))) & !
% 163.21/22.60 | [v0: $i] : ( ~ (aElementOf0(v0, all_56_0) = 0) | ~ $i(v0) | ? [v1:
% 163.21/22.60 | $i] : (sdtasdt0(xb, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & !
% 163.21/22.60 | [v0: $i] : ( ~ (aElementOf0(v0, all_56_1) = 0) | ~ $i(v0) | ? [v1:
% 163.21/22.60 | $i] : (sdtasdt0(xa, v1) = v0 & aElement0(v1) = 0 & $i(v1))) & !
% 163.21/22.60 | [v0: $i] : ( ~ (aElementOf0(v0, xI) = 0) | ~ $i(v0) | ? [v1: $i] :
% 163.21/22.60 | ? [v2: $i] : (aElementOf0(v2, all_56_0) = 0 & aElementOf0(v1,
% 163.21/22.60 | all_56_1) = 0 & sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1)))
% 163.21/22.60 |
% 163.21/22.60 | ALPHA: (92) implies:
% 163.21/22.60 | (93) aSet0(xI) = 0
% 163.21/22.60 | (94) sdtpldt1(all_56_1, all_56_0) = xI
% 163.21/22.60 | (95) aIdeal0(xI) = 0
% 163.21/22.60 | (96) slsdtgt0(xa) = all_56_1
% 163.21/22.60 | (97) slsdtgt0(xb) = all_56_0
% 163.21/22.60 |
% 163.21/22.60 | DELTA: instantiating (20) with fresh symbols all_59_0, all_59_1 gives:
% 163.21/22.61 | (98) aGcdOfAnd0(xc, xa, xb) = 0 & aDivisorOf0(xc, xb) = 0 & aDivisorOf0(xc,
% 163.21/22.61 | xa) = 0 & doDivides0(xc, xb) = 0 & doDivides0(xc, xa) = 0 &
% 163.21/22.61 | sdtasdt0(xc, all_59_0) = xa & sdtasdt0(xc, all_59_1) = xb &
% 163.21/22.61 | aElement0(all_59_0) = 0 & aElement0(all_59_1) = 0 & aElement0(xc) = 0
% 163.21/22.61 | & $i(all_59_0) & $i(all_59_1) & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 163.21/22.61 | ~ (doDivides0(v0, xc) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 163.21/22.61 | any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 163.21/22.61 | (aDivisorOf0(v0, xb) = v6 & aDivisorOf0(v0, xa) = v4 &
% 163.21/22.61 | doDivides0(v0, xb) = v5 & doDivides0(v0, xa) = v3 & aElement0(v0)
% 163.21/22.61 | = v2 & (( ~ (v6 = 0) & ~ (v5 = 0) & ! [v7: $i] : ( ~
% 163.21/22.61 | (sdtasdt0(v0, v7) = xb) | ~ $i(v7) | ? [v8: int] : ( ~ (v8
% 163.21/22.61 | = 0) & aElement0(v7) = v8)) & ! [v7: $i] : ( ~
% 163.21/22.61 | (aElement0(v7) = 0) | ~ $i(v7) | ? [v8: $i] : ( ~ (v8 =
% 163.21/22.61 | xb) & sdtasdt0(v0, v7) = v8 & $i(v8)))) | ( ~ (v4 = 0) &
% 163.21/22.61 | ( ~ (v2 = 0) | ( ~ (v3 = 0) & ! [v7: $i] : ( ~ (sdtasdt0(v0,
% 163.21/22.61 | v7) = xa) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0)
% 163.21/22.61 | & aElement0(v7) = v8)) & ! [v7: $i] : ( ~
% 163.21/22.61 | (aElement0(v7) = 0) | ~ $i(v7) | ? [v8: $i] : ( ~ (v8
% 163.21/22.61 | = xa) & sdtasdt0(v0, v7) = v8 & $i(v8))))))))) & !
% 163.21/22.61 | [v0: $i] : ! [v1: any] : ( ~ (aDivisorOf0(v0, xb) = v1) | ~ $i(v0) |
% 163.21/22.61 | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6:
% 163.21/22.61 | any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : (aDivisorOf0(v0,
% 163.21/22.61 | xa) = v4 & doDivides0(v0, xc) = v6 & doDivides0(v0, xb) = v5 &
% 163.21/22.61 | doDivides0(v0, xa) = v3 & aElement0(v0) = v2 & $i(v7) & ((v9 = xc
% 163.21/22.61 | & v8 = 0 & v6 = 0 & sdtasdt0(v0, v7) = xc & aElement0(v7) = 0)
% 163.21/22.61 | | ( ~ (v5 = 0) & ~ (v1 = 0) & ! [v10: $i] : ( ~ (sdtasdt0(v0,
% 163.21/22.61 | v10) = xb) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0)
% 163.21/22.61 | & aElement0(v10) = v11)) & ! [v10: $i] : ( ~
% 163.21/22.61 | (aElement0(v10) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~ (v11
% 163.21/22.61 | = xb) & sdtasdt0(v0, v10) = v11 & $i(v11)))) | ( ~ (v4 =
% 163.21/22.61 | 0) & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ! [v10: $i] : ( ~
% 163.21/22.61 | (sdtasdt0(v0, v10) = xa) | ~ $i(v10) | ? [v11: int] :
% 163.21/22.61 | ( ~ (v11 = 0) & aElement0(v10) = v11)) & ! [v10: $i] :
% 163.21/22.61 | ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~
% 163.21/22.61 | (v11 = xa) & sdtasdt0(v0, v10) = v11 & $i(v11)))))))))
% 163.21/22.61 | & ! [v0: $i] : ! [v1: any] : ( ~ (aDivisorOf0(v0, xa) = v1) | ~
% 163.21/22.61 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 163.21/22.61 | ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] :
% 163.21/22.61 | (aDivisorOf0(v0, xb) = v5 & doDivides0(v0, xc) = v6 & doDivides0(v0,
% 163.21/22.61 | xb) = v4 & doDivides0(v0, xa) = v3 & aElement0(v0) = v2 & $i(v7)
% 163.21/22.61 | & ((v9 = xc & v8 = 0 & v6 = 0 & sdtasdt0(v0, v7) = xc &
% 163.21/22.61 | aElement0(v7) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & ! [v10: $i]
% 163.21/22.61 | : ( ~ (sdtasdt0(v0, v10) = xb) | ~ $i(v10) | ? [v11: int] :
% 163.21/22.61 | ( ~ (v11 = 0) & aElement0(v10) = v11)) & ! [v10: $i] : ( ~
% 163.21/22.61 | (aElement0(v10) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~ (v11
% 163.21/22.61 | = xb) & sdtasdt0(v0, v10) = v11 & $i(v11)))) | ( ~ (v1 =
% 163.21/22.61 | 0) & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ! [v10: $i] : ( ~
% 163.21/22.61 | (sdtasdt0(v0, v10) = xa) | ~ $i(v10) | ? [v11: int] :
% 163.21/22.61 | ( ~ (v11 = 0) & aElement0(v10) = v11)) & ! [v10: $i] :
% 163.21/22.61 | ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~
% 163.21/22.61 | (v11 = xa) & sdtasdt0(v0, v10) = v11 & $i(v11)))))))))
% 163.21/22.61 | & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (doDivides0(v0, xc) =
% 163.21/22.61 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ?
% 163.21/22.61 | [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i]
% 163.21/22.61 | : ($i(v7) & ((v9 = xc & v8 = 0 & sdtasdt0(v0, v7) = xc &
% 163.21/22.61 | aElement0(v7) = 0) | (aDivisorOf0(v0, xb) = v6 &
% 163.21/22.61 | aDivisorOf0(v0, xa) = v4 & doDivides0(v0, xb) = v5 &
% 163.21/22.61 | doDivides0(v0, xa) = v3 & aElement0(v0) = v2 & (( ~ (v6 = 0) &
% 163.21/22.61 | ~ (v5 = 0) & ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xb)
% 163.21/22.61 | | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0) &
% 163.21/22.61 | aElement0(v10) = v11)) & ! [v10: $i] : ( ~
% 163.21/22.61 | (aElement0(v10) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~
% 163.21/22.61 | (v11 = xb) & sdtasdt0(v0, v10) = v11 & $i(v11)))) | (
% 163.21/22.61 | ~ (v4 = 0) & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ! [v10: $i] :
% 163.21/22.61 | ( ~ (sdtasdt0(v0, v10) = xa) | ~ $i(v10) | ? [v11:
% 163.21/22.61 | int] : ( ~ (v11 = 0) & aElement0(v10) = v11)) & !
% 163.21/22.61 | [v10: $i] : ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ?
% 163.21/22.61 | [v11: $i] : ( ~ (v11 = xa) & sdtasdt0(v0, v10) = v11
% 163.21/22.61 | & $i(v11))))))))))) & ! [v0: $i] : ! [v1: any] :
% 163.21/22.61 | ( ~ (doDivides0(v0, xb) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 163.21/22.61 | any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] :
% 163.21/22.61 | ? [v8: int] : ? [v9: $i] : (aDivisorOf0(v0, xb) = v5 &
% 163.21/22.61 | aDivisorOf0(v0, xa) = v4 & doDivides0(v0, xc) = v6 &
% 163.21/22.61 | doDivides0(v0, xa) = v3 & aElement0(v0) = v2 & $i(v7) & ((v9 = xc
% 163.21/22.61 | & v8 = 0 & v6 = 0 & sdtasdt0(v0, v7) = xc & aElement0(v7) = 0)
% 163.21/22.61 | | ( ~ (v5 = 0) & ~ (v1 = 0) & ! [v10: $i] : ( ~ (sdtasdt0(v0,
% 163.21/22.61 | v10) = xb) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0)
% 163.21/22.61 | & aElement0(v10) = v11)) & ! [v10: $i] : ( ~
% 163.21/22.61 | (aElement0(v10) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~ (v11
% 163.21/22.61 | = xb) & sdtasdt0(v0, v10) = v11 & $i(v11)))) | ( ~ (v4 =
% 163.21/22.61 | 0) & ( ~ (v2 = 0) | ( ~ (v3 = 0) & ! [v10: $i] : ( ~
% 163.21/22.61 | (sdtasdt0(v0, v10) = xa) | ~ $i(v10) | ? [v11: int] :
% 163.21/22.61 | ( ~ (v11 = 0) & aElement0(v10) = v11)) & ! [v10: $i] :
% 163.21/22.61 | ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~
% 163.21/22.61 | (v11 = xa) & sdtasdt0(v0, v10) = v11 & $i(v11)))))))))
% 163.21/22.61 | & ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xa) = v1) | ~
% 163.21/22.61 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 163.21/22.61 | ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] :
% 163.21/22.61 | (aDivisorOf0(v0, xb) = v5 & aDivisorOf0(v0, xa) = v3 &
% 163.21/22.61 | doDivides0(v0, xc) = v6 & doDivides0(v0, xb) = v4 & aElement0(v0)
% 163.21/22.61 | = v2 & $i(v7) & ((v9 = xc & v8 = 0 & v6 = 0 & sdtasdt0(v0, v7) =
% 163.21/22.61 | xc & aElement0(v7) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & !
% 163.21/22.61 | [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xb) | ~ $i(v10) | ?
% 163.21/22.61 | [v11: int] : ( ~ (v11 = 0) & aElement0(v10) = v11)) & !
% 163.21/22.61 | [v10: $i] : ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ? [v11:
% 163.21/22.61 | $i] : ( ~ (v11 = xb) & sdtasdt0(v0, v10) = v11 &
% 163.21/22.61 | $i(v11)))) | ( ~ (v3 = 0) & ( ~ (v2 = 0) | ( ~ (v1 = 0) &
% 163.21/22.61 | ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xa) | ~ $i(v10) |
% 163.21/22.61 | ? [v11: int] : ( ~ (v11 = 0) & aElement0(v10) = v11)) &
% 163.21/22.61 | ! [v10: $i] : ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ?
% 163.21/22.61 | [v11: $i] : ( ~ (v11 = xa) & sdtasdt0(v0, v10) = v11 &
% 163.21/22.61 | $i(v11))))))))) & ! [v0: $i] : ! [v1: any] : ( ~
% 163.21/22.61 | (aElement0(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 163.21/22.61 | [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: int]
% 163.21/22.61 | : ? [v9: $i] : (aDivisorOf0(v0, xb) = v5 & aDivisorOf0(v0, xa) = v3
% 163.21/22.61 | & doDivides0(v0, xc) = v6 & doDivides0(v0, xb) = v4 &
% 163.21/22.61 | doDivides0(v0, xa) = v2 & $i(v7) & ((v9 = xc & v8 = 0 & v6 = 0 &
% 163.21/22.61 | sdtasdt0(v0, v7) = xc & aElement0(v7) = 0) | ( ~ (v5 = 0) & ~
% 163.21/22.61 | (v4 = 0) & ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xb) | ~
% 163.21/22.61 | $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & aElement0(v10) =
% 163.21/22.61 | v11)) & ! [v10: $i] : ( ~ (aElement0(v10) = 0) | ~
% 163.21/22.61 | $i(v10) | ? [v11: $i] : ( ~ (v11 = xb) & sdtasdt0(v0, v10)
% 163.21/22.61 | = v11 & $i(v11)))) | ( ~ (v3 = 0) & ( ~ (v1 = 0) | ( ~ (v2
% 163.21/22.61 | = 0) & ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xa) | ~
% 163.21/22.61 | $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & aElement0(v10)
% 163.21/22.61 | = v11)) & ! [v10: $i] : ( ~ (aElement0(v10) = 0) | ~
% 163.21/22.61 | $i(v10) | ? [v11: $i] : ( ~ (v11 = xa) & sdtasdt0(v0,
% 163.21/22.61 | v10) = v11 & $i(v11)))))))))
% 163.21/22.61 |
% 163.21/22.61 | ALPHA: (98) implies:
% 163.21/22.61 | (99) $i(all_59_0)
% 163.21/22.61 | (100) aElement0(all_59_0) = 0
% 163.21/22.61 | (101) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xa) = v1) | ~
% 163.21/22.61 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any]
% 163.21/22.61 | : ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] :
% 163.21/22.61 | (aDivisorOf0(v0, xb) = v5 & aDivisorOf0(v0, xa) = v3 &
% 163.21/22.61 | doDivides0(v0, xc) = v6 & doDivides0(v0, xb) = v4 & aElement0(v0)
% 163.21/22.61 | = v2 & $i(v7) & ((v9 = xc & v8 = 0 & v6 = 0 & sdtasdt0(v0, v7) =
% 163.21/22.61 | xc & aElement0(v7) = 0) | ( ~ (v5 = 0) & ~ (v4 = 0) & !
% 163.21/22.61 | [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xb) | ~ $i(v10) | ?
% 163.21/22.61 | [v11: int] : ( ~ (v11 = 0) & aElement0(v10) = v11)) & !
% 163.21/22.61 | [v10: $i] : ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ? [v11:
% 163.21/22.61 | $i] : ( ~ (v11 = xb) & sdtasdt0(v0, v10) = v11 &
% 163.21/22.61 | $i(v11)))) | ( ~ (v3 = 0) & ( ~ (v2 = 0) | ( ~ (v1 = 0) &
% 163.21/22.61 | ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xa) | ~ $i(v10)
% 163.21/22.61 | | ? [v11: int] : ( ~ (v11 = 0) & aElement0(v10) =
% 163.21/22.61 | v11)) & ! [v10: $i] : ( ~ (aElement0(v10) = 0) | ~
% 163.21/22.61 | $i(v10) | ? [v11: $i] : ( ~ (v11 = xa) & sdtasdt0(v0,
% 163.21/22.61 | v10) = v11 & $i(v11)))))))))
% 163.21/22.62 | (102) ! [v0: $i] : ! [v1: any] : ( ~ (doDivides0(v0, xb) = v1) | ~
% 163.21/22.62 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any]
% 163.21/22.62 | : ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] :
% 163.21/22.62 | (aDivisorOf0(v0, xb) = v5 & aDivisorOf0(v0, xa) = v4 &
% 163.21/22.62 | doDivides0(v0, xc) = v6 & doDivides0(v0, xa) = v3 & aElement0(v0)
% 163.21/22.62 | = v2 & $i(v7) & ((v9 = xc & v8 = 0 & v6 = 0 & sdtasdt0(v0, v7) =
% 163.21/22.62 | xc & aElement0(v7) = 0) | ( ~ (v5 = 0) & ~ (v1 = 0) & !
% 163.21/22.62 | [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xb) | ~ $i(v10) | ?
% 163.21/22.62 | [v11: int] : ( ~ (v11 = 0) & aElement0(v10) = v11)) & !
% 163.21/22.62 | [v10: $i] : ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ? [v11:
% 163.21/22.62 | $i] : ( ~ (v11 = xb) & sdtasdt0(v0, v10) = v11 &
% 163.21/22.62 | $i(v11)))) | ( ~ (v4 = 0) & ( ~ (v2 = 0) | ( ~ (v3 = 0) &
% 163.21/22.62 | ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xa) | ~ $i(v10)
% 163.21/22.62 | | ? [v11: int] : ( ~ (v11 = 0) & aElement0(v10) =
% 163.21/22.62 | v11)) & ! [v10: $i] : ( ~ (aElement0(v10) = 0) | ~
% 163.21/22.62 | $i(v10) | ? [v11: $i] : ( ~ (v11 = xa) & sdtasdt0(v0,
% 163.21/22.62 | v10) = v11 & $i(v11)))))))))
% 163.21/22.62 | (103) ! [v0: $i] : ! [v1: any] : ( ~ (aDivisorOf0(v0, xb) = v1) | ~
% 163.21/22.62 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : ? [v5: any]
% 163.21/22.62 | : ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] :
% 163.21/22.62 | (aDivisorOf0(v0, xa) = v4 & doDivides0(v0, xc) = v6 &
% 163.21/22.62 | doDivides0(v0, xb) = v5 & doDivides0(v0, xa) = v3 & aElement0(v0)
% 163.21/22.62 | = v2 & $i(v7) & ((v9 = xc & v8 = 0 & v6 = 0 & sdtasdt0(v0, v7) =
% 163.21/22.62 | xc & aElement0(v7) = 0) | ( ~ (v5 = 0) & ~ (v1 = 0) & !
% 163.21/22.62 | [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xb) | ~ $i(v10) | ?
% 163.21/22.62 | [v11: int] : ( ~ (v11 = 0) & aElement0(v10) = v11)) & !
% 163.21/22.62 | [v10: $i] : ( ~ (aElement0(v10) = 0) | ~ $i(v10) | ? [v11:
% 163.21/22.62 | $i] : ( ~ (v11 = xb) & sdtasdt0(v0, v10) = v11 &
% 163.21/22.62 | $i(v11)))) | ( ~ (v4 = 0) & ( ~ (v2 = 0) | ( ~ (v3 = 0) &
% 163.21/22.62 | ! [v10: $i] : ( ~ (sdtasdt0(v0, v10) = xa) | ~ $i(v10)
% 163.21/22.62 | | ? [v11: int] : ( ~ (v11 = 0) & aElement0(v10) =
% 163.21/22.62 | v11)) & ! [v10: $i] : ( ~ (aElement0(v10) = 0) | ~
% 163.21/22.62 | $i(v10) | ? [v11: $i] : ( ~ (v11 = xa) & sdtasdt0(v0,
% 163.21/22.62 | v10) = v11 & $i(v11)))))))))
% 163.21/22.62 |
% 163.21/22.62 | REDUCE: (35), (59) imply:
% 163.21/22.62 | (104) sdtpldt0(all_41_3, sz00) = xb
% 163.21/22.62 |
% 163.21/22.62 | REDUCE: (33), (35) imply:
% 163.21/22.62 | (105) $i(sz00)
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (37) with all_41_1, all_50_2, xu, simplifying with
% 163.21/22.62 | (61), (84) gives:
% 163.21/22.62 | (106) all_50_2 = all_41_1
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (41) with 0, all_45_3, xa, xu, simplifying with
% 163.21/22.62 | (45), (74) gives:
% 163.21/22.62 | (107) all_45_3 = 0
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (41) with all_38_0, all_45_1, xb, xu, simplifying
% 163.21/22.62 | with (55), (75) gives:
% 163.21/22.62 | (108) all_45_1 = all_38_0
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (38) with all_50_4, all_53_5, xa, simplifying with
% 163.21/22.62 | (85), (90) gives:
% 163.21/22.62 | (109) all_53_5 = all_50_4
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (38) with all_53_5, all_56_1, xa, simplifying with
% 163.21/22.62 | (90), (96) gives:
% 163.21/22.62 | (110) all_56_1 = all_53_5
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (38) with all_43_5, all_56_1, xa, simplifying with
% 163.21/22.62 | (71), (96) gives:
% 163.21/22.62 | (111) all_56_1 = all_43_5
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (38) with all_50_3, all_53_4, xb, simplifying with
% 163.21/22.62 | (86), (91) gives:
% 163.21/22.62 | (112) all_53_4 = all_50_3
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (38) with all_53_4, all_56_0, xb, simplifying with
% 163.21/22.62 | (91), (97) gives:
% 163.21/22.62 | (113) all_56_0 = all_53_4
% 163.21/22.62 |
% 163.21/22.62 | GROUND_INST: instantiating (38) with all_43_4, all_56_0, xb, simplifying with
% 163.21/22.62 | (72), (97) gives:
% 163.21/22.62 | (114) all_56_0 = all_43_4
% 163.21/22.62 |
% 163.21/22.62 | COMBINE_EQS: (113), (114) imply:
% 163.21/22.62 | (115) all_53_4 = all_43_4
% 163.21/22.62 |
% 163.21/22.62 | SIMP: (115) implies:
% 163.21/22.62 | (116) all_53_4 = all_43_4
% 163.21/22.62 |
% 163.21/22.62 | COMBINE_EQS: (110), (111) imply:
% 163.21/22.62 | (117) all_53_5 = all_43_5
% 163.21/22.62 |
% 163.21/22.62 | SIMP: (117) implies:
% 163.21/22.62 | (118) all_53_5 = all_43_5
% 163.21/22.62 |
% 163.21/22.62 | COMBINE_EQS: (112), (116) imply:
% 163.21/22.62 | (119) all_50_3 = all_43_4
% 163.21/22.62 |
% 163.21/22.62 | COMBINE_EQS: (109), (118) imply:
% 163.21/22.62 | (120) all_50_4 = all_43_5
% 163.21/22.62 |
% 163.21/22.62 | REDUCE: (94), (111), (114) imply:
% 163.21/22.62 | (121) sdtpldt1(all_43_5, all_43_4) = xI
% 163.21/22.62 |
% 163.21/22.62 | REDUCE: (89), (116), (118) imply:
% 163.21/22.62 | (122) sdtpldt1(all_43_5, all_43_4) = all_53_3
% 163.21/22.62 |
% 163.21/22.62 | BETA: splitting (77) gives:
% 163.21/22.62 |
% 163.21/22.62 | Case 1:
% 163.21/22.62 | |
% 163.46/22.62 | | (123) ~ (all_45_0 = 0) & ~ (all_45_1 = 0) & ! [v0: $i] : ( ~
% 163.46/22.62 | | (sdtasdt0(xu, v0) = xb) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 163.46/22.62 | | & aElement0(v0) = v1)) & ! [v0: $i] : ( ~ (aElement0(v0) = 0)
% 163.46/22.62 | | | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xb) & sdtasdt0(xu, v0) = v1
% 163.46/22.62 | | & $i(v1)))
% 163.46/22.62 | |
% 163.46/22.62 | | ALPHA: (123) implies:
% 163.46/22.62 | | (124) ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (
% 163.46/22.62 | | ~ (v1 = xb) & sdtasdt0(xu, v0) = v1 & $i(v1)))
% 163.46/22.62 | |
% 163.46/22.63 | | GROUND_INST: instantiating (40) with xI, all_53_3, all_43_4, all_43_5,
% 163.46/22.63 | | simplifying with (121), (122) gives:
% 163.46/22.63 | | (125) all_53_3 = xI
% 163.46/22.63 | |
% 163.46/22.63 | | REDUCE: (88), (125) imply:
% 163.46/22.63 | | (126) $i(xI)
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (124) with xq, simplifying with (32), (58) gives:
% 163.46/22.63 | | (127) ? [v0: $i] : ( ~ (v0 = xb) & sdtasdt0(xu, xq) = v0 & $i(v0))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (14) with all_59_0, sz10, simplifying with (1),
% 163.46/22.63 | | (17), (99), (100) gives:
% 163.46/22.63 | | (128) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 163.46/22.63 | | : ? [v4: $i] : ? [v5: any] : (iLess0(v4, v0) = v5 & sbrdtbr0(v2)
% 163.46/22.63 | | = v4 & sbrdtbr0(sz10) = v0 & sdtasdt0(v1, sz10) = v3 &
% 163.46/22.63 | | sdtpldt0(v3, v2) = all_59_0 & aElement0(v2) = 0 & aElement0(v1) =
% 163.46/22.63 | | 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v5 = 0 | v2 =
% 163.46/22.63 | | sz00))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (mSortsB) with all_36_1, all_36_0, xu,
% 163.46/22.63 | | simplifying with (49), (50), (51) gives:
% 163.46/22.63 | | (129) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_36_0) =
% 163.46/22.63 | | v1 & aElement0(all_36_1) = v0 & aElement0(xu) = v2 & ( ~ (v1 = 0)
% 163.46/22.63 | | | ~ (v0 = 0) | v2 = 0))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (4) with all_41_3, xb, simplifying with (57),
% 163.46/22.63 | | (104) gives:
% 163.46/22.63 | | (130) ? [v0: any] : ? [v1: $i] : (sdtpldt0(sz00, all_41_3) = v1 &
% 163.46/22.63 | | aElement0(all_41_3) = v0 & $i(v1) & ( ~ (v0 = 0) | (v1 = xb &
% 163.46/22.63 | | all_41_3 = xb)))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (3) with sz00, all_41_3, xb, simplifying with
% 163.46/22.63 | | (57), (104), (105) gives:
% 163.46/22.63 | | (131) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(sz00,
% 163.46/22.63 | | all_41_3) = v2 & aElement0(all_41_3) = v1 & aElement0(sz00) =
% 163.46/22.63 | | v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xb))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (2) with all_41_3, sz00, xb, simplifying with
% 163.46/22.63 | | (57), (104), (105) gives:
% 163.46/22.63 | | (132) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(sz00,
% 163.46/22.63 | | all_41_3) = v2 & aElement0(all_41_3) = v0 & aElement0(sz00) =
% 163.46/22.63 | | v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xb))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (mSortsB) with all_41_3, sz00, xb, simplifying
% 163.46/22.63 | | with (57), (104), (105) gives:
% 163.46/22.63 | | (133) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_41_3) =
% 163.46/22.63 | | v0 & aElement0(xb) = v2 & aElement0(sz00) = v1 & ( ~ (v1 = 0) |
% 163.46/22.63 | | ~ (v0 = 0) | v2 = 0))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (mSortsB) with all_50_1, all_50_0, xu,
% 163.46/22.63 | | simplifying with (80), (81), (82) gives:
% 163.46/22.63 | | (134) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_50_0) =
% 163.46/22.63 | | v1 & aElement0(all_50_1) = v0 & aElement0(xu) = v2 & ( ~ (v1 = 0)
% 163.46/22.63 | | | ~ (v0 = 0) | v2 = 0))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (9) with all_36_2, all_41_3, sz00, xb, all_36_0,
% 163.46/22.63 | | simplifying with (48), (53), (57), (104), (105) gives:
% 163.46/22.63 | | (135) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.63 | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 163.46/22.63 | | [v9: $i] : (sdtasdt0(all_41_3, all_36_2) = v7 & sdtasdt0(all_36_2,
% 163.46/22.63 | | all_41_3) = v4 & sdtasdt0(all_36_2, xb) = v3 &
% 163.46/22.63 | | sdtasdt0(all_36_2, sz00) = v5 & sdtasdt0(sz00, all_36_2) = v8 &
% 163.46/22.63 | | sdtpldt0(v7, v8) = v9 & sdtpldt0(v4, v5) = v6 &
% 163.46/22.63 | | aElement0(all_41_3) = v1 & aElement0(all_36_2) = v0 &
% 163.46/22.63 | | aElement0(sz00) = v2 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 163.46/22.63 | | & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) |
% 163.46/22.63 | | (v9 = all_36_0 & v6 = v3)))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (9) with all_43_3, all_41_3, sz00, xb, xb,
% 163.46/22.63 | | simplifying with (57), (63), (69), (104), (105) gives:
% 163.46/22.63 | | (136) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.63 | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 163.46/22.63 | | [v9: $i] : (sdtasdt0(all_43_3, all_41_3) = v4 & sdtasdt0(all_43_3,
% 163.46/22.63 | | xb) = v3 & sdtasdt0(all_43_3, sz00) = v5 & sdtasdt0(all_41_3,
% 163.46/22.63 | | all_43_3) = v7 & sdtasdt0(sz00, all_43_3) = v8 & sdtpldt0(v7,
% 163.46/22.63 | | v8) = v9 & sdtpldt0(v4, v5) = v6 & aElement0(all_43_3) = v0 &
% 163.46/22.63 | | aElement0(all_41_3) = v1 & aElement0(sz00) = v2 & $i(v9) & $i(v8)
% 163.46/22.63 | | & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~
% 163.46/22.63 | | (v1 = 0) | ~ (v0 = 0) | (v9 = xb & v6 = v3)))
% 163.46/22.63 | |
% 163.46/22.63 | | GROUND_INST: instantiating (9) with all_43_2, all_41_3, sz00, xb, sz00,
% 163.46/22.63 | | simplifying with (57), (64), (70), (104), (105) gives:
% 163.46/22.64 | | (137) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.64 | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 163.46/22.64 | | [v9: $i] : (sdtasdt0(all_43_2, all_41_3) = v4 & sdtasdt0(all_43_2,
% 163.46/22.64 | | xb) = v3 & sdtasdt0(all_43_2, sz00) = v5 & sdtasdt0(all_41_3,
% 163.46/22.64 | | all_43_2) = v7 & sdtasdt0(sz00, all_43_2) = v8 & sdtpldt0(v7,
% 163.46/22.64 | | v8) = v9 & sdtpldt0(v4, v5) = v6 & aElement0(all_43_2) = v0 &
% 163.46/22.64 | | aElement0(all_41_3) = v1 & aElement0(sz00) = v2 & $i(v9) & $i(v8)
% 163.46/22.64 | | & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~
% 163.46/22.64 | | (v1 = 0) | ~ (v0 = 0) | (v9 = sz00 & v6 = v3)))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (7) with xu, all_34_0, all_43_0, xa, sz00,
% 163.46/22.64 | | simplifying with (31), (43), (44), (66), (68) gives:
% 163.46/22.64 | | (138) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.64 | | $i] : (sdtasdt0(all_34_0, all_43_0) = v3 & sdtasdt0(xu, v3) = v4
% 163.46/22.64 | | & aElement0(all_43_0) = v2 & aElement0(all_34_0) = v1 &
% 163.46/22.64 | | aElement0(xu) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0)
% 163.46/22.64 | | | ~ (v0 = 0) | v4 = sz00))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (7) with xu, all_34_0, all_43_1, xa, xa,
% 163.46/22.64 | | simplifying with (31), (43), (44), (65), (67) gives:
% 163.46/22.64 | | (139) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.64 | | $i] : (sdtasdt0(all_34_0, all_43_1) = v3 & sdtasdt0(xu, v3) = v4
% 163.46/22.64 | | & aElement0(all_43_1) = v2 & aElement0(all_34_0) = v1 &
% 163.46/22.64 | | aElement0(xu) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0)
% 163.46/22.64 | | | ~ (v0 = 0) | v4 = xa))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (7) with xu, all_34_0, all_36_3, xa, all_36_1,
% 163.46/22.64 | | simplifying with (31), (43), (44), (47), (52) gives:
% 163.46/22.64 | | (140) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.64 | | $i] : (sdtasdt0(all_34_0, all_36_3) = v3 & sdtasdt0(xu, v3) = v4
% 163.46/22.64 | | & aElement0(all_36_3) = v2 & aElement0(all_34_0) = v1 &
% 163.46/22.64 | | aElement0(xu) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0)
% 163.46/22.64 | | | ~ (v0 = 0) | v4 = all_36_1))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (6) with all_34_0, xu, xa, simplifying with (31),
% 163.46/22.64 | | (43), (44) gives:
% 163.46/22.64 | | (141) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_34_0, xu)
% 163.46/22.64 | | = v2 & aElement0(all_34_0) = v0 & aElement0(xu) = v1 & $i(v2) & (
% 163.46/22.64 | | ~ (v1 = 0) | ~ (v0 = 0) | v2 = xa))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (5) with xu, all_34_0, xa, simplifying with (31),
% 163.46/22.64 | | (43), (44) gives:
% 163.46/22.64 | | (142) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_34_0, xu)
% 163.46/22.64 | | = v2 & aElement0(all_34_0) = v1 & aElement0(xu) = v0 & $i(v2) & (
% 163.46/22.64 | | ~ (v1 = 0) | ~ (v0 = 0) | v2 = xa))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (mSortsB_02) with xu, all_34_0, xa, simplifying
% 163.46/22.64 | | with (31), (43), (44) gives:
% 163.46/22.64 | | (143) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_34_0) =
% 163.46/22.64 | | v1 & aElement0(xu) = v0 & aElement0(xa) = v2 & ( ~ (v1 = 0) | ~
% 163.46/22.64 | | (v0 = 0) | v2 = 0))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (8) with xq, all_50_1, all_50_0, xu, all_41_3,
% 163.46/22.64 | | simplifying with (32), (60), (80), (81), (82) gives:
% 163.46/22.64 | | (144) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.64 | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 163.46/22.64 | | [v9: $i] : (sdtasdt0(all_50_0, xq) = v8 & sdtasdt0(all_50_1, xq) =
% 163.46/22.64 | | v7 & sdtasdt0(xq, all_50_0) = v4 & sdtasdt0(xq, all_50_1) = v3 &
% 163.46/22.64 | | sdtasdt0(xu, xq) = v6 & sdtpldt0(v7, v8) = v9 & sdtpldt0(v3, v4)
% 163.46/22.64 | | = v5 & aElement0(all_50_0) = v2 & aElement0(all_50_1) = v1 &
% 163.46/22.64 | | aElement0(xq) = v0 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 163.46/22.64 | | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v9
% 163.46/22.64 | | = v6 & v5 = all_41_3)))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (8) with xq, all_36_1, all_36_0, xu, all_41_3,
% 163.46/22.64 | | simplifying with (32), (49), (50), (51), (60) gives:
% 163.46/22.64 | | (145) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 163.46/22.64 | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 163.46/22.64 | | [v9: $i] : (sdtasdt0(all_36_0, xq) = v8 & sdtasdt0(all_36_1, xq) =
% 163.46/22.64 | | v7 & sdtasdt0(xq, all_36_0) = v4 & sdtasdt0(xq, all_36_1) = v3 &
% 163.46/22.64 | | sdtasdt0(xu, xq) = v6 & sdtpldt0(v7, v8) = v9 & sdtpldt0(v3, v4)
% 163.46/22.64 | | = v5 & aElement0(all_36_0) = v2 & aElement0(all_36_1) = v1 &
% 163.46/22.64 | | aElement0(xq) = v0 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 163.46/22.64 | | $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v9
% 163.46/22.64 | | = v6 & v5 = all_41_3)))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (6) with xu, xq, all_41_3, simplifying with (31),
% 163.46/22.64 | | (32), (60) gives:
% 163.46/22.64 | | (146) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xu, xq) = v2
% 163.46/22.64 | | & aElement0(xq) = v1 & aElement0(xu) = v0 & $i(v2) & ( ~ (v1 = 0)
% 163.46/22.64 | | | ~ (v0 = 0) | v2 = all_41_3))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (5) with xq, xu, all_41_3, simplifying with (31),
% 163.46/22.64 | | (32), (60) gives:
% 163.46/22.64 | | (147) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xu, xq) = v2
% 163.46/22.64 | | & aElement0(xq) = v0 & aElement0(xu) = v1 & $i(v2) & ( ~ (v1 = 0)
% 163.46/22.64 | | | ~ (v0 = 0) | v2 = all_41_3))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (mSortsB_02) with xq, xu, all_41_3, simplifying
% 163.46/22.64 | | with (31), (32), (60) gives:
% 163.46/22.64 | | (148) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aElement0(all_41_3) =
% 163.46/22.64 | | v2 & aElement0(xq) = v0 & aElement0(xu) = v1 & ( ~ (v1 = 0) | ~
% 163.46/22.64 | | (v0 = 0) | v2 = 0))
% 163.46/22.64 | |
% 163.46/22.64 | | GROUND_INST: instantiating (11) with xI, xu, simplifying with (31), (83),
% 163.46/22.64 | | (93), (126) gives:
% 163.46/22.64 | | (149) aElement0(xu) = 0
% 163.46/22.64 | |
% 163.46/22.65 | | GROUND_INST: instantiating (12) with xI, xu, xq, all_41_3, simplifying with
% 163.46/22.65 | | (31), (32), (60), (83), (95), (126) gives:
% 163.46/22.65 | | (150) ? [v0: any] : ? [v1: any] : (aElementOf0(all_41_3, xI) = v1 &
% 163.46/22.65 | | aElement0(xq) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 163.46/22.65 | |
% 163.46/22.65 | | GROUND_INST: instantiating (13) with xu, all_41_1, simplifying with (31),
% 163.46/22.65 | | (61) gives:
% 163.46/22.65 | | (151) xu = sz00 | ? [v0: any] : ? [v1: any] :
% 163.46/22.65 | | (aNaturalNumber0(all_41_1) = v1 & aElement0(xu) = v0 & ( ~ (v0 = 0)
% 163.46/22.65 | | | v1 = 0))
% 163.46/22.65 | |
% 163.46/22.65 | | GROUND_INST: instantiating (16) with xa, xu, 0, simplifying with (18), (27),
% 163.46/22.65 | | (31), (45) gives:
% 163.46/22.65 | | (152) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xa) = v0 &
% 163.46/22.65 | | aElement0(xu) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 163.46/22.65 | |
% 163.46/22.65 | | GROUND_INST: instantiating (15) with xa, xu, simplifying with (18), (27),
% 163.46/22.65 | | (31), (45) gives:
% 163.46/22.65 | | (153) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xa) = v1 &
% 163.46/22.65 | | aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 163.46/22.65 | |
% 163.46/22.65 | | GROUND_INST: instantiating (101) with xu, 0, simplifying with (31), (45)
% 163.46/22.65 | | gives:
% 163.46/22.65 | | (154) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 163.46/22.65 | | any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] :
% 163.46/22.65 | | (aDivisorOf0(xu, xb) = v3 & aDivisorOf0(xu, xa) = v1 &
% 163.46/22.65 | | doDivides0(xu, xc) = v4 & doDivides0(xu, xb) = v2 & aElement0(xu)
% 163.46/22.65 | | = v0 & $i(v5) & ((v7 = xc & v6 = 0 & v4 = 0 & sdtasdt0(xu, v5) =
% 163.46/22.65 | | xc & aElement0(v5) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & !
% 163.46/22.65 | | [v8: $i] : ( ~ (sdtasdt0(xu, v8) = xb) | ~ $i(v8) | ? [v9:
% 163.46/22.65 | | int] : ( ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v8: $i]
% 163.46/22.65 | | : ( ~ (aElement0(v8) = 0) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9
% 163.46/22.65 | | = xb) & sdtasdt0(xu, v8) = v9 & $i(v9)))) | ( ~ (v1 =
% 163.46/22.65 | | 0) & ~ (v0 = 0))))
% 163.46/22.65 | |
% 163.46/22.65 | | GROUND_INST: instantiating (16) with xb, xu, all_38_0, simplifying with
% 163.46/22.65 | | (19), (30), (31), (55) gives:
% 163.46/22.65 | | (155) ? [v0: any] : ? [v1: any] : (aDivisorOf0(xu, xb) = v0 &
% 163.46/22.65 | | aElement0(xu) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_38_0 = 0)))
% 163.46/22.65 | |
% 163.46/22.65 | | GROUND_INST: instantiating (102) with xu, all_38_0, simplifying with (31),
% 163.46/22.65 | | (55) gives:
% 163.46/22.65 | | (156) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 163.46/22.65 | | any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] :
% 163.46/22.65 | | (aDivisorOf0(xu, xb) = v3 & aDivisorOf0(xu, xa) = v2 &
% 163.46/22.65 | | doDivides0(xu, xc) = v4 & doDivides0(xu, xa) = v1 & aElement0(xu)
% 163.46/22.65 | | = v0 & $i(v5) & ((v7 = xc & v6 = 0 & v4 = 0 & sdtasdt0(xu, v5) =
% 163.46/22.65 | | xc & aElement0(v5) = 0) | ( ~ (v3 = 0) & ~ (all_38_0 = 0) &
% 163.46/22.65 | | ! [v8: $i] : ( ~ (sdtasdt0(xu, v8) = xb) | ~ $i(v8) | ?
% 163.46/22.65 | | [v9: int] : ( ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v8:
% 163.46/22.65 | | $i] : ( ~ (aElement0(v8) = 0) | ~ $i(v8) | ? [v9: $i] : (
% 163.46/22.65 | | ~ (v9 = xb) & sdtasdt0(xu, v8) = v9 & $i(v9)))) | ( ~ (v2
% 163.46/22.65 | | = 0) & ( ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v8: $i] : ( ~
% 163.46/22.65 | | (sdtasdt0(xu, v8) = xa) | ~ $i(v8) | ? [v9: int] : (
% 163.46/22.65 | | ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v8: $i] : ( ~
% 163.46/22.65 | | (aElement0(v8) = 0) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9
% 163.46/22.65 | | = xa) & sdtasdt0(xu, v8) = v9 & $i(v9))))))))
% 163.46/22.65 | |
% 163.46/22.65 | | GROUND_INST: instantiating (103) with xu, all_45_0, simplifying with (31),
% 163.46/22.65 | | (76) gives:
% 163.58/22.65 | | (157) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 163.58/22.65 | | any] : ? [v5: $i] : ? [v6: int] : ? [v7: $i] :
% 163.58/22.65 | | (aDivisorOf0(xu, xa) = v2 & doDivides0(xu, xc) = v4 &
% 163.58/22.65 | | doDivides0(xu, xb) = v3 & doDivides0(xu, xa) = v1 & aElement0(xu)
% 163.58/22.65 | | = v0 & $i(v5) & ((v7 = xc & v6 = 0 & v4 = 0 & sdtasdt0(xu, v5) =
% 163.58/22.65 | | xc & aElement0(v5) = 0) | ( ~ (v3 = 0) & ~ (all_45_0 = 0) &
% 163.58/22.65 | | ! [v8: $i] : ( ~ (sdtasdt0(xu, v8) = xb) | ~ $i(v8) | ?
% 163.58/22.65 | | [v9: int] : ( ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v8:
% 163.58/22.65 | | $i] : ( ~ (aElement0(v8) = 0) | ~ $i(v8) | ? [v9: $i] : (
% 163.58/22.65 | | ~ (v9 = xb) & sdtasdt0(xu, v8) = v9 & $i(v9)))) | ( ~ (v2
% 163.58/22.65 | | = 0) & ( ~ (v0 = 0) | ( ~ (v1 = 0) & ! [v8: $i] : ( ~
% 163.58/22.65 | | (sdtasdt0(xu, v8) = xa) | ~ $i(v8) | ? [v9: int] : (
% 163.58/22.65 | | ~ (v9 = 0) & aElement0(v8) = v9)) & ! [v8: $i] : ( ~
% 163.58/22.65 | | (aElement0(v8) = 0) | ~ $i(v8) | ? [v9: $i] : ( ~ (v9
% 163.58/22.65 | | = xa) & sdtasdt0(xu, v8) = v9 & $i(v9))))))))
% 163.58/22.65 | |
% 163.58/22.65 | | DELTA: instantiating (127) with fresh symbol all_233_0 gives:
% 163.58/22.65 | | (158) ~ (all_233_0 = xb) & sdtasdt0(xu, xq) = all_233_0 & $i(all_233_0)
% 163.58/22.65 | |
% 163.58/22.65 | | ALPHA: (158) implies:
% 163.58/22.65 | | (159) ~ (all_233_0 = xb)
% 163.58/22.65 | | (160) sdtasdt0(xu, xq) = all_233_0
% 163.58/22.65 | |
% 163.58/22.65 | | DELTA: instantiating (153) with fresh symbols all_337_0, all_337_1 gives:
% 163.58/22.65 | | (161) aDivisorOf0(xu, xa) = all_337_0 & aElement0(xu) = all_337_1 & ( ~
% 163.58/22.65 | | (all_337_1 = 0) | all_337_0 = 0)
% 163.58/22.65 | |
% 163.58/22.65 | | ALPHA: (161) implies:
% 163.58/22.65 | | (162) aElement0(xu) = all_337_1
% 163.58/22.65 | |
% 163.58/22.65 | | DELTA: instantiating (152) with fresh symbols all_339_0, all_339_1 gives:
% 163.58/22.65 | | (163) aDivisorOf0(xu, xa) = all_339_1 & aElement0(xu) = all_339_0 & ( ~
% 163.58/22.65 | | (all_339_1 = 0) | all_339_0 = 0)
% 163.58/22.65 | |
% 163.58/22.65 | | ALPHA: (163) implies:
% 163.58/22.66 | | (164) aElement0(xu) = all_339_0
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (150) with fresh symbols all_1119_0, all_1119_1 gives:
% 163.58/22.66 | | (165) aElementOf0(all_41_3, xI) = all_1119_0 & aElement0(xq) = all_1119_1
% 163.58/22.66 | | & ( ~ (all_1119_1 = 0) | all_1119_0 = 0)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (165) implies:
% 163.58/22.66 | | (166) aElement0(xq) = all_1119_1
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (155) with fresh symbols all_1211_0, all_1211_1 gives:
% 163.58/22.66 | | (167) aDivisorOf0(xu, xb) = all_1211_1 & aElement0(xu) = all_1211_0 & ( ~
% 163.58/22.66 | | (all_1211_1 = 0) | (all_1211_0 = 0 & all_38_0 = 0))
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (167) implies:
% 163.58/22.66 | | (168) aElement0(xu) = all_1211_0
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (133) with fresh symbols all_1230_0, all_1230_1,
% 163.58/22.66 | | all_1230_2 gives:
% 163.58/22.66 | | (169) aElement0(all_41_3) = all_1230_2 & aElement0(xb) = all_1230_0 &
% 163.58/22.66 | | aElement0(sz00) = all_1230_1 & ( ~ (all_1230_1 = 0) | ~
% 163.58/22.66 | | (all_1230_2 = 0) | all_1230_0 = 0)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (169) implies:
% 163.58/22.66 | | (170) aElement0(all_41_3) = all_1230_2
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (143) with fresh symbols all_1232_0, all_1232_1,
% 163.58/22.66 | | all_1232_2 gives:
% 163.58/22.66 | | (171) aElement0(all_34_0) = all_1232_1 & aElement0(xu) = all_1232_2 &
% 163.58/22.66 | | aElement0(xa) = all_1232_0 & ( ~ (all_1232_1 = 0) | ~ (all_1232_2
% 163.58/22.66 | | = 0) | all_1232_0 = 0)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (171) implies:
% 163.58/22.66 | | (172) aElement0(xu) = all_1232_2
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (130) with fresh symbols all_1234_0, all_1234_1 gives:
% 163.58/22.66 | | (173) sdtpldt0(sz00, all_41_3) = all_1234_0 & aElement0(all_41_3) =
% 163.58/22.66 | | all_1234_1 & $i(all_1234_0) & ( ~ (all_1234_1 = 0) | (all_1234_0 =
% 163.58/22.66 | | xb & all_41_3 = xb))
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (173) implies:
% 163.58/22.66 | | (174) aElement0(all_41_3) = all_1234_1
% 163.58/22.66 | | (175) ~ (all_1234_1 = 0) | (all_1234_0 = xb & all_41_3 = xb)
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (129) with fresh symbols all_1237_0, all_1237_1,
% 163.58/22.66 | | all_1237_2 gives:
% 163.58/22.66 | | (176) aElement0(all_36_0) = all_1237_1 & aElement0(all_36_1) = all_1237_2
% 163.58/22.66 | | & aElement0(xu) = all_1237_0 & ( ~ (all_1237_1 = 0) | ~
% 163.58/22.66 | | (all_1237_2 = 0) | all_1237_0 = 0)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (176) implies:
% 163.58/22.66 | | (177) aElement0(xu) = all_1237_0
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (148) with fresh symbols all_1255_0, all_1255_1,
% 163.58/22.66 | | all_1255_2 gives:
% 163.58/22.66 | | (178) aElement0(all_41_3) = all_1255_0 & aElement0(xq) = all_1255_2 &
% 163.58/22.66 | | aElement0(xu) = all_1255_1 & ( ~ (all_1255_1 = 0) | ~ (all_1255_2
% 163.58/22.66 | | = 0) | all_1255_0 = 0)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (178) implies:
% 163.58/22.66 | | (179) aElement0(xu) = all_1255_1
% 163.58/22.66 | | (180) aElement0(xq) = all_1255_2
% 163.58/22.66 | | (181) aElement0(all_41_3) = all_1255_0
% 163.58/22.66 | | (182) ~ (all_1255_1 = 0) | ~ (all_1255_2 = 0) | all_1255_0 = 0
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (134) with fresh symbols all_1257_0, all_1257_1,
% 163.58/22.66 | | all_1257_2 gives:
% 163.58/22.66 | | (183) aElement0(all_50_0) = all_1257_1 & aElement0(all_50_1) = all_1257_2
% 163.58/22.66 | | & aElement0(xu) = all_1257_0 & ( ~ (all_1257_1 = 0) | ~
% 163.58/22.66 | | (all_1257_2 = 0) | all_1257_0 = 0)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (183) implies:
% 163.58/22.66 | | (184) aElement0(xu) = all_1257_0
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (132) with fresh symbols all_1280_0, all_1280_1,
% 163.58/22.66 | | all_1280_2 gives:
% 163.58/22.66 | | (185) sdtpldt0(sz00, all_41_3) = all_1280_0 & aElement0(all_41_3) =
% 163.58/22.66 | | all_1280_2 & aElement0(sz00) = all_1280_1 & $i(all_1280_0) & ( ~
% 163.58/22.66 | | (all_1280_1 = 0) | ~ (all_1280_2 = 0) | all_1280_0 = xb)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (185) implies:
% 163.58/22.66 | | (186) aElement0(all_41_3) = all_1280_2
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (142) with fresh symbols all_1284_0, all_1284_1,
% 163.58/22.66 | | all_1284_2 gives:
% 163.58/22.66 | | (187) sdtasdt0(all_34_0, xu) = all_1284_0 & aElement0(all_34_0) =
% 163.58/22.66 | | all_1284_1 & aElement0(xu) = all_1284_2 & $i(all_1284_0) & ( ~
% 163.58/22.66 | | (all_1284_1 = 0) | ~ (all_1284_2 = 0) | all_1284_0 = xa)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (187) implies:
% 163.58/22.66 | | (188) aElement0(xu) = all_1284_2
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (141) with fresh symbols all_1286_0, all_1286_1,
% 163.58/22.66 | | all_1286_2 gives:
% 163.58/22.66 | | (189) sdtasdt0(all_34_0, xu) = all_1286_0 & aElement0(all_34_0) =
% 163.58/22.66 | | all_1286_2 & aElement0(xu) = all_1286_1 & $i(all_1286_0) & ( ~
% 163.58/22.66 | | (all_1286_1 = 0) | ~ (all_1286_2 = 0) | all_1286_0 = xa)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (189) implies:
% 163.58/22.66 | | (190) aElement0(xu) = all_1286_1
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (131) with fresh symbols all_1296_0, all_1296_1,
% 163.58/22.66 | | all_1296_2 gives:
% 163.58/22.66 | | (191) sdtpldt0(sz00, all_41_3) = all_1296_0 & aElement0(all_41_3) =
% 163.58/22.66 | | all_1296_1 & aElement0(sz00) = all_1296_2 & $i(all_1296_0) & ( ~
% 163.58/22.66 | | (all_1296_1 = 0) | ~ (all_1296_2 = 0) | all_1296_0 = xb)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (191) implies:
% 163.58/22.66 | | (192) aElement0(all_41_3) = all_1296_1
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (146) with fresh symbols all_1308_0, all_1308_1,
% 163.58/22.66 | | all_1308_2 gives:
% 163.58/22.66 | | (193) sdtasdt0(xu, xq) = all_1308_0 & aElement0(xq) = all_1308_1 &
% 163.58/22.66 | | aElement0(xu) = all_1308_2 & $i(all_1308_0) & ( ~ (all_1308_1 = 0)
% 163.58/22.66 | | | ~ (all_1308_2 = 0) | all_1308_0 = all_41_3)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (193) implies:
% 163.58/22.66 | | (194) aElement0(xu) = all_1308_2
% 163.58/22.66 | | (195) aElement0(xq) = all_1308_1
% 163.58/22.66 | | (196) sdtasdt0(xu, xq) = all_1308_0
% 163.58/22.66 | | (197) ~ (all_1308_1 = 0) | ~ (all_1308_2 = 0) | all_1308_0 = all_41_3
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (147) with fresh symbols all_1320_0, all_1320_1,
% 163.58/22.66 | | all_1320_2 gives:
% 163.58/22.66 | | (198) sdtasdt0(xu, xq) = all_1320_0 & aElement0(xq) = all_1320_2 &
% 163.58/22.66 | | aElement0(xu) = all_1320_1 & $i(all_1320_0) & ( ~ (all_1320_1 = 0)
% 163.58/22.66 | | | ~ (all_1320_2 = 0) | all_1320_0 = all_41_3)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (198) implies:
% 163.58/22.66 | | (199) aElement0(xu) = all_1320_1
% 163.58/22.66 | | (200) aElement0(xq) = all_1320_2
% 163.58/22.66 | | (201) sdtasdt0(xu, xq) = all_1320_0
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (138) with fresh symbols all_1386_0, all_1386_1,
% 163.58/22.66 | | all_1386_2, all_1386_3, all_1386_4 gives:
% 163.58/22.66 | | (202) sdtasdt0(all_34_0, all_43_0) = all_1386_1 & sdtasdt0(xu,
% 163.58/22.66 | | all_1386_1) = all_1386_0 & aElement0(all_43_0) = all_1386_2 &
% 163.58/22.66 | | aElement0(all_34_0) = all_1386_3 & aElement0(xu) = all_1386_4 &
% 163.58/22.66 | | $i(all_1386_0) & $i(all_1386_1) & ( ~ (all_1386_2 = 0) | ~
% 163.58/22.66 | | (all_1386_3 = 0) | ~ (all_1386_4 = 0) | all_1386_0 = sz00)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (202) implies:
% 163.58/22.66 | | (203) aElement0(xu) = all_1386_4
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (140) with fresh symbols all_1476_0, all_1476_1,
% 163.58/22.66 | | all_1476_2, all_1476_3, all_1476_4 gives:
% 163.58/22.66 | | (204) sdtasdt0(all_34_0, all_36_3) = all_1476_1 & sdtasdt0(xu,
% 163.58/22.66 | | all_1476_1) = all_1476_0 & aElement0(all_36_3) = all_1476_2 &
% 163.58/22.66 | | aElement0(all_34_0) = all_1476_3 & aElement0(xu) = all_1476_4 &
% 163.58/22.66 | | $i(all_1476_0) & $i(all_1476_1) & ( ~ (all_1476_2 = 0) | ~
% 163.58/22.66 | | (all_1476_3 = 0) | ~ (all_1476_4 = 0) | all_1476_0 = all_36_1)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (204) implies:
% 163.58/22.66 | | (205) aElement0(xu) = all_1476_4
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (139) with fresh symbols all_1478_0, all_1478_1,
% 163.58/22.66 | | all_1478_2, all_1478_3, all_1478_4 gives:
% 163.58/22.66 | | (206) sdtasdt0(all_34_0, all_43_1) = all_1478_1 & sdtasdt0(xu,
% 163.58/22.66 | | all_1478_1) = all_1478_0 & aElement0(all_43_1) = all_1478_2 &
% 163.58/22.66 | | aElement0(all_34_0) = all_1478_3 & aElement0(xu) = all_1478_4 &
% 163.58/22.66 | | $i(all_1478_0) & $i(all_1478_1) & ( ~ (all_1478_2 = 0) | ~
% 163.58/22.66 | | (all_1478_3 = 0) | ~ (all_1478_4 = 0) | all_1478_0 = xa)
% 163.58/22.66 | |
% 163.58/22.66 | | ALPHA: (206) implies:
% 163.58/22.66 | | (207) aElement0(xu) = all_1478_4
% 163.58/22.66 | |
% 163.58/22.66 | | DELTA: instantiating (136) with fresh symbols all_1946_0, all_1946_1,
% 163.58/22.66 | | all_1946_2, all_1946_3, all_1946_4, all_1946_5, all_1946_6,
% 163.58/22.66 | | all_1946_7, all_1946_8, all_1946_9 gives:
% 163.58/22.67 | | (208) sdtasdt0(all_43_3, all_41_3) = all_1946_5 & sdtasdt0(all_43_3, xb)
% 163.58/22.67 | | = all_1946_6 & sdtasdt0(all_43_3, sz00) = all_1946_4 &
% 163.58/22.67 | | sdtasdt0(all_41_3, all_43_3) = all_1946_2 & sdtasdt0(sz00,
% 163.58/22.67 | | all_43_3) = all_1946_1 & sdtpldt0(all_1946_2, all_1946_1) =
% 163.58/22.67 | | all_1946_0 & sdtpldt0(all_1946_5, all_1946_4) = all_1946_3 &
% 163.58/22.67 | | aElement0(all_43_3) = all_1946_9 & aElement0(all_41_3) = all_1946_8
% 163.58/22.67 | | & aElement0(sz00) = all_1946_7 & $i(all_1946_0) & $i(all_1946_1) &
% 163.58/22.67 | | $i(all_1946_2) & $i(all_1946_3) & $i(all_1946_4) & $i(all_1946_5) &
% 163.58/22.67 | | $i(all_1946_6) & ( ~ (all_1946_7 = 0) | ~ (all_1946_8 = 0) | ~
% 163.58/22.67 | | (all_1946_9 = 0) | (all_1946_0 = xb & all_1946_3 = all_1946_6))
% 163.58/22.67 | |
% 163.58/22.67 | | ALPHA: (208) implies:
% 163.58/22.67 | | (209) aElement0(all_41_3) = all_1946_8
% 163.58/22.67 | |
% 163.58/22.67 | | DELTA: instantiating (144) with fresh symbols all_1948_0, all_1948_1,
% 163.58/22.67 | | all_1948_2, all_1948_3, all_1948_4, all_1948_5, all_1948_6,
% 163.58/22.67 | | all_1948_7, all_1948_8, all_1948_9 gives:
% 163.58/22.67 | | (210) sdtasdt0(all_50_0, xq) = all_1948_1 & sdtasdt0(all_50_1, xq) =
% 163.58/22.67 | | all_1948_2 & sdtasdt0(xq, all_50_0) = all_1948_5 & sdtasdt0(xq,
% 163.58/22.67 | | all_50_1) = all_1948_6 & sdtasdt0(xu, xq) = all_1948_3 &
% 163.58/22.67 | | sdtpldt0(all_1948_2, all_1948_1) = all_1948_0 &
% 163.58/22.67 | | sdtpldt0(all_1948_6, all_1948_5) = all_1948_4 & aElement0(all_50_0)
% 163.58/22.67 | | = all_1948_7 & aElement0(all_50_1) = all_1948_8 & aElement0(xq) =
% 163.58/22.67 | | all_1948_9 & $i(all_1948_0) & $i(all_1948_1) & $i(all_1948_2) &
% 163.58/22.67 | | $i(all_1948_3) & $i(all_1948_4) & $i(all_1948_5) & $i(all_1948_6) &
% 163.58/22.67 | | ( ~ (all_1948_7 = 0) | ~ (all_1948_8 = 0) | ~ (all_1948_9 = 0) |
% 163.58/22.67 | | (all_1948_0 = all_1948_3 & all_1948_4 = all_41_3))
% 163.58/22.67 | |
% 163.58/22.67 | | ALPHA: (210) implies:
% 163.58/22.67 | | (211) aElement0(xq) = all_1948_9
% 163.58/22.67 | | (212) sdtasdt0(xu, xq) = all_1948_3
% 163.58/22.67 | |
% 163.58/22.67 | | DELTA: instantiating (135) with fresh symbols all_1950_0, all_1950_1,
% 163.58/22.67 | | all_1950_2, all_1950_3, all_1950_4, all_1950_5, all_1950_6,
% 163.58/22.67 | | all_1950_7, all_1950_8, all_1950_9 gives:
% 163.58/22.67 | | (213) sdtasdt0(all_41_3, all_36_2) = all_1950_2 & sdtasdt0(all_36_2,
% 163.58/22.67 | | all_41_3) = all_1950_5 & sdtasdt0(all_36_2, xb) = all_1950_6 &
% 163.58/22.67 | | sdtasdt0(all_36_2, sz00) = all_1950_4 & sdtasdt0(sz00, all_36_2) =
% 163.58/22.67 | | all_1950_1 & sdtpldt0(all_1950_2, all_1950_1) = all_1950_0 &
% 163.58/22.67 | | sdtpldt0(all_1950_5, all_1950_4) = all_1950_3 & aElement0(all_41_3)
% 163.58/22.67 | | = all_1950_8 & aElement0(all_36_2) = all_1950_9 & aElement0(sz00) =
% 163.58/22.67 | | all_1950_7 & $i(all_1950_0) & $i(all_1950_1) & $i(all_1950_2) &
% 163.58/22.67 | | $i(all_1950_3) & $i(all_1950_4) & $i(all_1950_5) & $i(all_1950_6) &
% 163.58/22.67 | | ( ~ (all_1950_7 = 0) | ~ (all_1950_8 = 0) | ~ (all_1950_9 = 0) |
% 163.58/22.67 | | (all_1950_0 = all_36_0 & all_1950_3 = all_1950_6))
% 163.58/22.67 | |
% 163.58/22.67 | | ALPHA: (213) implies:
% 163.58/22.67 | | (214) aElement0(all_41_3) = all_1950_8
% 163.58/22.67 | |
% 163.58/22.67 | | DELTA: instantiating (137) with fresh symbols all_1952_0, all_1952_1,
% 163.58/22.67 | | all_1952_2, all_1952_3, all_1952_4, all_1952_5, all_1952_6,
% 163.58/22.67 | | all_1952_7, all_1952_8, all_1952_9 gives:
% 163.58/22.67 | | (215) sdtasdt0(all_43_2, all_41_3) = all_1952_5 & sdtasdt0(all_43_2, xb)
% 163.58/22.67 | | = all_1952_6 & sdtasdt0(all_43_2, sz00) = all_1952_4 &
% 163.58/22.67 | | sdtasdt0(all_41_3, all_43_2) = all_1952_2 & sdtasdt0(sz00,
% 163.58/22.67 | | all_43_2) = all_1952_1 & sdtpldt0(all_1952_2, all_1952_1) =
% 163.58/22.67 | | all_1952_0 & sdtpldt0(all_1952_5, all_1952_4) = all_1952_3 &
% 163.58/22.67 | | aElement0(all_43_2) = all_1952_9 & aElement0(all_41_3) = all_1952_8
% 163.58/22.67 | | & aElement0(sz00) = all_1952_7 & $i(all_1952_0) & $i(all_1952_1) &
% 163.58/22.67 | | $i(all_1952_2) & $i(all_1952_3) & $i(all_1952_4) & $i(all_1952_5) &
% 163.58/22.67 | | $i(all_1952_6) & ( ~ (all_1952_7 = 0) | ~ (all_1952_8 = 0) | ~
% 163.58/22.67 | | (all_1952_9 = 0) | (all_1952_0 = sz00 & all_1952_3 = all_1952_6))
% 163.58/22.67 | |
% 163.58/22.67 | | ALPHA: (215) implies:
% 163.58/22.67 | | (216) aElement0(all_41_3) = all_1952_8
% 163.58/22.67 | |
% 163.58/22.67 | | DELTA: instantiating (145) with fresh symbols all_1956_0, all_1956_1,
% 163.58/22.67 | | all_1956_2, all_1956_3, all_1956_4, all_1956_5, all_1956_6,
% 163.58/22.67 | | all_1956_7, all_1956_8, all_1956_9 gives:
% 163.58/22.67 | | (217) sdtasdt0(all_36_0, xq) = all_1956_1 & sdtasdt0(all_36_1, xq) =
% 163.58/22.67 | | all_1956_2 & sdtasdt0(xq, all_36_0) = all_1956_5 & sdtasdt0(xq,
% 163.58/22.67 | | all_36_1) = all_1956_6 & sdtasdt0(xu, xq) = all_1956_3 &
% 163.58/22.67 | | sdtpldt0(all_1956_2, all_1956_1) = all_1956_0 &
% 163.58/22.67 | | sdtpldt0(all_1956_6, all_1956_5) = all_1956_4 & aElement0(all_36_0)
% 163.58/22.67 | | = all_1956_7 & aElement0(all_36_1) = all_1956_8 & aElement0(xq) =
% 163.58/22.67 | | all_1956_9 & $i(all_1956_0) & $i(all_1956_1) & $i(all_1956_2) &
% 163.58/22.67 | | $i(all_1956_3) & $i(all_1956_4) & $i(all_1956_5) & $i(all_1956_6) &
% 163.58/22.67 | | ( ~ (all_1956_7 = 0) | ~ (all_1956_8 = 0) | ~ (all_1956_9 = 0) |
% 163.58/22.67 | | (all_1956_0 = all_1956_3 & all_1956_4 = all_41_3))
% 163.58/22.67 | |
% 163.58/22.67 | | ALPHA: (217) implies:
% 163.58/22.67 | | (218) aElement0(xq) = all_1956_9
% 163.58/22.67 | | (219) sdtasdt0(xu, xq) = all_1956_3
% 163.58/22.67 | |
% 163.58/22.67 | | DELTA: instantiating (154) with fresh symbols all_2100_0, all_2100_1,
% 163.58/22.67 | | all_2100_2, all_2100_3, all_2100_4, all_2100_5, all_2100_6,
% 163.58/22.67 | | all_2100_7 gives:
% 163.58/22.67 | | (220) aDivisorOf0(xu, xb) = all_2100_4 & aDivisorOf0(xu, xa) = all_2100_6
% 163.58/22.67 | | & doDivides0(xu, xc) = all_2100_3 & doDivides0(xu, xb) = all_2100_5
% 163.58/22.67 | | & aElement0(xu) = all_2100_7 & $i(all_2100_2) & ((all_2100_0 = xc &
% 163.58/22.67 | | all_2100_1 = 0 & all_2100_3 = 0 & sdtasdt0(xu, all_2100_2) = xc
% 163.58/22.67 | | & aElement0(all_2100_2) = 0) | ( ~ (all_2100_4 = 0) & ~
% 163.58/22.67 | | (all_2100_5 = 0) & ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xb) |
% 163.58/22.67 | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = v1))
% 163.58/22.67 | | & ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1:
% 163.58/22.67 | | $i] : ( ~ (v1 = xb) & sdtasdt0(xu, v0) = v1 & $i(v1)))) | (
% 163.58/22.67 | | ~ (all_2100_6 = 0) & ~ (all_2100_7 = 0)))
% 163.58/22.67 | |
% 163.58/22.67 | | ALPHA: (220) implies:
% 163.58/22.67 | | (221) aElement0(xu) = all_2100_7
% 163.58/22.67 | |
% 163.58/22.67 | | DELTA: instantiating (156) with fresh symbols all_2164_0, all_2164_1,
% 163.58/22.67 | | all_2164_2, all_2164_3, all_2164_4, all_2164_5, all_2164_6,
% 163.58/22.67 | | all_2164_7 gives:
% 163.58/22.67 | | (222) aDivisorOf0(xu, xb) = all_2164_4 & aDivisorOf0(xu, xa) = all_2164_5
% 163.58/22.67 | | & doDivides0(xu, xc) = all_2164_3 & doDivides0(xu, xa) = all_2164_6
% 163.58/22.67 | | & aElement0(xu) = all_2164_7 & $i(all_2164_2) & ((all_2164_0 = xc &
% 163.58/22.67 | | all_2164_1 = 0 & all_2164_3 = 0 & sdtasdt0(xu, all_2164_2) = xc
% 163.58/22.67 | | & aElement0(all_2164_2) = 0) | ( ~ (all_2164_4 = 0) & ~
% 163.58/22.67 | | (all_38_0 = 0) & ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xb) | ~
% 163.58/22.67 | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = v1)) &
% 163.58/22.67 | | ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 163.58/22.67 | | : ( ~ (v1 = xb) & sdtasdt0(xu, v0) = v1 & $i(v1)))) | ( ~
% 163.58/22.67 | | (all_2164_5 = 0) & ( ~ (all_2164_7 = 0) | ( ~ (all_2164_6 = 0)
% 163.58/22.67 | | & ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xa) | ~ $i(v0) |
% 163.58/22.67 | | ? [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = v1)) & !
% 163.58/22.67 | | [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1:
% 163.58/22.67 | | $i] : ( ~ (v1 = xa) & sdtasdt0(xu, v0) = v1 &
% 163.58/22.67 | | $i(v1)))))))
% 163.58/22.67 | |
% 163.58/22.67 | | ALPHA: (222) implies:
% 163.58/22.67 | | (223) aElement0(xu) = all_2164_7
% 163.58/22.67 | |
% 163.58/22.67 | | DELTA: instantiating (157) with fresh symbols all_2166_0, all_2166_1,
% 163.58/22.67 | | all_2166_2, all_2166_3, all_2166_4, all_2166_5, all_2166_6,
% 163.58/22.67 | | all_2166_7 gives:
% 163.58/22.68 | | (224) aDivisorOf0(xu, xa) = all_2166_5 & doDivides0(xu, xc) = all_2166_3
% 163.58/22.68 | | & doDivides0(xu, xb) = all_2166_4 & doDivides0(xu, xa) = all_2166_6
% 163.58/22.68 | | & aElement0(xu) = all_2166_7 & $i(all_2166_2) & ((all_2166_0 = xc &
% 163.58/22.68 | | all_2166_1 = 0 & all_2166_3 = 0 & sdtasdt0(xu, all_2166_2) = xc
% 163.58/22.68 | | & aElement0(all_2166_2) = 0) | ( ~ (all_2166_4 = 0) & ~
% 163.58/22.68 | | (all_45_0 = 0) & ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xb) | ~
% 163.58/22.68 | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = v1)) &
% 163.58/22.68 | | ! [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 163.58/22.68 | | : ( ~ (v1 = xb) & sdtasdt0(xu, v0) = v1 & $i(v1)))) | ( ~
% 163.58/22.68 | | (all_2166_5 = 0) & ( ~ (all_2166_7 = 0) | ( ~ (all_2166_6 = 0)
% 163.58/22.68 | | & ! [v0: $i] : ( ~ (sdtasdt0(xu, v0) = xa) | ~ $i(v0) |
% 163.58/22.68 | | ? [v1: int] : ( ~ (v1 = 0) & aElement0(v0) = v1)) & !
% 163.58/22.68 | | [v0: $i] : ( ~ (aElement0(v0) = 0) | ~ $i(v0) | ? [v1:
% 163.58/22.68 | | $i] : ( ~ (v1 = xa) & sdtasdt0(xu, v0) = v1 &
% 163.58/22.68 | | $i(v1)))))))
% 163.58/22.68 | |
% 163.58/22.68 | | ALPHA: (224) implies:
% 163.58/22.68 | | (225) aElement0(xu) = all_2166_7
% 163.58/22.68 | |
% 163.58/22.68 | | BETA: splitting (151) gives:
% 163.58/22.68 | |
% 163.58/22.68 | | Case 1:
% 163.58/22.68 | | |
% 163.58/22.68 | | | (226) xu = sz00
% 163.58/22.68 | | |
% 163.58/22.68 | | | REDUCE: (79), (226) imply:
% 163.58/22.68 | | | (227) $false
% 163.58/22.68 | | |
% 163.58/22.68 | | | CLOSE: (227) is inconsistent.
% 163.58/22.68 | | |
% 163.58/22.68 | | Case 2:
% 163.58/22.68 | | |
% 163.58/22.68 | | | (228) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_41_1) = v1 &
% 163.58/22.68 | | | aElement0(xu) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 163.58/22.68 | | |
% 163.58/22.68 | | | DELTA: instantiating (228) with fresh symbols all_2284_0, all_2284_1
% 163.58/22.68 | | | gives:
% 163.58/22.68 | | | (229) aNaturalNumber0(all_41_1) = all_2284_0 & aElement0(xu) =
% 163.58/22.68 | | | all_2284_1 & ( ~ (all_2284_1 = 0) | all_2284_0 = 0)
% 163.58/22.68 | | |
% 163.58/22.68 | | | ALPHA: (229) implies:
% 163.58/22.68 | | | (230) aElement0(xu) = all_2284_1
% 163.58/22.68 | | |
% 163.58/22.68 | | | BETA: splitting (128) gives:
% 163.58/22.68 | | |
% 163.58/22.68 | | | Case 1:
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | (231) sz10 = sz00
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | REDUCE: (10), (231) imply:
% 163.58/22.68 | | | | (232) $false
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | CLOSE: (232) is inconsistent.
% 163.58/22.68 | | | |
% 163.58/22.68 | | | Case 2:
% 163.58/22.68 | | | |
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with 0, all_339_0, xu, simplifying with
% 163.58/22.68 | | | | (149), (164) gives:
% 163.58/22.68 | | | | (233) all_339_0 = 0
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_339_0, all_1211_0, xu,
% 163.58/22.68 | | | | simplifying with (164), (168) gives:
% 163.58/22.68 | | | | (234) all_1211_0 = all_339_0
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1211_0, all_1232_2, xu,
% 163.58/22.68 | | | | simplifying with (168), (172) gives:
% 163.58/22.68 | | | | (235) all_1232_2 = all_1211_0
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1232_2, all_1237_0, xu,
% 163.58/22.68 | | | | simplifying with (172), (177) gives:
% 163.58/22.68 | | | | (236) all_1237_0 = all_1232_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1237_0, all_1255_1, xu,
% 163.58/22.68 | | | | simplifying with (177), (179) gives:
% 163.58/22.68 | | | | (237) all_1255_1 = all_1237_0
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1255_1, all_1257_0, xu,
% 163.58/22.68 | | | | simplifying with (179), (184) gives:
% 163.58/22.68 | | | | (238) all_1257_0 = all_1255_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1386_4, all_1476_4, xu,
% 163.58/22.68 | | | | simplifying with (203), (205) gives:
% 163.58/22.68 | | | | (239) all_1476_4 = all_1386_4
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1308_2, all_1476_4, xu,
% 163.58/22.68 | | | | simplifying with (194), (205) gives:
% 163.58/22.68 | | | | (240) all_1476_4 = all_1308_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1386_4, all_1478_4, xu,
% 163.58/22.68 | | | | simplifying with (203), (207) gives:
% 163.58/22.68 | | | | (241) all_1478_4 = all_1386_4
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1478_4, all_2100_7, xu,
% 163.58/22.68 | | | | simplifying with (207), (221) gives:
% 163.58/22.68 | | | | (242) all_2100_7 = all_1478_4
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_2100_7, all_2164_7, xu,
% 163.58/22.68 | | | | simplifying with (221), (223) gives:
% 163.58/22.68 | | | | (243) all_2164_7 = all_2100_7
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1284_2, all_2164_7, xu,
% 163.58/22.68 | | | | simplifying with (188), (223) gives:
% 163.58/22.68 | | | | (244) all_2164_7 = all_1284_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1308_2, all_2166_7, xu,
% 163.58/22.68 | | | | simplifying with (194), (225) gives:
% 163.58/22.68 | | | | (245) all_2166_7 = all_1308_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1286_1, all_2166_7, xu,
% 163.58/22.68 | | | | simplifying with (190), (225) gives:
% 163.58/22.68 | | | | (246) all_2166_7 = all_1286_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1257_0, all_2166_7, xu,
% 163.58/22.68 | | | | simplifying with (184), (225) gives:
% 163.58/22.68 | | | | (247) all_2166_7 = all_1257_0
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_337_1, all_2166_7, xu,
% 163.58/22.68 | | | | simplifying with (162), (225) gives:
% 163.58/22.68 | | | | (248) all_2166_7 = all_337_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1476_4, all_2284_1, xu,
% 163.58/22.68 | | | | simplifying with (205), (230) gives:
% 163.58/22.68 | | | | (249) all_2284_1 = all_1476_4
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1320_1, all_2284_1, xu,
% 163.58/22.68 | | | | simplifying with (199), (230) gives:
% 163.58/22.68 | | | | (250) all_2284_1 = all_1320_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with 0, all_1255_2, xq, simplifying with
% 163.58/22.68 | | | | (58), (180) gives:
% 163.58/22.68 | | | | (251) all_1255_2 = 0
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1255_2, all_1308_1, xq,
% 163.58/22.68 | | | | simplifying with (180), (195) gives:
% 163.58/22.68 | | | | (252) all_1308_1 = all_1255_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1308_1, all_1320_2, xq,
% 163.58/22.68 | | | | simplifying with (195), (200) gives:
% 163.58/22.68 | | | | (253) all_1320_2 = all_1308_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1320_2, all_1948_9, xq,
% 163.58/22.68 | | | | simplifying with (200), (211) gives:
% 163.58/22.68 | | | | (254) all_1948_9 = all_1320_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1948_9, all_1956_9, xq,
% 163.58/22.68 | | | | simplifying with (211), (218) gives:
% 163.58/22.68 | | | | (255) all_1956_9 = all_1948_9
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1119_1, all_1956_9, xq,
% 163.58/22.68 | | | | simplifying with (166), (218) gives:
% 163.58/22.68 | | | | (256) all_1956_9 = all_1119_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1234_1, all_1280_2, all_41_3,
% 163.58/22.68 | | | | simplifying with (174), (186) gives:
% 163.58/22.68 | | | | (257) all_1280_2 = all_1234_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1946_8, all_1950_8, all_41_3,
% 163.58/22.68 | | | | simplifying with (209), (214) gives:
% 163.58/22.68 | | | | (258) all_1950_8 = all_1946_8
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1296_1, all_1950_8, all_41_3,
% 163.58/22.68 | | | | simplifying with (192), (214) gives:
% 163.58/22.68 | | | | (259) all_1950_8 = all_1296_1
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1280_2, all_1950_8, all_41_3,
% 163.58/22.68 | | | | simplifying with (186), (214) gives:
% 163.58/22.68 | | | | (260) all_1950_8 = all_1280_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1230_2, all_1950_8, all_41_3,
% 163.58/22.68 | | | | simplifying with (170), (214) gives:
% 163.58/22.68 | | | | (261) all_1950_8 = all_1230_2
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1946_8, all_1952_8, all_41_3,
% 163.58/22.68 | | | | simplifying with (209), (216) gives:
% 163.58/22.68 | | | | (262) all_1952_8 = all_1946_8
% 163.58/22.68 | | | |
% 163.58/22.68 | | | | GROUND_INST: instantiating (36) with all_1255_0, all_1952_8, all_41_3,
% 163.58/22.68 | | | | simplifying with (181), (216) gives:
% 163.58/22.68 | | | | (263) all_1952_8 = all_1255_0
% 163.58/22.68 | | | |
% 163.58/22.69 | | | | GROUND_INST: instantiating (39) with all_233_0, all_1948_3, xq, xu,
% 163.58/22.69 | | | | simplifying with (160), (212) gives:
% 163.58/22.69 | | | | (264) all_1948_3 = all_233_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | GROUND_INST: instantiating (39) with all_1948_3, all_1956_3, xq, xu,
% 163.58/22.69 | | | | simplifying with (212), (219) gives:
% 163.58/22.69 | | | | (265) all_1956_3 = all_1948_3
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | GROUND_INST: instantiating (39) with all_1320_0, all_1956_3, xq, xu,
% 163.58/22.69 | | | | simplifying with (201), (219) gives:
% 163.58/22.69 | | | | (266) all_1956_3 = all_1320_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | GROUND_INST: instantiating (39) with all_1308_0, all_1956_3, xq, xu,
% 163.58/22.69 | | | | simplifying with (196), (219) gives:
% 163.58/22.69 | | | | (267) all_1956_3 = all_1308_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (249), (250) imply:
% 163.58/22.69 | | | | (268) all_1476_4 = all_1320_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (268) implies:
% 163.58/22.69 | | | | (269) all_1476_4 = all_1320_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (245), (246) imply:
% 163.58/22.69 | | | | (270) all_1308_2 = all_1286_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (270) implies:
% 163.58/22.69 | | | | (271) all_1308_2 = all_1286_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (246), (248) imply:
% 163.58/22.69 | | | | (272) all_1286_1 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (246), (247) imply:
% 163.58/22.69 | | | | (273) all_1286_1 = all_1257_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (243), (244) imply:
% 163.58/22.69 | | | | (274) all_2100_7 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (274) implies:
% 163.58/22.69 | | | | (275) all_2100_7 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (242), (275) imply:
% 163.58/22.69 | | | | (276) all_1478_4 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (276) implies:
% 163.58/22.69 | | | | (277) all_1478_4 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (265), (266) imply:
% 163.58/22.69 | | | | (278) all_1948_3 = all_1320_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (278) implies:
% 163.58/22.69 | | | | (279) all_1948_3 = all_1320_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (266), (267) imply:
% 163.58/22.69 | | | | (280) all_1320_0 = all_1308_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (255), (256) imply:
% 163.58/22.69 | | | | (281) all_1948_9 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (281) implies:
% 163.58/22.69 | | | | (282) all_1948_9 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (262), (263) imply:
% 163.58/22.69 | | | | (283) all_1946_8 = all_1255_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (283) implies:
% 163.58/22.69 | | | | (284) all_1946_8 = all_1255_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (259), (260) imply:
% 163.58/22.69 | | | | (285) all_1296_1 = all_1280_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (259), (261) imply:
% 163.58/22.69 | | | | (286) all_1296_1 = all_1230_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (258), (259) imply:
% 163.58/22.69 | | | | (287) all_1946_8 = all_1296_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (287) implies:
% 163.58/22.69 | | | | (288) all_1946_8 = all_1296_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (264), (279) imply:
% 163.58/22.69 | | | | (289) all_1320_0 = all_233_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (289) implies:
% 163.58/22.69 | | | | (290) all_1320_0 = all_233_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (254), (282) imply:
% 163.58/22.69 | | | | (291) all_1320_2 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (291) implies:
% 163.58/22.69 | | | | (292) all_1320_2 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (284), (288) imply:
% 163.58/22.69 | | | | (293) all_1296_1 = all_1255_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (293) implies:
% 163.58/22.69 | | | | (294) all_1296_1 = all_1255_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (241), (277) imply:
% 163.58/22.69 | | | | (295) all_1386_4 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (295) implies:
% 163.58/22.69 | | | | (296) all_1386_4 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (239), (269) imply:
% 163.58/22.69 | | | | (297) all_1386_4 = all_1320_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (297) implies:
% 163.58/22.69 | | | | (298) all_1386_4 = all_1320_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (240), (269) imply:
% 163.58/22.69 | | | | (299) all_1320_1 = all_1308_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (296), (298) imply:
% 163.58/22.69 | | | | (300) all_1320_1 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (300) implies:
% 163.58/22.69 | | | | (301) all_1320_1 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (280), (290) imply:
% 163.58/22.69 | | | | (302) all_1308_0 = all_233_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (299), (301) imply:
% 163.58/22.69 | | | | (303) all_1308_2 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (303) implies:
% 163.58/22.69 | | | | (304) all_1308_2 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (253), (292) imply:
% 163.58/22.69 | | | | (305) all_1308_1 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (305) implies:
% 163.58/22.69 | | | | (306) all_1308_1 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (252), (306) imply:
% 163.58/22.69 | | | | (307) all_1255_2 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (307) implies:
% 163.58/22.69 | | | | (308) all_1255_2 = all_1119_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (271), (304) imply:
% 163.58/22.69 | | | | (309) all_1286_1 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (309) implies:
% 163.58/22.69 | | | | (310) all_1286_1 = all_1284_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (286), (294) imply:
% 163.58/22.69 | | | | (311) all_1255_0 = all_1230_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (285), (294) imply:
% 163.58/22.69 | | | | (312) all_1280_2 = all_1255_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (312) implies:
% 163.58/22.69 | | | | (313) all_1280_2 = all_1255_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (272), (310) imply:
% 163.58/22.69 | | | | (314) all_1284_2 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (273), (310) imply:
% 163.58/22.69 | | | | (315) all_1284_2 = all_1257_0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (314), (315) imply:
% 163.58/22.69 | | | | (316) all_1257_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (316) implies:
% 163.58/22.69 | | | | (317) all_1257_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (257), (313) imply:
% 163.58/22.69 | | | | (318) all_1255_0 = all_1234_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (318) implies:
% 163.58/22.69 | | | | (319) all_1255_0 = all_1234_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (238), (317) imply:
% 163.58/22.69 | | | | (320) all_1255_1 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (320) implies:
% 163.58/22.69 | | | | (321) all_1255_1 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (311), (319) imply:
% 163.58/22.69 | | | | (322) all_1234_1 = all_1230_2
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (237), (321) imply:
% 163.58/22.69 | | | | (323) all_1237_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (323) implies:
% 163.58/22.69 | | | | (324) all_1237_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (251), (308) imply:
% 163.58/22.69 | | | | (325) all_1119_1 = 0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (325) implies:
% 163.58/22.69 | | | | (326) all_1119_1 = 0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (236), (324) imply:
% 163.58/22.69 | | | | (327) all_1232_2 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (327) implies:
% 163.58/22.69 | | | | (328) all_1232_2 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (235), (328) imply:
% 163.58/22.69 | | | | (329) all_1211_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (329) implies:
% 163.58/22.69 | | | | (330) all_1211_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (234), (330) imply:
% 163.58/22.69 | | | | (331) all_339_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | SIMP: (331) implies:
% 163.58/22.69 | | | | (332) all_339_0 = all_337_1
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (233), (332) imply:
% 163.58/22.69 | | | | (333) all_337_1 = 0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (321), (333) imply:
% 163.58/22.69 | | | | (334) all_1255_1 = 0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (314), (333) imply:
% 163.58/22.69 | | | | (335) all_1284_2 = 0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (304), (335) imply:
% 163.58/22.69 | | | | (336) all_1308_2 = 0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | COMBINE_EQS: (306), (326) imply:
% 163.58/22.69 | | | | (337) all_1308_1 = 0
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | BETA: splitting (182) gives:
% 163.58/22.69 | | | |
% 163.58/22.69 | | | | Case 1:
% 163.58/22.69 | | | | |
% 163.58/22.69 | | | | | (338) ~ (all_1255_1 = 0)
% 163.58/22.69 | | | | |
% 163.58/22.69 | | | | | REDUCE: (334), (338) imply:
% 163.58/22.69 | | | | | (339) $false
% 163.58/22.69 | | | | |
% 163.58/22.69 | | | | | CLOSE: (339) is inconsistent.
% 163.58/22.69 | | | | |
% 163.58/22.69 | | | | Case 2:
% 163.58/22.69 | | | | |
% 163.58/22.69 | | | | | (340) ~ (all_1255_2 = 0) | all_1255_0 = 0
% 163.58/22.69 | | | | |
% 163.58/22.69 | | | | | BETA: splitting (340) gives:
% 163.58/22.69 | | | | |
% 163.58/22.69 | | | | | Case 1:
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | (341) ~ (all_1255_2 = 0)
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | REDUCE: (251), (341) imply:
% 163.58/22.69 | | | | | | (342) $false
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | CLOSE: (342) is inconsistent.
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | Case 2:
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | (343) all_1255_0 = 0
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | COMBINE_EQS: (311), (343) imply:
% 163.58/22.69 | | | | | | (344) all_1230_2 = 0
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | COMBINE_EQS: (322), (344) imply:
% 163.58/22.69 | | | | | | (345) all_1234_1 = 0
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | BETA: splitting (175) gives:
% 163.58/22.69 | | | | | |
% 163.58/22.69 | | | | | | Case 1:
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | | (346) ~ (all_1234_1 = 0)
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | | REDUCE: (345), (346) imply:
% 163.58/22.69 | | | | | | | (347) $false
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | | CLOSE: (347) is inconsistent.
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | Case 2:
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | | (348) all_1234_0 = xb & all_41_3 = xb
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | | ALPHA: (348) implies:
% 163.58/22.69 | | | | | | | (349) all_41_3 = xb
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | | BETA: splitting (197) gives:
% 163.58/22.69 | | | | | | |
% 163.58/22.69 | | | | | | | Case 1:
% 163.58/22.69 | | | | | | | |
% 163.58/22.69 | | | | | | | | (350) ~ (all_1308_1 = 0)
% 163.58/22.69 | | | | | | | |
% 163.58/22.69 | | | | | | | | REDUCE: (337), (350) imply:
% 163.58/22.69 | | | | | | | | (351) $false
% 163.58/22.69 | | | | | | | |
% 163.58/22.69 | | | | | | | | CLOSE: (351) is inconsistent.
% 163.58/22.69 | | | | | | | |
% 163.58/22.69 | | | | | | | Case 2:
% 163.58/22.69 | | | | | | | |
% 163.58/22.69 | | | | | | | | (352) ~ (all_1308_2 = 0) | all_1308_0 = all_41_3
% 163.58/22.69 | | | | | | | |
% 163.58/22.69 | | | | | | | | BETA: splitting (352) gives:
% 163.58/22.69 | | | | | | | |
% 163.58/22.69 | | | | | | | | Case 1:
% 163.58/22.69 | | | | | | | | |
% 163.58/22.69 | | | | | | | | | (353) ~ (all_1308_2 = 0)
% 163.58/22.69 | | | | | | | | |
% 163.58/22.69 | | | | | | | | | REDUCE: (336), (353) imply:
% 163.58/22.69 | | | | | | | | | (354) $false
% 163.58/22.69 | | | | | | | | |
% 163.58/22.69 | | | | | | | | | CLOSE: (354) is inconsistent.
% 163.58/22.69 | | | | | | | | |
% 163.58/22.69 | | | | | | | | Case 2:
% 163.58/22.69 | | | | | | | | |
% 163.58/22.70 | | | | | | | | | (355) all_1308_0 = all_41_3
% 163.58/22.70 | | | | | | | | |
% 163.58/22.70 | | | | | | | | | COMBINE_EQS: (302), (355) imply:
% 163.58/22.70 | | | | | | | | | (356) all_233_0 = all_41_3
% 163.58/22.70 | | | | | | | | |
% 163.58/22.70 | | | | | | | | | COMBINE_EQS: (349), (356) imply:
% 163.58/22.70 | | | | | | | | | (357) all_233_0 = xb
% 163.58/22.70 | | | | | | | | |
% 163.58/22.70 | | | | | | | | | REDUCE: (159), (357) imply:
% 163.58/22.70 | | | | | | | | | (358) $false
% 163.58/22.70 | | | | | | | | |
% 163.58/22.70 | | | | | | | | | CLOSE: (358) is inconsistent.
% 163.58/22.70 | | | | | | | | |
% 163.58/22.70 | | | | | | | | End of split
% 163.58/22.70 | | | | | | | |
% 163.58/22.70 | | | | | | | End of split
% 163.58/22.70 | | | | | | |
% 163.58/22.70 | | | | | | End of split
% 163.58/22.70 | | | | | |
% 163.58/22.70 | | | | | End of split
% 163.58/22.70 | | | | |
% 163.58/22.70 | | | | End of split
% 163.58/22.70 | | | |
% 163.58/22.70 | | | End of split
% 163.58/22.70 | | |
% 163.58/22.70 | | End of split
% 163.58/22.70 | |
% 163.58/22.70 | Case 2:
% 163.58/22.70 | |
% 163.58/22.70 | | (359) ~ (all_45_2 = 0) & ~ (all_45_3 = 0) & ! [v0: $i] : ( ~
% 163.58/22.70 | | (sdtasdt0(xu, v0) = xa) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 163.58/22.70 | | & aElement0(v0) = v1)) & ! [v0: $i] : ( ~ (aElement0(v0) = 0)
% 163.58/22.70 | | | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xa) & sdtasdt0(xu, v0) = v1
% 163.58/22.70 | | & $i(v1)))
% 163.58/22.70 | |
% 163.58/22.70 | | ALPHA: (359) implies:
% 163.58/22.70 | | (360) ~ (all_45_3 = 0)
% 163.58/22.70 | |
% 163.58/22.70 | | REDUCE: (107), (360) imply:
% 163.58/22.70 | | (361) $false
% 163.58/22.70 | |
% 163.58/22.70 | | CLOSE: (361) is inconsistent.
% 163.58/22.70 | |
% 163.58/22.70 | End of split
% 163.58/22.70 |
% 163.58/22.70 End of proof
% 163.58/22.70 % SZS output end Proof for theBenchmark
% 163.58/22.70
% 163.58/22.70 22103ms
%------------------------------------------------------------------------------