TSTP Solution File: NUM501+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:48:12 EDT 2023
% Result : Theorem 23.16s 3.96s
% Output : Proof 58.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.38 % Computer : n024.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Fri Aug 25 17:47:24 EDT 2023
% 0.14/0.38 % CPUTime :
% 0.22/0.66 ________ _____
% 0.22/0.66 ___ __ \_________(_)________________________________
% 0.22/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.66
% 0.22/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.66 (2023-06-19)
% 0.22/0.66
% 0.22/0.66 (c) Philipp Rümmer, 2009-2023
% 0.22/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.66 Amanda Stjerna.
% 0.22/0.66 Free software under BSD-3-Clause.
% 0.22/0.66
% 0.22/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.66
% 0.22/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.68 Running up to 7 provers in parallel.
% 0.22/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.61/1.36 Prover 1: Preprocessing ...
% 3.61/1.36 Prover 4: Preprocessing ...
% 3.61/1.42 Prover 6: Preprocessing ...
% 3.61/1.42 Prover 0: Preprocessing ...
% 3.61/1.42 Prover 3: Preprocessing ...
% 3.61/1.42 Prover 2: Preprocessing ...
% 3.61/1.42 Prover 5: Preprocessing ...
% 12.30/2.50 Prover 1: Constructing countermodel ...
% 12.53/2.59 Prover 3: Constructing countermodel ...
% 12.53/2.59 Prover 6: Proving ...
% 12.53/2.69 Prover 5: Constructing countermodel ...
% 17.56/3.19 Prover 2: Proving ...
% 18.39/3.37 Prover 4: Constructing countermodel ...
% 20.38/3.59 Prover 0: Proving ...
% 23.16/3.95 Prover 3: proved (3262ms)
% 23.16/3.95
% 23.16/3.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.16/3.96
% 23.16/3.96 Prover 5: stopped
% 23.16/3.96 Prover 0: stopped
% 23.16/3.97 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.16/3.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.16/3.97 Prover 2: stopped
% 23.16/3.98 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.16/3.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.16/3.98 Prover 6: stopped
% 23.16/4.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.11/4.13 Prover 8: Preprocessing ...
% 24.71/4.18 Prover 7: Preprocessing ...
% 24.71/4.18 Prover 10: Preprocessing ...
% 24.96/4.20 Prover 13: Preprocessing ...
% 24.96/4.22 Prover 11: Preprocessing ...
% 26.94/4.48 Prover 8: Warning: ignoring some quantifiers
% 27.24/4.51 Prover 8: Constructing countermodel ...
% 27.24/4.52 Prover 10: Constructing countermodel ...
% 27.75/4.63 Prover 7: Constructing countermodel ...
% 27.75/4.68 Prover 13: Constructing countermodel ...
% 31.21/5.04 Prover 11: Constructing countermodel ...
% 57.47/8.46 Prover 1: Found proof (size 423)
% 57.47/8.46 Prover 1: proved (7777ms)
% 57.47/8.46 Prover 13: stopped
% 57.47/8.46 Prover 11: stopped
% 57.47/8.46 Prover 4: stopped
% 57.47/8.46 Prover 7: stopped
% 57.47/8.46 Prover 10: stopped
% 57.47/8.48 Prover 8: stopped
% 57.47/8.48
% 57.47/8.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.47/8.48
% 58.07/8.52 % SZS output start Proof for theBenchmark
% 58.07/8.52 Assumptions after simplification:
% 58.07/8.52 ---------------------------------
% 58.07/8.52
% 58.07/8.52 (mAddAsso)
% 58.07/8.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 58.07/8.55 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 58.07/8.55 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 58.07/8.55 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 &
% 58.07/8.55 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 58.07/8.55 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 58.07/8.55 v4)))
% 58.07/8.55
% 58.07/8.55 (mAddComm)
% 58.07/8.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 58.07/8.55 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 58.07/8.55 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 58.07/8.55 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 58.07/8.55
% 58.07/8.55 (mDefDiv)
% 58.07/8.56 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~
% 58.07/8.56 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4
% 58.07/8.56 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0)
% 58.07/8.56 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 &
% 58.07/8.56 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~
% 58.07/8.56 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)))))
% 58.07/8.56
% 58.07/8.56 (mDefPrime)
% 58.07/8.56 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) |
% 58.07/8.56 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~
% 58.07/8.56 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 |
% 58.07/8.56 v2 = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] :
% 58.07/8.56 ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = 0 | v0 = sz10 |
% 58.07/8.56 v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) &
% 58.07/8.56 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & $i(v2)))))
% 58.07/8.56
% 58.07/8.56 (mDefQuot)
% 58.07/8.56 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~
% 58.07/8.56 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 58.07/8.56 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4
% 58.07/8.56 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) |
% 58.07/8.56 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4:
% 58.07/8.56 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~
% 58.07/8.56 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) =
% 58.07/8.56 0))))
% 58.07/8.56
% 58.07/8.56 (mDivTrans)
% 58.07/8.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 58.07/8.57 (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ~ $i(v2) | ~
% 58.07/8.57 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7:
% 58.07/8.57 any] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 &
% 58.07/8.57 aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~
% 58.07/8.57 (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 58.07/8.57
% 58.07/8.57 (mMulAsso)
% 58.07/8.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 58.07/8.57 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 58.07/8.57 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 58.07/8.57 [v9: $i] : (sdtasdt0(v1, v2) = v8 & sdtasdt0(v0, v8) = v9 &
% 58.07/8.57 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 58.07/8.57 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 58.07/8.57 v4)))
% 58.07/8.57
% 58.07/8.57 (mMulCanc)
% 58.07/8.57 $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0)
% 58.07/8.57 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~
% 58.07/8.57 (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~
% 58.07/8.57 $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] :
% 58.07/8.57 (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6
% 58.07/8.57 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 =
% 58.07/8.57 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))))
% 58.07/8.57
% 58.07/8.57 (mMulComm)
% 58.07/8.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 58.07/8.57 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 58.07/8.57 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 58.07/8.57 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 58.07/8.57
% 58.07/8.57 (mPrimDiv)
% 58.07/8.57 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~
% 58.07/8.57 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 &
% 58.07/8.57 doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0 & $i(v1)))
% 58.07/8.57
% 58.07/8.57 (mSortsB)
% 58.07/8.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 58.07/8.57 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 58.07/8.57 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 58.07/8.57 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 58.07/8.57
% 58.07/8.57 (mSortsB_02)
% 58.07/8.57 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 58.07/8.57 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 58.07/8.57 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 58.07/8.57 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 58.07/8.57
% 58.07/8.57 (m__)
% 58.07/8.57 $i(xr) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 58.07/8.57 doDivides0(xr, v0) = v1 & sdtasdt0(xn, xm) = v0 & $i(v0) & ! [v2: $i] : ( ~
% 58.07/8.57 (sdtasdt0(xr, v2) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 58.07/8.57 aNaturalNumber0(v2) = v3)))
% 58.07/8.57
% 58.07/8.57 (m__1799)
% 58.07/8.58 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] :
% 58.07/8.58 (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i]
% 58.07/8.58 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5,
% 58.07/8.58 v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 58.07/8.58 $i(v2) | ? [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ?
% 58.07/8.58 [v11: $i] : ? [v12: any] : ? [v13: any] : ? [v14: any] : ? [v15: any]
% 58.07/8.58 : (isPrime0(v4) = v10 & doDivides0(v4, v11) = v12 & doDivides0(v4, v3) =
% 58.07/8.58 v15 & doDivides0(v4, v2) = v14 & iLess0(v6, v1) = v13 & sdtasdt0(v2, v3)
% 58.07/8.58 = v11 & aNaturalNumber0(v4) = v9 & aNaturalNumber0(v3) = v8 &
% 58.07/8.58 aNaturalNumber0(v2) = v7 & $i(v11) & ( ~ (v13 = 0) | ~ (v9 = 0) | ~
% 58.07/8.58 (v8 = 0) | ~ (v7 = 0) | (v15 = 0 & ? [v16: $i] : (sdtasdt0(v4, v16)
% 58.07/8.58 = v3 & aNaturalNumber0(v16) = 0 & $i(v16))) | (v14 = 0 & ? [v16:
% 58.07/8.58 $i] : (sdtasdt0(v4, v16) = v2 & aNaturalNumber0(v16) = 0 &
% 58.07/8.58 $i(v16))) | ( ~ (v12 = 0) & ! [v16: $i] : ( ~ (sdtasdt0(v4, v16)
% 58.07/8.58 = v11) | ~ $i(v16) | ? [v17: int] : ( ~ (v17 = 0) &
% 58.07/8.58 aNaturalNumber0(v16) = v17))) | ( ~ (v10 = 0) & (v4 = sz10 | v4
% 58.07/8.58 = sz00 | ? [v16: $i] : ( ~ (v16 = v4) & ~ (v16 = sz10) &
% 58.07/8.58 doDivides0(v16, v4) = 0 & aNaturalNumber0(v16) = 0 & $i(v16) &
% 58.07/8.58 ? [v17: $i] : (sdtasdt0(v16, v17) = v4 & aNaturalNumber0(v17) =
% 58.07/8.58 0 & $i(v17)))))))))
% 58.07/8.58
% 58.07/8.58 (m__1837)
% 58.07/8.58 aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 &
% 58.07/8.58 $i(xp) & $i(xm) & $i(xn)
% 58.07/8.58
% 58.07/8.58 (m__1860)
% 58.07/8.58 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ( ~ (xp = sz10)
% 58.07/8.58 & ~ (xp = sz00) & isPrime0(xp) = 0 & doDivides0(xp, v0) = 0 & sdtasdt0(xn,
% 58.07/8.58 xm) = v0 & $i(v0) & ! [v1: $i] : ! [v2: any] : (v1 = xp | v1 = sz10 | ~
% 58.07/8.58 (doDivides0(v1, xp) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 58.07/8.58 aNaturalNumber0(v1) = v3) | ( ~ (v2 = 0) & ! [v3: $i] : ( ~
% 58.07/8.58 (sdtasdt0(v1, v3) = xp) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) &
% 58.07/8.58 aNaturalNumber0(v3) = v4)))) & ? [v1: $i] : (sdtasdt0(xp, v1) = v0
% 58.07/8.58 & aNaturalNumber0(v1) = 0 & $i(v1)))
% 58.07/8.58
% 58.07/8.58 (m__2287)
% 58.07/8.58 ~ (xp = xm) & ~ (xp = xn) & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0
% 58.07/8.58 & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtpldt0(xm, v0) = xp &
% 58.07/8.58 aNaturalNumber0(v0) = 0 & $i(v0)) & ? [v0: $i] : (sdtpldt0(xn, v0) = xp &
% 58.07/8.58 aNaturalNumber0(v0) = 0 & $i(v0))
% 58.07/8.58
% 58.07/8.58 (m__2306)
% 58.07/8.58 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 58.07/8.58 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & aNaturalNumber0(xk) = 0 &
% 58.07/8.58 $i(v0))
% 58.07/8.58
% 58.07/8.58 (m__2342)
% 58.07/8.59 ~ (xr = sz10) & ~ (xr = sz00) & isPrime0(xr) = 0 & doDivides0(xr, xk) = 0 &
% 58.07/8.59 aNaturalNumber0(xr) = 0 & $i(xr) & $i(xk) & $i(sz10) & $i(sz00) & ! [v0: $i]
% 58.07/8.59 : ! [v1: any] : (v0 = xr | v0 = sz10 | ~ (doDivides0(v0, xr) = v1) | ~
% 58.07/8.59 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | ( ~ (v1 =
% 58.07/8.59 0) & ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = xr) | ~ $i(v2) | ? [v3:
% 58.07/8.59 int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & ? [v0: $i] :
% 58.07/8.59 (sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0 & $i(v0))
% 58.07/8.59
% 58.07/8.59 (function-axioms)
% 58.07/8.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 58.07/8.59 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 58.07/8.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 58.07/8.59 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 58.07/8.59 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 58.07/8.59 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 58.07/8.59 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 58.07/8.59 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 58.07/8.59 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 58.07/8.59 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 58.07/8.59 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 58.07/8.59 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 58.07/8.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 58.07/8.59 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 58.07/8.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~
% 58.07/8.59 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 58.07/8.59 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 58.07/8.59 | ~ (aNaturalNumber0(v2) = v0))
% 58.07/8.59
% 58.07/8.59 Further assumptions not needed in the proof:
% 58.07/8.59 --------------------------------------------
% 58.07/8.59 mAMDistr, mAddCanc, mDefDiff, mDefLE, mDivAsso, mDivLE, mDivMin, mDivSum, mIH,
% 58.07/8.59 mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2,
% 58.07/8.59 mNatSort, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit,
% 58.07/8.59 m_MulZero, m__1870, m__2075, m__2315, m__2327
% 58.07/8.59
% 58.07/8.59 Those formulas are unsatisfiable:
% 58.07/8.59 ---------------------------------
% 58.07/8.59
% 58.07/8.59 Begin of proof
% 58.07/8.59 |
% 58.07/8.59 | ALPHA: (mMulCanc) implies:
% 58.49/8.59 | (1) ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) |
% 58.49/8.59 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~
% 58.49/8.59 | (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) |
% 58.49/8.59 | ~ $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i]
% 58.49/8.59 | : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 &
% 58.49/8.59 | aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & $i(v8) &
% 58.49/8.59 | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 =
% 58.49/8.59 | v3))))))
% 58.49/8.59 |
% 58.49/8.59 | ALPHA: (mDefQuot) implies:
% 58.49/8.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1,
% 58.49/8.60 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 58.49/8.60 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 &
% 58.49/8.60 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 58.49/8.60 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) |
% 58.49/8.60 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) =
% 58.49/8.60 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) |
% 58.49/8.60 | (v3 = v1 & aNaturalNumber0(v2) = 0))))
% 58.49/8.60 |
% 58.49/8.60 | ALPHA: (mDefPrime) implies:
% 58.49/8.60 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | ~ $i(v0) | ?
% 58.49/8.60 | [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ (v1 = 0)
% 58.49/8.60 | | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | v2
% 58.49/8.60 | = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3:
% 58.49/8.60 | int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 =
% 58.49/8.60 | 0 | v0 = sz10 | v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2
% 58.49/8.60 | = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 &
% 58.49/8.60 | $i(v2)))))
% 58.49/8.60 |
% 58.49/8.60 | ALPHA: (mPrimDiv) implies:
% 58.49/8.60 | (4) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) |
% 58.49/8.60 | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 &
% 58.49/8.60 | aNaturalNumber0(v1) = 0 & $i(v1)))
% 58.49/8.60 |
% 58.49/8.60 | ALPHA: (m__1837) implies:
% 58.49/8.60 | (5) aNaturalNumber0(xn) = 0
% 58.49/8.60 | (6) aNaturalNumber0(xm) = 0
% 58.49/8.60 | (7) aNaturalNumber0(xp) = 0
% 58.49/8.60 |
% 58.49/8.60 | ALPHA: (m__1799) implies:
% 58.49/8.60 | (8) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) =
% 58.49/8.60 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 58.49/8.60 | [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~
% 58.49/8.60 | (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ?
% 58.49/8.60 | [v7: any] : ? [v8: any] : ? [v9: any] : ? [v10: any] : ? [v11:
% 58.49/8.60 | $i] : ? [v12: any] : ? [v13: any] : ? [v14: any] : ? [v15:
% 58.49/8.60 | any] : (isPrime0(v4) = v10 & doDivides0(v4, v11) = v12 &
% 58.49/8.60 | doDivides0(v4, v3) = v15 & doDivides0(v4, v2) = v14 & iLess0(v6,
% 58.49/8.60 | v1) = v13 & sdtasdt0(v2, v3) = v11 & aNaturalNumber0(v4) = v9 &
% 58.49/8.60 | aNaturalNumber0(v3) = v8 & aNaturalNumber0(v2) = v7 & $i(v11) & (
% 58.49/8.60 | ~ (v13 = 0) | ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | (v15 =
% 58.49/8.60 | 0 & ? [v16: $i] : (sdtasdt0(v4, v16) = v3 &
% 58.49/8.60 | aNaturalNumber0(v16) = 0 & $i(v16))) | (v14 = 0 & ? [v16:
% 58.49/8.60 | $i] : (sdtasdt0(v4, v16) = v2 & aNaturalNumber0(v16) = 0 &
% 58.49/8.60 | $i(v16))) | ( ~ (v12 = 0) & ! [v16: $i] : ( ~
% 58.49/8.60 | (sdtasdt0(v4, v16) = v11) | ~ $i(v16) | ? [v17: int] : (
% 58.49/8.60 | ~ (v17 = 0) & aNaturalNumber0(v16) = v17))) | ( ~ (v10 =
% 58.49/8.60 | 0) & (v4 = sz10 | v4 = sz00 | ? [v16: $i] : ( ~ (v16 = v4)
% 58.49/8.60 | & ~ (v16 = sz10) & doDivides0(v16, v4) = 0 &
% 58.49/8.60 | aNaturalNumber0(v16) = 0 & $i(v16) & ? [v17: $i] :
% 58.49/8.60 | (sdtasdt0(v16, v17) = v4 & aNaturalNumber0(v17) = 0 &
% 58.49/8.60 | $i(v17)))))))))
% 58.49/8.60 |
% 58.49/8.60 | ALPHA: (m__1860) implies:
% 58.49/8.61 | (9) ? [v0: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) & isPrime0(xp) = 0 &
% 58.49/8.61 | doDivides0(xp, v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0) & ! [v1: $i]
% 58.49/8.61 | : ! [v2: any] : (v1 = xp | v1 = sz10 | ~ (doDivides0(v1, xp) = v2)
% 58.49/8.61 | | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aNaturalNumber0(v1) =
% 58.49/8.61 | v3) | ( ~ (v2 = 0) & ! [v3: $i] : ( ~ (sdtasdt0(v1, v3) = xp) |
% 58.49/8.61 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) =
% 58.49/8.61 | v4)))) & ? [v1: $i] : (sdtasdt0(xp, v1) = v0 &
% 58.49/8.61 | aNaturalNumber0(v1) = 0 & $i(v1)))
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (m__2287) implies:
% 58.49/8.61 | (10) ? [v0: $i] : (sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0 &
% 58.49/8.61 | $i(v0))
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (m__2306) implies:
% 58.49/8.61 | (11) $i(xp)
% 58.49/8.61 | (12) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 &
% 58.49/8.61 | sdtasdt0(xn, xm) = v0 & aNaturalNumber0(xk) = 0 & $i(v0))
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (m__2342) implies:
% 58.49/8.61 | (13) ~ (xr = sz00)
% 58.49/8.61 | (14) ~ (xr = sz10)
% 58.49/8.61 | (15) $i(xk)
% 58.49/8.61 | (16) aNaturalNumber0(xr) = 0
% 58.49/8.61 | (17) doDivides0(xr, xk) = 0
% 58.49/8.61 | (18) ? [v0: $i] : (sdtasdt0(xr, v0) = xk & aNaturalNumber0(v0) = 0 &
% 58.49/8.61 | $i(v0))
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (m__) implies:
% 58.49/8.61 | (19) $i(xn)
% 58.49/8.61 | (20) $i(xm)
% 58.49/8.61 | (21) $i(xr)
% 58.49/8.61 | (22) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & doDivides0(xr, v0) = v1 &
% 58.49/8.61 | sdtasdt0(xn, xm) = v0 & $i(v0) & ! [v2: $i] : ( ~ (sdtasdt0(xr, v2)
% 58.49/8.61 | = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 58.49/8.61 | aNaturalNumber0(v2) = v3)))
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (function-axioms) implies:
% 58.49/8.61 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 58.49/8.61 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 58.49/8.61 | v0))
% 58.49/8.61 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 58.49/8.61 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 58.49/8.61 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 58.49/8.61 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~
% 58.49/8.61 | (doDivides0(v3, v2) = v0))
% 58.49/8.61 |
% 58.49/8.61 | DELTA: instantiating (18) with fresh symbol all_41_0 gives:
% 58.49/8.61 | (26) sdtasdt0(xr, all_41_0) = xk & aNaturalNumber0(all_41_0) = 0 &
% 58.49/8.61 | $i(all_41_0)
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (26) implies:
% 58.49/8.61 | (27) $i(all_41_0)
% 58.49/8.61 | (28) aNaturalNumber0(all_41_0) = 0
% 58.49/8.61 | (29) sdtasdt0(xr, all_41_0) = xk
% 58.49/8.61 |
% 58.49/8.61 | DELTA: instantiating (10) with fresh symbol all_43_0 gives:
% 58.49/8.61 | (30) sdtpldt0(xm, all_43_0) = xp & aNaturalNumber0(all_43_0) = 0 &
% 58.49/8.61 | $i(all_43_0)
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (30) implies:
% 58.49/8.61 | (31) $i(all_43_0)
% 58.49/8.61 | (32) sdtpldt0(xm, all_43_0) = xp
% 58.49/8.61 |
% 58.49/8.61 | DELTA: instantiating (12) with fresh symbol all_45_0 gives:
% 58.49/8.61 | (33) sdtsldt0(all_45_0, xp) = xk & sdtasdt0(xp, xk) = all_45_0 &
% 58.49/8.61 | sdtasdt0(xn, xm) = all_45_0 & aNaturalNumber0(xk) = 0 & $i(all_45_0)
% 58.49/8.61 |
% 58.49/8.61 | ALPHA: (33) implies:
% 58.49/8.61 | (34) aNaturalNumber0(xk) = 0
% 58.49/8.61 | (35) sdtasdt0(xn, xm) = all_45_0
% 58.49/8.61 | (36) sdtasdt0(xp, xk) = all_45_0
% 58.49/8.61 | (37) sdtsldt0(all_45_0, xp) = xk
% 58.49/8.61 |
% 58.49/8.61 | DELTA: instantiating (22) with fresh symbols all_53_0, all_53_1 gives:
% 58.49/8.62 | (38) ~ (all_53_0 = 0) & doDivides0(xr, all_53_1) = all_53_0 & sdtasdt0(xn,
% 58.49/8.62 | xm) = all_53_1 & $i(all_53_1) & ! [v0: $i] : ( ~ (sdtasdt0(xr, v0)
% 58.49/8.62 | = all_53_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 58.49/8.62 | aNaturalNumber0(v0) = v1))
% 58.49/8.62 |
% 58.49/8.62 | ALPHA: (38) implies:
% 58.49/8.62 | (39) ~ (all_53_0 = 0)
% 58.49/8.62 | (40) $i(all_53_1)
% 58.49/8.62 | (41) sdtasdt0(xn, xm) = all_53_1
% 58.49/8.62 | (42) doDivides0(xr, all_53_1) = all_53_0
% 58.49/8.62 |
% 58.49/8.62 | DELTA: instantiating (9) with fresh symbol all_56_0 gives:
% 58.49/8.62 | (43) ~ (xp = sz10) & ~ (xp = sz00) & isPrime0(xp) = 0 & doDivides0(xp,
% 58.49/8.62 | all_56_0) = 0 & sdtasdt0(xn, xm) = all_56_0 & $i(all_56_0) & ! [v0:
% 58.49/8.62 | $i] : ! [v1: any] : (v0 = xp | v0 = sz10 | ~ (doDivides0(v0, xp) =
% 58.49/8.62 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 58.49/8.62 | aNaturalNumber0(v0) = v2) | ( ~ (v1 = 0) & ! [v2: $i] : ( ~
% 58.49/8.62 | (sdtasdt0(v0, v2) = xp) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 =
% 58.49/8.62 | 0) & aNaturalNumber0(v2) = v3)))) & ? [v0: $i] :
% 58.49/8.62 | (sdtasdt0(xp, v0) = all_56_0 & aNaturalNumber0(v0) = 0 & $i(v0))
% 58.49/8.62 |
% 58.49/8.62 | ALPHA: (43) implies:
% 58.49/8.62 | (44) ~ (xp = sz00)
% 58.49/8.62 | (45) sdtasdt0(xn, xm) = all_56_0
% 58.49/8.62 | (46) doDivides0(xp, all_56_0) = 0
% 58.49/8.62 | (47) ? [v0: $i] : (sdtasdt0(xp, v0) = all_56_0 & aNaturalNumber0(v0) = 0 &
% 58.49/8.62 | $i(v0))
% 58.49/8.62 |
% 58.49/8.62 | DELTA: instantiating (8) with fresh symbols all_59_0, all_59_1 gives:
% 58.49/8.62 | (48) sdtpldt0(all_59_1, xp) = all_59_0 & sdtpldt0(xn, xm) = all_59_1 &
% 58.49/8.62 | $i(all_59_0) & $i(all_59_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 58.49/8.62 | : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v2) = v4) | ~
% 58.49/8.62 | (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 58.49/8.62 | [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: $i]
% 58.49/8.62 | : ? [v10: any] : ? [v11: any] : ? [v12: any] : ? [v13: any] :
% 58.49/8.62 | (isPrime0(v2) = v8 & doDivides0(v2, v9) = v10 & doDivides0(v2, v1) =
% 58.49/8.62 | v13 & doDivides0(v2, v0) = v12 & iLess0(v4, all_59_0) = v11 &
% 58.49/8.62 | sdtasdt0(v0, v1) = v9 & aNaturalNumber0(v2) = v7 &
% 58.49/8.62 | aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & ( ~
% 58.49/8.62 | (v11 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | (v13 = 0 &
% 58.49/8.62 | ? [v14: $i] : (sdtasdt0(v2, v14) = v1 & aNaturalNumber0(v14)
% 58.49/8.62 | = 0 & $i(v14))) | (v12 = 0 & ? [v14: $i] : (sdtasdt0(v2,
% 58.49/8.62 | v14) = v0 & aNaturalNumber0(v14) = 0 & $i(v14))) | ( ~
% 58.49/8.62 | (v10 = 0) & ! [v14: $i] : ( ~ (sdtasdt0(v2, v14) = v9) | ~
% 58.49/8.62 | $i(v14) | ? [v15: int] : ( ~ (v15 = 0) &
% 58.49/8.62 | aNaturalNumber0(v14) = v15))) | ( ~ (v8 = 0) & (v2 = sz10
% 58.49/8.62 | | v2 = sz00 | ? [v14: $i] : ( ~ (v14 = v2) & ~ (v14 =
% 58.49/8.62 | sz10) & doDivides0(v14, v2) = 0 & aNaturalNumber0(v14) =
% 58.49/8.62 | 0 & $i(v14) & ? [v15: $i] : (sdtasdt0(v14, v15) = v2 &
% 58.49/8.62 | aNaturalNumber0(v15) = 0 & $i(v15))))))))
% 58.49/8.62 |
% 58.49/8.62 | ALPHA: (48) implies:
% 58.49/8.62 | (49) $i(all_59_1)
% 58.49/8.62 | (50) sdtpldt0(xn, xm) = all_59_1
% 58.49/8.62 | (51) sdtpldt0(all_59_1, xp) = all_59_0
% 58.49/8.62 | (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.49/8.62 | ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 58.49/8.62 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 58.49/8.62 | ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: any] : ?
% 58.49/8.62 | [v12: any] : ? [v13: any] : (isPrime0(v2) = v8 & doDivides0(v2, v9)
% 58.49/8.62 | = v10 & doDivides0(v2, v1) = v13 & doDivides0(v2, v0) = v12 &
% 58.49/8.62 | iLess0(v4, all_59_0) = v11 & sdtasdt0(v0, v1) = v9 &
% 58.49/8.62 | aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 &
% 58.49/8.62 | aNaturalNumber0(v0) = v5 & $i(v9) & ( ~ (v11 = 0) | ~ (v7 = 0) |
% 58.49/8.62 | ~ (v6 = 0) | ~ (v5 = 0) | (v13 = 0 & ? [v14: $i] :
% 58.49/8.62 | (sdtasdt0(v2, v14) = v1 & aNaturalNumber0(v14) = 0 & $i(v14)))
% 58.49/8.62 | | (v12 = 0 & ? [v14: $i] : (sdtasdt0(v2, v14) = v0 &
% 58.49/8.62 | aNaturalNumber0(v14) = 0 & $i(v14))) | ( ~ (v10 = 0) & !
% 58.49/8.62 | [v14: $i] : ( ~ (sdtasdt0(v2, v14) = v9) | ~ $i(v14) | ?
% 58.49/8.62 | [v15: int] : ( ~ (v15 = 0) & aNaturalNumber0(v14) = v15))) |
% 58.49/8.62 | ( ~ (v8 = 0) & (v2 = sz10 | v2 = sz00 | ? [v14: $i] : ( ~ (v14
% 58.49/8.62 | = v2) & ~ (v14 = sz10) & doDivides0(v14, v2) = 0 &
% 58.49/8.62 | aNaturalNumber0(v14) = 0 & $i(v14) & ? [v15: $i] :
% 58.49/8.62 | (sdtasdt0(v14, v15) = v2 & aNaturalNumber0(v15) = 0 &
% 58.49/8.62 | $i(v15))))))))
% 58.49/8.62 |
% 58.49/8.62 | DELTA: instantiating (47) with fresh symbol all_62_0 gives:
% 58.49/8.63 | (53) sdtasdt0(xp, all_62_0) = all_56_0 & aNaturalNumber0(all_62_0) = 0 &
% 58.49/8.63 | $i(all_62_0)
% 58.49/8.63 |
% 58.49/8.63 | ALPHA: (53) implies:
% 58.49/8.63 | (54) $i(all_62_0)
% 58.49/8.63 | (55) aNaturalNumber0(all_62_0) = 0
% 58.49/8.63 | (56) sdtasdt0(xp, all_62_0) = all_56_0
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (24) with all_53_1, all_56_0, xm, xn, simplifying
% 58.49/8.63 | with (41), (45) gives:
% 58.49/8.63 | (57) all_56_0 = all_53_1
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (24) with all_45_0, all_56_0, xm, xn, simplifying
% 58.49/8.63 | with (35), (45) gives:
% 58.49/8.63 | (58) all_56_0 = all_45_0
% 58.49/8.63 |
% 58.49/8.63 | COMBINE_EQS: (57), (58) imply:
% 58.49/8.63 | (59) all_53_1 = all_45_0
% 58.49/8.63 |
% 58.49/8.63 | SIMP: (59) implies:
% 58.49/8.63 | (60) all_53_1 = all_45_0
% 58.49/8.63 |
% 58.49/8.63 | REDUCE: (42), (60) imply:
% 58.49/8.63 | (61) doDivides0(xr, all_45_0) = all_53_0
% 58.49/8.63 |
% 58.49/8.63 | REDUCE: (46), (58) imply:
% 58.49/8.63 | (62) doDivides0(xp, all_45_0) = 0
% 58.49/8.63 |
% 58.49/8.63 | REDUCE: (56), (58) imply:
% 58.49/8.63 | (63) sdtasdt0(xp, all_62_0) = all_45_0
% 58.49/8.63 |
% 58.49/8.63 | REDUCE: (40), (60) imply:
% 58.49/8.63 | (64) $i(all_45_0)
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (1) with xp, simplifying with (7), (11) gives:
% 58.49/8.63 | (65) xp = sz00 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 58.49/8.63 | (v1 = v0 | ~ (sdtasdt0(xp, v1) = v3) | ~ (sdtasdt0(xp, v0) = v2) |
% 58.49/8.63 | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] :
% 58.49/8.63 | ? [v7: $i] : (sdtasdt0(v1, xp) = v7 & sdtasdt0(v0, xp) = v6 &
% 58.49/8.63 | aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & $i(v7) &
% 58.49/8.63 | $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ( ~ (v7 = v6) & ~ (v3 =
% 58.49/8.63 | v2)))))
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (4) with xr, simplifying with (16), (21) gives:
% 58.49/8.63 | (66) xr = sz10 | xr = sz00 | ? [v0: $i] : (isPrime0(v0) = 0 &
% 58.49/8.63 | doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0 & $i(v0))
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_59_1, simplifying with
% 58.49/8.63 | (19), (20), (50) gives:
% 58.49/8.63 | (67) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xm, xn) = v2 &
% 58.49/8.63 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 58.49/8.63 | (v1 = 0) | ~ (v0 = 0) | v2 = all_59_1))
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_59_1, simplifying with
% 58.49/8.63 | (19), (20), (50) gives:
% 58.49/8.63 | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.63 | (aNaturalNumber0(all_59_1) = v2 & aNaturalNumber0(xm) = v1 &
% 58.49/8.63 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (mAddComm) with xm, all_43_0, xp, simplifying with
% 58.49/8.63 | (20), (31), (32) gives:
% 58.49/8.63 | (69) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_43_0, xm) =
% 58.49/8.63 | v2 & aNaturalNumber0(all_43_0) = v1 & aNaturalNumber0(xm) = v0 &
% 58.49/8.63 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xp))
% 58.49/8.63 |
% 58.49/8.63 | GROUND_INST: instantiating (52) with xn, xm, xp, all_59_1, all_59_0,
% 58.49/8.63 | simplifying with (11), (19), (20), (50), (51) gives:
% 58.49/8.63 | (70) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 58.49/8.63 | $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 58.49/8.63 | (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 & doDivides0(xp, xm) = v8
% 58.49/8.63 | & doDivides0(xp, xn) = v7 & iLess0(all_59_0, all_59_0) = v6 &
% 58.49/8.63 | sdtasdt0(xn, xm) = v4 & aNaturalNumber0(xp) = v2 &
% 58.49/8.63 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4) & ( ~
% 58.49/8.63 | (v6 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v8 = 0 & ?
% 58.49/8.63 | [v9: $i] : (sdtasdt0(xp, v9) = xm & aNaturalNumber0(v9) = 0 &
% 58.49/8.63 | $i(v9))) | (v7 = 0 & ? [v9: $i] : (sdtasdt0(xp, v9) = xn &
% 58.49/8.64 | aNaturalNumber0(v9) = 0 & $i(v9))) | ( ~ (v5 = 0) & ! [v9:
% 58.49/8.64 | $i] : ( ~ (sdtasdt0(xp, v9) = v4) | ~ $i(v9) | ? [v10: int]
% 58.49/8.64 | : ( ~ (v10 = 0) & aNaturalNumber0(v9) = v10))) | ( ~ (v3 = 0)
% 58.49/8.64 | & (xp = sz10 | xp = sz00 | ? [v9: $i] : ( ~ (v9 = xp) & ~ (v9
% 58.49/8.64 | = sz10) & doDivides0(v9, xp) = 0 & aNaturalNumber0(v9) = 0
% 58.49/8.64 | & $i(v9) & ? [v10: $i] : (sdtasdt0(v9, v10) = xp &
% 58.49/8.64 | aNaturalNumber0(v10) = 0 & $i(v10)))))))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xp, all_59_1, all_59_0,
% 58.49/8.64 | simplifying with (11), (19), (20), (50), (51) gives:
% 58.49/8.64 | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 58.49/8.64 | : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp)
% 58.49/8.64 | = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4)
% 58.49/8.64 | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 58.49/8.64 | all_59_0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mAddComm) with all_59_1, xp, all_59_0, simplifying
% 58.49/8.64 | with (11), (49), (51) gives:
% 58.49/8.64 | (72) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xp, all_59_1) =
% 58.49/8.64 | v2 & aNaturalNumber0(all_59_1) = v0 & aNaturalNumber0(xp) = v1 &
% 58.49/8.64 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_59_0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mSortsB) with all_59_1, xp, all_59_0, simplifying
% 58.49/8.64 | with (11), (49), (51) gives:
% 58.49/8.64 | (73) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.64 | (aNaturalNumber0(all_59_0) = v2 & aNaturalNumber0(all_59_1) = v0 &
% 58.49/8.64 | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_45_0, simplifying with
% 58.49/8.64 | (19), (20), (35) gives:
% 58.49/8.64 | (74) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 &
% 58.49/8.64 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 58.49/8.64 | (v1 = 0) | ~ (v0 = 0) | v2 = all_45_0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_45_0, simplifying
% 58.49/8.64 | with (19), (20), (35) gives:
% 58.49/8.64 | (75) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.64 | (aNaturalNumber0(all_45_0) = v2 & aNaturalNumber0(xm) = v1 &
% 58.49/8.64 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mMulComm) with xp, xk, all_45_0, simplifying with
% 58.49/8.64 | (11), (15), (36) gives:
% 58.49/8.64 | (76) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xk, xp) = v2 &
% 58.49/8.64 | aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & $i(v2) & ( ~
% 58.49/8.64 | (v1 = 0) | ~ (v0 = 0) | v2 = all_45_0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mSortsB_02) with xp, xk, all_45_0, simplifying
% 58.49/8.64 | with (11), (15), (36) gives:
% 58.49/8.64 | (77) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.64 | (aNaturalNumber0(all_45_0) = v2 & aNaturalNumber0(xk) = v1 &
% 58.49/8.64 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mMulComm) with xp, all_62_0, all_45_0, simplifying
% 58.49/8.64 | with (11), (54), (63) gives:
% 58.49/8.64 | (78) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_62_0, xp) =
% 58.49/8.64 | v2 & aNaturalNumber0(all_62_0) = v1 & aNaturalNumber0(xp) = v0 &
% 58.49/8.64 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_45_0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mSortsB_02) with xp, all_62_0, all_45_0,
% 58.49/8.64 | simplifying with (11), (54), (63) gives:
% 58.49/8.64 | (79) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.64 | (aNaturalNumber0(all_62_0) = v1 & aNaturalNumber0(all_45_0) = v2 &
% 58.49/8.64 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mMulComm) with xr, all_41_0, xk, simplifying with
% 58.49/8.64 | (21), (27), (29) gives:
% 58.49/8.64 | (80) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(all_41_0, xr) =
% 58.49/8.64 | v2 & aNaturalNumber0(all_41_0) = v1 & aNaturalNumber0(xr) = v0 &
% 58.49/8.64 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = xk))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mDefDiv) with xp, all_45_0, 0, simplifying with
% 58.49/8.64 | (11), (62), (64) gives:
% 58.49/8.64 | (81) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_45_0) = v1 &
% 58.49/8.64 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 58.49/8.64 | $i] : (sdtasdt0(xp, v0) = all_45_0 & aNaturalNumber0(v0) = 0 &
% 58.49/8.64 | $i(v0))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (mDivTrans) with xr, xk, all_45_0, all_53_0,
% 58.49/8.64 | simplifying with (15), (17), (21), (61), (64) gives:
% 58.49/8.64 | (82) all_53_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 58.49/8.64 | any] : (doDivides0(xk, all_45_0) = v3 & aNaturalNumber0(all_45_0) =
% 58.49/8.64 | v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~ (v3 =
% 58.49/8.64 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 58.49/8.64 |
% 58.49/8.64 | GROUND_INST: instantiating (2) with xp, all_45_0, xk, simplifying with (11),
% 58.49/8.64 | (37), (64) gives:
% 58.49/8.65 | (83) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.65 | (doDivides0(xp, all_45_0) = v2 & aNaturalNumber0(all_45_0) = v1 &
% 58.49/8.65 | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 58.49/8.65 | 0))) | ( ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 58.49/8.65 | all_45_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 58.49/8.65 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xp, xk)
% 58.49/8.65 | = v0) | ~ $i(xk) | (v0 = all_45_0 & aNaturalNumber0(xk) = 0)))
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (79) with fresh symbols all_73_0, all_73_1, all_73_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (84) aNaturalNumber0(all_62_0) = all_73_1 & aNaturalNumber0(all_45_0) =
% 58.49/8.65 | all_73_0 & aNaturalNumber0(xp) = all_73_2 & ( ~ (all_73_1 = 0) | ~
% 58.49/8.65 | (all_73_2 = 0) | all_73_0 = 0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (84) implies:
% 58.49/8.65 | (85) aNaturalNumber0(xp) = all_73_2
% 58.49/8.65 | (86) aNaturalNumber0(all_45_0) = all_73_0
% 58.49/8.65 | (87) aNaturalNumber0(all_62_0) = all_73_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (77) with fresh symbols all_75_0, all_75_1, all_75_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (88) aNaturalNumber0(all_45_0) = all_75_0 & aNaturalNumber0(xk) = all_75_1
% 58.49/8.65 | & aNaturalNumber0(xp) = all_75_2 & ( ~ (all_75_1 = 0) | ~ (all_75_2 =
% 58.49/8.65 | 0) | all_75_0 = 0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (88) implies:
% 58.49/8.65 | (89) aNaturalNumber0(xp) = all_75_2
% 58.49/8.65 | (90) aNaturalNumber0(xk) = all_75_1
% 58.49/8.65 | (91) aNaturalNumber0(all_45_0) = all_75_0
% 58.49/8.65 | (92) ~ (all_75_1 = 0) | ~ (all_75_2 = 0) | all_75_0 = 0
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (75) with fresh symbols all_77_0, all_77_1, all_77_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (93) aNaturalNumber0(all_45_0) = all_77_0 & aNaturalNumber0(xm) = all_77_1
% 58.49/8.65 | & aNaturalNumber0(xn) = all_77_2 & ( ~ (all_77_1 = 0) | ~ (all_77_2 =
% 58.49/8.65 | 0) | all_77_0 = 0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (93) implies:
% 58.49/8.65 | (94) aNaturalNumber0(xm) = all_77_1
% 58.49/8.65 | (95) aNaturalNumber0(all_45_0) = all_77_0
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (73) with fresh symbols all_79_0, all_79_1, all_79_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (96) aNaturalNumber0(all_59_0) = all_79_0 & aNaturalNumber0(all_59_1) =
% 58.49/8.65 | all_79_2 & aNaturalNumber0(xp) = all_79_1 & ( ~ (all_79_1 = 0) | ~
% 58.49/8.65 | (all_79_2 = 0) | all_79_0 = 0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (96) implies:
% 58.49/8.65 | (97) aNaturalNumber0(xp) = all_79_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (68) with fresh symbols all_81_0, all_81_1, all_81_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (98) aNaturalNumber0(all_59_1) = all_81_0 & aNaturalNumber0(xm) = all_81_1
% 58.49/8.65 | & aNaturalNumber0(xn) = all_81_2 & ( ~ (all_81_1 = 0) | ~ (all_81_2 =
% 58.49/8.65 | 0) | all_81_0 = 0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (98) implies:
% 58.49/8.65 | (99) aNaturalNumber0(xm) = all_81_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (67) with fresh symbols all_85_0, all_85_1, all_85_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (100) sdtpldt0(xm, xn) = all_85_0 & aNaturalNumber0(xm) = all_85_1 &
% 58.49/8.65 | aNaturalNumber0(xn) = all_85_2 & $i(all_85_0) & ( ~ (all_85_1 = 0) |
% 58.49/8.65 | ~ (all_85_2 = 0) | all_85_0 = all_59_1)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (100) implies:
% 58.49/8.65 | (101) aNaturalNumber0(xn) = all_85_2
% 58.49/8.65 | (102) aNaturalNumber0(xm) = all_85_1
% 58.49/8.65 | (103) sdtpldt0(xm, xn) = all_85_0
% 58.49/8.65 | (104) ~ (all_85_1 = 0) | ~ (all_85_2 = 0) | all_85_0 = all_59_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (78) with fresh symbols all_87_0, all_87_1, all_87_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (105) sdtasdt0(all_62_0, xp) = all_87_0 & aNaturalNumber0(all_62_0) =
% 58.49/8.65 | all_87_1 & aNaturalNumber0(xp) = all_87_2 & $i(all_87_0) & ( ~
% 58.49/8.65 | (all_87_1 = 0) | ~ (all_87_2 = 0) | all_87_0 = all_45_0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (105) implies:
% 58.49/8.65 | (106) $i(all_87_0)
% 58.49/8.65 | (107) aNaturalNumber0(xp) = all_87_2
% 58.49/8.65 | (108) aNaturalNumber0(all_62_0) = all_87_1
% 58.49/8.65 | (109) sdtasdt0(all_62_0, xp) = all_87_0
% 58.49/8.65 | (110) ~ (all_87_1 = 0) | ~ (all_87_2 = 0) | all_87_0 = all_45_0
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (74) with fresh symbols all_89_0, all_89_1, all_89_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (111) sdtasdt0(xm, xn) = all_89_0 & aNaturalNumber0(xm) = all_89_1 &
% 58.49/8.65 | aNaturalNumber0(xn) = all_89_2 & $i(all_89_0) & ( ~ (all_89_1 = 0) |
% 58.49/8.65 | ~ (all_89_2 = 0) | all_89_0 = all_45_0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (111) implies:
% 58.49/8.65 | (112) aNaturalNumber0(xm) = all_89_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (76) with fresh symbols all_91_0, all_91_1, all_91_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (113) sdtasdt0(xk, xp) = all_91_0 & aNaturalNumber0(xk) = all_91_1 &
% 58.49/8.65 | aNaturalNumber0(xp) = all_91_2 & $i(all_91_0) & ( ~ (all_91_1 = 0) |
% 58.49/8.65 | ~ (all_91_2 = 0) | all_91_0 = all_45_0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (113) implies:
% 58.49/8.65 | (114) aNaturalNumber0(xp) = all_91_2
% 58.49/8.65 | (115) aNaturalNumber0(xk) = all_91_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (72) with fresh symbols all_93_0, all_93_1, all_93_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (116) sdtpldt0(xp, all_59_1) = all_93_0 & aNaturalNumber0(all_59_1) =
% 58.49/8.65 | all_93_2 & aNaturalNumber0(xp) = all_93_1 & $i(all_93_0) & ( ~
% 58.49/8.65 | (all_93_1 = 0) | ~ (all_93_2 = 0) | all_93_0 = all_59_0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (116) implies:
% 58.49/8.65 | (117) aNaturalNumber0(xp) = all_93_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (80) with fresh symbols all_95_0, all_95_1, all_95_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (118) sdtasdt0(all_41_0, xr) = all_95_0 & aNaturalNumber0(all_41_0) =
% 58.49/8.65 | all_95_1 & aNaturalNumber0(xr) = all_95_2 & $i(all_95_0) & ( ~
% 58.49/8.65 | (all_95_1 = 0) | ~ (all_95_2 = 0) | all_95_0 = xk)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (118) implies:
% 58.49/8.65 | (119) $i(all_95_0)
% 58.49/8.65 | (120) aNaturalNumber0(xr) = all_95_2
% 58.49/8.65 | (121) aNaturalNumber0(all_41_0) = all_95_1
% 58.49/8.65 | (122) sdtasdt0(all_41_0, xr) = all_95_0
% 58.49/8.65 | (123) ~ (all_95_1 = 0) | ~ (all_95_2 = 0) | all_95_0 = xk
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (69) with fresh symbols all_97_0, all_97_1, all_97_2
% 58.49/8.65 | gives:
% 58.49/8.65 | (124) sdtpldt0(all_43_0, xm) = all_97_0 & aNaturalNumber0(all_43_0) =
% 58.49/8.65 | all_97_1 & aNaturalNumber0(xm) = all_97_2 & $i(all_97_0) & ( ~
% 58.49/8.65 | (all_97_1 = 0) | ~ (all_97_2 = 0) | all_97_0 = xp)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (124) implies:
% 58.49/8.65 | (125) aNaturalNumber0(xm) = all_97_2
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (71) with fresh symbols all_99_0, all_99_1, all_99_2,
% 58.49/8.65 | all_99_3, all_99_4 gives:
% 58.49/8.65 | (126) sdtpldt0(xm, xp) = all_99_1 & sdtpldt0(xn, all_99_1) = all_99_0 &
% 58.49/8.65 | aNaturalNumber0(xp) = all_99_2 & aNaturalNumber0(xm) = all_99_3 &
% 58.49/8.65 | aNaturalNumber0(xn) = all_99_4 & $i(all_99_0) & $i(all_99_1) & ( ~
% 58.49/8.65 | (all_99_2 = 0) | ~ (all_99_3 = 0) | ~ (all_99_4 = 0) | all_99_0 =
% 58.49/8.65 | all_59_0)
% 58.49/8.65 |
% 58.49/8.65 | ALPHA: (126) implies:
% 58.49/8.65 | (127) aNaturalNumber0(xm) = all_99_3
% 58.49/8.65 | (128) aNaturalNumber0(xp) = all_99_2
% 58.49/8.65 | (129) sdtpldt0(xm, xp) = all_99_1
% 58.49/8.65 |
% 58.49/8.65 | DELTA: instantiating (70) with fresh symbols all_101_0, all_101_1, all_101_2,
% 58.49/8.65 | all_101_3, all_101_4, all_101_5, all_101_6, all_101_7, all_101_8 gives:
% 58.49/8.66 | (130) isPrime0(xp) = all_101_5 & doDivides0(xp, all_101_4) = all_101_3 &
% 58.49/8.66 | doDivides0(xp, xm) = all_101_0 & doDivides0(xp, xn) = all_101_1 &
% 58.49/8.66 | iLess0(all_59_0, all_59_0) = all_101_2 & sdtasdt0(xn, xm) = all_101_4
% 58.49/8.66 | & aNaturalNumber0(xp) = all_101_6 & aNaturalNumber0(xm) = all_101_7 &
% 58.49/8.66 | aNaturalNumber0(xn) = all_101_8 & $i(all_101_4) & ( ~ (all_101_2 = 0)
% 58.49/8.66 | | ~ (all_101_6 = 0) | ~ (all_101_7 = 0) | ~ (all_101_8 = 0) |
% 58.49/8.66 | (all_101_0 = 0 & ? [v0: $i] : (sdtasdt0(xp, v0) = xm &
% 58.49/8.66 | aNaturalNumber0(v0) = 0 & $i(v0))) | (all_101_1 = 0 & ? [v0:
% 58.49/8.66 | $i] : (sdtasdt0(xp, v0) = xn & aNaturalNumber0(v0) = 0 &
% 58.49/8.66 | $i(v0))) | ( ~ (all_101_3 = 0) & ! [v0: $i] : ( ~
% 58.49/8.66 | (sdtasdt0(xp, v0) = all_101_4) | ~ $i(v0) | ? [v1: int] : ( ~
% 58.49/8.66 | (v1 = 0) & aNaturalNumber0(v0) = v1))) | ( ~ (all_101_5 = 0)
% 58.49/8.66 | & (xp = sz10 | xp = sz00 | ? [v0: $i] : ( ~ (v0 = xp) & ~ (v0 =
% 58.49/8.66 | sz10) & doDivides0(v0, xp) = 0 & aNaturalNumber0(v0) = 0 &
% 58.49/8.66 | $i(v0) & ? [v1: $i] : (sdtasdt0(v0, v1) = xp &
% 58.49/8.66 | aNaturalNumber0(v1) = 0 & $i(v1))))))
% 58.49/8.66 |
% 58.49/8.66 | ALPHA: (130) implies:
% 58.49/8.66 | (131) aNaturalNumber0(xn) = all_101_8
% 58.49/8.66 | (132) aNaturalNumber0(xm) = all_101_7
% 58.49/8.66 | (133) aNaturalNumber0(xp) = all_101_6
% 58.49/8.66 | (134) sdtasdt0(xn, xm) = all_101_4
% 58.49/8.66 | (135) doDivides0(xp, all_101_4) = all_101_3
% 58.49/8.66 |
% 58.49/8.66 | BETA: splitting (65) gives:
% 58.49/8.66 |
% 58.49/8.66 | Case 1:
% 58.49/8.66 | |
% 58.49/8.66 | | (136) xp = sz00
% 58.49/8.66 | |
% 58.49/8.66 | | REDUCE: (44), (136) imply:
% 58.49/8.66 | | (137) $false
% 58.49/8.66 | |
% 58.49/8.66 | | CLOSE: (137) is inconsistent.
% 58.49/8.66 | |
% 58.49/8.66 | Case 2:
% 58.49/8.66 | |
% 58.49/8.66 | | (138) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 58.49/8.66 | | ~ (sdtasdt0(xp, v1) = v3) | ~ (sdtasdt0(xp, v0) = v2) | ~
% 58.49/8.66 | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] :
% 58.49/8.66 | | ? [v7: $i] : (sdtasdt0(v1, xp) = v7 & sdtasdt0(v0, xp) = v6 &
% 58.49/8.66 | | aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & $i(v7) &
% 58.49/8.66 | | $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ( ~ (v7 = v6) & ~ (v3 =
% 58.49/8.66 | | v2)))))
% 58.49/8.66 | |
% 58.49/8.66 | | GROUND_INST: instantiating (138) with xk, all_62_0, all_45_0, all_45_0,
% 58.49/8.66 | | simplifying with (15), (36), (54), (63) gives:
% 58.49/8.66 | | (139) all_62_0 = xk | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 58.49/8.66 | | $i] : (sdtasdt0(all_62_0, xp) = v3 & sdtasdt0(xk, xp) = v2 &
% 58.49/8.66 | | aNaturalNumber0(all_62_0) = v1 & aNaturalNumber0(xk) = v0 &
% 58.49/8.66 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 58.49/8.66 | |
% 58.49/8.66 | | GROUND_INST: instantiating (138) with all_62_0, xk, all_45_0, all_45_0,
% 58.49/8.66 | | simplifying with (15), (36), (54), (63) gives:
% 58.49/8.66 | | (140) all_62_0 = xk | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 58.49/8.66 | | $i] : (sdtasdt0(all_62_0, xp) = v2 & sdtasdt0(xk, xp) = v3 &
% 58.49/8.66 | | aNaturalNumber0(all_62_0) = v0 & aNaturalNumber0(xk) = v1 &
% 58.49/8.66 | | $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 58.49/8.66 | |
% 58.49/8.66 | | BETA: splitting (66) gives:
% 58.49/8.66 | |
% 58.49/8.66 | | Case 1:
% 58.49/8.66 | | |
% 58.49/8.66 | | | (141) xr = sz00
% 58.49/8.66 | | |
% 58.49/8.66 | | | REDUCE: (13), (141) imply:
% 58.49/8.66 | | | (142) $false
% 58.49/8.66 | | |
% 58.49/8.66 | | | CLOSE: (142) is inconsistent.
% 58.49/8.66 | | |
% 58.49/8.66 | | Case 2:
% 58.49/8.66 | | |
% 58.49/8.66 | | | (143) xr = sz10 | ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0, xr)
% 58.49/8.66 | | | = 0 & aNaturalNumber0(v0) = 0 & $i(v0))
% 58.49/8.66 | | |
% 58.49/8.66 | | | BETA: splitting (82) gives:
% 58.49/8.66 | | |
% 58.49/8.66 | | | Case 1:
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | (144) all_53_0 = 0
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | REDUCE: (39), (144) imply:
% 58.49/8.66 | | | | (145) $false
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | CLOSE: (145) is inconsistent.
% 58.49/8.66 | | | |
% 58.49/8.66 | | | Case 2:
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | (146) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 58.49/8.66 | | | | (doDivides0(xk, all_45_0) = v3 & aNaturalNumber0(all_45_0) = v2
% 58.49/8.66 | | | | & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~
% 58.49/8.66 | | | | (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | DELTA: instantiating (146) with fresh symbols all_132_0, all_132_1,
% 58.49/8.66 | | | | all_132_2, all_132_3 gives:
% 58.49/8.66 | | | | (147) doDivides0(xk, all_45_0) = all_132_0 &
% 58.49/8.66 | | | | aNaturalNumber0(all_45_0) = all_132_1 & aNaturalNumber0(xr) =
% 58.49/8.66 | | | | all_132_3 & aNaturalNumber0(xk) = all_132_2 & ( ~ (all_132_0 =
% 58.49/8.66 | | | | 0) | ~ (all_132_1 = 0) | ~ (all_132_2 = 0) | ~
% 58.49/8.66 | | | | (all_132_3 = 0))
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | ALPHA: (147) implies:
% 58.49/8.66 | | | | (148) aNaturalNumber0(xk) = all_132_2
% 58.49/8.66 | | | | (149) aNaturalNumber0(xr) = all_132_3
% 58.49/8.66 | | | | (150) aNaturalNumber0(all_45_0) = all_132_1
% 58.49/8.66 | | | | (151) doDivides0(xk, all_45_0) = all_132_0
% 58.49/8.66 | | | | (152) ~ (all_132_0 = 0) | ~ (all_132_1 = 0) | ~ (all_132_2 = 0) |
% 58.49/8.66 | | | | ~ (all_132_3 = 0)
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | BETA: splitting (143) gives:
% 58.49/8.66 | | | |
% 58.49/8.66 | | | | Case 1:
% 58.49/8.66 | | | | |
% 58.49/8.66 | | | | | (153) xr = sz10
% 58.49/8.66 | | | | |
% 58.49/8.66 | | | | | REDUCE: (14), (153) imply:
% 58.49/8.66 | | | | | (154) $false
% 58.49/8.66 | | | | |
% 58.49/8.66 | | | | | CLOSE: (154) is inconsistent.
% 58.49/8.66 | | | | |
% 58.49/8.66 | | | | Case 2:
% 58.49/8.66 | | | | |
% 58.49/8.66 | | | | | (155) ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0, xr) = 0 &
% 58.49/8.66 | | | | | aNaturalNumber0(v0) = 0 & $i(v0))
% 58.49/8.66 | | | | |
% 58.49/8.66 | | | | | DELTA: instantiating (155) with fresh symbol all_148_0 gives:
% 58.49/8.66 | | | | | (156) isPrime0(all_148_0) = 0 & doDivides0(all_148_0, xr) = 0 &
% 58.49/8.66 | | | | | aNaturalNumber0(all_148_0) = 0 & $i(all_148_0)
% 58.49/8.66 | | | | |
% 58.49/8.66 | | | | | ALPHA: (156) implies:
% 58.49/8.67 | | | | | (157) $i(all_148_0)
% 58.49/8.67 | | | | | (158) aNaturalNumber0(all_148_0) = 0
% 58.49/8.67 | | | | | (159) isPrime0(all_148_0) = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with 0, all_101_8, xn, simplifying
% 58.49/8.67 | | | | | with (5), (131) gives:
% 58.49/8.67 | | | | | (160) all_101_8 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_85_2, all_101_8, xn,
% 58.49/8.67 | | | | | simplifying with (101), (131) gives:
% 58.49/8.67 | | | | | (161) all_101_8 = all_85_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_85_1, all_89_1, xm,
% 58.49/8.67 | | | | | simplifying with (102), (112) gives:
% 58.49/8.67 | | | | | (162) all_89_1 = all_85_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_89_1, all_97_2, xm,
% 58.49/8.67 | | | | | simplifying with (112), (125) gives:
% 58.49/8.67 | | | | | (163) all_97_2 = all_89_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with 0, all_99_3, xm, simplifying with
% 58.49/8.67 | | | | | (6), (127) gives:
% 58.49/8.67 | | | | | (164) all_99_3 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_89_1, all_99_3, xm,
% 58.49/8.67 | | | | | simplifying with (112), (127) gives:
% 58.49/8.67 | | | | | (165) all_99_3 = all_89_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_81_1, all_99_3, xm,
% 58.49/8.67 | | | | | simplifying with (99), (127) gives:
% 58.49/8.67 | | | | | (166) all_99_3 = all_81_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_97_2, all_101_7, xm,
% 58.49/8.67 | | | | | simplifying with (125), (132) gives:
% 58.49/8.67 | | | | | (167) all_101_7 = all_97_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_77_1, all_101_7, xm,
% 58.49/8.67 | | | | | simplifying with (94), (132) gives:
% 58.49/8.67 | | | | | (168) all_101_7 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with 0, all_75_2, xp, simplifying with
% 58.49/8.67 | | | | | (7), (89) gives:
% 58.49/8.67 | | | | | (169) all_75_2 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_75_2, all_79_1, xp,
% 58.49/8.67 | | | | | simplifying with (89), (97) gives:
% 58.49/8.67 | | | | | (170) all_79_1 = all_75_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_79_1, all_87_2, xp,
% 58.49/8.67 | | | | | simplifying with (97), (107) gives:
% 58.49/8.67 | | | | | (171) all_87_2 = all_79_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_87_2, all_91_2, xp,
% 58.49/8.67 | | | | | simplifying with (107), (114) gives:
% 58.49/8.67 | | | | | (172) all_91_2 = all_87_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_91_2, all_93_1, xp,
% 58.49/8.67 | | | | | simplifying with (114), (117) gives:
% 58.49/8.67 | | | | | (173) all_93_1 = all_91_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_99_2, all_101_6, xp,
% 58.49/8.67 | | | | | simplifying with (128), (133) gives:
% 58.49/8.67 | | | | | (174) all_101_6 = all_99_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_93_1, all_101_6, xp,
% 58.49/8.67 | | | | | simplifying with (117), (133) gives:
% 58.49/8.67 | | | | | (175) all_101_6 = all_93_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_73_2, all_101_6, xp,
% 58.49/8.67 | | | | | simplifying with (85), (133) gives:
% 58.49/8.67 | | | | | (176) all_101_6 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with 0, all_91_1, xk, simplifying with
% 58.49/8.67 | | | | | (34), (115) gives:
% 58.49/8.67 | | | | | (177) all_91_1 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_91_1, all_132_2, xk,
% 58.49/8.67 | | | | | simplifying with (115), (148) gives:
% 58.49/8.67 | | | | | (178) all_132_2 = all_91_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_75_1, all_132_2, xk,
% 58.49/8.67 | | | | | simplifying with (90), (148) gives:
% 58.49/8.67 | | | | | (179) all_132_2 = all_75_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with 0, all_132_3, xr, simplifying
% 58.49/8.67 | | | | | with (16), (149) gives:
% 58.49/8.67 | | | | | (180) all_132_3 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_95_2, all_132_3, xr,
% 58.49/8.67 | | | | | simplifying with (120), (149) gives:
% 58.49/8.67 | | | | | (181) all_132_3 = all_95_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with 0, all_95_1, all_41_0,
% 58.49/8.67 | | | | | simplifying with (28), (121) gives:
% 58.49/8.67 | | | | | (182) all_95_1 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_77_0, all_132_1, all_45_0,
% 58.49/8.67 | | | | | simplifying with (95), (150) gives:
% 58.49/8.67 | | | | | (183) all_132_1 = all_77_0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_75_0, all_132_1, all_45_0,
% 58.49/8.67 | | | | | simplifying with (91), (150) gives:
% 58.49/8.67 | | | | | (184) all_132_1 = all_75_0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_73_0, all_132_1, all_45_0,
% 58.49/8.67 | | | | | simplifying with (86), (150) gives:
% 58.49/8.67 | | | | | (185) all_132_1 = all_73_0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with 0, all_87_1, all_62_0,
% 58.49/8.67 | | | | | simplifying with (55), (108) gives:
% 58.49/8.67 | | | | | (186) all_87_1 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (23) with all_73_1, all_87_1, all_62_0,
% 58.49/8.67 | | | | | simplifying with (87), (108) gives:
% 58.49/8.67 | | | | | (187) all_87_1 = all_73_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | GROUND_INST: instantiating (24) with all_45_0, all_101_4, xm, xn,
% 58.49/8.67 | | | | | simplifying with (35), (134) gives:
% 58.49/8.67 | | | | | (188) all_101_4 = all_45_0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (183), (185) imply:
% 58.49/8.67 | | | | | (189) all_77_0 = all_73_0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (183), (184) imply:
% 58.49/8.67 | | | | | (190) all_77_0 = all_75_0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (178), (179) imply:
% 58.49/8.67 | | | | | (191) all_91_1 = all_75_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (191) implies:
% 58.49/8.67 | | | | | (192) all_91_1 = all_75_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (180), (181) imply:
% 58.49/8.67 | | | | | (193) all_95_2 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (174), (175) imply:
% 58.49/8.67 | | | | | (194) all_99_2 = all_93_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (174), (176) imply:
% 58.49/8.67 | | | | | (195) all_99_2 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (167), (168) imply:
% 58.49/8.67 | | | | | (196) all_97_2 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (196) implies:
% 58.49/8.67 | | | | | (197) all_97_2 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (160), (161) imply:
% 58.49/8.67 | | | | | (198) all_85_2 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (198) implies:
% 58.49/8.67 | | | | | (199) all_85_2 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (194), (195) imply:
% 58.49/8.67 | | | | | (200) all_93_1 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (200) implies:
% 58.49/8.67 | | | | | (201) all_93_1 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (164), (166) imply:
% 58.49/8.67 | | | | | (202) all_81_1 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (165), (166) imply:
% 58.49/8.67 | | | | | (203) all_89_1 = all_81_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (203) implies:
% 58.49/8.67 | | | | | (204) all_89_1 = all_81_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (163), (197) imply:
% 58.49/8.67 | | | | | (205) all_89_1 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (205) implies:
% 58.49/8.67 | | | | | (206) all_89_1 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (173), (201) imply:
% 58.49/8.67 | | | | | (207) all_91_2 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (207) implies:
% 58.49/8.67 | | | | | (208) all_91_2 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (177), (192) imply:
% 58.49/8.67 | | | | | (209) all_75_1 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (172), (208) imply:
% 58.49/8.67 | | | | | (210) all_87_2 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (210) implies:
% 58.49/8.67 | | | | | (211) all_87_2 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (162), (206) imply:
% 58.49/8.67 | | | | | (212) all_85_1 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (162), (204) imply:
% 58.49/8.67 | | | | | (213) all_85_1 = all_81_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (186), (187) imply:
% 58.49/8.67 | | | | | (214) all_73_1 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (171), (211) imply:
% 58.49/8.67 | | | | | (215) all_79_1 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (215) implies:
% 58.49/8.67 | | | | | (216) all_79_1 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (212), (213) imply:
% 58.49/8.67 | | | | | (217) all_81_1 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (217) implies:
% 58.49/8.67 | | | | | (218) all_81_1 = all_77_1
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (202), (218) imply:
% 58.49/8.67 | | | | | (219) all_77_1 = 0
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (170), (216) imply:
% 58.49/8.67 | | | | | (220) all_75_2 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | SIMP: (220) implies:
% 58.49/8.67 | | | | | (221) all_75_2 = all_73_2
% 58.49/8.67 | | | | |
% 58.49/8.67 | | | | | COMBINE_EQS: (189), (190) imply:
% 58.49/8.68 | | | | | (222) all_75_0 = all_73_0
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | SIMP: (222) implies:
% 58.49/8.68 | | | | | (223) all_75_0 = all_73_0
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | COMBINE_EQS: (169), (221) imply:
% 58.49/8.68 | | | | | (224) all_73_2 = 0
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | COMBINE_EQS: (212), (219) imply:
% 58.49/8.68 | | | | | (225) all_85_1 = 0
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | COMBINE_EQS: (211), (224) imply:
% 58.49/8.68 | | | | | (226) all_87_2 = 0
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | COMBINE_EQS: (179), (209) imply:
% 58.49/8.68 | | | | | (227) all_132_2 = 0
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | REDUCE: (135), (188) imply:
% 58.49/8.68 | | | | | (228) doDivides0(xp, all_45_0) = all_101_3
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | BETA: splitting (92) gives:
% 58.49/8.68 | | | | |
% 58.49/8.68 | | | | | Case 1:
% 58.49/8.68 | | | | | |
% 58.49/8.68 | | | | | | (229) ~ (all_75_1 = 0)
% 58.49/8.68 | | | | | |
% 58.49/8.68 | | | | | | REDUCE: (209), (229) imply:
% 58.49/8.68 | | | | | | (230) $false
% 58.49/8.68 | | | | | |
% 58.49/8.68 | | | | | | CLOSE: (230) is inconsistent.
% 58.49/8.68 | | | | | |
% 58.49/8.68 | | | | | Case 2:
% 58.49/8.68 | | | | | |
% 58.49/8.68 | | | | | | (231) ~ (all_75_2 = 0) | all_75_0 = 0
% 58.49/8.68 | | | | | |
% 58.49/8.68 | | | | | | BETA: splitting (110) gives:
% 58.49/8.68 | | | | | |
% 58.49/8.68 | | | | | | Case 1:
% 58.49/8.68 | | | | | | |
% 58.49/8.68 | | | | | | | (232) ~ (all_87_1 = 0)
% 58.49/8.68 | | | | | | |
% 58.49/8.68 | | | | | | | REDUCE: (186), (232) imply:
% 58.49/8.68 | | | | | | | (233) $false
% 58.49/8.68 | | | | | | |
% 58.49/8.68 | | | | | | | CLOSE: (233) is inconsistent.
% 58.49/8.68 | | | | | | |
% 58.49/8.68 | | | | | | Case 2:
% 58.49/8.68 | | | | | | |
% 58.49/8.68 | | | | | | | (234) ~ (all_87_2 = 0) | all_87_0 = all_45_0
% 58.49/8.68 | | | | | | |
% 58.49/8.68 | | | | | | | BETA: splitting (139) gives:
% 58.49/8.68 | | | | | | |
% 58.49/8.68 | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | |
% 58.49/8.68 | | | | | | | | (235) all_62_0 = xk
% 58.49/8.68 | | | | | | | |
% 58.49/8.68 | | | | | | | | REDUCE: (109), (235) imply:
% 58.49/8.68 | | | | | | | | (236) sdtasdt0(xk, xp) = all_87_0
% 58.49/8.68 | | | | | | | |
% 58.49/8.68 | | | | | | | | BETA: splitting (231) gives:
% 58.49/8.68 | | | | | | | |
% 58.49/8.68 | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | (237) ~ (all_75_2 = 0)
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | REDUCE: (169), (237) imply:
% 58.49/8.68 | | | | | | | | | (238) $false
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | CLOSE: (238) is inconsistent.
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | (239) all_75_0 = 0
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | COMBINE_EQS: (223), (239) imply:
% 58.49/8.68 | | | | | | | | | (240) all_73_0 = 0
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | COMBINE_EQS: (185), (240) imply:
% 58.49/8.68 | | | | | | | | | (241) all_132_1 = 0
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | REDUCE: (86), (240) imply:
% 58.49/8.68 | | | | | | | | | (242) aNaturalNumber0(all_45_0) = 0
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | DELTA: instantiating (18) with fresh symbol all_198_0 gives:
% 58.49/8.68 | | | | | | | | | (243) sdtasdt0(xr, all_198_0) = xk &
% 58.49/8.68 | | | | | | | | | aNaturalNumber0(all_198_0) = 0 & $i(all_198_0)
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | ALPHA: (243) implies:
% 58.49/8.68 | | | | | | | | | (244) $i(all_198_0)
% 58.49/8.68 | | | | | | | | | (245) sdtasdt0(xr, all_198_0) = xk
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | BETA: splitting (152) gives:
% 58.49/8.68 | | | | | | | | |
% 58.49/8.68 | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | (246) ~ (all_132_0 = 0)
% 58.49/8.68 | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | BETA: splitting (83) gives:
% 58.49/8.68 | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | (247) xp = sz00
% 58.49/8.68 | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | REDUCE: (44), (247) imply:
% 58.49/8.68 | | | | | | | | | | | (248) $false
% 58.49/8.68 | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 58.49/8.68 | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | (249) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.68 | | | | | | | | | | | (doDivides0(xp, all_45_0) = v2 &
% 58.49/8.68 | | | | | | | | | | | aNaturalNumber0(all_45_0) = v1 &
% 58.49/8.68 | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 58.49/8.68 | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 =
% 58.49/8.68 | | | | | | | | | | | xk | ~ (sdtasdt0(xp, v0) = all_45_0) | ~
% 58.49/8.68 | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 58.49/8.68 | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : (
% 58.49/8.68 | | | | | | | | | | | ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | (v0 =
% 58.49/8.68 | | | | | | | | | | | all_45_0 & aNaturalNumber0(xk) = 0)))
% 58.49/8.68 | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | BETA: splitting (104) gives:
% 58.49/8.68 | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | (250) ~ (all_85_1 = 0)
% 58.49/8.68 | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | REDUCE: (225), (250) imply:
% 58.49/8.68 | | | | | | | | | | | | (251) $false
% 58.49/8.68 | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | CLOSE: (251) is inconsistent.
% 58.49/8.68 | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | (252) ~ (all_85_2 = 0) | all_85_0 = all_59_1
% 58.49/8.68 | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | BETA: splitting (234) gives:
% 58.49/8.68 | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | (253) ~ (all_87_2 = 0)
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | REDUCE: (226), (253) imply:
% 58.49/8.68 | | | | | | | | | | | | | (254) $false
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | CLOSE: (254) is inconsistent.
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | (255) all_87_0 = all_45_0
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | REDUCE: (236), (255) imply:
% 58.49/8.68 | | | | | | | | | | | | | (256) sdtasdt0(xk, xp) = all_45_0
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | BETA: splitting (81) gives:
% 58.49/8.68 | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | (257) ? [v0: any] : ? [v1: any] :
% 58.49/8.68 | | | | | | | | | | | | | | (aNaturalNumber0(all_45_0) = v1 &
% 58.49/8.68 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0
% 58.49/8.68 | | | | | | | | | | | | | | = 0)))
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | DELTA: instantiating (257) with fresh symbols all_264_0,
% 58.49/8.68 | | | | | | | | | | | | | | all_264_1 gives:
% 58.49/8.68 | | | | | | | | | | | | | | (258) aNaturalNumber0(all_45_0) = all_264_0 &
% 58.49/8.68 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_264_1 & ( ~ (all_264_0 =
% 58.49/8.68 | | | | | | | | | | | | | | 0) | ~ (all_264_1 = 0))
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | ALPHA: (258) implies:
% 58.49/8.68 | | | | | | | | | | | | | | (259) aNaturalNumber0(xp) = all_264_1
% 58.49/8.68 | | | | | | | | | | | | | | (260) aNaturalNumber0(all_45_0) = all_264_0
% 58.49/8.68 | | | | | | | | | | | | | | (261) ~ (all_264_0 = 0) | ~ (all_264_1 = 0)
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_264_1, xp,
% 58.49/8.68 | | | | | | | | | | | | | | simplifying with (7), (259) gives:
% 58.49/8.68 | | | | | | | | | | | | | | (262) all_264_1 = 0
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_264_0, all_45_0,
% 58.49/8.68 | | | | | | | | | | | | | | simplifying with (242), (260) gives:
% 58.49/8.68 | | | | | | | | | | | | | | (263) all_264_0 = 0
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | (264) ~ (all_264_0 = 0)
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | REDUCE: (263), (264) imply:
% 58.49/8.68 | | | | | | | | | | | | | | | (265) $false
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent.
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | (266) ~ (all_264_1 = 0)
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | REDUCE: (262), (266) imply:
% 58.49/8.68 | | | | | | | | | | | | | | | (267) $false
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | End of split
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | (268) ? [v0: $i] : (sdtasdt0(xp, v0) = all_45_0 &
% 58.49/8.68 | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0))
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | DELTA: instantiating (268) with fresh symbol all_264_0
% 58.49/8.68 | | | | | | | | | | | | | | gives:
% 58.49/8.68 | | | | | | | | | | | | | | (269) sdtasdt0(xp, all_264_0) = all_45_0 &
% 58.49/8.68 | | | | | | | | | | | | | | aNaturalNumber0(all_264_0) = 0 & $i(all_264_0)
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | ALPHA: (269) implies:
% 58.49/8.68 | | | | | | | | | | | | | | (270) $i(all_264_0)
% 58.49/8.68 | | | | | | | | | | | | | | (271) sdtasdt0(xp, all_264_0) = all_45_0
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 58.49/8.68 | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | (272) ~ (all_85_2 = 0)
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | REDUCE: (199), (272) imply:
% 58.49/8.68 | | | | | | | | | | | | | | | (273) $false
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent.
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | (274) all_85_0 = all_59_1
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | REDUCE: (103), (274) imply:
% 58.49/8.68 | | | | | | | | | | | | | | | (275) sdtpldt0(xm, xn) = all_59_1
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 58.49/8.68 | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | (276) ~ (all_95_1 = 0)
% 58.49/8.68 | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | REDUCE: (182), (276) imply:
% 58.49/8.68 | | | | | | | | | | | | | | | | (277) $false
% 58.49/8.68 | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent.
% 58.49/8.68 | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | (278) ~ (all_95_2 = 0) | all_95_0 = xk
% 58.49/8.68 | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 58.49/8.68 | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | (279) ~ (all_95_2 = 0)
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | REDUCE: (193), (279) imply:
% 58.49/8.68 | | | | | | | | | | | | | | | | | (280) $false
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | CLOSE: (280) is inconsistent.
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | (281) all_95_0 = xk
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | REDUCE: (122), (281) imply:
% 58.49/8.68 | | | | | | | | | | | | | | | | | (282) sdtasdt0(all_41_0, xr) = xk
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_101_3, all_45_0,
% 58.49/8.68 | | | | | | | | | | | | | | | | | xp, simplifying with (62), (228) gives:
% 58.49/8.68 | | | | | | | | | | | | | | | | | (283) all_101_3 = 0
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 58.49/8.68 | | | | | | | | | | | | | | | | |
% 58.49/8.68 | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.68 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (284) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (doDivides0(xp, all_45_0) = v2 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_45_0) = v1 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 58.49/8.69 | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0)))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | DELTA: instantiating (284) with fresh symbols all_338_0,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | all_338_1, all_338_2 gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (285) doDivides0(xp, all_45_0) = all_338_0 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_45_0) = all_338_1 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_338_2 & ( ~ (all_338_0 =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | 0) | ~ (all_338_1 = 0) | ~ (all_338_2 = 0))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (286) aNaturalNumber0(xp) = all_338_2
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (287) aNaturalNumber0(all_45_0) = all_338_1
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (288) doDivides0(xp, all_45_0) = all_338_0
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (289) ~ (all_338_0 = 0) | ~ (all_338_1 = 0) | ~
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (all_338_2 = 0)
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_338_2, xp,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | simplifying with (7), (286) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (290) all_338_2 = 0
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_338_1, all_45_0,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | simplifying with (242), (287) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (291) all_338_1 = 0
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_338_0, all_45_0,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | xp, simplifying with (62), (288) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (292) all_338_0 = 0
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | (293) ~ (all_338_0 = 0)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | REDUCE: (292), (293) imply:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | (294) $false
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | (295) ~ (all_338_1 = 0) | ~ (all_338_2 = 0)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | (296) ~ (all_338_1 = 0)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (296) imply:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | (297) $false
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | (298) ~ (all_338_2 = 0)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | REDUCE: (290), (298) imply:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | (299) $false
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | | CLOSE: (299) is inconsistent.
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.69 | | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_148_0, simplifying with
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (157), (158) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (300) all_148_0 = sz10 | all_148_0 = sz00 | ? [v0: $i]
% 58.49/8.69 | | | | | | | | | | | | | | | | | | : (isPrime0(v0) = 0 & doDivides0(v0, all_148_0) =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | 0 & aNaturalNumber0(v0) = 0 & $i(v0))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with xm, xn, xp, all_59_1,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | all_59_0, simplifying with (11), (19), (20), (51),
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (275) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (301) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 58.49/8.69 | | | | | | | | | | | | | | | | | | [v3: any] : ? [v4: $i] : ? [v5: any] : ? [v6:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | any] : ? [v7: any] : ? [v8: any] :
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (isPrime0(xp) = v3 & doDivides0(xp, v4) = v5 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | doDivides0(xp, xm) = v7 & doDivides0(xp, xn) =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | v8 & iLess0(all_59_0, all_59_0) = v6 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | sdtasdt0(xm, xn) = v4 & aNaturalNumber0(xp) = v2
% 58.49/8.69 | | | | | | | | | | | | | | | | | | & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | = v1 & $i(v4) & ( ~ (v6 = 0) | ~ (v2 = 0) | ~
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | (v8 = 0 & ? [v9: $i]
% 58.49/8.69 | | | | | | | | | | | | | | | | | | : (sdtasdt0(xp, v9) = xn &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v9) = 0 & $i(v9))) | (v7 =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | 0 & ? [v9: $i] : (sdtasdt0(xp, v9) = xm &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v9) = 0 & $i(v9))) | ( ~
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (v5 = 0) & ! [v9: $i] : ( ~ (sdtasdt0(xp,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | v9) = v4) | ~ $i(v9) | ? [v10: int]
% 58.49/8.69 | | | | | | | | | | | | | | | | | | : ( ~ (v10 = 0) & aNaturalNumber0(v9) =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | v10))) | ( ~ (v3 = 0) & (xp = sz10 | xp
% 58.49/8.69 | | | | | | | | | | | | | | | | | | = sz00 | ? [v9: $i] : ( ~ (v9 = xp) & ~
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (v9 = sz10) & doDivides0(v9, xp) = 0 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v9) = 0 & $i(v9) & ?
% 58.49/8.69 | | | | | | | | | | | | | | | | | | [v10: $i] : (sdtasdt0(v9, v10) = xp &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v10) = 0 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | $i(v10)))))))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddAsso) with xm, xn, xp,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | all_59_1, all_59_0, simplifying with (11), (19),
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (20), (51), (275) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (302) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 58.49/8.69 | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtpldt0(xm, v3) = v4 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | sdtpldt0(xn, xp) = v3 & aNaturalNumber0(xp) = v2
% 58.49/8.69 | | | | | | | | | | | | | | | | | | & aNaturalNumber0(xm) = v0 & aNaturalNumber0(xn)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | = v1 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_59_0))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddComm) with xm, xp, all_99_1,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | simplifying with (11), (20), (129) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (303) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (sdtpldt0(xp, xm) = v2 & aNaturalNumber0(xp) = v1
% 58.49/8.69 | | | | | | | | | | | | | | | | | | & aNaturalNumber0(xm) = v0 & $i(v2) & ( ~ (v1 =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v2 = all_99_1))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mSortsB) with xm, xp, all_99_1,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | simplifying with (11), (20), (129) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (304) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_99_1) = v2 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v1 & aNaturalNumber0(xm) =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_264_0,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | all_45_0, simplifying with (11), (270), (271)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (305) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (sdtasdt0(all_264_0, xp) = v2 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_264_0) = v1 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & $i(v2) & ( ~ (v1 = 0)
% 58.49/8.69 | | | | | | | | | | | | | | | | | | | ~ (v0 = 0) | v2 = all_45_0))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xr, all_41_0, xp,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | xk, all_45_0, simplifying with (11), (21), (27),
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (29), (256) gives:
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (306) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 58.49/8.69 | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_41_0, xp) =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | v3 & sdtasdt0(xr, v3) = v4 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_41_0) = v1 &
% 58.49/8.69 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 58.49/8.69 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_45_0))
% 58.49/8.69 | | | | | | | | | | | | | | | | | |
% 58.49/8.69 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with xr, all_198_0, xp,
% 58.49/8.69 | | | | | | | | | | | | | | | | | | xk, all_45_0, simplifying with (11), (21), (244),
% 58.49/8.69 | | | | | | | | | | | | | | | | | | (245), (256) gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (307) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 58.49/8.70 | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_198_0, xp)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = v3 & sdtasdt0(xr, v3) = v4 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_198_0) = v1 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v0 & aNaturalNumber0(xp) =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_45_0))
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mMulAsso) with all_41_0, xr, xp,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | xk, all_45_0, simplifying with (11), (21), (27),
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (256), (282) gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (308) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 58.49/8.70 | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtasdt0(all_41_0, v3) =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | v4 & sdtasdt0(xr, xp) = v3 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_41_0) = v0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v1 & aNaturalNumber0(xp) =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | 0) | ~ (v0 = 0) | v4 = all_45_0))
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mDefDiv) with xk, all_45_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_132_0, simplifying with (15), (64), (151)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (309) ? [v0: any] : ? [v1: any] :
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_45_0) = v1 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = 0))) | (( ~ (all_132_0 = 0) | ? [v0: $i]
% 58.49/8.70 | | | | | | | | | | | | | | | | | | : (sdtasdt0(xk, v0) = all_45_0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0))) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_132_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xk,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | v0) = all_45_0) | ~ $i(v0) | ? [v1:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = v1))))
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_148_0, 0, simplifying
% 58.49/8.70 | | | | | | | | | | | | | | | | | | with (157), (159) gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (310) ? [v0: int] : ( ~ (v0 = 0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_148_0) = v0) | ( ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_148_0 = sz10) & ~ (all_148_0 = sz00) & !
% 58.49/8.70 | | | | | | | | | | | | | | | | | | [v0: any] : (v0 = all_148_0 | v0 = sz10 | ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (doDivides0(v0, all_148_0) = 0) | ~ $i(v0) |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ? [v1: int] : ( ~ (v1 = 0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)))
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (304) with fresh symbols all_343_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_343_1, all_343_2 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (311) aNaturalNumber0(all_99_1) = all_343_0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_343_1 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_343_2 & ( ~ (all_343_1 =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | 0) | ~ (all_343_2 = 0) | all_343_0 = 0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (312) aNaturalNumber0(xp) = all_343_1
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (303) with fresh symbols all_347_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_347_1, all_347_2 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (313) sdtpldt0(xp, xm) = all_347_0 & aNaturalNumber0(xp)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = all_347_1 & aNaturalNumber0(xm) = all_347_2 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | $i(all_347_0) & ( ~ (all_347_1 = 0) | ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_347_2 = 0) | all_347_0 = all_99_1)
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (314) aNaturalNumber0(xp) = all_347_1
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (305) with fresh symbols all_355_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_355_1, all_355_2 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (315) sdtasdt0(all_264_0, xp) = all_355_0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_264_0) = all_355_1 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_355_2 & $i(all_355_0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ( ~ (all_355_1 = 0) | ~ (all_355_2 = 0) |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_355_0 = all_45_0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (316) aNaturalNumber0(xp) = all_355_2
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (302) with fresh symbols all_371_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_371_1, all_371_2, all_371_3, all_371_4 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (317) sdtpldt0(xm, all_371_1) = all_371_0 & sdtpldt0(xn,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | xp) = all_371_1 & aNaturalNumber0(xp) =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_371_2 & aNaturalNumber0(xm) = all_371_4 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_371_3 & $i(all_371_0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | $i(all_371_1) & ( ~ (all_371_2 = 0) | ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_371_3 = 0) | ~ (all_371_4 = 0) | all_371_0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = all_59_0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (318) aNaturalNumber0(xp) = all_371_2
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (308) with fresh symbols all_373_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_373_1, all_373_2, all_373_3, all_373_4 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (319) sdtasdt0(all_41_0, all_373_1) = all_373_0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | sdtasdt0(xr, xp) = all_373_1 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_41_0) = all_373_4 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_373_3 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_373_2 & $i(all_373_0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | $i(all_373_1) & ( ~ (all_373_2 = 0) | ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_373_3 = 0) | ~ (all_373_4 = 0) | all_373_0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = all_45_0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (320) aNaturalNumber0(xp) = all_373_2
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (307) with fresh symbols all_387_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_387_1, all_387_2, all_387_3, all_387_4 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (321) sdtasdt0(all_198_0, xp) = all_387_1 & sdtasdt0(xr,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_387_1) = all_387_0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_198_0) = all_387_3 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_387_4 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_387_2 & $i(all_387_0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | $i(all_387_1) & ( ~ (all_387_2 = 0) | ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_387_3 = 0) | ~ (all_387_4 = 0) | all_387_0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = all_45_0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (322) aNaturalNumber0(xp) = all_387_2
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (306) with fresh symbols all_389_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_389_1, all_389_2, all_389_3, all_389_4 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (323) sdtasdt0(all_41_0, xp) = all_389_1 & sdtasdt0(xr,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_389_1) = all_389_0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_41_0) = all_389_3 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = all_389_4 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_389_2 & $i(all_389_0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | $i(all_389_1) & ( ~ (all_389_2 = 0) | ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_389_3 = 0) | ~ (all_389_4 = 0) | all_389_0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = all_45_0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (324) aNaturalNumber0(xp) = all_389_2
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | DELTA: instantiating (301) with fresh symbols all_391_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_391_1, all_391_2, all_391_3, all_391_4,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_391_5, all_391_6, all_391_7, all_391_8 gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (325) isPrime0(xp) = all_391_5 & doDivides0(xp,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_391_4) = all_391_3 & doDivides0(xp, xm) =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | all_391_1 & doDivides0(xp, xn) = all_391_0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | iLess0(all_59_0, all_59_0) = all_391_2 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | sdtasdt0(xm, xn) = all_391_4 & aNaturalNumber0(xp)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = all_391_6 & aNaturalNumber0(xm) = all_391_8 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xn) = all_391_7 & $i(all_391_4) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ( ~ (all_391_2 = 0) | ~ (all_391_6 = 0) | ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_391_7 = 0) | ~ (all_391_8 = 0) |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_391_0 = 0 & ? [v0: $i] : (sdtasdt0(xp, v0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = xn & aNaturalNumber0(v0) = 0 & $i(v0))) |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_391_1 = 0 & ? [v0: $i] : (sdtasdt0(xp, v0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | = xm & aNaturalNumber0(v0) = 0 & $i(v0))) |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ( ~ (all_391_3 = 0) & ! [v0: $i] : ( ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (sdtasdt0(xp, v0) = all_391_4) | ~ $i(v0) |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ? [v1: int] : ( ~ (v1 = 0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1))) | ( ~
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (all_391_5 = 0) & (xp = sz10 | xp = sz00 | ?
% 58.49/8.70 | | | | | | | | | | | | | | | | | | [v0: $i] : ( ~ (v0 = xp) & ~ (v0 = sz10) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | doDivides0(v0, xp) = 0 &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0) & ? [v1:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | $i] : (sdtasdt0(v0, v1) = xp &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | aNaturalNumber0(v1) = 0 & $i(v1))))))
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | (326) aNaturalNumber0(xp) = all_391_6
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | (327) ? [v0: int] : ( ~ (v0 = 0) &
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_148_0) = v0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (327) with fresh symbol all_418_0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | (328) ~ (all_418_0 = 0) & aNaturalNumber0(all_148_0) =
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | all_418_0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | (329) ~ (all_418_0 = 0)
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | (330) aNaturalNumber0(all_148_0) = all_418_0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_418_0, all_148_0,
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | simplifying with (158), (330) gives:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | (331) all_418_0 = 0
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (329), (331) imply:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | (332) $false
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent.
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.70 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (333) ( ~ (all_132_0 = 0) | ? [v0: $i] : (sdtasdt0(xk,
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | v0) = all_45_0 & aNaturalNumber0(v0) = 0 &
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | $i(v0))) & (all_132_0 = 0 | ! [v0: $i] : ( ~
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (sdtasdt0(xk, v0) = all_45_0) | ~ $i(v0) | ?
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | = v1)))
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (23), (246), (256), (312), (314),
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (316), (318), (320), (322), (324), (326), (333)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1.
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | (334) ~ (all_148_0 = sz10) & ~ (all_148_0 = sz00) & !
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | [v0: any] : (v0 = all_148_0 | v0 = sz10 | ~
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | (doDivides0(v0, all_148_0) = 0) | ~ $i(v0) | ?
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) =
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | v1))
% 58.49/8.71 | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | (335) ~ (all_148_0 = sz00)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | (336) ~ (all_148_0 = sz10)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (337) ? [v0: any] : ? [v1: any] :
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (aNaturalNumber0(all_45_0) = v1 &
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xk) = v0 & ( ~ (v1 = 0) | ~ (v0
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | = 0)))
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (337) with fresh symbols all_421_0,
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | all_421_1 gives:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (338) aNaturalNumber0(all_45_0) = all_421_0 &
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xk) = all_421_1 & ( ~ (all_421_0 =
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_421_1 = 0))
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (339) aNaturalNumber0(xk) = all_421_1
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (340) aNaturalNumber0(all_45_0) = all_421_0
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (341) ~ (all_421_0 = 0) | ~ (all_421_1 = 0)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | (342) all_148_0 = sz00
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (335), (342) imply:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | (343) $false
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | CLOSE: (343) is inconsistent.
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | (344) all_148_0 = sz10 | ? [v0: $i] : (isPrime0(v0) = 0
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | & doDivides0(v0, all_148_0) = 0 &
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0))
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | (345) all_148_0 = sz10
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (345) imply:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | (346) $false
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (346) is inconsistent.
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_421_1, xk,
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | simplifying with (34), (339) gives:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | (347) all_421_1 = 0
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_421_0, all_45_0,
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | simplifying with (242), (340) gives:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | (348) all_421_0 = 0
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | (349) ~ (all_421_0 = 0)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (349) imply:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | (350) $false
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (350) is inconsistent.
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | (351) ~ (all_421_1 = 0)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (351) imply:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | (352) $false
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (352) is inconsistent.
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (353) ( ~ (all_132_0 = 0) | ? [v0: $i] : (sdtasdt0(xk,
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | v0) = all_45_0 & aNaturalNumber0(v0) = 0 &
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | $i(v0))) & (all_132_0 = 0 | ! [v0: $i] : ( ~
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (sdtasdt0(xk, v0) = all_45_0) | ~ $i(v0) | ?
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | = v1)))
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (23), (246), (256), (312), (314),
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | (316), (318), (320), (322), (324), (326), (353)
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1.
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | (354) ~ (all_132_1 = 0) | ~ (all_132_2 = 0) | ~
% 58.49/8.71 | | | | | | | | | | (all_132_3 = 0)
% 58.49/8.71 | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | BETA: splitting (354) gives:
% 58.49/8.71 | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | Case 1:
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | (355) ~ (all_132_1 = 0)
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | REDUCE: (241), (355) imply:
% 58.49/8.71 | | | | | | | | | | | (356) $false
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | CLOSE: (356) is inconsistent.
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | (357) ~ (all_132_2 = 0) | ~ (all_132_3 = 0)
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | BETA: splitting (357) gives:
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | Case 1:
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | (358) ~ (all_132_2 = 0)
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | REDUCE: (227), (358) imply:
% 58.49/8.71 | | | | | | | | | | | | (359) $false
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | CLOSE: (359) is inconsistent.
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | (360) ~ (all_132_3 = 0)
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | REDUCE: (180), (360) imply:
% 58.49/8.71 | | | | | | | | | | | | (361) $false
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | | CLOSE: (361) is inconsistent.
% 58.49/8.71 | | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | | |
% 58.49/8.71 | | | | | | | | | End of split
% 58.49/8.71 | | | | | | | | |
% 58.49/8.71 | | | | | | | | End of split
% 58.49/8.71 | | | | | | | |
% 58.49/8.71 | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | |
% 58.49/8.71 | | | | | | | | (362) ~ (all_62_0 = xk)
% 58.49/8.71 | | | | | | | | (363) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i]
% 58.49/8.71 | | | | | | | | : (sdtasdt0(all_62_0, xp) = v3 & sdtasdt0(xk, xp) = v2
% 58.49/8.71 | | | | | | | | & aNaturalNumber0(all_62_0) = v1 &
% 58.49/8.71 | | | | | | | | aNaturalNumber0(xk) = v0 & $i(v3) & $i(v2) & ( ~ (v1
% 58.49/8.71 | | | | | | | | = 0) | ~ (v0 = 0)))
% 58.49/8.71 | | | | | | | |
% 58.49/8.71 | | | | | | | | DELTA: instantiating (363) with fresh symbols all_175_0,
% 58.49/8.71 | | | | | | | | all_175_1, all_175_2, all_175_3 gives:
% 58.49/8.71 | | | | | | | | (364) sdtasdt0(all_62_0, xp) = all_175_0 & sdtasdt0(xk, xp) =
% 58.49/8.71 | | | | | | | | all_175_1 & aNaturalNumber0(all_62_0) = all_175_2 &
% 58.49/8.71 | | | | | | | | aNaturalNumber0(xk) = all_175_3 & $i(all_175_0) &
% 58.49/8.71 | | | | | | | | $i(all_175_1) & ( ~ (all_175_2 = 0) | ~ (all_175_3 =
% 58.49/8.71 | | | | | | | | 0))
% 58.49/8.71 | | | | | | | |
% 58.49/8.71 | | | | | | | | ALPHA: (364) implies:
% 58.49/8.71 | | | | | | | | (365) aNaturalNumber0(xk) = all_175_3
% 58.49/8.71 | | | | | | | | (366) aNaturalNumber0(all_62_0) = all_175_2
% 58.49/8.71 | | | | | | | |
% 58.49/8.71 | | | | | | | | BETA: splitting (140) gives:
% 58.49/8.71 | | | | | | | |
% 58.49/8.71 | | | | | | | | Case 1:
% 58.49/8.71 | | | | | | | | |
% 58.49/8.71 | | | | | | | | | (367) all_62_0 = xk
% 58.49/8.71 | | | | | | | | |
% 58.49/8.71 | | | | | | | | | REDUCE: (362), (367) imply:
% 58.49/8.71 | | | | | | | | | (368) $false
% 58.49/8.71 | | | | | | | | |
% 58.49/8.71 | | | | | | | | | CLOSE: (368) is inconsistent.
% 58.49/8.71 | | | | | | | | |
% 58.49/8.71 | | | | | | | | Case 2:
% 58.49/8.71 | | | | | | | | |
% 58.49/8.71 | | | | | | | | | (369) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 58.49/8.71 | | | | | | | | | $i] : (sdtasdt0(all_62_0, xp) = v2 & sdtasdt0(xk,
% 58.49/8.71 | | | | | | | | | xp) = v3 & aNaturalNumber0(all_62_0) = v0 &
% 58.49/8.71 | | | | | | | | | aNaturalNumber0(xk) = v1 & $i(v3) & $i(v2) & ( ~
% 58.49/8.71 | | | | | | | | | (v1 = 0) | ~ (v0 = 0)))
% 58.49/8.71 | | | | | | | | |
% 58.49/8.71 | | | | | | | | | DELTA: instantiating (369) with fresh symbols all_205_0,
% 58.49/8.71 | | | | | | | | | all_205_1, all_205_2, all_205_3 gives:
% 58.49/8.72 | | | | | | | | | (370) sdtasdt0(all_62_0, xp) = all_205_1 & sdtasdt0(xk, xp)
% 58.49/8.72 | | | | | | | | | = all_205_0 & aNaturalNumber0(all_62_0) = all_205_3 &
% 58.49/8.72 | | | | | | | | | aNaturalNumber0(xk) = all_205_2 & $i(all_205_0) &
% 58.49/8.72 | | | | | | | | | $i(all_205_1) & ( ~ (all_205_2 = 0) | ~ (all_205_3 =
% 58.49/8.72 | | | | | | | | | 0))
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | ALPHA: (370) implies:
% 58.49/8.72 | | | | | | | | | (371) aNaturalNumber0(xk) = all_205_2
% 58.49/8.72 | | | | | | | | | (372) aNaturalNumber0(all_62_0) = all_205_3
% 58.49/8.72 | | | | | | | | | (373) ~ (all_205_2 = 0) | ~ (all_205_3 = 0)
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_205_2, xk,
% 58.49/8.72 | | | | | | | | | simplifying with (34), (371) gives:
% 58.49/8.72 | | | | | | | | | (374) all_205_2 = 0
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | GROUND_INST: instantiating (23) with all_175_3, all_205_2, xk,
% 58.49/8.72 | | | | | | | | | simplifying with (365), (371) gives:
% 58.49/8.72 | | | | | | | | | (375) all_205_2 = all_175_3
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_205_3, all_62_0,
% 58.49/8.72 | | | | | | | | | simplifying with (55), (372) gives:
% 58.49/8.72 | | | | | | | | | (376) all_205_3 = 0
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | GROUND_INST: instantiating (23) with all_175_2, all_205_3,
% 58.49/8.72 | | | | | | | | | all_62_0, simplifying with (366), (372) gives:
% 58.49/8.72 | | | | | | | | | (377) all_205_3 = all_175_2
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | COMBINE_EQS: (374), (375) imply:
% 58.49/8.72 | | | | | | | | | (378) all_175_3 = 0
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | COMBINE_EQS: (376), (377) imply:
% 58.49/8.72 | | | | | | | | | (379) all_175_2 = 0
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | BETA: splitting (373) gives:
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | | Case 1:
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | | (380) ~ (all_205_2 = 0)
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | | REDUCE: (374), (380) imply:
% 58.49/8.72 | | | | | | | | | | (381) $false
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | | CLOSE: (381) is inconsistent.
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | Case 2:
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | | (382) ~ (all_205_3 = 0)
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | | REDUCE: (376), (382) imply:
% 58.49/8.72 | | | | | | | | | | (383) $false
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | | CLOSE: (383) is inconsistent.
% 58.49/8.72 | | | | | | | | | |
% 58.49/8.72 | | | | | | | | | End of split
% 58.49/8.72 | | | | | | | | |
% 58.49/8.72 | | | | | | | | End of split
% 58.49/8.72 | | | | | | | |
% 58.49/8.72 | | | | | | | End of split
% 58.49/8.72 | | | | | | |
% 58.49/8.72 | | | | | | End of split
% 58.49/8.72 | | | | | |
% 58.49/8.72 | | | | | End of split
% 58.49/8.72 | | | | |
% 58.49/8.72 | | | | End of split
% 58.49/8.72 | | | |
% 58.49/8.72 | | | End of split
% 58.49/8.72 | | |
% 58.49/8.72 | | End of split
% 58.49/8.72 | |
% 58.49/8.72 | End of split
% 58.49/8.72 |
% 58.49/8.72 End of proof
% 58.49/8.72
% 58.49/8.72 Sub-proof #1 shows that the following formulas are inconsistent:
% 58.49/8.72 ----------------------------------------------------------------
% 58.49/8.72 (1) sdtasdt0(xk, xp) = all_45_0
% 58.49/8.72 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 58.49/8.72 (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 58.49/8.72 (3) ~ (all_132_0 = 0)
% 58.49/8.72 (4) aNaturalNumber0(xp) = all_387_2
% 58.49/8.72 (5) aNaturalNumber0(xp) = all_355_2
% 58.49/8.72 (6) ( ~ (all_132_0 = 0) | ? [v0: $i] : (sdtasdt0(xk, v0) = all_45_0 &
% 58.49/8.72 aNaturalNumber0(v0) = 0 & $i(v0))) & (all_132_0 = 0 | ! [v0: $i] : (
% 58.49/8.72 ~ (sdtasdt0(xk, v0) = all_45_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 58.49/8.72 = 0) & aNaturalNumber0(v0) = v1)))
% 58.49/8.72 (7) aNaturalNumber0(xp) = all_373_2
% 58.49/8.72 (8) $i(xp)
% 58.49/8.72 (9) aNaturalNumber0(xp) = 0
% 58.49/8.72 (10) aNaturalNumber0(xp) = all_391_6
% 58.49/8.72 (11) aNaturalNumber0(xp) = all_389_2
% 58.49/8.72 (12) aNaturalNumber0(xp) = all_347_1
% 58.49/8.72 (13) aNaturalNumber0(xp) = all_343_1
% 58.49/8.72 (14) aNaturalNumber0(xp) = all_371_2
% 58.49/8.72
% 58.49/8.72 Begin of proof
% 58.49/8.72 |
% 58.49/8.72 | ALPHA: (6) implies:
% 58.49/8.72 | (15) all_132_0 = 0 | ! [v0: $i] : ( ~ (sdtasdt0(xk, v0) = all_45_0) | ~
% 58.49/8.72 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 58.49/8.72 |
% 58.49/8.72 | BETA: splitting (15) gives:
% 58.49/8.72 |
% 58.49/8.72 | Case 1:
% 58.49/8.72 | |
% 58.49/8.72 | | (16) all_132_0 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | REDUCE: (3), (16) imply:
% 58.49/8.72 | | (17) $false
% 58.49/8.72 | |
% 58.49/8.72 | | CLOSE: (17) is inconsistent.
% 58.49/8.72 | |
% 58.49/8.72 | Case 2:
% 58.49/8.72 | |
% 58.49/8.72 | | (18) ! [v0: $i] : ( ~ (sdtasdt0(xk, v0) = all_45_0) | ~ $i(v0) | ?
% 58.49/8.72 | | [v1: int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (18) with xp, simplifying with (1), (8) gives:
% 58.49/8.72 | | (19) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0)
% 58.49/8.72 | |
% 58.49/8.72 | | DELTA: instantiating (19) with fresh symbol all_444_0 gives:
% 58.49/8.72 | | (20) ~ (all_444_0 = 0) & aNaturalNumber0(xp) = all_444_0
% 58.49/8.72 | |
% 58.49/8.72 | | ALPHA: (20) implies:
% 58.49/8.72 | | (21) ~ (all_444_0 = 0)
% 58.49/8.72 | | (22) aNaturalNumber0(xp) = all_444_0
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_347_1, all_355_2, xp, simplifying
% 58.49/8.72 | | with (5), (12) gives:
% 58.49/8.72 | | (23) all_355_2 = all_347_1
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_355_2, all_371_2, xp, simplifying
% 58.49/8.72 | | with (5), (14) gives:
% 58.49/8.72 | | (24) all_371_2 = all_355_2
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_371_2, all_373_2, xp, simplifying
% 58.49/8.72 | | with (7), (14) gives:
% 58.49/8.72 | | (25) all_373_2 = all_371_2
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_347_1, all_387_2, xp, simplifying
% 58.49/8.72 | | with (4), (12) gives:
% 58.49/8.72 | | (26) all_387_2 = all_347_1
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with 0, all_391_6, xp, simplifying with (9),
% 58.49/8.72 | | (10) gives:
% 58.49/8.72 | | (27) all_391_6 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_389_2, all_391_6, xp, simplifying
% 58.49/8.72 | | with (10), (11) gives:
% 58.49/8.72 | | (28) all_391_6 = all_389_2
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_373_2, all_391_6, xp, simplifying
% 58.49/8.72 | | with (7), (10) gives:
% 58.49/8.72 | | (29) all_391_6 = all_373_2
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_387_2, all_444_0, xp, simplifying
% 58.49/8.72 | | with (4), (22) gives:
% 58.49/8.72 | | (30) all_444_0 = all_387_2
% 58.49/8.72 | |
% 58.49/8.72 | | GROUND_INST: instantiating (2) with all_343_1, all_444_0, xp, simplifying
% 58.49/8.72 | | with (13), (22) gives:
% 58.49/8.72 | | (31) all_444_0 = all_343_1
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (30), (31) imply:
% 58.49/8.72 | | (32) all_387_2 = all_343_1
% 58.49/8.72 | |
% 58.49/8.72 | | SIMP: (32) implies:
% 58.49/8.72 | | (33) all_387_2 = all_343_1
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (27), (28) imply:
% 58.49/8.72 | | (34) all_389_2 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (28), (29) imply:
% 58.49/8.72 | | (35) all_389_2 = all_373_2
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (34), (35) imply:
% 58.49/8.72 | | (36) all_373_2 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | SIMP: (36) implies:
% 58.49/8.72 | | (37) all_373_2 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (26), (33) imply:
% 58.49/8.72 | | (38) all_347_1 = all_343_1
% 58.49/8.72 | |
% 58.49/8.72 | | SIMP: (38) implies:
% 58.49/8.72 | | (39) all_347_1 = all_343_1
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (25), (37) imply:
% 58.49/8.72 | | (40) all_371_2 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | SIMP: (40) implies:
% 58.49/8.72 | | (41) all_371_2 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (24), (41) imply:
% 58.49/8.72 | | (42) all_355_2 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | SIMP: (42) implies:
% 58.49/8.72 | | (43) all_355_2 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (23), (43) imply:
% 58.49/8.72 | | (44) all_347_1 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | SIMP: (44) implies:
% 58.49/8.72 | | (45) all_347_1 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (39), (45) imply:
% 58.49/8.72 | | (46) all_343_1 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | SIMP: (46) implies:
% 58.49/8.72 | | (47) all_343_1 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | COMBINE_EQS: (31), (47) imply:
% 58.49/8.72 | | (48) all_444_0 = 0
% 58.49/8.72 | |
% 58.49/8.72 | | REDUCE: (21), (48) imply:
% 58.49/8.72 | | (49) $false
% 58.49/8.72 | |
% 58.49/8.72 | | CLOSE: (49) is inconsistent.
% 58.49/8.72 | |
% 58.49/8.72 | End of split
% 58.49/8.72 |
% 58.49/8.72 End of proof
% 58.49/8.72 % SZS output end Proof for theBenchmark
% 58.49/8.72
% 58.49/8.72 8063ms
%------------------------------------------------------------------------------