TSTP Solution File: NUM505+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.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 11:48:14 EDT 2023
% Result : Theorem 14.30s 2.67s
% Output : Proof 39.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 09:08:25 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.59/1.20 Prover 4: Preprocessing ...
% 3.59/1.20 Prover 1: Preprocessing ...
% 4.02/1.25 Prover 6: Preprocessing ...
% 4.02/1.25 Prover 0: Preprocessing ...
% 4.02/1.25 Prover 2: Preprocessing ...
% 4.02/1.25 Prover 5: Preprocessing ...
% 4.02/1.25 Prover 3: Preprocessing ...
% 8.74/1.96 Prover 1: Constructing countermodel ...
% 8.74/1.98 Prover 3: Constructing countermodel ...
% 9.15/2.07 Prover 6: Proving ...
% 10.30/2.17 Prover 5: Constructing countermodel ...
% 11.41/2.31 Prover 2: Proving ...
% 13.21/2.55 Prover 4: Constructing countermodel ...
% 14.30/2.67 Prover 6: proved (2023ms)
% 14.30/2.67
% 14.30/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.30/2.67
% 14.30/2.68 Prover 3: stopped
% 14.30/2.69 Prover 5: stopped
% 14.30/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.30/2.70 Prover 2: stopped
% 14.30/2.70 Prover 0: Proving ...
% 14.30/2.70 Prover 0: stopped
% 14.30/2.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.30/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.30/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.30/2.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.74/2.85 Prover 10: Preprocessing ...
% 14.74/2.86 Prover 8: Preprocessing ...
% 15.74/2.88 Prover 11: Preprocessing ...
% 15.74/2.88 Prover 7: Preprocessing ...
% 15.74/2.89 Prover 13: Preprocessing ...
% 17.20/3.10 Prover 10: Constructing countermodel ...
% 17.20/3.12 Prover 7: Constructing countermodel ...
% 17.20/3.12 Prover 8: Warning: ignoring some quantifiers
% 17.20/3.13 Prover 8: Constructing countermodel ...
% 17.20/3.15 Prover 13: Constructing countermodel ...
% 20.43/3.54 Prover 11: Constructing countermodel ...
% 37.65/5.83 Prover 1: Found proof (size 325)
% 37.65/5.83 Prover 1: proved (5191ms)
% 37.65/5.83 Prover 7: stopped
% 37.65/5.83 Prover 8: stopped
% 37.65/5.83 Prover 13: stopped
% 37.65/5.83 Prover 11: stopped
% 37.65/5.83 Prover 4: stopped
% 37.65/5.83 Prover 10: stopped
% 37.65/5.84
% 37.65/5.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.65/5.84
% 38.17/5.87 % SZS output start Proof for theBenchmark
% 38.17/5.87 Assumptions after simplification:
% 38.17/5.87 ---------------------------------
% 38.17/5.87
% 38.17/5.87 (mAddAsso)
% 38.17/5.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 38.17/5.90 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 38.17/5.90 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 38.17/5.90 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 &
% 38.17/5.90 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 38.17/5.90 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 38.17/5.90 v4)))
% 38.17/5.90
% 38.17/5.90 (mAddComm)
% 38.17/5.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 38.17/5.90 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 38.17/5.90 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 38.17/5.90 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 38.17/5.90
% 38.17/5.90 (mDefDiv)
% 38.17/5.90 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~
% 38.17/5.90 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4
% 38.17/5.90 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0)
% 38.17/5.90 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 &
% 38.17/5.90 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~
% 38.17/5.90 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)))))
% 38.17/5.90
% 38.17/5.90 (mDefLE)
% 38.17/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (sdtlseqdt0(v0, v1) = v2) | ~
% 38.17/5.91 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4
% 38.17/5.91 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0)
% 38.17/5.91 | ? [v3: $i] : (sdtpldt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 &
% 38.17/5.91 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtpldt0(v0, v3) = v1) | ~
% 38.17/5.91 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)))))
% 38.17/5.91
% 38.17/5.91 (mDefPrime)
% 38.17/5.91 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) |
% 38.17/5.91 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~
% 38.17/5.91 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 |
% 38.17/5.91 v2 = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] :
% 38.17/5.91 ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = 0 | v0 = sz10 |
% 38.17/5.91 v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) &
% 38.17/5.91 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & $i(v2)))))
% 38.17/5.91
% 38.17/5.91 (mDefQuot)
% 38.17/5.92 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~
% 38.17/5.92 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 38.17/5.92 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4
% 38.45/5.92 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) |
% 38.45/5.92 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4:
% 38.45/5.92 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~
% 38.45/5.92 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) =
% 38.45/5.92 0))))
% 38.45/5.92
% 38.45/5.92 (mDivLE)
% 38.45/5.92 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (doDivides0(v0, v1) =
% 38.45/5.92 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 38.45/5.92 (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) =
% 38.45/5.92 v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 38.45/5.92
% 38.45/5.92 (mLETotal)
% 38.45/5.92 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) =
% 38.45/5.92 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 38.45/5.92 (sdtlseqdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 38.45/5.92 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v5 = 0 & ~ (v1 = v0)))))
% 38.45/5.92
% 38.45/5.92 (mMulCanc)
% 38.45/5.92 $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0)
% 38.45/5.92 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~
% 38.45/5.92 (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~
% 38.45/5.92 $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] :
% 38.45/5.92 (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6
% 38.45/5.92 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 =
% 38.45/5.92 0) | ( ~ (v8 = v7) & ~ (v4 = v3))))))
% 38.45/5.92
% 38.45/5.92 (mMulComm)
% 38.45/5.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 38.45/5.92 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 38.45/5.92 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 38.45/5.92 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 38.45/5.92
% 38.45/5.92 (mPrimDiv)
% 38.45/5.92 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~
% 38.45/5.92 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 &
% 38.45/5.92 doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0 & $i(v1)))
% 38.45/5.92
% 38.45/5.92 (mSortsB)
% 38.45/5.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 38.45/5.92 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 38.45/5.92 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 38.45/5.92 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 38.45/5.92
% 38.45/5.92 (mSortsB_02)
% 38.45/5.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 38.45/5.93 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 38.45/5.93 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 38.45/5.93 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 38.45/5.93
% 38.45/5.93 (m__)
% 38.45/5.93 $i(xk) & $i(xp) & ? [v0: int] : ? [v1: any] : ( ~ (v0 = 0) & sdtlseqdt0(xk,
% 38.45/5.93 xp) = v1 & sdtlseqdt0(xp, xk) = v0 & ( ~ (v1 = 0) | xk = xp))
% 38.45/5.93
% 38.45/5.93 (m__1799)
% 38.45/5.93 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1
% 38.45/5.93 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : !
% 38.45/5.93 [v4: $i] : ! [v5: $i] : ( ~ (doDivides0(v4, v5) = 0) | ~ (sdtasdt0(v2, v3)
% 38.45/5.93 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 38.45/5.93 : ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 38.45/5.93 any] : ? [v13: any] : ? [v14: any] : (isPrime0(v4) = v9 &
% 38.45/5.93 doDivides0(v4, v3) = v14 & doDivides0(v4, v2) = v13 & iLess0(v11, v1) =
% 38.45/5.93 v12 & sdtpldt0(v10, v4) = v11 & sdtpldt0(v2, v3) = v10 &
% 38.45/5.93 aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 &
% 38.45/5.93 aNaturalNumber0(v2) = v6 & $i(v11) & $i(v10) & ( ~ (v12 = 0) | ~ (v9 =
% 38.45/5.93 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v14 = 0 | v13 = 0))))
% 38.45/5.93
% 38.45/5.93 (m__1837)
% 38.45/5.93 aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 &
% 38.45/5.93 $i(xp) & $i(xm) & $i(xn)
% 38.45/5.93
% 38.45/5.93 (m__1860)
% 38.45/5.93 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp,
% 38.45/5.93 v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0))
% 38.45/5.93
% 38.45/5.93 (m__2287)
% 38.45/5.93 ~ (xp = xm) & ~ (xp = xn) & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0
% 38.45/5.93 & $i(xp) & $i(xm) & $i(xn)
% 38.45/5.93
% 38.45/5.93 (m__2306)
% 38.45/5.93 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 38.45/5.93 sdtasdt0(xn, xm) = v0 & $i(v0))
% 38.45/5.93
% 38.45/5.93 (m__2315)
% 38.45/5.93 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00)
% 38.45/5.93
% 38.45/5.93 (m__2327)
% 38.45/5.93 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00)
% 38.45/5.93
% 38.45/5.93 (m__2342)
% 38.45/5.93 isPrime0(xr) = 0 & doDivides0(xr, xk) = 0 & aNaturalNumber0(xr) = 0 & $i(xr) &
% 38.45/5.93 $i(xk)
% 38.45/5.93
% 38.45/5.93 (m__2362)
% 38.45/5.93 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : (doDivides0(xr, v0) = 0 &
% 38.45/5.93 sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0))
% 38.45/5.93
% 38.45/5.93 (function-axioms)
% 38.45/5.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.45/5.94 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 38.45/5.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 38.45/5.94 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 38.45/5.94 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 38.45/5.94 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 38.45/5.94 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.45/5.94 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 38.45/5.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 38.45/5.94 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 38.45/5.94 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.45/5.94 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 38.45/5.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 38.45/5.94 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.45/5.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~
% 38.45/5.94 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.45/5.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 38.45/5.94 | ~ (aNaturalNumber0(v2) = v0))
% 38.45/5.94
% 38.45/5.94 Further assumptions not needed in the proof:
% 38.45/5.94 --------------------------------------------
% 38.45/5.94 mAMDistr, mAddCanc, mDefDiff, mDivAsso, mDivMin, mDivSum, mDivTrans, mIH,
% 38.45/5.94 mIH_03, mLEAsym, mLENTr, mLERefl, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso,
% 38.45/5.94 mNatSort, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit,
% 38.45/5.94 m_MulZero, m__1870, m__2075
% 38.45/5.94
% 38.45/5.94 Those formulas are unsatisfiable:
% 38.45/5.94 ---------------------------------
% 38.45/5.94
% 38.45/5.94 Begin of proof
% 38.45/5.94 |
% 38.45/5.94 | ALPHA: (mMulCanc) implies:
% 38.45/5.94 | (1) ! [v0: $i] : (v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) |
% 38.45/5.94 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~
% 38.45/5.94 | (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) |
% 38.45/5.94 | ~ $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i]
% 38.45/5.94 | : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 &
% 38.45/5.94 | aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & $i(v8) &
% 38.45/5.94 | $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v7) & ~ (v4 =
% 38.45/5.94 | v3))))))
% 38.45/5.94 |
% 38.45/5.94 | ALPHA: (mDefQuot) implies:
% 38.45/5.94 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1,
% 38.45/5.94 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 38.45/5.94 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 &
% 38.45/5.94 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 38.45/5.94 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) |
% 38.45/5.94 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) =
% 38.45/5.94 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) |
% 38.45/5.94 | (v3 = v1 & aNaturalNumber0(v2) = 0))))
% 38.45/5.94 |
% 38.45/5.94 | ALPHA: (mDivLE) implies:
% 38.45/5.95 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) |
% 38.45/5.95 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 38.45/5.95 | (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 &
% 38.45/5.95 | aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 38.45/5.95 |
% 38.45/5.95 | ALPHA: (mDefPrime) implies:
% 38.45/5.95 | (4) ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | ~ $i(v0) | ?
% 38.45/5.95 | [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ (v1 = 0)
% 38.45/5.95 | | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | v2
% 38.45/5.95 | = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3:
% 38.45/5.95 | int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 =
% 38.45/5.95 | 0 | v0 = sz10 | v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2
% 38.45/5.95 | = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 &
% 38.45/5.95 | $i(v2)))))
% 38.45/5.95 |
% 38.45/5.95 | ALPHA: (mPrimDiv) implies:
% 38.45/5.95 | (5) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) |
% 38.45/5.95 | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 &
% 38.45/5.95 | aNaturalNumber0(v1) = 0 & $i(v1)))
% 38.45/5.95 |
% 38.45/5.95 | ALPHA: (m__1837) implies:
% 38.45/5.95 | (6) aNaturalNumber0(xn) = 0
% 38.45/5.95 | (7) aNaturalNumber0(xm) = 0
% 38.45/5.95 | (8) aNaturalNumber0(xp) = 0
% 38.45/5.95 |
% 38.45/5.95 | ALPHA: (m__1799) implies:
% 38.45/5.95 | (9) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) =
% 38.45/5.95 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 38.45/5.95 | [v5: $i] : ( ~ (doDivides0(v4, v5) = 0) | ~ (sdtasdt0(v2, v3) = v5)
% 38.45/5.95 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] :
% 38.45/5.95 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ?
% 38.45/5.95 | [v12: any] : ? [v13: any] : ? [v14: any] : (isPrime0(v4) = v9 &
% 38.45/5.95 | doDivides0(v4, v3) = v14 & doDivides0(v4, v2) = v13 & iLess0(v11,
% 38.45/5.95 | v1) = v12 & sdtpldt0(v10, v4) = v11 & sdtpldt0(v2, v3) = v10 &
% 38.45/5.95 | aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 &
% 38.45/5.95 | aNaturalNumber0(v2) = v6 & $i(v11) & $i(v10) & ( ~ (v12 = 0) | ~
% 38.45/5.95 | (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v14 = 0 |
% 38.45/5.95 | v13 = 0))))
% 38.45/5.95 |
% 38.45/5.95 | ALPHA: (m__1860) implies:
% 38.45/5.95 | (10) ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp, v0) = 0 &
% 38.45/5.95 | sdtasdt0(xn, xm) = v0 & $i(v0))
% 38.45/5.95 |
% 38.45/5.95 | ALPHA: (m__2287) implies:
% 38.45/5.95 | (11) sdtlseqdt0(xm, xp) = 0
% 38.45/5.95 |
% 38.45/5.95 | ALPHA: (m__2306) implies:
% 38.45/5.96 | (12) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xn, xm) = v0 & $i(v0))
% 38.45/5.96 |
% 38.45/5.96 | ALPHA: (m__2327) implies:
% 38.45/5.96 | (13) ~ (xk = sz00)
% 38.45/5.96 |
% 38.45/5.96 | ALPHA: (m__2342) implies:
% 38.65/5.96 | (14) aNaturalNumber0(xr) = 0
% 38.65/5.96 | (15) doDivides0(xr, xk) = 0
% 38.65/5.96 | (16) isPrime0(xr) = 0
% 38.65/5.96 |
% 38.65/5.96 | ALPHA: (m__2362) implies:
% 38.65/5.96 | (17) $i(xn)
% 38.65/5.96 | (18) $i(xm)
% 38.65/5.96 | (19) $i(xr)
% 38.65/5.96 | (20) ? [v0: $i] : (doDivides0(xr, v0) = 0 & sdtlseqdt0(xr, xk) = 0 &
% 38.65/5.96 | sdtasdt0(xn, xm) = v0 & $i(v0))
% 38.65/5.96 |
% 38.65/5.96 | ALPHA: (m__) implies:
% 38.65/5.96 | (21) $i(xp)
% 38.65/5.96 | (22) $i(xk)
% 38.65/5.96 | (23) ? [v0: int] : ? [v1: any] : ( ~ (v0 = 0) & sdtlseqdt0(xk, xp) = v1 &
% 38.65/5.96 | sdtlseqdt0(xp, xk) = v0 & ( ~ (v1 = 0) | xk = xp))
% 38.65/5.96 |
% 38.65/5.96 | ALPHA: (function-axioms) implies:
% 38.65/5.96 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 38.65/5.96 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 38.65/5.96 | v0))
% 38.65/5.96 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.65/5.96 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 38.65/5.96 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.65/5.96 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 38.65/5.96 | (27) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 38.65/5.96 | : ! [v3: $i] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~
% 38.65/5.96 | (sdtlseqdt0(v3, v2) = v0))
% 38.65/5.96 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 38.65/5.96 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~
% 38.65/5.96 | (doDivides0(v3, v2) = v0))
% 38.65/5.96 |
% 38.65/5.96 | DELTA: instantiating (12) with fresh symbol all_42_0 gives:
% 38.65/5.96 | (29) sdtsldt0(all_42_0, xp) = xk & sdtasdt0(xn, xm) = all_42_0 &
% 38.65/5.96 | $i(all_42_0)
% 38.65/5.96 |
% 38.65/5.96 | ALPHA: (29) implies:
% 38.65/5.96 | (30) sdtasdt0(xn, xm) = all_42_0
% 38.65/5.96 | (31) sdtsldt0(all_42_0, xp) = xk
% 38.65/5.96 |
% 38.65/5.96 | DELTA: instantiating (10) with fresh symbol all_44_0 gives:
% 38.65/5.96 | (32) isPrime0(xp) = 0 & doDivides0(xp, all_44_0) = 0 & sdtasdt0(xn, xm) =
% 38.65/5.96 | all_44_0 & $i(all_44_0)
% 38.65/5.96 |
% 38.65/5.96 | ALPHA: (32) implies:
% 38.65/5.96 | (33) $i(all_44_0)
% 38.65/5.96 | (34) sdtasdt0(xn, xm) = all_44_0
% 38.65/5.96 | (35) doDivides0(xp, all_44_0) = 0
% 38.65/5.96 | (36) isPrime0(xp) = 0
% 38.65/5.96 |
% 38.65/5.96 | DELTA: instantiating (20) with fresh symbol all_46_0 gives:
% 38.65/5.96 | (37) doDivides0(xr, all_46_0) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn,
% 38.65/5.96 | xm) = all_46_0 & $i(all_46_0)
% 38.65/5.96 |
% 38.65/5.96 | ALPHA: (37) implies:
% 38.65/5.97 | (38) sdtasdt0(xn, xm) = all_46_0
% 38.65/5.97 | (39) doDivides0(xr, all_46_0) = 0
% 38.65/5.97 |
% 38.65/5.97 | DELTA: instantiating (23) with fresh symbols all_48_0, all_48_1 gives:
% 38.65/5.97 | (40) ~ (all_48_1 = 0) & sdtlseqdt0(xk, xp) = all_48_0 & sdtlseqdt0(xp, xk)
% 38.65/5.97 | = all_48_1 & ( ~ (all_48_0 = 0) | xk = xp)
% 38.65/5.97 |
% 38.65/5.97 | ALPHA: (40) implies:
% 38.65/5.97 | (41) ~ (all_48_1 = 0)
% 38.65/5.97 | (42) sdtlseqdt0(xp, xk) = all_48_1
% 38.65/5.97 | (43) sdtlseqdt0(xk, xp) = all_48_0
% 38.65/5.97 | (44) ~ (all_48_0 = 0) | xk = xp
% 38.65/5.97 |
% 38.65/5.97 | DELTA: instantiating (9) with fresh symbols all_50_0, all_50_1 gives:
% 38.65/5.97 | (45) sdtpldt0(all_50_1, xp) = all_50_0 & sdtpldt0(xn, xm) = all_50_1 &
% 38.65/5.97 | $i(all_50_0) & $i(all_50_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 38.65/5.97 | : ! [v3: $i] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) =
% 38.65/5.97 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 38.65/5.97 | any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] :
% 38.65/5.97 | ? [v10: any] : ? [v11: any] : ? [v12: any] : (isPrime0(v2) = v7 &
% 38.65/5.97 | doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9,
% 38.65/5.97 | all_50_0) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8
% 38.65/5.97 | & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 &
% 38.65/5.97 | aNaturalNumber0(v0) = v4 & $i(v9) & $i(v8) & ( ~ (v10 = 0) | ~
% 38.65/5.97 | (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 |
% 38.65/5.97 | v11 = 0)))
% 38.65/5.97 |
% 38.65/5.97 | ALPHA: (45) implies:
% 38.65/5.97 | (46) $i(all_50_1)
% 38.65/5.97 | (47) sdtpldt0(xn, xm) = all_50_1
% 38.65/5.97 | (48) sdtpldt0(all_50_1, xp) = all_50_0
% 38.65/5.97 | (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 38.65/5.97 | (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) |
% 38.65/5.97 | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 38.65/5.97 | ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: any] : ? [v11:
% 38.65/5.97 | any] : ? [v12: any] : (isPrime0(v2) = v7 & doDivides0(v2, v1) =
% 38.65/5.97 | v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_50_0) = v10 &
% 38.65/5.97 | sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 &
% 38.65/5.97 | aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 &
% 38.65/5.97 | aNaturalNumber0(v0) = v4 & $i(v9) & $i(v8) & ( ~ (v10 = 0) | ~
% 38.65/5.97 | (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 |
% 38.65/5.97 | v11 = 0)))
% 38.65/5.97 |
% 38.65/5.97 | GROUND_INST: instantiating (26) with all_44_0, all_46_0, xm, xn, simplifying
% 38.65/5.97 | with (34), (38) gives:
% 38.65/5.97 | (50) all_46_0 = all_44_0
% 38.65/5.97 |
% 38.65/5.97 | GROUND_INST: instantiating (26) with all_42_0, all_46_0, xm, xn, simplifying
% 38.65/5.97 | with (30), (38) gives:
% 38.65/5.97 | (51) all_46_0 = all_42_0
% 38.65/5.97 |
% 38.65/5.97 | COMBINE_EQS: (50), (51) imply:
% 38.65/5.97 | (52) all_44_0 = all_42_0
% 38.65/5.97 |
% 38.65/5.97 | SIMP: (52) implies:
% 38.65/5.97 | (53) all_44_0 = all_42_0
% 38.65/5.97 |
% 38.65/5.97 | REDUCE: (39), (51) imply:
% 38.65/5.97 | (54) doDivides0(xr, all_42_0) = 0
% 38.65/5.97 |
% 38.65/5.97 | REDUCE: (35), (53) imply:
% 38.65/5.97 | (55) doDivides0(xp, all_42_0) = 0
% 38.65/5.97 |
% 38.65/5.97 | REDUCE: (33), (53) imply:
% 38.65/5.97 | (56) $i(all_42_0)
% 38.65/5.97 |
% 38.65/5.97 | GROUND_INST: instantiating (1) with xp, simplifying with (8), (21) gives:
% 38.65/5.98 | (57) xp = sz00 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 38.65/5.98 | (v1 = v0 | ~ (sdtasdt0(xp, v1) = v3) | ~ (sdtasdt0(xp, v0) = v2) |
% 38.65/5.98 | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] :
% 38.65/5.98 | ? [v7: $i] : (sdtasdt0(v1, xp) = v7 & sdtasdt0(v0, xp) = v6 &
% 38.65/5.98 | aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & $i(v7) &
% 38.65/5.98 | $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ( ~ (v7 = v6) & ~ (v3 =
% 38.65/5.98 | v2)))))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (5) with xr, simplifying with (14), (19) gives:
% 38.65/5.98 | (58) xr = sz10 | xr = sz00 | ? [v0: $i] : (isPrime0(v0) = 0 &
% 38.65/5.98 | doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0 & $i(v0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_50_1, simplifying with
% 38.65/5.98 | (17), (18), (47) gives:
% 38.65/5.98 | (59) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xm, xn) = v2 &
% 38.65/5.98 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 38.65/5.98 | (v1 = 0) | ~ (v0 = 0) | v2 = all_50_1))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_50_1, simplifying with
% 38.65/5.98 | (17), (18), (47) gives:
% 38.65/5.98 | (60) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/5.98 | (aNaturalNumber0(all_50_1) = v2 & aNaturalNumber0(xm) = v1 &
% 38.65/5.98 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xp, all_50_1, all_50_0,
% 38.65/5.98 | simplifying with (17), (18), (21), (47), (48) gives:
% 38.65/5.98 | (61) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 38.65/5.98 | : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp)
% 38.65/5.98 | = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4)
% 38.65/5.98 | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 38.65/5.98 | all_50_0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mAddComm) with all_50_1, xp, all_50_0, simplifying
% 38.65/5.98 | with (21), (46), (48) gives:
% 38.65/5.98 | (62) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xp, all_50_1) =
% 38.65/5.98 | v2 & aNaturalNumber0(all_50_1) = v0 & aNaturalNumber0(xp) = v1 &
% 38.65/5.98 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_50_0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mSortsB) with all_50_1, xp, all_50_0, simplifying
% 38.65/5.98 | with (21), (46), (48) gives:
% 38.65/5.98 | (63) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/5.98 | (aNaturalNumber0(all_50_0) = v2 & aNaturalNumber0(all_50_1) = v0 &
% 38.65/5.98 | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_42_0, simplifying with
% 38.65/5.98 | (17), (18), (30) gives:
% 38.65/5.98 | (64) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 &
% 38.65/5.98 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 38.65/5.98 | (v1 = 0) | ~ (v0 = 0) | v2 = all_42_0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_42_0, simplifying
% 38.65/5.98 | with (17), (18), (30) gives:
% 38.65/5.98 | (65) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/5.98 | (aNaturalNumber0(all_42_0) = v2 & aNaturalNumber0(xm) = v1 &
% 38.65/5.98 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mDefLE) with xm, xp, 0, simplifying with (11),
% 38.65/5.98 | (18), (21) gives:
% 38.65/5.98 | (66) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xp) = v1 &
% 38.65/5.98 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 38.65/5.98 | $i] : (sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0) = 0 & $i(v0))
% 38.65/5.98 |
% 38.65/5.98 | GROUND_INST: instantiating (mLETotal) with xp, xk, all_48_1, simplifying with
% 38.65/5.98 | (21), (22), (42) gives:
% 38.65/5.99 | (67) all_48_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/5.99 | (sdtlseqdt0(xk, xp) = v2 & aNaturalNumber0(xk) = v1 &
% 38.65/5.99 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~
% 38.65/5.99 | (xk = xp))))
% 38.65/5.99 |
% 38.65/5.99 | GROUND_INST: instantiating (49) with xn, xm, xp, all_42_0, simplifying with
% 38.65/5.99 | (17), (18), (21), (30), (55) gives:
% 38.65/5.99 | (68) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 38.65/5.99 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 38.65/5.99 | (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7
% 38.65/5.99 | & iLess0(v5, all_50_0) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn,
% 38.65/5.99 | xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 &
% 38.65/5.99 | aNaturalNumber0(xn) = v0 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | ~ (v3 =
% 38.65/5.99 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 38.65/5.99 |
% 38.65/5.99 | GROUND_INST: instantiating (mDefDiv) with xp, all_42_0, 0, simplifying with
% 38.65/5.99 | (21), (55), (56) gives:
% 38.65/5.99 | (69) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_42_0) = v1 &
% 38.65/5.99 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 38.65/5.99 | $i] : (sdtasdt0(xp, v0) = all_42_0 & aNaturalNumber0(v0) = 0 &
% 38.65/5.99 | $i(v0))
% 38.65/5.99 |
% 38.65/5.99 | GROUND_INST: instantiating (3) with xr, xk, simplifying with (15), (19), (22)
% 38.65/5.99 | gives:
% 38.65/5.99 | (70) xk = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/5.99 | (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 &
% 38.65/5.99 | aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.65/5.99 |
% 38.65/5.99 | GROUND_INST: instantiating (49) with xn, xm, xr, all_42_0, simplifying with
% 38.65/5.99 | (17), (18), (19), (30), (54) gives:
% 38.65/5.99 | (71) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 38.65/5.99 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 38.65/5.99 | (isPrime0(xr) = v3 & doDivides0(xr, xm) = v8 & doDivides0(xr, xn) = v7
% 38.65/5.99 | & iLess0(v5, all_50_0) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xn,
% 38.65/5.99 | xm) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 &
% 38.65/5.99 | aNaturalNumber0(xn) = v0 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | ~ (v3 =
% 38.65/5.99 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 38.65/5.99 |
% 38.65/5.99 | GROUND_INST: instantiating (2) with xp, all_42_0, xk, simplifying with (21),
% 38.65/5.99 | (31), (56) gives:
% 38.65/5.99 | (72) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/5.99 | (doDivides0(xp, all_42_0) = v2 & aNaturalNumber0(all_42_0) = v1 &
% 38.65/5.99 | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 38.65/5.99 | 0))) | ( ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 38.65/5.99 | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 38.65/5.99 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xp, xk)
% 38.65/5.99 | = v0) | ~ $i(xk) | (v0 = all_42_0 & aNaturalNumber0(xk) = 0)))
% 38.65/5.99 |
% 38.65/5.99 | GROUND_INST: instantiating (4) with xp, 0, simplifying with (21), (36) gives:
% 38.65/5.99 | (73) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | ( ~ (xp =
% 38.65/5.99 | sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 38.65/5.99 | (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 38.65/5.99 | & aNaturalNumber0(v0) = v1)))
% 38.65/5.99 |
% 38.65/5.99 | GROUND_INST: instantiating (4) with xr, 0, simplifying with (16), (19) gives:
% 38.65/5.99 | (74) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0) | ( ~ (xr =
% 38.65/5.99 | sz10) & ~ (xr = sz00) & ! [v0: $i] : (v0 = xr | v0 = sz10 | ~
% 38.65/5.99 | (doDivides0(v0, xr) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 38.65/5.99 | & aNaturalNumber0(v0) = v1)))
% 38.65/5.99 |
% 38.65/5.99 | DELTA: instantiating (65) with fresh symbols all_62_0, all_62_1, all_62_2
% 38.65/5.99 | gives:
% 38.65/5.99 | (75) aNaturalNumber0(all_42_0) = all_62_0 & aNaturalNumber0(xm) = all_62_1
% 38.65/5.99 | & aNaturalNumber0(xn) = all_62_2 & ( ~ (all_62_1 = 0) | ~ (all_62_2 =
% 38.65/5.99 | 0) | all_62_0 = 0)
% 38.65/5.99 |
% 38.65/5.99 | ALPHA: (75) implies:
% 38.65/5.99 | (76) aNaturalNumber0(xn) = all_62_2
% 38.65/5.99 | (77) aNaturalNumber0(xm) = all_62_1
% 38.65/5.99 | (78) aNaturalNumber0(all_42_0) = all_62_0
% 38.65/5.99 | (79) ~ (all_62_1 = 0) | ~ (all_62_2 = 0) | all_62_0 = 0
% 38.65/5.99 |
% 38.65/5.99 | DELTA: instantiating (63) with fresh symbols all_64_0, all_64_1, all_64_2
% 38.65/5.99 | gives:
% 38.65/5.99 | (80) aNaturalNumber0(all_50_0) = all_64_0 & aNaturalNumber0(all_50_1) =
% 38.65/5.99 | all_64_2 & aNaturalNumber0(xp) = all_64_1 & ( ~ (all_64_1 = 0) | ~
% 38.65/5.99 | (all_64_2 = 0) | all_64_0 = 0)
% 38.65/5.99 |
% 38.65/5.99 | ALPHA: (80) implies:
% 38.65/5.99 | (81) aNaturalNumber0(xp) = all_64_1
% 38.65/5.99 | (82) aNaturalNumber0(all_50_1) = all_64_2
% 38.65/5.99 | (83) ~ (all_64_1 = 0) | ~ (all_64_2 = 0) | all_64_0 = 0
% 38.65/5.99 |
% 38.65/5.99 | DELTA: instantiating (60) with fresh symbols all_66_0, all_66_1, all_66_2
% 38.65/5.99 | gives:
% 38.65/6.00 | (84) aNaturalNumber0(all_50_1) = all_66_0 & aNaturalNumber0(xm) = all_66_1
% 38.65/6.00 | & aNaturalNumber0(xn) = all_66_2 & ( ~ (all_66_1 = 0) | ~ (all_66_2 =
% 38.65/6.00 | 0) | all_66_0 = 0)
% 38.65/6.00 |
% 38.65/6.00 | ALPHA: (84) implies:
% 38.65/6.00 | (85) aNaturalNumber0(xn) = all_66_2
% 38.65/6.00 | (86) aNaturalNumber0(xm) = all_66_1
% 38.65/6.00 | (87) aNaturalNumber0(all_50_1) = all_66_0
% 38.65/6.00 | (88) ~ (all_66_1 = 0) | ~ (all_66_2 = 0) | all_66_0 = 0
% 38.65/6.00 |
% 38.65/6.00 | DELTA: instantiating (62) with fresh symbols all_68_0, all_68_1, all_68_2
% 38.65/6.00 | gives:
% 38.65/6.00 | (89) sdtpldt0(xp, all_50_1) = all_68_0 & aNaturalNumber0(all_50_1) =
% 38.65/6.00 | all_68_2 & aNaturalNumber0(xp) = all_68_1 & $i(all_68_0) & ( ~
% 38.65/6.00 | (all_68_1 = 0) | ~ (all_68_2 = 0) | all_68_0 = all_50_0)
% 38.65/6.00 |
% 38.65/6.00 | ALPHA: (89) implies:
% 38.65/6.00 | (90) aNaturalNumber0(xp) = all_68_1
% 38.65/6.00 | (91) aNaturalNumber0(all_50_1) = all_68_2
% 38.65/6.00 | (92) sdtpldt0(xp, all_50_1) = all_68_0
% 38.65/6.00 | (93) ~ (all_68_1 = 0) | ~ (all_68_2 = 0) | all_68_0 = all_50_0
% 38.65/6.00 |
% 38.65/6.00 | DELTA: instantiating (64) with fresh symbols all_70_0, all_70_1, all_70_2
% 38.65/6.00 | gives:
% 38.65/6.00 | (94) sdtasdt0(xm, xn) = all_70_0 & aNaturalNumber0(xm) = all_70_1 &
% 38.65/6.00 | aNaturalNumber0(xn) = all_70_2 & $i(all_70_0) & ( ~ (all_70_1 = 0) |
% 38.65/6.00 | ~ (all_70_2 = 0) | all_70_0 = all_42_0)
% 38.65/6.00 |
% 38.65/6.00 | ALPHA: (94) implies:
% 38.65/6.00 | (95) aNaturalNumber0(xn) = all_70_2
% 38.65/6.00 | (96) aNaturalNumber0(xm) = all_70_1
% 38.65/6.00 |
% 38.65/6.00 | DELTA: instantiating (59) with fresh symbols all_72_0, all_72_1, all_72_2
% 38.65/6.00 | gives:
% 38.65/6.00 | (97) sdtpldt0(xm, xn) = all_72_0 & aNaturalNumber0(xm) = all_72_1 &
% 38.65/6.00 | aNaturalNumber0(xn) = all_72_2 & $i(all_72_0) & ( ~ (all_72_1 = 0) |
% 38.65/6.00 | ~ (all_72_2 = 0) | all_72_0 = all_50_1)
% 38.65/6.00 |
% 38.65/6.00 | ALPHA: (97) implies:
% 38.65/6.00 | (98) aNaturalNumber0(xn) = all_72_2
% 38.65/6.00 | (99) aNaturalNumber0(xm) = all_72_1
% 38.65/6.00 |
% 38.65/6.00 | DELTA: instantiating (61) with fresh symbols all_74_0, all_74_1, all_74_2,
% 38.65/6.00 | all_74_3, all_74_4 gives:
% 38.65/6.00 | (100) sdtpldt0(xm, xp) = all_74_1 & sdtpldt0(xn, all_74_1) = all_74_0 &
% 38.65/6.00 | aNaturalNumber0(xp) = all_74_2 & aNaturalNumber0(xm) = all_74_3 &
% 38.65/6.00 | aNaturalNumber0(xn) = all_74_4 & $i(all_74_0) & $i(all_74_1) & ( ~
% 38.65/6.00 | (all_74_2 = 0) | ~ (all_74_3 = 0) | ~ (all_74_4 = 0) | all_74_0 =
% 38.65/6.00 | all_50_0)
% 38.65/6.00 |
% 38.65/6.00 | ALPHA: (100) implies:
% 38.65/6.00 | (101) aNaturalNumber0(xn) = all_74_4
% 38.65/6.00 | (102) aNaturalNumber0(xm) = all_74_3
% 38.65/6.00 | (103) aNaturalNumber0(xp) = all_74_2
% 38.65/6.00 |
% 38.65/6.00 | DELTA: instantiating (71) with fresh symbols all_76_0, all_76_1, all_76_2,
% 38.65/6.00 | all_76_3, all_76_4, all_76_5, all_76_6, all_76_7, all_76_8 gives:
% 38.65/6.00 | (104) isPrime0(xr) = all_76_5 & doDivides0(xr, xm) = all_76_0 &
% 38.65/6.00 | doDivides0(xr, xn) = all_76_1 & iLess0(all_76_3, all_50_0) = all_76_2
% 38.65/6.00 | & sdtpldt0(all_76_4, xr) = all_76_3 & sdtpldt0(xn, xm) = all_76_4 &
% 38.65/6.00 | aNaturalNumber0(xr) = all_76_6 & aNaturalNumber0(xm) = all_76_7 &
% 38.65/6.00 | aNaturalNumber0(xn) = all_76_8 & $i(all_76_3) & $i(all_76_4) & ( ~
% 38.65/6.00 | (all_76_2 = 0) | ~ (all_76_5 = 0) | ~ (all_76_6 = 0) | ~
% 38.65/6.00 | (all_76_7 = 0) | ~ (all_76_8 = 0) | all_76_0 = 0 | all_76_1 = 0)
% 38.65/6.00 |
% 38.65/6.00 | ALPHA: (104) implies:
% 38.65/6.00 | (105) $i(all_76_4)
% 38.65/6.00 | (106) aNaturalNumber0(xn) = all_76_8
% 38.65/6.00 | (107) aNaturalNumber0(xm) = all_76_7
% 38.65/6.00 | (108) aNaturalNumber0(xr) = all_76_6
% 38.65/6.00 | (109) sdtpldt0(xn, xm) = all_76_4
% 38.65/6.00 |
% 38.65/6.00 | DELTA: instantiating (68) with fresh symbols all_78_0, all_78_1, all_78_2,
% 38.65/6.00 | all_78_3, all_78_4, all_78_5, all_78_6, all_78_7, all_78_8 gives:
% 38.65/6.00 | (110) isPrime0(xp) = all_78_5 & doDivides0(xp, xm) = all_78_0 &
% 38.65/6.00 | doDivides0(xp, xn) = all_78_1 & iLess0(all_78_3, all_50_0) = all_78_2
% 38.65/6.00 | & sdtpldt0(all_78_4, xp) = all_78_3 & sdtpldt0(xn, xm) = all_78_4 &
% 38.65/6.00 | aNaturalNumber0(xp) = all_78_6 & aNaturalNumber0(xm) = all_78_7 &
% 38.65/6.00 | aNaturalNumber0(xn) = all_78_8 & $i(all_78_3) & $i(all_78_4) & ( ~
% 38.65/6.00 | (all_78_2 = 0) | ~ (all_78_5 = 0) | ~ (all_78_6 = 0) | ~
% 38.65/6.00 | (all_78_7 = 0) | ~ (all_78_8 = 0) | all_78_0 = 0 | all_78_1 = 0)
% 38.65/6.00 |
% 38.65/6.00 | ALPHA: (110) implies:
% 38.65/6.00 | (111) aNaturalNumber0(xn) = all_78_8
% 38.65/6.00 | (112) aNaturalNumber0(xm) = all_78_7
% 38.65/6.00 | (113) aNaturalNumber0(xp) = all_78_6
% 38.65/6.00 | (114) sdtpldt0(xn, xm) = all_78_4
% 38.65/6.00 |
% 38.65/6.00 | BETA: splitting (70) gives:
% 38.65/6.00 |
% 38.65/6.00 | Case 1:
% 38.65/6.00 | |
% 38.65/6.00 | | (115) xk = sz00
% 38.65/6.00 | |
% 38.65/6.00 | | REDUCE: (13), (115) imply:
% 38.65/6.00 | | (116) $false
% 38.65/6.00 | |
% 38.65/6.00 | | CLOSE: (116) is inconsistent.
% 38.65/6.00 | |
% 38.65/6.00 | Case 2:
% 38.65/6.00 | |
% 38.65/6.00 | | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xr, xk) =
% 38.65/6.00 | | v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~
% 38.65/6.00 | | (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 38.65/6.00 | |
% 38.65/6.00 | | DELTA: instantiating (117) with fresh symbols all_88_0, all_88_1, all_88_2
% 38.65/6.00 | | gives:
% 38.65/6.01 | | (118) sdtlseqdt0(xr, xk) = all_88_0 & aNaturalNumber0(xr) = all_88_2 &
% 38.65/6.01 | | aNaturalNumber0(xk) = all_88_1 & ( ~ (all_88_1 = 0) | ~ (all_88_2
% 38.65/6.01 | | = 0) | all_88_0 = 0)
% 38.65/6.01 | |
% 38.65/6.01 | | ALPHA: (118) implies:
% 38.65/6.01 | | (119) aNaturalNumber0(xk) = all_88_1
% 38.65/6.01 | | (120) aNaturalNumber0(xr) = all_88_2
% 38.65/6.01 | |
% 38.65/6.01 | | BETA: splitting (67) gives:
% 38.65/6.01 | |
% 38.65/6.01 | | Case 1:
% 38.65/6.01 | | |
% 38.65/6.01 | | | (121) all_48_1 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | REDUCE: (41), (121) imply:
% 38.65/6.01 | | | (122) $false
% 38.65/6.01 | | |
% 38.65/6.01 | | | CLOSE: (122) is inconsistent.
% 38.65/6.01 | | |
% 38.65/6.01 | | Case 2:
% 38.65/6.01 | | |
% 38.65/6.01 | | | (123) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xk, xp)
% 38.65/6.01 | | | = v2 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xp) = v0 & (
% 38.65/6.01 | | | ~ (v1 = 0) | ~ (v0 = 0) | (v2 = 0 & ~ (xk = xp))))
% 38.65/6.01 | | |
% 38.65/6.01 | | | DELTA: instantiating (123) with fresh symbols all_93_0, all_93_1, all_93_2
% 38.65/6.01 | | | gives:
% 38.65/6.01 | | | (124) sdtlseqdt0(xk, xp) = all_93_0 & aNaturalNumber0(xk) = all_93_1 &
% 38.65/6.01 | | | aNaturalNumber0(xp) = all_93_2 & ( ~ (all_93_1 = 0) | ~
% 38.65/6.01 | | | (all_93_2 = 0) | (all_93_0 = 0 & ~ (xk = xp)))
% 38.65/6.01 | | |
% 38.65/6.01 | | | ALPHA: (124) implies:
% 38.65/6.01 | | | (125) aNaturalNumber0(xp) = all_93_2
% 38.65/6.01 | | | (126) aNaturalNumber0(xk) = all_93_1
% 38.65/6.01 | | | (127) sdtlseqdt0(xk, xp) = all_93_0
% 38.65/6.01 | | | (128) ~ (all_93_1 = 0) | ~ (all_93_2 = 0) | (all_93_0 = 0 & ~ (xk =
% 38.65/6.01 | | | xp))
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_62_2, all_66_2, xn, simplifying
% 38.65/6.01 | | | with (76), (85) gives:
% 38.65/6.01 | | | (129) all_66_2 = all_62_2
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_72_2, all_74_4, xn, simplifying
% 38.65/6.01 | | | with (98), (101) gives:
% 38.65/6.01 | | | (130) all_74_4 = all_72_2
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_70_2, all_74_4, xn, simplifying
% 38.65/6.01 | | | with (95), (101) gives:
% 38.65/6.01 | | | (131) all_74_4 = all_70_2
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_66_2, all_74_4, xn, simplifying
% 38.65/6.01 | | | with (85), (101) gives:
% 38.65/6.01 | | | (132) all_74_4 = all_66_2
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with 0, all_78_8, xn, simplifying with
% 38.65/6.01 | | | (6), (111) gives:
% 38.65/6.01 | | | (133) all_78_8 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_76_8, all_78_8, xn, simplifying
% 38.65/6.01 | | | with (106), (111) gives:
% 38.65/6.01 | | | (134) all_78_8 = all_76_8
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_72_2, all_78_8, xn, simplifying
% 38.65/6.01 | | | with (98), (111) gives:
% 38.65/6.01 | | | (135) all_78_8 = all_72_2
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_66_1, all_72_1, xm, simplifying
% 38.65/6.01 | | | with (86), (99) gives:
% 38.65/6.01 | | | (136) all_72_1 = all_66_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_70_1, all_74_3, xm, simplifying
% 38.65/6.01 | | | with (96), (102) gives:
% 38.65/6.01 | | | (137) all_74_3 = all_70_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_66_1, all_74_3, xm, simplifying
% 38.65/6.01 | | | with (86), (102) gives:
% 38.65/6.01 | | | (138) all_74_3 = all_66_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_62_1, all_74_3, xm, simplifying
% 38.65/6.01 | | | with (77), (102) gives:
% 38.65/6.01 | | | (139) all_74_3 = all_62_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_72_1, all_76_7, xm, simplifying
% 38.65/6.01 | | | with (99), (107) gives:
% 38.65/6.01 | | | (140) all_76_7 = all_72_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with 0, all_78_7, xm, simplifying with
% 38.65/6.01 | | | (7), (112) gives:
% 38.65/6.01 | | | (141) all_78_7 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_76_7, all_78_7, xm, simplifying
% 38.65/6.01 | | | with (107), (112) gives:
% 38.65/6.01 | | | (142) all_78_7 = all_76_7
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_64_1, all_68_1, xp, simplifying
% 38.65/6.01 | | | with (81), (90) gives:
% 38.65/6.01 | | | (143) all_68_1 = all_64_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_74_2, all_78_6, xp, simplifying
% 38.65/6.01 | | | with (103), (113) gives:
% 38.65/6.01 | | | (144) all_78_6 = all_74_2
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_68_1, all_78_6, xp, simplifying
% 38.65/6.01 | | | with (90), (113) gives:
% 38.65/6.01 | | | (145) all_78_6 = all_68_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with 0, all_93_2, xp, simplifying with
% 38.65/6.01 | | | (8), (125) gives:
% 38.65/6.01 | | | (146) all_93_2 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_78_6, all_93_2, xp, simplifying
% 38.65/6.01 | | | with (113), (125) gives:
% 38.65/6.01 | | | (147) all_93_2 = all_78_6
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_88_1, all_93_1, xk, simplifying
% 38.65/6.01 | | | with (119), (126) gives:
% 38.65/6.01 | | | (148) all_93_1 = all_88_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with 0, all_88_2, xr, simplifying with
% 38.65/6.01 | | | (14), (120) gives:
% 38.65/6.01 | | | (149) all_88_2 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_76_6, all_88_2, xr, simplifying
% 38.65/6.01 | | | with (108), (120) gives:
% 38.65/6.01 | | | (150) all_88_2 = all_76_6
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_66_0, all_68_2, all_50_1,
% 38.65/6.01 | | | simplifying with (87), (91) gives:
% 38.65/6.01 | | | (151) all_68_2 = all_66_0
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (24) with all_64_2, all_68_2, all_50_1,
% 38.65/6.01 | | | simplifying with (82), (91) gives:
% 38.65/6.01 | | | (152) all_68_2 = all_64_2
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (25) with all_50_1, all_78_4, xm, xn,
% 38.65/6.01 | | | simplifying with (47), (114) gives:
% 38.65/6.01 | | | (153) all_78_4 = all_50_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (25) with all_76_4, all_78_4, xm, xn,
% 38.65/6.01 | | | simplifying with (109), (114) gives:
% 38.65/6.01 | | | (154) all_78_4 = all_76_4
% 38.65/6.01 | | |
% 38.65/6.01 | | | GROUND_INST: instantiating (27) with all_48_0, all_93_0, xp, xk,
% 38.65/6.01 | | | simplifying with (43), (127) gives:
% 38.65/6.01 | | | (155) all_93_0 = all_48_0
% 38.65/6.01 | | |
% 38.65/6.01 | | | COMBINE_EQS: (146), (147) imply:
% 38.65/6.01 | | | (156) all_78_6 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | SIMP: (156) implies:
% 38.65/6.01 | | | (157) all_78_6 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | COMBINE_EQS: (149), (150) imply:
% 38.65/6.01 | | | (158) all_76_6 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | COMBINE_EQS: (153), (154) imply:
% 38.65/6.01 | | | (159) all_76_4 = all_50_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | SIMP: (159) implies:
% 38.65/6.01 | | | (160) all_76_4 = all_50_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | COMBINE_EQS: (144), (145) imply:
% 38.65/6.01 | | | (161) all_74_2 = all_68_1
% 38.65/6.01 | | |
% 38.65/6.01 | | | COMBINE_EQS: (144), (157) imply:
% 38.65/6.01 | | | (162) all_74_2 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | COMBINE_EQS: (141), (142) imply:
% 38.65/6.01 | | | (163) all_76_7 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | SIMP: (163) implies:
% 38.65/6.01 | | | (164) all_76_7 = 0
% 38.65/6.01 | | |
% 38.65/6.01 | | | COMBINE_EQS: (133), (134) imply:
% 38.65/6.01 | | | (165) all_76_8 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (134), (135) imply:
% 38.65/6.02 | | | (166) all_76_8 = all_72_2
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (140), (164) imply:
% 38.65/6.02 | | | (167) all_72_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (167) implies:
% 38.65/6.02 | | | (168) all_72_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (165), (166) imply:
% 38.65/6.02 | | | (169) all_72_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (169) implies:
% 38.65/6.02 | | | (170) all_72_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (161), (162) imply:
% 38.65/6.02 | | | (171) all_68_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (171) implies:
% 38.65/6.02 | | | (172) all_68_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (137), (139) imply:
% 38.65/6.02 | | | (173) all_70_1 = all_62_1
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (137), (138) imply:
% 38.65/6.02 | | | (174) all_70_1 = all_66_1
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (130), (131) imply:
% 38.65/6.02 | | | (175) all_72_2 = all_70_2
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (175) implies:
% 38.65/6.02 | | | (176) all_72_2 = all_70_2
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (131), (132) imply:
% 38.65/6.02 | | | (177) all_70_2 = all_66_2
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (136), (168) imply:
% 38.65/6.02 | | | (178) all_66_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (178) implies:
% 38.65/6.02 | | | (179) all_66_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (170), (176) imply:
% 38.65/6.02 | | | (180) all_70_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (180) implies:
% 38.65/6.02 | | | (181) all_70_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (173), (174) imply:
% 38.65/6.02 | | | (182) all_66_1 = all_62_1
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (182) implies:
% 38.65/6.02 | | | (183) all_66_1 = all_62_1
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (177), (181) imply:
% 38.65/6.02 | | | (184) all_66_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (184) implies:
% 38.65/6.02 | | | (185) all_66_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (143), (172) imply:
% 38.65/6.02 | | | (186) all_64_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (151), (152) imply:
% 38.65/6.02 | | | (187) all_66_0 = all_64_2
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (179), (183) imply:
% 38.65/6.02 | | | (188) all_62_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (188) implies:
% 38.65/6.02 | | | (189) all_62_1 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | COMBINE_EQS: (129), (185) imply:
% 38.65/6.02 | | | (190) all_62_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | SIMP: (190) implies:
% 38.65/6.02 | | | (191) all_62_2 = 0
% 38.65/6.02 | | |
% 38.65/6.02 | | | BETA: splitting (73) gives:
% 38.65/6.02 | | |
% 38.65/6.02 | | | Case 1:
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | (192) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0)
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | DELTA: instantiating (192) with fresh symbol all_133_0 gives:
% 38.65/6.02 | | | | (193) ~ (all_133_0 = 0) & aNaturalNumber0(xp) = all_133_0
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | ALPHA: (193) implies:
% 38.65/6.02 | | | | (194) ~ (all_133_0 = 0)
% 38.65/6.02 | | | | (195) aNaturalNumber0(xp) = all_133_0
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | GROUND_INST: instantiating (24) with 0, all_133_0, xp, simplifying with
% 38.65/6.02 | | | | (8), (195) gives:
% 38.65/6.02 | | | | (196) all_133_0 = 0
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | REDUCE: (194), (196) imply:
% 38.65/6.02 | | | | (197) $false
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | CLOSE: (197) is inconsistent.
% 38.65/6.02 | | | |
% 38.65/6.02 | | | Case 2:
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | (198) ~ (xp = sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 =
% 38.65/6.02 | | | | sz10 | ~ (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int]
% 38.65/6.02 | | | | : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | ALPHA: (198) implies:
% 38.65/6.02 | | | | (199) ~ (xp = sz00)
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | BETA: splitting (74) gives:
% 38.65/6.02 | | | |
% 38.65/6.02 | | | | Case 1:
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | | (200) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xr) = v0)
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | | BETA: splitting (57) gives:
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | | Case 1:
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | (201) xp = sz00
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | REDUCE: (199), (201) imply:
% 38.65/6.02 | | | | | | (202) $false
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | CLOSE: (202) is inconsistent.
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | Case 2:
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | DELTA: instantiating (200) with fresh symbol all_142_0 gives:
% 38.65/6.02 | | | | | | (203) ~ (all_142_0 = 0) & aNaturalNumber0(xr) = all_142_0
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | ALPHA: (203) implies:
% 38.65/6.02 | | | | | | (204) ~ (all_142_0 = 0)
% 38.65/6.02 | | | | | | (205) aNaturalNumber0(xr) = all_142_0
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | GROUND_INST: instantiating (24) with 0, all_142_0, xr, simplifying
% 38.65/6.02 | | | | | | with (14), (205) gives:
% 38.65/6.02 | | | | | | (206) all_142_0 = 0
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | REDUCE: (204), (206) imply:
% 38.65/6.02 | | | | | | (207) $false
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | CLOSE: (207) is inconsistent.
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | End of split
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | Case 2:
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | | (208) ~ (xr = sz10) & ~ (xr = sz00) & ! [v0: $i] : (v0 = xr | v0
% 38.65/6.02 | | | | | = sz10 | ~ (doDivides0(v0, xr) = 0) | ~ $i(v0) | ? [v1:
% 38.65/6.02 | | | | | int] : ( ~ (v1 = 0) & aNaturalNumber0(v0) = v1))
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | | ALPHA: (208) implies:
% 38.65/6.02 | | | | | (209) ~ (xr = sz00)
% 38.65/6.02 | | | | | (210) ~ (xr = sz10)
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | | BETA: splitting (66) gives:
% 38.65/6.02 | | | | |
% 38.65/6.02 | | | | | Case 1:
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | (211) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xp) = v1 &
% 38.65/6.02 | | | | | | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | DELTA: instantiating (211) with fresh symbols all_147_0, all_147_1
% 38.65/6.02 | | | | | | gives:
% 38.65/6.02 | | | | | | (212) aNaturalNumber0(xp) = all_147_0 & aNaturalNumber0(xm) =
% 38.65/6.02 | | | | | | all_147_1 & ( ~ (all_147_0 = 0) | ~ (all_147_1 = 0))
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | ALPHA: (212) implies:
% 38.65/6.02 | | | | | | (213) aNaturalNumber0(xm) = all_147_1
% 38.65/6.02 | | | | | | (214) aNaturalNumber0(xp) = all_147_0
% 38.65/6.02 | | | | | | (215) ~ (all_147_0 = 0) | ~ (all_147_1 = 0)
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | GROUND_INST: instantiating (24) with 0, all_147_1, xm, simplifying
% 38.65/6.02 | | | | | | with (7), (213) gives:
% 38.65/6.02 | | | | | | (216) all_147_1 = 0
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | GROUND_INST: instantiating (24) with 0, all_147_0, xp, simplifying
% 38.65/6.02 | | | | | | with (8), (214) gives:
% 38.65/6.02 | | | | | | (217) all_147_0 = 0
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | BETA: splitting (215) gives:
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | Case 1:
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | | (218) ~ (all_147_0 = 0)
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | | REDUCE: (217), (218) imply:
% 38.65/6.02 | | | | | | | (219) $false
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | | CLOSE: (219) is inconsistent.
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | Case 2:
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | | (220) ~ (all_147_1 = 0)
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | | REDUCE: (216), (220) imply:
% 38.65/6.02 | | | | | | | (221) $false
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | | CLOSE: (221) is inconsistent.
% 38.65/6.02 | | | | | | |
% 38.65/6.02 | | | | | | End of split
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | Case 2:
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | (222) ? [v0: $i] : (sdtpldt0(xm, v0) = xp & aNaturalNumber0(v0)
% 38.65/6.02 | | | | | | = 0 & $i(v0))
% 38.65/6.02 | | | | | |
% 38.65/6.02 | | | | | | DELTA: instantiating (222) with fresh symbol all_147_0 gives:
% 38.65/6.02 | | | | | | (223) sdtpldt0(xm, all_147_0) = xp & aNaturalNumber0(all_147_0) =
% 38.65/6.03 | | | | | | 0 & $i(all_147_0)
% 38.65/6.03 | | | | | |
% 38.65/6.03 | | | | | | ALPHA: (223) implies:
% 38.65/6.03 | | | | | | (224) $i(all_147_0)
% 38.65/6.03 | | | | | | (225) aNaturalNumber0(all_147_0) = 0
% 38.65/6.03 | | | | | | (226) sdtpldt0(xm, all_147_0) = xp
% 38.65/6.03 | | | | | |
% 38.65/6.03 | | | | | | BETA: splitting (79) gives:
% 38.65/6.03 | | | | | |
% 38.65/6.03 | | | | | | Case 1:
% 38.65/6.03 | | | | | | |
% 38.65/6.03 | | | | | | | (227) ~ (all_62_1 = 0)
% 38.65/6.03 | | | | | | |
% 38.65/6.03 | | | | | | | REDUCE: (189), (227) imply:
% 38.65/6.03 | | | | | | | (228) $false
% 38.65/6.03 | | | | | | |
% 38.65/6.03 | | | | | | | CLOSE: (228) is inconsistent.
% 38.65/6.03 | | | | | | |
% 38.65/6.03 | | | | | | Case 2:
% 38.65/6.03 | | | | | | |
% 38.65/6.03 | | | | | | | (229) ~ (all_62_2 = 0) | all_62_0 = 0
% 38.65/6.03 | | | | | | |
% 38.65/6.03 | | | | | | | BETA: splitting (229) gives:
% 38.65/6.03 | | | | | | |
% 38.65/6.03 | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | | (230) ~ (all_62_2 = 0)
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | | REDUCE: (191), (230) imply:
% 38.65/6.03 | | | | | | | | (231) $false
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | | CLOSE: (231) is inconsistent.
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | | (232) all_62_0 = 0
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | | REDUCE: (78), (232) imply:
% 38.65/6.03 | | | | | | | | (233) aNaturalNumber0(all_42_0) = 0
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | | BETA: splitting (58) gives:
% 38.65/6.03 | | | | | | | |
% 38.65/6.03 | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | |
% 38.65/6.03 | | | | | | | | | (234) xr = sz00
% 38.65/6.03 | | | | | | | | |
% 38.65/6.03 | | | | | | | | | REDUCE: (209), (234) imply:
% 38.65/6.03 | | | | | | | | | (235) $false
% 38.65/6.03 | | | | | | | | |
% 38.65/6.03 | | | | | | | | | CLOSE: (235) is inconsistent.
% 38.65/6.03 | | | | | | | | |
% 38.65/6.03 | | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | | |
% 38.65/6.03 | | | | | | | | | (236) xr = sz10 | ? [v0: $i] : (isPrime0(v0) = 0 &
% 38.65/6.03 | | | | | | | | | doDivides0(v0, xr) = 0 & aNaturalNumber0(v0) = 0 &
% 38.65/6.03 | | | | | | | | | $i(v0))
% 38.65/6.03 | | | | | | | | |
% 38.65/6.03 | | | | | | | | | BETA: splitting (88) gives:
% 38.65/6.03 | | | | | | | | |
% 38.65/6.03 | | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | (237) ~ (all_66_1 = 0)
% 38.65/6.03 | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | REDUCE: (179), (237) imply:
% 38.65/6.03 | | | | | | | | | | (238) $false
% 38.65/6.03 | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | CLOSE: (238) is inconsistent.
% 38.65/6.03 | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | (239) ~ (all_66_2 = 0) | all_66_0 = 0
% 38.65/6.03 | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | BETA: splitting (69) gives:
% 38.65/6.03 | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | (240) ? [v0: any] : ? [v1: any] :
% 38.65/6.03 | | | | | | | | | | | (aNaturalNumber0(all_42_0) = v1 &
% 38.65/6.03 | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0
% 38.65/6.03 | | | | | | | | | | | = 0)))
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | DELTA: instantiating (240) with fresh symbols all_186_0,
% 38.65/6.03 | | | | | | | | | | | all_186_1 gives:
% 38.65/6.03 | | | | | | | | | | | (241) aNaturalNumber0(all_42_0) = all_186_0 &
% 38.65/6.03 | | | | | | | | | | | aNaturalNumber0(xp) = all_186_1 & ( ~ (all_186_0 =
% 38.65/6.03 | | | | | | | | | | | 0) | ~ (all_186_1 = 0))
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | ALPHA: (241) implies:
% 38.65/6.03 | | | | | | | | | | | (242) aNaturalNumber0(xp) = all_186_1
% 38.65/6.03 | | | | | | | | | | | (243) aNaturalNumber0(all_42_0) = all_186_0
% 38.65/6.03 | | | | | | | | | | | (244) ~ (all_186_0 = 0) | ~ (all_186_1 = 0)
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_186_1, xp,
% 38.65/6.03 | | | | | | | | | | | simplifying with (8), (242) gives:
% 38.65/6.03 | | | | | | | | | | | (245) all_186_1 = 0
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_186_0, all_42_0,
% 38.65/6.03 | | | | | | | | | | | simplifying with (233), (243) gives:
% 38.65/6.03 | | | | | | | | | | | (246) all_186_0 = 0
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | BETA: splitting (244) gives:
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | (247) ~ (all_186_0 = 0)
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | REDUCE: (246), (247) imply:
% 38.65/6.03 | | | | | | | | | | | | (248) $false
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | (249) ~ (all_186_1 = 0)
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | REDUCE: (245), (249) imply:
% 38.65/6.03 | | | | | | | | | | | | (250) $false
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | End of split
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | (251) ? [v0: $i] : (sdtasdt0(xp, v0) = all_42_0 &
% 38.65/6.03 | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0))
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | DELTA: instantiating (251) with fresh symbol all_186_0
% 38.65/6.03 | | | | | | | | | | | gives:
% 38.65/6.03 | | | | | | | | | | | (252) sdtasdt0(xp, all_186_0) = all_42_0 &
% 38.65/6.03 | | | | | | | | | | | aNaturalNumber0(all_186_0) = 0 & $i(all_186_0)
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | ALPHA: (252) implies:
% 38.65/6.03 | | | | | | | | | | | (253) $i(all_186_0)
% 38.65/6.03 | | | | | | | | | | | (254) aNaturalNumber0(all_186_0) = 0
% 38.65/6.03 | | | | | | | | | | | (255) sdtasdt0(xp, all_186_0) = all_42_0
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | BETA: splitting (72) gives:
% 38.65/6.03 | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | (256) xp = sz00
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | REDUCE: (199), (256) imply:
% 38.65/6.03 | | | | | | | | | | | | (257) $false
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | CLOSE: (257) is inconsistent.
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | (258) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/6.03 | | | | | | | | | | | | (doDivides0(xp, all_42_0) = v2 &
% 38.65/6.03 | | | | | | | | | | | | aNaturalNumber0(all_42_0) = v1 &
% 38.65/6.03 | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 38.65/6.03 | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 =
% 38.65/6.03 | | | | | | | | | | | | xk | ~ (sdtasdt0(xp, v0) = all_42_0) | ~
% 38.65/6.03 | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 38.65/6.03 | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : (
% 38.65/6.03 | | | | | | | | | | | | ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | (v0 =
% 38.65/6.03 | | | | | | | | | | | | all_42_0 & aNaturalNumber0(xk) = 0)))
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | BETA: splitting (239) gives:
% 38.65/6.03 | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | (259) ~ (all_66_2 = 0)
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | REDUCE: (185), (259) imply:
% 38.65/6.03 | | | | | | | | | | | | | (260) $false
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | CLOSE: (260) is inconsistent.
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | (261) all_66_0 = 0
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | COMBINE_EQS: (187), (261) imply:
% 38.65/6.03 | | | | | | | | | | | | | (262) all_64_2 = 0
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | SIMP: (262) implies:
% 38.65/6.03 | | | | | | | | | | | | | (263) all_64_2 = 0
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | COMBINE_EQS: (152), (263) imply:
% 38.65/6.03 | | | | | | | | | | | | | (264) all_68_2 = 0
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | REDUCE: (82), (263) imply:
% 38.65/6.03 | | | | | | | | | | | | | (265) aNaturalNumber0(all_50_1) = 0
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | BETA: splitting (236) gives:
% 38.65/6.03 | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | (266) xr = sz10
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | REDUCE: (210), (266) imply:
% 38.65/6.03 | | | | | | | | | | | | | | (267) $false
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | Case 2:
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | (268) ? [v0: $i] : (isPrime0(v0) = 0 & doDivides0(v0,
% 38.65/6.03 | | | | | | | | | | | | | | xr) = 0 & aNaturalNumber0(v0) = 0 & $i(v0))
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | DELTA: instantiating (268) with fresh symbol all_213_0
% 38.65/6.03 | | | | | | | | | | | | | | gives:
% 38.65/6.03 | | | | | | | | | | | | | | (269) isPrime0(all_213_0) = 0 & doDivides0(all_213_0,
% 38.65/6.03 | | | | | | | | | | | | | | xr) = 0 & aNaturalNumber0(all_213_0) = 0 &
% 38.65/6.03 | | | | | | | | | | | | | | $i(all_213_0)
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | ALPHA: (269) implies:
% 38.65/6.03 | | | | | | | | | | | | | | (270) $i(all_213_0)
% 38.65/6.03 | | | | | | | | | | | | | | (271) doDivides0(all_213_0, xr) = 0
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 38.65/6.03 | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | Case 1:
% 38.65/6.03 | | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | | (272) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 38.65/6.03 | | | | | | | | | | | | | | | (doDivides0(xp, all_42_0) = v2 &
% 38.65/6.03 | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = v1 &
% 38.65/6.03 | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 38.65/6.03 | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0)))
% 38.65/6.03 | | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | | DELTA: instantiating (272) with fresh symbols all_222_0,
% 38.65/6.03 | | | | | | | | | | | | | | | all_222_1, all_222_2 gives:
% 38.65/6.03 | | | | | | | | | | | | | | | (273) doDivides0(xp, all_42_0) = all_222_0 &
% 38.65/6.03 | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = all_222_1 &
% 38.65/6.03 | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_222_2 & ( ~ (all_222_0 =
% 38.65/6.03 | | | | | | | | | | | | | | | 0) | ~ (all_222_1 = 0) | ~ (all_222_2 = 0))
% 38.65/6.03 | | | | | | | | | | | | | | |
% 38.65/6.03 | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 38.65/6.03 | | | | | | | | | | | | | | | (274) aNaturalNumber0(xp) = all_222_2
% 38.65/6.04 | | | | | | | | | | | | | | | (275) aNaturalNumber0(all_42_0) = all_222_1
% 38.65/6.04 | | | | | | | | | | | | | | | (276) doDivides0(xp, all_42_0) = all_222_0
% 38.65/6.04 | | | | | | | | | | | | | | | (277) ~ (all_222_0 = 0) | ~ (all_222_1 = 0) | ~
% 38.65/6.04 | | | | | | | | | | | | | | | (all_222_2 = 0)
% 38.65/6.04 | | | | | | | | | | | | | | |
% 38.65/6.04 | | | | | | | | | | | | | | | DELTA: instantiating (272) with fresh symbols all_224_0,
% 38.65/6.04 | | | | | | | | | | | | | | | all_224_1, all_224_2 gives:
% 38.65/6.04 | | | | | | | | | | | | | | | (278) doDivides0(xp, all_42_0) = all_224_0 &
% 38.65/6.04 | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = all_224_1 &
% 38.65/6.04 | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_224_2 & ( ~ (all_224_0 =
% 38.65/6.04 | | | | | | | | | | | | | | | 0) | ~ (all_224_1 = 0) | ~ (all_224_2 = 0))
% 38.65/6.04 | | | | | | | | | | | | | | |
% 38.65/6.04 | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 38.65/6.04 | | | | | | | | | | | | | | | (279) aNaturalNumber0(xp) = all_224_2
% 38.65/6.04 | | | | | | | | | | | | | | | (280) aNaturalNumber0(all_42_0) = all_224_1
% 38.65/6.04 | | | | | | | | | | | | | | | (281) doDivides0(xp, all_42_0) = all_224_0
% 38.65/6.04 | | | | | | | | | | | | | | |
% 38.65/6.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_224_2, xp,
% 38.65/6.04 | | | | | | | | | | | | | | | simplifying with (8), (279) gives:
% 38.65/6.04 | | | | | | | | | | | | | | | (282) all_224_2 = 0
% 38.65/6.04 | | | | | | | | | | | | | | |
% 38.65/6.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_222_2, all_224_2, xp,
% 38.65/6.04 | | | | | | | | | | | | | | | simplifying with (274), (279) gives:
% 38.65/6.04 | | | | | | | | | | | | | | | (283) all_224_2 = all_222_2
% 38.65/6.04 | | | | | | | | | | | | | | |
% 38.65/6.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_222_1, all_224_1,
% 38.65/6.04 | | | | | | | | | | | | | | | all_42_0, simplifying with (275), (280) gives:
% 38.65/6.04 | | | | | | | | | | | | | | | (284) all_224_1 = all_222_1
% 38.65/6.04 | | | | | | | | | | | | | | |
% 38.65/6.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_224_1, all_42_0,
% 38.65/6.04 | | | | | | | | | | | | | | | simplifying with (233), (280) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | (285) all_224_1 = 0
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_224_0, all_42_0,
% 39.03/6.04 | | | | | | | | | | | | | | | xp, simplifying with (55), (281) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | (286) all_224_0 = 0
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_222_0, all_224_0,
% 39.03/6.04 | | | | | | | | | | | | | | | all_42_0, xp, simplifying with (276), (281) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | (287) all_224_0 = all_222_0
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | COMBINE_EQS: (286), (287) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | (288) all_222_0 = 0
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | COMBINE_EQS: (284), (285) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | (289) all_222_1 = 0
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | SIMP: (289) implies:
% 39.03/6.04 | | | | | | | | | | | | | | | (290) all_222_1 = 0
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | COMBINE_EQS: (282), (283) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | (291) all_222_2 = 0
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | Case 1:
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | (292) ~ (all_222_0 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | REDUCE: (288), (292) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | (293) $false
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | (294) ~ (all_222_1 = 0) | ~ (all_222_2 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | (295) ~ (all_222_1 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | REDUCE: (290), (295) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | | (296) $false
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | (297) ~ (all_222_2 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | REDUCE: (291), (297) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | | (298) $false
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | CLOSE: (298) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | End of split
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | End of split
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | (299) ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 39.03/6.04 | | | | | | | | | | | | | | | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 39.03/6.04 | | | | | | | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1)) & ! [v0:
% 39.03/6.04 | | | | | | | | | | | | | | | $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) |
% 39.03/6.04 | | | | | | | | | | | | | | | (v0 = all_42_0 & aNaturalNumber0(xk) = 0))
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 39.03/6.04 | | | | | | | | | | | | | | | (300) ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 39.03/6.04 | | | | | | | | | | | | | | | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 39.03/6.04 | | | | | | | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1))
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 39.03/6.04 | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | Case 1:
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | (301) ~ (all_68_1 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | REDUCE: (172), (301) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | (302) $false
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | CLOSE: (302) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | (303) ~ (all_68_2 = 0) | all_68_0 = all_50_0
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | (304) ~ (all_64_1 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | REDUCE: (186), (304) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | | (305) $false
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | CLOSE: (305) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | (306) ~ (all_64_2 = 0) | all_64_0 = 0
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | (307) ~ (all_68_2 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | REDUCE: (264), (307) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | (308) $false
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | (309) all_68_0 = all_50_0
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | REDUCE: (92), (309) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | (310) sdtpldt0(xp, all_50_1) = all_50_0
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (311) ~ (all_64_2 = 0)
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | REDUCE: (263), (311) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (312) $false
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | CLOSE: (312) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mAddAsso) with xm, all_147_0,
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | all_50_1, xp, all_50_0, simplifying with (18),
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (46), (224), (226), (310) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (313) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | [v3: $i] : ? [v4: $i] : (sdtpldt0(all_147_0,
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | all_50_1) = v3 & sdtpldt0(xm, v3) = v4 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_147_0) = v1 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_1) = v2 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = v0 & $i(v4) & $i(v3) & ( ~
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | all_50_0))
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (300) with all_186_0, simplifying
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | with (253), (255) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (314) all_186_0 = xk | ? [v0: int] : ( ~ (v0 = 0) &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_186_0) = v0)
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_213_0, xr, simplifying
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | with (19), (270), (271) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (315) xr = sz00 | ? [v0: any] : ? [v1: any] : ? [v2:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | any] : (sdtlseqdt0(all_213_0, xr) = v2 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_213_0) = v0 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | = 0) | v2 = 0))
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (313) with fresh symbols all_278_0,
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | all_278_1, all_278_2, all_278_3, all_278_4 gives:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (316) sdtpldt0(all_147_0, all_50_1) = all_278_1 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | sdtpldt0(xm, all_278_1) = all_278_0 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_147_0) = all_278_3 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_1) = all_278_2 &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | aNaturalNumber0(xm) = all_278_4 & $i(all_278_0) &
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | $i(all_278_1) & ( ~ (all_278_2 = 0) | ~
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (all_278_3 = 0) | ~ (all_278_4 = 0) | all_278_0
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | = all_50_0)
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (317) aNaturalNumber0(all_50_1) = all_278_2
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (318) aNaturalNumber0(all_147_0) = all_278_3
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (319) ~ (all_278_2 = 0) | ~ (all_278_3 = 0) | ~
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | (all_278_4 = 0) | all_278_0 = all_50_0
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | | (320) xr = sz00
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | | REDUCE: (209), (320) imply:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | | (321) $false
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent.
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.04 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_278_2, all_50_1,
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | simplifying with (265), (317) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | (322) all_278_2 = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_278_3, all_147_0,
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | simplifying with (225), (318) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | (323) all_278_3 = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (324) all_186_0 = xk
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (324) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (325) aNaturalNumber0(xk) = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | (326) ~ (all_278_2 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (326) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | (327) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (327) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | (328) ~ (all_278_3 = 0) | ~ (all_278_4 = 0) |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | all_278_0 = all_50_0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | (329) ~ (all_278_3 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (323), (329) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | (330) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (330) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_88_1, 0, xk,
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (119), (325) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | (331) all_88_1 = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (331) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | (332) all_93_1 = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | (333) ~ (all_48_0 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | (334) ~ (all_93_1 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (332), (334) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | (335) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (335) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | (336) ~ (all_93_2 = 0) | (all_93_0 = 0 & ~ (xk = xp))
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (336) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (337) ~ (all_93_2 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (337) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (338) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (338) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (339) all_93_0 = 0 & ~ (xk = xp)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (340) all_93_0 = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (340) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (341) all_48_0 = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (333), (341) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (342) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (342) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | (343) xk = xp
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | (344) ~ (all_93_1 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (332), (344) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | (345) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (345) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | (346) ~ (all_93_2 = 0) | (all_93_0 = 0 & ~ (xk = xp))
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (347) ~ (all_93_2 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (347) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (348) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (348) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_93_0 = 0 & ~ (xk = xp)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (350) ~ (xk = xp)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (350) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (351) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (351) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | Case 2:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (352) ? [v0: int] : ( ~ (v0 = 0) &
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_186_0) = v0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (352) with fresh symbol all_351_0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (353) ~ (all_351_0 = 0) & aNaturalNumber0(all_186_0) =
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | all_351_0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (354) ~ (all_351_0 = 0)
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (355) aNaturalNumber0(all_186_0) = all_351_0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with 0, all_351_0, all_186_0,
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | simplifying with (254), (355) gives:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (356) all_351_0 = 0
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (356) imply:
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | (357) $false
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent.
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | | |
% 39.03/6.05 | | | | | | | | | End of split
% 39.03/6.05 | | | | | | | | |
% 39.03/6.05 | | | | | | | | End of split
% 39.03/6.05 | | | | | | | |
% 39.03/6.05 | | | | | | | End of split
% 39.03/6.05 | | | | | | |
% 39.03/6.05 | | | | | | End of split
% 39.03/6.05 | | | | | |
% 39.03/6.05 | | | | | End of split
% 39.03/6.05 | | | | |
% 39.03/6.05 | | | | End of split
% 39.03/6.05 | | | |
% 39.03/6.05 | | | End of split
% 39.03/6.05 | | |
% 39.03/6.05 | | End of split
% 39.03/6.05 | |
% 39.03/6.05 | End of split
% 39.03/6.05 |
% 39.03/6.05 End of proof
% 39.03/6.05 % SZS output end Proof for theBenchmark
% 39.03/6.05
% 39.03/6.05 5431ms
%------------------------------------------------------------------------------