TSTP Solution File: NUM508+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM508+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 : n005.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 11:48:15 EDT 2023
% Result : Theorem 13.59s 2.59s
% Output : Proof 50.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM508+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 08:57:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.61 ________ _____
% 0.18/0.61 ___ __ \_________(_)________________________________
% 0.18/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61
% 0.18/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61 (2023-06-19)
% 0.18/0.61
% 0.18/0.61 (c) Philipp Rümmer, 2009-2023
% 0.18/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61 Amanda Stjerna.
% 0.18/0.61 Free software under BSD-3-Clause.
% 0.18/0.61
% 0.18/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61
% 0.18/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.62 Running up to 7 provers in parallel.
% 0.18/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.46/1.17 Prover 1: Preprocessing ...
% 3.46/1.17 Prover 4: Preprocessing ...
% 3.46/1.20 Prover 6: Preprocessing ...
% 3.46/1.20 Prover 5: Preprocessing ...
% 3.46/1.20 Prover 0: Preprocessing ...
% 3.46/1.20 Prover 2: Preprocessing ...
% 3.46/1.21 Prover 3: Preprocessing ...
% 8.28/1.87 Prover 1: Constructing countermodel ...
% 8.28/1.88 Prover 3: Constructing countermodel ...
% 9.06/1.91 Prover 6: Proving ...
% 9.06/1.97 Prover 5: Constructing countermodel ...
% 9.61/2.09 Prover 2: Proving ...
% 11.13/2.23 Prover 4: Constructing countermodel ...
% 11.28/2.31 Prover 0: Proving ...
% 13.59/2.56 Prover 3: proved (1927ms)
% 13.59/2.57
% 13.59/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.59/2.59
% 13.59/2.59 Prover 5: stopped
% 13.59/2.59 Prover 2: stopped
% 13.59/2.59 Prover 0: stopped
% 13.59/2.60 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.59/2.60 Prover 6: stopped
% 13.59/2.60 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.59/2.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.59/2.60 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.59/2.61 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.59/2.67 Prover 7: Preprocessing ...
% 14.46/2.71 Prover 11: Preprocessing ...
% 14.46/2.72 Prover 8: Preprocessing ...
% 14.46/2.74 Prover 10: Preprocessing ...
% 14.46/2.74 Prover 13: Preprocessing ...
% 15.88/2.87 Prover 8: Warning: ignoring some quantifiers
% 15.88/2.87 Prover 7: Constructing countermodel ...
% 16.19/2.88 Prover 8: Constructing countermodel ...
% 16.19/2.89 Prover 10: Constructing countermodel ...
% 17.21/3.04 Prover 13: Constructing countermodel ...
% 18.07/3.16 Prover 11: Constructing countermodel ...
% 49.19/7.29 Prover 1: Found proof (size 432)
% 49.19/7.29 Prover 1: proved (6662ms)
% 49.19/7.29 Prover 7: stopped
% 49.19/7.29 Prover 10: stopped
% 49.19/7.29 Prover 8: stopped
% 49.19/7.29 Prover 13: stopped
% 49.19/7.29 Prover 11: stopped
% 49.19/7.30 Prover 4: stopped
% 49.19/7.30
% 49.19/7.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.19/7.30
% 49.89/7.36 % SZS output start Proof for theBenchmark
% 49.89/7.37 Assumptions after simplification:
% 49.89/7.37 ---------------------------------
% 49.89/7.37
% 49.89/7.37 (mAddAsso)
% 49.89/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 49.89/7.40 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 49.89/7.40 | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ?
% 49.89/7.40 [v9: $i] : (sdtpldt0(v1, v2) = v8 & sdtpldt0(v0, v8) = v9 &
% 49.89/7.40 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 49.89/7.40 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | v9 =
% 49.89/7.40 v4)))
% 49.89/7.40
% 49.89/7.40 (mAddComm)
% 50.19/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 50.19/7.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 50.19/7.40 (sdtpldt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 50.19/7.40 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 50.19/7.40
% 50.19/7.40 (mDefDiv)
% 50.19/7.40 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (doDivides0(v0, v1) = v2) | ~
% 50.19/7.40 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (aNaturalNumber0(v1) = v4
% 50.19/7.40 & aNaturalNumber0(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (( ~ (v2 = 0)
% 50.19/7.40 | ? [v3: $i] : (sdtasdt0(v0, v3) = v1 & aNaturalNumber0(v3) = 0 &
% 50.19/7.40 $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (sdtasdt0(v0, v3) = v1) | ~
% 50.19/7.40 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)))))
% 50.19/7.40
% 50.19/7.40 (mDefPrime)
% 50.19/7.41 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) |
% 50.19/7.41 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~
% 50.19/7.41 (v1 = 0) | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 |
% 50.19/7.41 v2 = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] :
% 50.19/7.41 ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 = 0 | v0 = sz10 |
% 50.19/7.41 v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2 = sz10) &
% 50.19/7.41 doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 & $i(v2)))))
% 50.19/7.41
% 50.19/7.41 (mDefQuot)
% 50.19/7.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~
% 50.19/7.41 (sdtsldt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 50.19/7.41 any] : ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4
% 50.19/7.41 & aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))) |
% 50.19/7.41 ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) | ~ $i(v3) | ? [v4:
% 50.19/7.41 int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3: $i] : ( ~
% 50.19/7.41 (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | (v3 = v1 & aNaturalNumber0(v2) =
% 50.19/7.41 0))))
% 50.19/7.41
% 50.19/7.41 (mDivLE)
% 50.19/7.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (doDivides0(v0, v1) =
% 50.19/7.41 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 50.19/7.41 (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) =
% 50.19/7.41 v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 50.19/7.41
% 50.19/7.41 (mDivTrans)
% 50.19/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 50.19/7.42 (doDivides0(v0, v2) = v3) | ~ (doDivides0(v0, v1) = 0) | ~ $i(v2) | ~
% 50.19/7.42 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7:
% 50.19/7.42 any] : (doDivides0(v1, v2) = v7 & aNaturalNumber0(v2) = v6 &
% 50.19/7.42 aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v7 = 0) | ~
% 50.19/7.42 (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 50.19/7.42
% 50.19/7.42 (mIH_03)
% 50.19/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (iLess0(v0,
% 50.19/7.42 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 50.19/7.42 [v5: any] : (sdtlseqdt0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 &
% 50.19/7.42 aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))))
% 50.19/7.42
% 50.19/7.42 (mLEAsym)
% 50.19/7.42 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1)
% 50.19/7.42 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (sdtlseqdt0(v1,
% 50.19/7.42 v0) = v4 & aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v4
% 50.19/7.42 = 0) | ~ (v3 = 0) | ~ (v2 = 0))))
% 50.19/7.42
% 50.19/7.42 (mMonAdd)
% 50.19/7.42 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1)
% 50.19/7.42 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (aNaturalNumber0(v1) = v3 &
% 50.19/7.42 aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))) | ! [v2: $i] : !
% 50.19/7.42 [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (sdtlseqdt0(v3, v4) = v5) | ~
% 50.19/7.42 (sdtpldt0(v1, v2) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ? [v6:
% 50.19/7.42 any] : ? [v7: $i] : ? [v8: $i] : ? [v9: any] : (sdtlseqdt0(v7, v8) =
% 50.19/7.42 v9 & sdtpldt0(v2, v1) = v8 & sdtpldt0(v2, v0) = v7 & aNaturalNumber0(v2)
% 50.19/7.42 = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0 & ~ (v8 = v7)
% 50.19/7.42 & ~ (v4 = v3))))))
% 50.19/7.42
% 50.19/7.42 (mMulComm)
% 50.19/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 50.19/7.42 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 50.19/7.42 (sdtasdt0(v1, v0) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) = v3
% 50.19/7.42 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 50.19/7.42
% 50.19/7.42 (mPrimDiv)
% 50.19/7.42 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~
% 50.19/7.42 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 &
% 50.19/7.42 doDivides0(v1, v0) = 0 & aNaturalNumber0(v1) = 0 & $i(v1)))
% 50.19/7.42
% 50.19/7.42 (mSortsB)
% 50.19/7.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 50.19/7.42 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 50.19/7.42 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 50.19/7.42 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 50.19/7.42
% 50.19/7.42 (mSortsB_02)
% 50.19/7.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 50.19/7.43 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 50.19/7.43 (aNaturalNumber0(v2) = v5 & aNaturalNumber0(v1) = v4 & aNaturalNumber0(v0) =
% 50.19/7.43 v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 50.19/7.43
% 50.19/7.43 (m__)
% 50.19/7.43 $i(xr) & $i(xm) & $i(xn) & ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0
% 50.19/7.43 = 0) & doDivides0(xr, xm) = v1 & doDivides0(xr, xn) = v0)
% 50.19/7.43
% 50.19/7.43 (m__1799)
% 50.19/7.43 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1
% 50.19/7.43 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : !
% 50.19/7.43 [v4: $i] : ! [v5: $i] : ( ~ (doDivides0(v4, v5) = 0) | ~ (sdtasdt0(v2, v3)
% 50.19/7.43 = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 50.19/7.43 : ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 50.19/7.43 any] : ? [v13: any] : ? [v14: any] : (isPrime0(v4) = v9 &
% 50.19/7.43 doDivides0(v4, v3) = v14 & doDivides0(v4, v2) = v13 & iLess0(v11, v1) =
% 50.19/7.43 v12 & sdtpldt0(v10, v4) = v11 & sdtpldt0(v2, v3) = v10 &
% 50.19/7.43 aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 &
% 50.19/7.43 aNaturalNumber0(v2) = v6 & $i(v11) & $i(v10) & ( ~ (v12 = 0) | ~ (v9 =
% 50.19/7.43 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v14 = 0 | v13 = 0))))
% 50.19/7.43
% 50.19/7.43 (m__1837)
% 50.19/7.43 aNaturalNumber0(xp) = 0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(xn) = 0 &
% 50.19/7.43 $i(xp) & $i(xm) & $i(xn)
% 50.19/7.43
% 50.19/7.43 (m__1860)
% 50.19/7.43 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp,
% 50.19/7.43 v0) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0))
% 50.19/7.43
% 50.19/7.43 (m__2287)
% 50.19/7.43 ~ (xp = xm) & ~ (xp = xn) & sdtlseqdt0(xm, xp) = 0 & sdtlseqdt0(xn, xp) = 0
% 50.19/7.43 & $i(xp) & $i(xm) & $i(xn)
% 50.19/7.43
% 50.19/7.43 (m__2306)
% 50.19/7.43 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 50.19/7.43 sdtasdt0(xn, xm) = v0 & $i(v0))
% 50.19/7.43
% 50.19/7.43 (m__2315)
% 50.19/7.43 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00)
% 50.19/7.43
% 50.19/7.43 (m__2327)
% 50.19/7.43 ~ (xk = sz10) & ~ (xk = sz00) & $i(xk) & $i(sz10) & $i(sz00)
% 50.19/7.43
% 50.19/7.43 (m__2342)
% 50.19/7.43 isPrime0(xr) = 0 & doDivides0(xr, xk) = 0 & aNaturalNumber0(xr) = 0 & $i(xr) &
% 50.19/7.43 $i(xk)
% 50.19/7.43
% 50.19/7.43 (m__2362)
% 50.19/7.43 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : (doDivides0(xr, v0) = 0 &
% 50.19/7.43 sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn, xm) = v0 & $i(v0))
% 50.19/7.43
% 50.19/7.43 (m__2377)
% 50.19/7.43 ~ (xk = xp) & sdtlseqdt0(xk, xp) = 0 & $i(xk) & $i(xp)
% 50.19/7.43
% 50.19/7.43 (m__2478)
% 50.19/7.44 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 50.19/7.44 ( ~ (v2 = v1) & sdtlseqdt0(v1, v2) = 0 & sdtpldt0(v0, xr) = v1 & sdtpldt0(v0,
% 50.19/7.44 xp) = v2 & sdtpldt0(xn, xm) = v0 & $i(v2) & $i(v1) & $i(v0))
% 50.19/7.44
% 50.19/7.44 (function-axioms)
% 50.19/7.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.19/7.44 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 50.19/7.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.19/7.44 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 50.19/7.44 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 50.19/7.44 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 50.19/7.44 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.19/7.44 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 50.19/7.44 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.19/7.44 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 50.19/7.44 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.19/7.44 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 50.19/7.44 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 50.19/7.44 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.19/7.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~
% 50.19/7.44 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.19/7.44 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 50.19/7.44 | ~ (aNaturalNumber0(v2) = v0))
% 50.19/7.44
% 50.19/7.44 Further assumptions not needed in the proof:
% 50.19/7.44 --------------------------------------------
% 50.19/7.44 mAMDistr, mAddCanc, mDefDiff, mDefLE, mDivAsso, mDivMin, mDivSum, mIH, mLENTr,
% 50.19/7.44 mLERefl, mLETotal, mLETran, mMonMul, mMonMul2, mMulAsso, mMulCanc, mNatSort,
% 50.19/7.44 mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero,
% 50.19/7.44 m__1870, m__2075
% 50.19/7.44
% 50.19/7.44 Those formulas are unsatisfiable:
% 50.19/7.44 ---------------------------------
% 50.19/7.44
% 50.19/7.44 Begin of proof
% 50.19/7.44 |
% 50.19/7.44 | ALPHA: (mDefQuot) implies:
% 50.19/7.45 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v0 = sz00 | ~ (sdtsldt0(v1,
% 50.19/7.45 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 50.19/7.45 | ? [v5: any] : (doDivides0(v0, v1) = v5 & aNaturalNumber0(v1) = v4 &
% 50.19/7.45 | aNaturalNumber0(v0) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 50.19/7.45 | 0))) | ( ! [v3: $i] : (v3 = v2 | ~ (sdtasdt0(v0, v3) = v1) |
% 50.19/7.45 | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & aNaturalNumber0(v3) =
% 50.19/7.45 | v4)) & ! [v3: $i] : ( ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) |
% 50.19/7.45 | (v3 = v1 & aNaturalNumber0(v2) = 0))))
% 50.19/7.45 |
% 50.19/7.45 | ALPHA: (mDivLE) implies:
% 50.19/7.45 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (doDivides0(v0, v1) = 0) |
% 50.19/7.45 | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 50.19/7.45 | (sdtlseqdt0(v0, v1) = v4 & aNaturalNumber0(v1) = v3 &
% 50.19/7.45 | aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 50.19/7.45 |
% 50.19/7.45 | ALPHA: (mDefPrime) implies:
% 50.19/7.45 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (isPrime0(v0) = v1) | ~ $i(v0) | ?
% 50.19/7.45 | [v2: int] : ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (( ~ (v1 = 0)
% 50.19/7.45 | | ( ~ (v0 = sz10) & ~ (v0 = sz00) & ! [v2: $i] : (v2 = v0 | v2
% 50.19/7.45 | = sz10 | ~ (doDivides0(v2, v0) = 0) | ~ $i(v2) | ? [v3:
% 50.19/7.45 | int] : ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3)))) & (v1 =
% 50.19/7.45 | 0 | v0 = sz10 | v0 = sz00 | ? [v2: $i] : ( ~ (v2 = v0) & ~ (v2
% 50.19/7.45 | = sz10) & doDivides0(v2, v0) = 0 & aNaturalNumber0(v2) = 0 &
% 50.19/7.45 | $i(v2)))))
% 50.19/7.45 |
% 50.19/7.45 | ALPHA: (mPrimDiv) implies:
% 50.19/7.45 | (4) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ (aNaturalNumber0(v0) = 0) |
% 50.19/7.45 | ~ $i(v0) | ? [v1: $i] : (isPrime0(v1) = 0 & doDivides0(v1, v0) = 0 &
% 50.19/7.45 | aNaturalNumber0(v1) = 0 & $i(v1)))
% 50.19/7.45 |
% 50.19/7.45 | ALPHA: (m__1837) implies:
% 50.19/7.45 | (5) aNaturalNumber0(xn) = 0
% 50.19/7.45 | (6) aNaturalNumber0(xm) = 0
% 50.19/7.45 | (7) aNaturalNumber0(xp) = 0
% 50.19/7.45 |
% 50.19/7.45 | ALPHA: (m__1799) implies:
% 50.19/7.45 | (8) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) =
% 50.19/7.45 | v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 50.19/7.45 | [v5: $i] : ( ~ (doDivides0(v4, v5) = 0) | ~ (sdtasdt0(v2, v3) = v5)
% 50.19/7.45 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any] :
% 50.19/7.45 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: $i] : ?
% 50.19/7.45 | [v12: any] : ? [v13: any] : ? [v14: any] : (isPrime0(v4) = v9 &
% 50.19/7.45 | doDivides0(v4, v3) = v14 & doDivides0(v4, v2) = v13 & iLess0(v11,
% 50.19/7.45 | v1) = v12 & sdtpldt0(v10, v4) = v11 & sdtpldt0(v2, v3) = v10 &
% 50.19/7.45 | aNaturalNumber0(v4) = v8 & aNaturalNumber0(v3) = v7 &
% 50.19/7.45 | aNaturalNumber0(v2) = v6 & $i(v11) & $i(v10) & ( ~ (v12 = 0) | ~
% 50.19/7.46 | (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | v14 = 0 |
% 50.19/7.46 | v13 = 0))))
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__1860) implies:
% 50.19/7.46 | (9) ? [v0: $i] : (isPrime0(xp) = 0 & doDivides0(xp, v0) = 0 & sdtasdt0(xn,
% 50.19/7.46 | xm) = v0 & $i(v0))
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__2287) implies:
% 50.19/7.46 | (10) ~ (xp = xn)
% 50.19/7.46 | (11) sdtlseqdt0(xn, xp) = 0
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__2306) implies:
% 50.19/7.46 | (12) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xn, xm) = v0 & $i(v0))
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__2327) implies:
% 50.19/7.46 | (13) ~ (xk = sz00)
% 50.19/7.46 | (14) ~ (xk = sz10)
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__2342) implies:
% 50.19/7.46 | (15) aNaturalNumber0(xr) = 0
% 50.19/7.46 | (16) doDivides0(xr, xk) = 0
% 50.19/7.46 | (17) isPrime0(xr) = 0
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__2362) implies:
% 50.19/7.46 | (18) ? [v0: $i] : (doDivides0(xr, v0) = 0 & sdtlseqdt0(xr, xk) = 0 &
% 50.19/7.46 | sdtasdt0(xn, xm) = v0 & $i(v0))
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__2377) implies:
% 50.19/7.46 | (19) ~ (xk = xp)
% 50.19/7.46 | (20) $i(xk)
% 50.19/7.46 | (21) sdtlseqdt0(xk, xp) = 0
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__2478) implies:
% 50.19/7.46 | (22) $i(xp)
% 50.19/7.46 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 50.19/7.46 | sdtlseqdt0(v1, v2) = 0 & sdtpldt0(v0, xr) = v1 & sdtpldt0(v0, xp) =
% 50.19/7.46 | v2 & sdtpldt0(xn, xm) = v0 & $i(v2) & $i(v1) & $i(v0))
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (m__) implies:
% 50.19/7.46 | (24) $i(xn)
% 50.19/7.46 | (25) $i(xm)
% 50.19/7.46 | (26) $i(xr)
% 50.19/7.46 | (27) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) &
% 50.19/7.46 | doDivides0(xr, xm) = v1 & doDivides0(xr, xn) = v0)
% 50.19/7.46 |
% 50.19/7.46 | ALPHA: (function-axioms) implies:
% 50.19/7.46 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 50.19/7.46 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 50.19/7.46 | v0))
% 50.19/7.46 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 50.19/7.46 | : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 50.19/7.46 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.19/7.46 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 50.51/7.46 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.51/7.46 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 50.51/7.46 | (32) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 50.51/7.46 | : ! [v3: $i] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~
% 50.51/7.46 | (sdtlseqdt0(v3, v2) = v0))
% 50.51/7.46 | (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 50.51/7.46 | : ! [v3: $i] : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~
% 50.51/7.46 | (doDivides0(v3, v2) = v0))
% 50.51/7.46 |
% 50.51/7.47 | DELTA: instantiating (12) with fresh symbol all_42_0 gives:
% 50.51/7.47 | (34) sdtsldt0(all_42_0, xp) = xk & sdtasdt0(xn, xm) = all_42_0 &
% 50.51/7.47 | $i(all_42_0)
% 50.51/7.47 |
% 50.51/7.47 | ALPHA: (34) implies:
% 50.51/7.47 | (35) sdtasdt0(xn, xm) = all_42_0
% 50.51/7.47 | (36) sdtsldt0(all_42_0, xp) = xk
% 50.51/7.47 |
% 50.51/7.47 | DELTA: instantiating (9) with fresh symbol all_44_0 gives:
% 50.51/7.47 | (37) isPrime0(xp) = 0 & doDivides0(xp, all_44_0) = 0 & sdtasdt0(xn, xm) =
% 50.51/7.47 | all_44_0 & $i(all_44_0)
% 50.51/7.47 |
% 50.51/7.47 | ALPHA: (37) implies:
% 50.51/7.47 | (38) $i(all_44_0)
% 50.51/7.47 | (39) sdtasdt0(xn, xm) = all_44_0
% 50.51/7.47 | (40) doDivides0(xp, all_44_0) = 0
% 50.51/7.47 | (41) isPrime0(xp) = 0
% 50.51/7.47 |
% 50.51/7.47 | DELTA: instantiating (18) with fresh symbol all_46_0 gives:
% 50.51/7.47 | (42) doDivides0(xr, all_46_0) = 0 & sdtlseqdt0(xr, xk) = 0 & sdtasdt0(xn,
% 50.51/7.47 | xm) = all_46_0 & $i(all_46_0)
% 50.51/7.47 |
% 50.51/7.47 | ALPHA: (42) implies:
% 50.51/7.47 | (43) sdtasdt0(xn, xm) = all_46_0
% 50.51/7.47 | (44) doDivides0(xr, all_46_0) = 0
% 50.51/7.47 |
% 50.51/7.47 | DELTA: instantiating (27) with fresh symbols all_48_0, all_48_1 gives:
% 50.51/7.47 | (45) ~ (all_48_0 = 0) & ~ (all_48_1 = 0) & doDivides0(xr, xm) = all_48_0
% 50.51/7.47 | & doDivides0(xr, xn) = all_48_1
% 50.51/7.47 |
% 50.51/7.47 | ALPHA: (45) implies:
% 50.51/7.47 | (46) ~ (all_48_1 = 0)
% 50.51/7.47 | (47) ~ (all_48_0 = 0)
% 50.51/7.47 | (48) doDivides0(xr, xn) = all_48_1
% 50.51/7.47 | (49) doDivides0(xr, xm) = all_48_0
% 50.51/7.47 |
% 50.51/7.47 | DELTA: instantiating (23) with fresh symbols all_50_0, all_50_1, all_50_2
% 50.51/7.47 | gives:
% 50.51/7.47 | (50) ~ (all_50_0 = all_50_1) & sdtlseqdt0(all_50_1, all_50_0) = 0 &
% 50.51/7.47 | sdtpldt0(all_50_2, xr) = all_50_1 & sdtpldt0(all_50_2, xp) = all_50_0
% 50.51/7.47 | & sdtpldt0(xn, xm) = all_50_2 & $i(all_50_0) & $i(all_50_1) &
% 50.51/7.47 | $i(all_50_2)
% 50.51/7.47 |
% 50.51/7.47 | ALPHA: (50) implies:
% 50.51/7.47 | (51) ~ (all_50_0 = all_50_1)
% 50.51/7.47 | (52) $i(all_50_1)
% 50.51/7.47 | (53) sdtpldt0(xn, xm) = all_50_2
% 50.51/7.47 | (54) sdtpldt0(all_50_2, xp) = all_50_0
% 50.51/7.47 | (55) sdtpldt0(all_50_2, xr) = all_50_1
% 50.51/7.47 | (56) sdtlseqdt0(all_50_1, all_50_0) = 0
% 50.51/7.47 |
% 50.51/7.47 | DELTA: instantiating (8) with fresh symbols all_52_0, all_52_1 gives:
% 50.51/7.47 | (57) sdtpldt0(all_52_1, xp) = all_52_0 & sdtpldt0(xn, xm) = all_52_1 &
% 50.51/7.47 | $i(all_52_0) & $i(all_52_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 50.51/7.47 | : ! [v3: $i] : ( ~ (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) =
% 50.51/7.47 | v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 50.51/7.47 | any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] :
% 50.51/7.47 | ? [v10: any] : ? [v11: any] : ? [v12: any] : (isPrime0(v2) = v7 &
% 50.51/7.47 | doDivides0(v2, v1) = v12 & doDivides0(v2, v0) = v11 & iLess0(v9,
% 50.51/7.47 | all_52_0) = v10 & sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8
% 50.51/7.47 | & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 &
% 50.51/7.47 | aNaturalNumber0(v0) = v4 & $i(v9) & $i(v8) & ( ~ (v10 = 0) | ~
% 50.51/7.47 | (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 |
% 50.51/7.47 | v11 = 0)))
% 50.51/7.47 |
% 50.51/7.47 | ALPHA: (57) implies:
% 50.51/7.47 | (58) $i(all_52_1)
% 50.51/7.47 | (59) $i(all_52_0)
% 50.51/7.47 | (60) sdtpldt0(xn, xm) = all_52_1
% 50.51/7.47 | (61) sdtpldt0(all_52_1, xp) = all_52_0
% 50.51/7.48 | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 50.51/7.48 | (doDivides0(v2, v3) = 0) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) |
% 50.51/7.48 | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 50.51/7.48 | ? [v7: any] : ? [v8: $i] : ? [v9: $i] : ? [v10: any] : ? [v11:
% 50.51/7.48 | any] : ? [v12: any] : (isPrime0(v2) = v7 & doDivides0(v2, v1) =
% 50.51/7.48 | v12 & doDivides0(v2, v0) = v11 & iLess0(v9, all_52_0) = v10 &
% 50.51/7.48 | sdtpldt0(v8, v2) = v9 & sdtpldt0(v0, v1) = v8 &
% 50.51/7.48 | aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 &
% 50.51/7.48 | aNaturalNumber0(v0) = v4 & $i(v9) & $i(v8) & ( ~ (v10 = 0) | ~
% 50.51/7.48 | (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | v12 = 0 |
% 50.51/7.48 | v11 = 0)))
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (30) with all_50_2, all_52_1, xm, xn, simplifying
% 50.51/7.48 | with (53), (60) gives:
% 50.51/7.48 | (63) all_52_1 = all_50_2
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (31) with all_44_0, all_46_0, xm, xn, simplifying
% 50.51/7.48 | with (39), (43) gives:
% 50.51/7.48 | (64) all_46_0 = all_44_0
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (31) with all_42_0, all_46_0, xm, xn, simplifying
% 50.51/7.48 | with (35), (43) gives:
% 50.51/7.48 | (65) all_46_0 = all_42_0
% 50.51/7.48 |
% 50.51/7.48 | COMBINE_EQS: (64), (65) imply:
% 50.51/7.48 | (66) all_44_0 = all_42_0
% 50.51/7.48 |
% 50.51/7.48 | REDUCE: (44), (65) imply:
% 50.51/7.48 | (67) doDivides0(xr, all_42_0) = 0
% 50.51/7.48 |
% 50.51/7.48 | REDUCE: (40), (66) imply:
% 50.51/7.48 | (68) doDivides0(xp, all_42_0) = 0
% 50.51/7.48 |
% 50.51/7.48 | REDUCE: (61), (63) imply:
% 50.51/7.48 | (69) sdtpldt0(all_50_2, xp) = all_52_0
% 50.51/7.48 |
% 50.51/7.48 | REDUCE: (58), (63) imply:
% 50.51/7.48 | (70) $i(all_50_2)
% 50.51/7.48 |
% 50.51/7.48 | REDUCE: (38), (66) imply:
% 50.51/7.48 | (71) $i(all_42_0)
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (30) with all_50_0, all_52_0, xp, all_50_2,
% 50.51/7.48 | simplifying with (54), (69) gives:
% 50.51/7.48 | (72) all_52_0 = all_50_0
% 50.51/7.48 |
% 50.51/7.48 | REDUCE: (59), (72) imply:
% 50.51/7.48 | (73) $i(all_50_0)
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (mAddComm) with xn, xm, all_50_2, simplifying with
% 50.51/7.48 | (24), (25), (53) gives:
% 50.51/7.48 | (74) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xm, xn) = v2 &
% 50.51/7.48 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 50.51/7.48 | (v1 = 0) | ~ (v0 = 0) | v2 = all_50_2))
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (mSortsB) with xn, xm, all_50_2, simplifying with
% 50.51/7.48 | (24), (25), (53) gives:
% 50.51/7.48 | (75) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.48 | (aNaturalNumber0(all_50_2) = v2 & aNaturalNumber0(xm) = v1 &
% 50.51/7.48 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xp, all_50_2, all_50_0,
% 50.51/7.48 | simplifying with (22), (24), (25), (53), (54) gives:
% 50.51/7.48 | (76) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 50.51/7.48 | : (sdtpldt0(xm, xp) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xp)
% 50.51/7.48 | = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4)
% 50.51/7.48 | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 50.51/7.48 | all_50_0))
% 50.51/7.48 |
% 50.51/7.48 | GROUND_INST: instantiating (mAddComm) with all_50_2, xp, all_50_0, simplifying
% 50.51/7.48 | with (22), (54), (70) gives:
% 50.51/7.49 | (77) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xp, all_50_2) =
% 50.51/7.49 | v2 & aNaturalNumber0(all_50_2) = v0 & aNaturalNumber0(xp) = v1 &
% 50.51/7.49 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_50_0))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mSortsB) with all_50_2, xp, all_50_0, simplifying
% 50.51/7.49 | with (22), (54), (70) gives:
% 50.51/7.49 | (78) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.49 | (aNaturalNumber0(all_50_0) = v2 & aNaturalNumber0(all_50_2) = v0 &
% 50.51/7.49 | aNaturalNumber0(xp) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mAddAsso) with xn, xm, xr, all_50_2, all_50_1,
% 50.51/7.49 | simplifying with (24), (25), (26), (53), (55) gives:
% 50.51/7.49 | (79) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ? [v4: $i]
% 50.51/7.49 | : (sdtpldt0(xm, xr) = v3 & sdtpldt0(xn, v3) = v4 & aNaturalNumber0(xr)
% 50.51/7.49 | = v2 & aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v4)
% 50.51/7.49 | & $i(v3) & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v4 =
% 50.51/7.49 | all_50_1))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mAddComm) with all_50_2, xr, all_50_1, simplifying
% 50.51/7.49 | with (26), (55), (70) gives:
% 50.51/7.49 | (80) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(xr, all_50_2) =
% 50.51/7.49 | v2 & aNaturalNumber0(all_50_2) = v0 & aNaturalNumber0(xr) = v1 &
% 50.51/7.49 | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = all_50_1))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mSortsB) with all_50_2, xr, all_50_1, simplifying
% 50.51/7.49 | with (26), (55), (70) gives:
% 50.51/7.49 | (81) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.49 | (aNaturalNumber0(all_50_1) = v2 & aNaturalNumber0(all_50_2) = v0 &
% 50.51/7.49 | aNaturalNumber0(xr) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mMulComm) with xn, xm, all_42_0, simplifying with
% 50.51/7.49 | (24), (25), (35) gives:
% 50.51/7.49 | (82) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtasdt0(xm, xn) = v2 &
% 50.51/7.49 | aNaturalNumber0(xm) = v1 & aNaturalNumber0(xn) = v0 & $i(v2) & ( ~
% 50.51/7.49 | (v1 = 0) | ~ (v0 = 0) | v2 = all_42_0))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_42_0, simplifying
% 50.51/7.49 | with (24), (25), (35) gives:
% 50.51/7.49 | (83) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.49 | (aNaturalNumber0(all_42_0) = v2 & aNaturalNumber0(xm) = v1 &
% 50.51/7.49 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mMonAdd) with xn, xp, simplifying with (11), (22),
% 50.51/7.49 | (24) gives:
% 50.51/7.49 | (84) xp = xn | ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xp) = v1 &
% 50.51/7.49 | aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ! [v0:
% 50.51/7.49 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (sdtlseqdt0(v1,
% 50.51/7.49 | v2) = v3) | ~ (sdtpldt0(xp, v0) = v2) | ~ (sdtpldt0(xn, v0) =
% 50.51/7.49 | v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ?
% 50.51/7.49 | [v7: any] : (sdtlseqdt0(v5, v6) = v7 & sdtpldt0(v0, xp) = v6 &
% 50.51/7.49 | sdtpldt0(v0, xn) = v5 & aNaturalNumber0(v0) = v4 & $i(v6) & $i(v5)
% 50.51/7.49 | & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0 & ~ (v6 = v5) & ~ (v2 =
% 50.51/7.49 | v1)))))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mLEAsym) with xk, xp, simplifying with (20), (21),
% 50.51/7.49 | (22) gives:
% 50.51/7.49 | (85) xk = xp | ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xp,
% 50.51/7.49 | xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) = v1 & (
% 50.51/7.49 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mLEAsym) with all_50_1, all_50_0, simplifying with
% 50.51/7.49 | (52), (56), (73) gives:
% 50.51/7.49 | (86) all_50_0 = all_50_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.49 | (sdtlseqdt0(all_50_0, all_50_1) = v2 & aNaturalNumber0(all_50_0) = v1
% 50.51/7.49 | & aNaturalNumber0(all_50_1) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 50.51/7.49 | (v0 = 0)))
% 50.51/7.49 |
% 50.51/7.49 | GROUND_INST: instantiating (mMonAdd) with all_50_1, all_50_0, simplifying with
% 50.51/7.49 | (52), (56), (73) gives:
% 50.51/7.50 | (87) all_50_0 = all_50_1 | ? [v0: any] : ? [v1: any] :
% 50.51/7.50 | (aNaturalNumber0(all_50_0) = v1 & aNaturalNumber0(all_50_1) = v0 & ( ~
% 50.51/7.50 | (v1 = 0) | ~ (v0 = 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 50.51/7.50 | : ! [v3: any] : ( ~ (sdtlseqdt0(v1, v2) = v3) | ~
% 50.51/7.50 | (sdtpldt0(all_50_0, v0) = v2) | ~ (sdtpldt0(all_50_1, v0) = v1) |
% 50.51/7.50 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: any] :
% 50.51/7.50 | (sdtlseqdt0(v5, v6) = v7 & sdtpldt0(v0, all_50_0) = v6 &
% 50.51/7.50 | sdtpldt0(v0, all_50_1) = v5 & aNaturalNumber0(v0) = v4 & $i(v6) &
% 50.51/7.50 | $i(v5) & ( ~ (v4 = 0) | (v7 = 0 & v3 = 0 & ~ (v6 = v5) & ~ (v2 =
% 50.51/7.50 | v1)))))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (62) with xn, xm, xp, all_42_0, simplifying with
% 50.51/7.50 | (22), (24), (25), (35), (68) gives:
% 50.51/7.50 | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 50.51/7.50 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 50.51/7.50 | (isPrime0(xp) = v3 & doDivides0(xp, xm) = v8 & doDivides0(xp, xn) = v7
% 50.51/7.50 | & iLess0(v5, all_52_0) = v6 & sdtpldt0(v4, xp) = v5 & sdtpldt0(xn,
% 50.51/7.50 | xm) = v4 & aNaturalNumber0(xp) = v2 & aNaturalNumber0(xm) = v1 &
% 50.51/7.50 | aNaturalNumber0(xn) = v0 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | ~ (v3 =
% 50.51/7.50 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (mDefDiv) with xp, all_42_0, 0, simplifying with
% 50.51/7.50 | (22), (68), (71) gives:
% 50.51/7.50 | (89) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(all_42_0) = v1 &
% 50.51/7.50 | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | ? [v0:
% 50.51/7.50 | $i] : (sdtasdt0(xp, v0) = all_42_0 & aNaturalNumber0(v0) = 0 &
% 50.51/7.50 | $i(v0))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (mDivTrans) with xr, xk, xm, all_48_0, simplifying
% 50.51/7.50 | with (16), (20), (25), (26), (49) gives:
% 50.51/7.50 | (90) all_48_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 50.51/7.50 | any] : (doDivides0(xk, xm) = v3 & aNaturalNumber0(xr) = v0 &
% 50.51/7.50 | aNaturalNumber0(xk) = v1 & aNaturalNumber0(xm) = v2 & ( ~ (v3 = 0) |
% 50.51/7.50 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (mDivTrans) with xr, xk, xn, all_48_1, simplifying
% 50.51/7.50 | with (16), (20), (24), (26), (48) gives:
% 50.51/7.50 | (91) all_48_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 50.51/7.50 | any] : (doDivides0(xk, xn) = v3 & aNaturalNumber0(xr) = v0 &
% 50.51/7.50 | aNaturalNumber0(xk) = v1 & aNaturalNumber0(xn) = v2 & ( ~ (v3 = 0) |
% 50.51/7.50 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (2) with xr, xk, simplifying with (16), (20), (26)
% 50.51/7.50 | gives:
% 50.51/7.50 | (92) xk = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.50 | (sdtlseqdt0(xr, xk) = v2 & aNaturalNumber0(xr) = v0 &
% 50.51/7.50 | aNaturalNumber0(xk) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (mDivTrans) with xr, all_42_0, xm, all_48_0,
% 50.51/7.50 | simplifying with (25), (26), (49), (67), (71) gives:
% 50.51/7.50 | (93) all_48_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 50.51/7.50 | any] : (doDivides0(all_42_0, xm) = v3 & aNaturalNumber0(all_42_0) =
% 50.51/7.50 | v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 =
% 50.51/7.50 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (mDivTrans) with xr, all_42_0, xn, all_48_1,
% 50.51/7.50 | simplifying with (24), (26), (48), (67), (71) gives:
% 50.51/7.50 | (94) all_48_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 50.51/7.50 | any] : (doDivides0(all_42_0, xn) = v3 & aNaturalNumber0(all_42_0) =
% 50.51/7.50 | v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) = v2 & ( ~ (v3 =
% 50.51/7.50 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (62) with xn, xm, xr, all_42_0, simplifying with
% 50.51/7.50 | (24), (25), (26), (35), (67) gives:
% 50.51/7.50 | (95) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 50.51/7.50 | $i] : ? [v5: $i] : ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 50.51/7.50 | (isPrime0(xr) = v3 & doDivides0(xr, xm) = v8 & doDivides0(xr, xn) = v7
% 50.51/7.50 | & iLess0(v5, all_52_0) = v6 & sdtpldt0(v4, xr) = v5 & sdtpldt0(xn,
% 50.51/7.50 | xm) = v4 & aNaturalNumber0(xr) = v2 & aNaturalNumber0(xm) = v1 &
% 50.51/7.50 | aNaturalNumber0(xn) = v0 & $i(v5) & $i(v4) & ( ~ (v6 = 0) | ~ (v3 =
% 50.51/7.50 | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | v8 = 0 | v7 = 0))
% 50.51/7.50 |
% 50.51/7.50 | GROUND_INST: instantiating (1) with xp, all_42_0, xk, simplifying with (22),
% 50.51/7.50 | (36), (71) gives:
% 50.51/7.51 | (96) xp = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.51 | (doDivides0(xp, all_42_0) = v2 & aNaturalNumber0(all_42_0) = v1 &
% 50.51/7.51 | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 50.51/7.51 | 0))) | ( ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 50.51/7.51 | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 50.51/7.51 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~ (sdtasdt0(xp, xk)
% 50.51/7.51 | = v0) | ~ $i(xk) | (v0 = all_42_0 & aNaturalNumber0(xk) = 0)))
% 50.51/7.51 |
% 50.51/7.51 | GROUND_INST: instantiating (3) with xp, 0, simplifying with (22), (41) gives:
% 50.51/7.51 | (97) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) = v0) | ( ~ (xp =
% 50.51/7.51 | sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 50.51/7.51 | (doDivides0(v0, xp) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0)
% 50.51/7.51 | & aNaturalNumber0(v0) = v1)))
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (83) with fresh symbols all_68_0, all_68_1, all_68_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (98) aNaturalNumber0(all_42_0) = all_68_0 & aNaturalNumber0(xm) = all_68_1
% 50.51/7.51 | & aNaturalNumber0(xn) = all_68_2 & ( ~ (all_68_1 = 0) | ~ (all_68_2 =
% 50.51/7.51 | 0) | all_68_0 = 0)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (98) implies:
% 50.51/7.51 | (99) aNaturalNumber0(xn) = all_68_2
% 50.51/7.51 | (100) aNaturalNumber0(xm) = all_68_1
% 50.51/7.51 | (101) aNaturalNumber0(all_42_0) = all_68_0
% 50.51/7.51 | (102) ~ (all_68_1 = 0) | ~ (all_68_2 = 0) | all_68_0 = 0
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (81) with fresh symbols all_70_0, all_70_1, all_70_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (103) aNaturalNumber0(all_50_1) = all_70_0 & aNaturalNumber0(all_50_2) =
% 50.51/7.51 | all_70_2 & aNaturalNumber0(xr) = all_70_1 & ( ~ (all_70_1 = 0) | ~
% 50.51/7.51 | (all_70_2 = 0) | all_70_0 = 0)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (103) implies:
% 50.51/7.51 | (104) aNaturalNumber0(xr) = all_70_1
% 50.51/7.51 | (105) aNaturalNumber0(all_50_2) = all_70_2
% 50.51/7.51 | (106) aNaturalNumber0(all_50_1) = all_70_0
% 50.51/7.51 | (107) ~ (all_70_1 = 0) | ~ (all_70_2 = 0) | all_70_0 = 0
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (78) with fresh symbols all_72_0, all_72_1, all_72_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (108) aNaturalNumber0(all_50_0) = all_72_0 & aNaturalNumber0(all_50_2) =
% 50.51/7.51 | all_72_2 & aNaturalNumber0(xp) = all_72_1 & ( ~ (all_72_1 = 0) | ~
% 50.51/7.51 | (all_72_2 = 0) | all_72_0 = 0)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (108) implies:
% 50.51/7.51 | (109) aNaturalNumber0(xp) = all_72_1
% 50.51/7.51 | (110) aNaturalNumber0(all_50_2) = all_72_2
% 50.51/7.51 | (111) aNaturalNumber0(all_50_0) = all_72_0
% 50.51/7.51 | (112) ~ (all_72_1 = 0) | ~ (all_72_2 = 0) | all_72_0 = 0
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (75) with fresh symbols all_74_0, all_74_1, all_74_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (113) aNaturalNumber0(all_50_2) = all_74_0 & aNaturalNumber0(xm) = all_74_1
% 50.51/7.51 | & aNaturalNumber0(xn) = all_74_2 & ( ~ (all_74_1 = 0) | ~ (all_74_2
% 50.51/7.51 | = 0) | all_74_0 = 0)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (113) implies:
% 50.51/7.51 | (114) aNaturalNumber0(xn) = all_74_2
% 50.51/7.51 | (115) aNaturalNumber0(xm) = all_74_1
% 50.51/7.51 | (116) aNaturalNumber0(all_50_2) = all_74_0
% 50.51/7.51 | (117) ~ (all_74_1 = 0) | ~ (all_74_2 = 0) | all_74_0 = 0
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (82) with fresh symbols all_76_0, all_76_1, all_76_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (118) sdtasdt0(xm, xn) = all_76_0 & aNaturalNumber0(xm) = all_76_1 &
% 50.51/7.51 | aNaturalNumber0(xn) = all_76_2 & $i(all_76_0) & ( ~ (all_76_1 = 0) |
% 50.51/7.51 | ~ (all_76_2 = 0) | all_76_0 = all_42_0)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (118) implies:
% 50.51/7.51 | (119) aNaturalNumber0(xn) = all_76_2
% 50.51/7.51 | (120) aNaturalNumber0(xm) = all_76_1
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (77) with fresh symbols all_78_0, all_78_1, all_78_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (121) sdtpldt0(xp, all_50_2) = all_78_0 & aNaturalNumber0(all_50_2) =
% 50.51/7.51 | all_78_2 & aNaturalNumber0(xp) = all_78_1 & $i(all_78_0) & ( ~
% 50.51/7.51 | (all_78_1 = 0) | ~ (all_78_2 = 0) | all_78_0 = all_50_0)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (121) implies:
% 50.51/7.51 | (122) aNaturalNumber0(xp) = all_78_1
% 50.51/7.51 | (123) aNaturalNumber0(all_50_2) = all_78_2
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (80) with fresh symbols all_80_0, all_80_1, all_80_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (124) sdtpldt0(xr, all_50_2) = all_80_0 & aNaturalNumber0(all_50_2) =
% 50.51/7.51 | all_80_2 & aNaturalNumber0(xr) = all_80_1 & $i(all_80_0) & ( ~
% 50.51/7.51 | (all_80_1 = 0) | ~ (all_80_2 = 0) | all_80_0 = all_50_1)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (124) implies:
% 50.51/7.51 | (125) aNaturalNumber0(xr) = all_80_1
% 50.51/7.51 | (126) aNaturalNumber0(all_50_2) = all_80_2
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (74) with fresh symbols all_82_0, all_82_1, all_82_2
% 50.51/7.51 | gives:
% 50.51/7.51 | (127) sdtpldt0(xm, xn) = all_82_0 & aNaturalNumber0(xm) = all_82_1 &
% 50.51/7.51 | aNaturalNumber0(xn) = all_82_2 & $i(all_82_0) & ( ~ (all_82_1 = 0) |
% 50.51/7.51 | ~ (all_82_2 = 0) | all_82_0 = all_50_2)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (127) implies:
% 50.51/7.51 | (128) aNaturalNumber0(xn) = all_82_2
% 50.51/7.51 | (129) aNaturalNumber0(xm) = all_82_1
% 50.51/7.51 |
% 50.51/7.51 | DELTA: instantiating (76) with fresh symbols all_84_0, all_84_1, all_84_2,
% 50.51/7.51 | all_84_3, all_84_4 gives:
% 50.51/7.51 | (130) sdtpldt0(xm, xp) = all_84_1 & sdtpldt0(xn, all_84_1) = all_84_0 &
% 50.51/7.51 | aNaturalNumber0(xp) = all_84_2 & aNaturalNumber0(xm) = all_84_3 &
% 50.51/7.51 | aNaturalNumber0(xn) = all_84_4 & $i(all_84_0) & $i(all_84_1) & ( ~
% 50.51/7.51 | (all_84_2 = 0) | ~ (all_84_3 = 0) | ~ (all_84_4 = 0) | all_84_0 =
% 50.51/7.51 | all_50_0)
% 50.51/7.51 |
% 50.51/7.51 | ALPHA: (130) implies:
% 50.51/7.52 | (131) aNaturalNumber0(xn) = all_84_4
% 50.51/7.52 | (132) aNaturalNumber0(xm) = all_84_3
% 50.51/7.52 | (133) aNaturalNumber0(xp) = all_84_2
% 50.51/7.52 |
% 50.51/7.52 | DELTA: instantiating (79) with fresh symbols all_86_0, all_86_1, all_86_2,
% 50.51/7.52 | all_86_3, all_86_4 gives:
% 50.51/7.52 | (134) sdtpldt0(xm, xr) = all_86_1 & sdtpldt0(xn, all_86_1) = all_86_0 &
% 50.51/7.52 | aNaturalNumber0(xr) = all_86_2 & aNaturalNumber0(xm) = all_86_3 &
% 50.51/7.52 | aNaturalNumber0(xn) = all_86_4 & $i(all_86_0) & $i(all_86_1) & ( ~
% 50.51/7.52 | (all_86_2 = 0) | ~ (all_86_3 = 0) | ~ (all_86_4 = 0) | all_86_0 =
% 50.51/7.52 | all_50_1)
% 50.51/7.52 |
% 50.51/7.52 | ALPHA: (134) implies:
% 50.51/7.52 | (135) aNaturalNumber0(xn) = all_86_4
% 50.51/7.52 | (136) aNaturalNumber0(xm) = all_86_3
% 50.51/7.52 | (137) aNaturalNumber0(xr) = all_86_2
% 50.51/7.52 |
% 50.51/7.52 | DELTA: instantiating (95) with fresh symbols all_88_0, all_88_1, all_88_2,
% 50.51/7.52 | all_88_3, all_88_4, all_88_5, all_88_6, all_88_7, all_88_8 gives:
% 50.51/7.52 | (138) isPrime0(xr) = all_88_5 & doDivides0(xr, xm) = all_88_0 &
% 50.51/7.52 | doDivides0(xr, xn) = all_88_1 & iLess0(all_88_3, all_52_0) = all_88_2
% 50.51/7.52 | & sdtpldt0(all_88_4, xr) = all_88_3 & sdtpldt0(xn, xm) = all_88_4 &
% 50.51/7.52 | aNaturalNumber0(xr) = all_88_6 & aNaturalNumber0(xm) = all_88_7 &
% 50.51/7.52 | aNaturalNumber0(xn) = all_88_8 & $i(all_88_3) & $i(all_88_4) & ( ~
% 50.51/7.52 | (all_88_2 = 0) | ~ (all_88_5 = 0) | ~ (all_88_6 = 0) | ~
% 50.51/7.52 | (all_88_7 = 0) | ~ (all_88_8 = 0) | all_88_0 = 0 | all_88_1 = 0)
% 50.51/7.52 |
% 50.51/7.52 | ALPHA: (138) implies:
% 50.51/7.52 | (139) $i(all_88_3)
% 50.51/7.52 | (140) aNaturalNumber0(xn) = all_88_8
% 50.51/7.52 | (141) aNaturalNumber0(xm) = all_88_7
% 50.51/7.52 | (142) aNaturalNumber0(xr) = all_88_6
% 50.51/7.52 | (143) sdtpldt0(xn, xm) = all_88_4
% 50.51/7.52 | (144) sdtpldt0(all_88_4, xr) = all_88_3
% 50.51/7.52 | (145) iLess0(all_88_3, all_52_0) = all_88_2
% 50.51/7.52 | (146) doDivides0(xr, xn) = all_88_1
% 50.51/7.52 | (147) doDivides0(xr, xm) = all_88_0
% 50.51/7.52 | (148) isPrime0(xr) = all_88_5
% 50.51/7.52 | (149) ~ (all_88_2 = 0) | ~ (all_88_5 = 0) | ~ (all_88_6 = 0) | ~
% 50.51/7.52 | (all_88_7 = 0) | ~ (all_88_8 = 0) | all_88_0 = 0 | all_88_1 = 0
% 50.51/7.52 |
% 50.51/7.52 | DELTA: instantiating (88) with fresh symbols all_90_0, all_90_1, all_90_2,
% 50.51/7.52 | all_90_3, all_90_4, all_90_5, all_90_6, all_90_7, all_90_8 gives:
% 50.51/7.52 | (150) isPrime0(xp) = all_90_5 & doDivides0(xp, xm) = all_90_0 &
% 50.51/7.52 | doDivides0(xp, xn) = all_90_1 & iLess0(all_90_3, all_52_0) = all_90_2
% 50.51/7.52 | & sdtpldt0(all_90_4, xp) = all_90_3 & sdtpldt0(xn, xm) = all_90_4 &
% 50.51/7.52 | aNaturalNumber0(xp) = all_90_6 & aNaturalNumber0(xm) = all_90_7 &
% 50.51/7.52 | aNaturalNumber0(xn) = all_90_8 & $i(all_90_3) & $i(all_90_4) & ( ~
% 50.51/7.52 | (all_90_2 = 0) | ~ (all_90_5 = 0) | ~ (all_90_6 = 0) | ~
% 50.51/7.52 | (all_90_7 = 0) | ~ (all_90_8 = 0) | all_90_0 = 0 | all_90_1 = 0)
% 50.51/7.52 |
% 50.51/7.52 | ALPHA: (150) implies:
% 50.51/7.52 | (151) $i(all_90_3)
% 50.51/7.52 | (152) aNaturalNumber0(xn) = all_90_8
% 50.51/7.52 | (153) aNaturalNumber0(xm) = all_90_7
% 50.51/7.52 | (154) aNaturalNumber0(xp) = all_90_6
% 50.51/7.52 | (155) sdtpldt0(xn, xm) = all_90_4
% 50.51/7.52 | (156) sdtpldt0(all_90_4, xp) = all_90_3
% 50.51/7.52 |
% 50.51/7.52 | REDUCE: (72), (145) imply:
% 50.51/7.52 | (157) iLess0(all_88_3, all_50_0) = all_88_2
% 50.51/7.52 |
% 50.51/7.52 | BETA: splitting (92) gives:
% 50.51/7.52 |
% 50.51/7.52 | Case 1:
% 50.51/7.52 | |
% 50.51/7.52 | | (158) xk = sz00
% 50.51/7.52 | |
% 50.51/7.52 | | REDUCE: (13), (158) imply:
% 50.51/7.52 | | (159) $false
% 50.51/7.52 | |
% 50.51/7.52 | | CLOSE: (159) is inconsistent.
% 50.51/7.52 | |
% 50.51/7.52 | Case 2:
% 50.51/7.52 | |
% 50.51/7.52 | | (160) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xr, xk) =
% 50.51/7.52 | | v2 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xk) = v1 & ( ~
% 50.51/7.52 | | (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 50.51/7.52 | |
% 50.51/7.52 | | DELTA: instantiating (160) with fresh symbols all_100_0, all_100_1,
% 50.51/7.52 | | all_100_2 gives:
% 50.51/7.52 | | (161) sdtlseqdt0(xr, xk) = all_100_0 & aNaturalNumber0(xr) = all_100_2 &
% 50.51/7.52 | | aNaturalNumber0(xk) = all_100_1 & ( ~ (all_100_1 = 0) | ~
% 50.51/7.52 | | (all_100_2 = 0) | all_100_0 = 0)
% 50.51/7.52 | |
% 50.51/7.52 | | ALPHA: (161) implies:
% 50.51/7.52 | | (162) aNaturalNumber0(xr) = all_100_2
% 50.51/7.52 | |
% 50.51/7.52 | | BETA: splitting (93) gives:
% 50.51/7.52 | |
% 50.51/7.52 | | Case 1:
% 50.51/7.52 | | |
% 50.51/7.52 | | | (163) all_48_0 = 0
% 50.51/7.52 | | |
% 50.51/7.52 | | | REDUCE: (47), (163) imply:
% 50.51/7.52 | | | (164) $false
% 50.51/7.52 | | |
% 50.51/7.52 | | | CLOSE: (164) is inconsistent.
% 50.51/7.52 | | |
% 50.51/7.52 | | Case 2:
% 50.51/7.52 | | |
% 50.51/7.52 | | | (165) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 50.51/7.52 | | | (doDivides0(all_42_0, xm) = v3 & aNaturalNumber0(all_42_0) = v1 &
% 50.51/7.52 | | | aNaturalNumber0(xr) = v0 & aNaturalNumber0(xm) = v2 & ( ~ (v3 =
% 50.51/7.52 | | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.52 | | |
% 50.51/7.52 | | | DELTA: instantiating (165) with fresh symbols all_105_0, all_105_1,
% 50.51/7.52 | | | all_105_2, all_105_3 gives:
% 50.51/7.52 | | | (166) doDivides0(all_42_0, xm) = all_105_0 & aNaturalNumber0(all_42_0)
% 50.51/7.52 | | | = all_105_2 & aNaturalNumber0(xr) = all_105_3 &
% 50.51/7.52 | | | aNaturalNumber0(xm) = all_105_1 & ( ~ (all_105_0 = 0) | ~
% 50.51/7.52 | | | (all_105_1 = 0) | ~ (all_105_2 = 0) | ~ (all_105_3 = 0))
% 50.51/7.52 | | |
% 50.51/7.52 | | | ALPHA: (166) implies:
% 50.51/7.52 | | | (167) aNaturalNumber0(xm) = all_105_1
% 50.51/7.52 | | | (168) aNaturalNumber0(xr) = all_105_3
% 50.51/7.53 | | | (169) aNaturalNumber0(all_42_0) = all_105_2
% 50.51/7.53 | | |
% 50.51/7.53 | | | BETA: splitting (85) gives:
% 50.51/7.53 | | |
% 50.51/7.53 | | | Case 1:
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | (170) xk = xp
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | REDUCE: (19), (170) imply:
% 50.51/7.53 | | | | (171) $false
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | CLOSE: (171) is inconsistent.
% 50.51/7.53 | | | |
% 50.51/7.53 | | | Case 2:
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | (172) ? [v0: any] : ? [v1: any] : ? [v2: any] : (sdtlseqdt0(xp,
% 50.51/7.53 | | | | xk) = v2 & aNaturalNumber0(xk) = v0 & aNaturalNumber0(xp) =
% 50.51/7.53 | | | | v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | DELTA: instantiating (172) with fresh symbols all_110_0, all_110_1,
% 50.51/7.53 | | | | all_110_2 gives:
% 50.51/7.53 | | | | (173) sdtlseqdt0(xp, xk) = all_110_0 & aNaturalNumber0(xk) =
% 50.51/7.53 | | | | all_110_2 & aNaturalNumber0(xp) = all_110_1 & ( ~ (all_110_0 =
% 50.51/7.53 | | | | 0) | ~ (all_110_1 = 0) | ~ (all_110_2 = 0))
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | ALPHA: (173) implies:
% 50.51/7.53 | | | | (174) aNaturalNumber0(xp) = all_110_1
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | BETA: splitting (86) gives:
% 50.51/7.53 | | | |
% 50.51/7.53 | | | | Case 1:
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | (175) all_50_0 = all_50_1
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | REDUCE: (51), (175) imply:
% 50.51/7.53 | | | | | (176) $false
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | CLOSE: (176) is inconsistent.
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | Case 2:
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | (177) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.51/7.53 | | | | | (sdtlseqdt0(all_50_0, all_50_1) = v2 &
% 50.51/7.53 | | | | | aNaturalNumber0(all_50_0) = v1 & aNaturalNumber0(all_50_1)
% 50.51/7.53 | | | | | = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | DELTA: instantiating (177) with fresh symbols all_115_0, all_115_1,
% 50.51/7.53 | | | | | all_115_2 gives:
% 50.51/7.53 | | | | | (178) sdtlseqdt0(all_50_0, all_50_1) = all_115_0 &
% 50.51/7.53 | | | | | aNaturalNumber0(all_50_0) = all_115_1 &
% 50.51/7.53 | | | | | aNaturalNumber0(all_50_1) = all_115_2 & ( ~ (all_115_0 = 0) |
% 50.51/7.53 | | | | | ~ (all_115_1 = 0) | ~ (all_115_2 = 0))
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | ALPHA: (178) implies:
% 50.51/7.53 | | | | | (179) aNaturalNumber0(all_50_1) = all_115_2
% 50.51/7.53 | | | | | (180) aNaturalNumber0(all_50_0) = all_115_1
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | BETA: splitting (94) gives:
% 50.51/7.53 | | | | |
% 50.51/7.53 | | | | | Case 1:
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | (181) all_48_1 = 0
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | REDUCE: (46), (181) imply:
% 50.51/7.53 | | | | | | (182) $false
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | CLOSE: (182) is inconsistent.
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | Case 2:
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | (183) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 50.51/7.53 | | | | | | (doDivides0(all_42_0, xn) = v3 & aNaturalNumber0(all_42_0)
% 50.51/7.53 | | | | | | = v1 & aNaturalNumber0(xr) = v0 & aNaturalNumber0(xn) =
% 50.51/7.53 | | | | | | v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 50.51/7.53 | | | | | | 0)))
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | DELTA: instantiating (183) with fresh symbols all_120_0, all_120_1,
% 50.51/7.53 | | | | | | all_120_2, all_120_3 gives:
% 50.51/7.53 | | | | | | (184) doDivides0(all_42_0, xn) = all_120_0 &
% 50.51/7.53 | | | | | | aNaturalNumber0(all_42_0) = all_120_2 & aNaturalNumber0(xr)
% 50.51/7.53 | | | | | | = all_120_3 & aNaturalNumber0(xn) = all_120_1 & ( ~
% 50.51/7.53 | | | | | | (all_120_0 = 0) | ~ (all_120_1 = 0) | ~ (all_120_2 = 0)
% 50.51/7.53 | | | | | | | ~ (all_120_3 = 0))
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | ALPHA: (184) implies:
% 50.51/7.53 | | | | | | (185) aNaturalNumber0(xn) = all_120_1
% 50.51/7.53 | | | | | | (186) aNaturalNumber0(xr) = all_120_3
% 50.51/7.53 | | | | | | (187) aNaturalNumber0(all_42_0) = all_120_2
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | BETA: splitting (90) gives:
% 50.51/7.53 | | | | | |
% 50.51/7.53 | | | | | | Case 1:
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | (188) all_48_0 = 0
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | REDUCE: (47), (188) imply:
% 50.51/7.53 | | | | | | | (189) $false
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | CLOSE: (189) is inconsistent.
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | Case 2:
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | (190) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any]
% 50.51/7.53 | | | | | | | : (doDivides0(xk, xm) = v3 & aNaturalNumber0(xr) = v0 &
% 50.51/7.53 | | | | | | | aNaturalNumber0(xk) = v1 & aNaturalNumber0(xm) = v2 & (
% 50.51/7.53 | | | | | | | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 50.51/7.53 | | | | | | | 0)))
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | DELTA: instantiating (190) with fresh symbols all_125_0,
% 50.51/7.53 | | | | | | | all_125_1, all_125_2, all_125_3 gives:
% 50.51/7.53 | | | | | | | (191) doDivides0(xk, xm) = all_125_0 & aNaturalNumber0(xr) =
% 50.51/7.53 | | | | | | | all_125_3 & aNaturalNumber0(xk) = all_125_2 &
% 50.51/7.53 | | | | | | | aNaturalNumber0(xm) = all_125_1 & ( ~ (all_125_0 = 0) |
% 50.51/7.53 | | | | | | | ~ (all_125_1 = 0) | ~ (all_125_2 = 0) | ~ (all_125_3
% 50.51/7.53 | | | | | | | = 0))
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | ALPHA: (191) implies:
% 50.51/7.53 | | | | | | | (192) aNaturalNumber0(xm) = all_125_1
% 50.51/7.53 | | | | | | | (193) aNaturalNumber0(xr) = all_125_3
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | BETA: splitting (91) gives:
% 50.51/7.53 | | | | | | |
% 50.51/7.53 | | | | | | | Case 1:
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | (194) all_48_1 = 0
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | REDUCE: (46), (194) imply:
% 50.51/7.53 | | | | | | | | (195) $false
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | CLOSE: (195) is inconsistent.
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | Case 2:
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | (196) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 50.51/7.53 | | | | | | | | any] : (doDivides0(xk, xn) = v3 & aNaturalNumber0(xr)
% 50.51/7.53 | | | | | | | | = v0 & aNaturalNumber0(xk) = v1 & aNaturalNumber0(xn)
% 50.51/7.53 | | | | | | | | = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~
% 50.51/7.53 | | | | | | | | (v0 = 0)))
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | DELTA: instantiating (196) with fresh symbols all_130_0,
% 50.51/7.53 | | | | | | | | all_130_1, all_130_2, all_130_3 gives:
% 50.51/7.53 | | | | | | | | (197) doDivides0(xk, xn) = all_130_0 & aNaturalNumber0(xr) =
% 50.51/7.53 | | | | | | | | all_130_3 & aNaturalNumber0(xk) = all_130_2 &
% 50.51/7.53 | | | | | | | | aNaturalNumber0(xn) = all_130_1 & ( ~ (all_130_0 = 0) |
% 50.51/7.53 | | | | | | | | ~ (all_130_1 = 0) | ~ (all_130_2 = 0) | ~
% 50.51/7.53 | | | | | | | | (all_130_3 = 0))
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | ALPHA: (197) implies:
% 50.51/7.53 | | | | | | | | (198) aNaturalNumber0(xn) = all_130_1
% 50.51/7.53 | | | | | | | | (199) aNaturalNumber0(xr) = all_130_3
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | GROUND_INST: instantiating (28) with 0, all_82_2, xn,
% 50.51/7.53 | | | | | | | | simplifying with (5), (128) gives:
% 50.51/7.53 | | | | | | | | (200) all_82_2 = 0
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | GROUND_INST: instantiating (28) with all_74_2, all_82_2, xn,
% 50.51/7.53 | | | | | | | | simplifying with (114), (128) gives:
% 50.51/7.53 | | | | | | | | (201) all_82_2 = all_74_2
% 50.51/7.53 | | | | | | | |
% 50.51/7.53 | | | | | | | | GROUND_INST: instantiating (28) with all_82_2, all_84_4, xn,
% 50.51/7.53 | | | | | | | | simplifying with (128), (131) gives:
% 50.51/7.53 | | | | | | | | (202) all_84_4 = all_82_2
% 50.51/7.53 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_84_4, all_88_8, xn,
% 50.51/7.54 | | | | | | | | simplifying with (131), (140) gives:
% 50.51/7.54 | | | | | | | | (203) all_88_8 = all_84_4
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_68_2, all_88_8, xn,
% 50.51/7.54 | | | | | | | | simplifying with (99), (140) gives:
% 50.51/7.54 | | | | | | | | (204) all_88_8 = all_68_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_86_4, all_120_1, xn,
% 50.51/7.54 | | | | | | | | simplifying with (135), (185) gives:
% 50.51/7.54 | | | | | | | | (205) all_120_1 = all_86_4
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_84_4, all_120_1, xn,
% 50.51/7.54 | | | | | | | | simplifying with (131), (185) gives:
% 50.51/7.54 | | | | | | | | (206) all_120_1 = all_84_4
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_76_2, all_120_1, xn,
% 50.51/7.54 | | | | | | | | simplifying with (119), (185) gives:
% 50.51/7.54 | | | | | | | | (207) all_120_1 = all_76_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_120_1, all_130_1, xn,
% 50.51/7.54 | | | | | | | | simplifying with (185), (198) gives:
% 50.51/7.54 | | | | | | | | (208) all_130_1 = all_120_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_90_8, all_130_1, xn,
% 50.51/7.54 | | | | | | | | simplifying with (152), (198) gives:
% 50.51/7.54 | | | | | | | | (209) all_130_1 = all_90_8
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_82_1, all_86_3, xm,
% 50.51/7.54 | | | | | | | | simplifying with (129), (136) gives:
% 50.51/7.54 | | | | | | | | (210) all_86_3 = all_82_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_74_1, all_86_3, xm,
% 50.51/7.54 | | | | | | | | simplifying with (115), (136) gives:
% 50.51/7.54 | | | | | | | | (211) all_86_3 = all_74_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with 0, all_88_7, xm,
% 50.51/7.54 | | | | | | | | simplifying with (6), (141) gives:
% 50.51/7.54 | | | | | | | | (212) all_88_7 = 0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_84_3, all_88_7, xm,
% 50.51/7.54 | | | | | | | | simplifying with (132), (141) gives:
% 50.51/7.54 | | | | | | | | (213) all_88_7 = all_84_3
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_82_1, all_88_7, xm,
% 50.51/7.54 | | | | | | | | simplifying with (129), (141) gives:
% 50.51/7.54 | | | | | | | | (214) all_88_7 = all_82_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_86_3, all_90_7, xm,
% 50.51/7.54 | | | | | | | | simplifying with (136), (153) gives:
% 50.51/7.54 | | | | | | | | (215) all_90_7 = all_86_3
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_90_7, all_105_1, xm,
% 50.51/7.54 | | | | | | | | simplifying with (153), (167) gives:
% 50.51/7.54 | | | | | | | | (216) all_105_1 = all_90_7
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_76_1, all_105_1, xm,
% 50.51/7.54 | | | | | | | | simplifying with (120), (167) gives:
% 50.51/7.54 | | | | | | | | (217) all_105_1 = all_76_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_74_1, all_125_1, xm,
% 50.51/7.54 | | | | | | | | simplifying with (115), (192) gives:
% 50.51/7.54 | | | | | | | | (218) all_125_1 = all_74_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_68_1, all_125_1, xm,
% 50.51/7.54 | | | | | | | | simplifying with (100), (192) gives:
% 50.51/7.54 | | | | | | | | (219) all_125_1 = all_68_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with 0, all_84_2, xp,
% 50.51/7.54 | | | | | | | | simplifying with (7), (133) gives:
% 50.51/7.54 | | | | | | | | (220) all_84_2 = 0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_78_1, all_84_2, xp,
% 50.51/7.54 | | | | | | | | simplifying with (122), (133) gives:
% 50.51/7.54 | | | | | | | | (221) all_84_2 = all_78_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_90_6, all_110_1, xp,
% 50.51/7.54 | | | | | | | | simplifying with (154), (174) gives:
% 50.51/7.54 | | | | | | | | (222) all_110_1 = all_90_6
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_84_2, all_110_1, xp,
% 50.51/7.54 | | | | | | | | simplifying with (133), (174) gives:
% 50.51/7.54 | | | | | | | | (223) all_110_1 = all_84_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_72_1, all_110_1, xp,
% 50.51/7.54 | | | | | | | | simplifying with (109), (174) gives:
% 50.51/7.54 | | | | | | | | (224) all_110_1 = all_72_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with 0, all_88_6, xr,
% 50.51/7.54 | | | | | | | | simplifying with (15), (142) gives:
% 50.51/7.54 | | | | | | | | (225) all_88_6 = 0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_80_1, all_88_6, xr,
% 50.51/7.54 | | | | | | | | simplifying with (125), (142) gives:
% 50.51/7.54 | | | | | | | | (226) all_88_6 = all_80_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_88_6, all_100_2, xr,
% 50.51/7.54 | | | | | | | | simplifying with (142), (162) gives:
% 50.51/7.54 | | | | | | | | (227) all_100_2 = all_88_6
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_88_6, all_105_3, xr,
% 50.51/7.54 | | | | | | | | simplifying with (142), (168) gives:
% 50.51/7.54 | | | | | | | | (228) all_105_3 = all_88_6
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_105_3, all_125_3, xr,
% 50.51/7.54 | | | | | | | | simplifying with (168), (193) gives:
% 50.51/7.54 | | | | | | | | (229) all_125_3 = all_105_3
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_70_1, all_125_3, xr,
% 50.51/7.54 | | | | | | | | simplifying with (104), (193) gives:
% 50.51/7.54 | | | | | | | | (230) all_125_3 = all_70_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_120_3, all_130_3, xr,
% 50.51/7.54 | | | | | | | | simplifying with (186), (199) gives:
% 50.51/7.54 | | | | | | | | (231) all_130_3 = all_120_3
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_100_2, all_130_3, xr,
% 50.51/7.54 | | | | | | | | simplifying with (162), (199) gives:
% 50.51/7.54 | | | | | | | | (232) all_130_3 = all_100_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_86_2, all_130_3, xr,
% 50.51/7.54 | | | | | | | | simplifying with (137), (199) gives:
% 50.51/7.54 | | | | | | | | (233) all_130_3 = all_86_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_105_2, all_120_2,
% 50.51/7.54 | | | | | | | | all_42_0, simplifying with (169), (187) gives:
% 50.51/7.54 | | | | | | | | (234) all_120_2 = all_105_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_68_0, all_120_2,
% 50.51/7.54 | | | | | | | | all_42_0, simplifying with (101), (187) gives:
% 50.51/7.54 | | | | | | | | (235) all_120_2 = all_68_0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_78_2, all_80_2,
% 50.51/7.54 | | | | | | | | all_50_2, simplifying with (123), (126) gives:
% 50.51/7.54 | | | | | | | | (236) all_80_2 = all_78_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_74_0, all_80_2,
% 50.51/7.54 | | | | | | | | all_50_2, simplifying with (116), (126) gives:
% 50.51/7.54 | | | | | | | | (237) all_80_2 = all_74_0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_72_2, all_80_2,
% 50.51/7.54 | | | | | | | | all_50_2, simplifying with (110), (126) gives:
% 50.51/7.54 | | | | | | | | (238) all_80_2 = all_72_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_70_2, all_80_2,
% 50.51/7.54 | | | | | | | | all_50_2, simplifying with (105), (126) gives:
% 50.51/7.54 | | | | | | | | (239) all_80_2 = all_70_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_70_0, all_115_2,
% 50.51/7.54 | | | | | | | | all_50_1, simplifying with (106), (179) gives:
% 50.51/7.54 | | | | | | | | (240) all_115_2 = all_70_0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (28) with all_72_0, all_115_1,
% 50.51/7.54 | | | | | | | | all_50_0, simplifying with (111), (180) gives:
% 50.51/7.54 | | | | | | | | (241) all_115_1 = all_72_0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (30) with all_50_2, all_90_4, xm, xn,
% 50.51/7.54 | | | | | | | | simplifying with (53), (155) gives:
% 50.51/7.54 | | | | | | | | (242) all_90_4 = all_50_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (30) with all_88_4, all_90_4, xm, xn,
% 50.51/7.54 | | | | | | | | simplifying with (143), (155) gives:
% 50.51/7.54 | | | | | | | | (243) all_90_4 = all_88_4
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (33) with all_48_1, all_88_1, xn, xr,
% 50.51/7.54 | | | | | | | | simplifying with (48), (146) gives:
% 50.51/7.54 | | | | | | | | (244) all_88_1 = all_48_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (33) with all_48_0, all_88_0, xm, xr,
% 50.51/7.54 | | | | | | | | simplifying with (49), (147) gives:
% 50.51/7.54 | | | | | | | | (245) all_88_0 = all_48_0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | GROUND_INST: instantiating (29) with 0, all_88_5, xr,
% 50.51/7.54 | | | | | | | | simplifying with (17), (148) gives:
% 50.51/7.54 | | | | | | | | (246) all_88_5 = 0
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | COMBINE_EQS: (208), (209) imply:
% 50.51/7.54 | | | | | | | | (247) all_120_1 = all_90_8
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | SIMP: (247) implies:
% 50.51/7.54 | | | | | | | | (248) all_120_1 = all_90_8
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | COMBINE_EQS: (231), (233) imply:
% 50.51/7.54 | | | | | | | | (249) all_120_3 = all_86_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | COMBINE_EQS: (231), (232) imply:
% 50.51/7.54 | | | | | | | | (250) all_120_3 = all_100_2
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | COMBINE_EQS: (218), (219) imply:
% 50.51/7.54 | | | | | | | | (251) all_74_1 = all_68_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | SIMP: (251) implies:
% 50.51/7.54 | | | | | | | | (252) all_74_1 = all_68_1
% 50.51/7.54 | | | | | | | |
% 50.51/7.54 | | | | | | | | COMBINE_EQS: (229), (230) imply:
% 50.51/7.55 | | | | | | | | (253) all_105_3 = all_70_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (253) implies:
% 50.51/7.55 | | | | | | | | (254) all_105_3 = all_70_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (207), (248) imply:
% 50.51/7.55 | | | | | | | | (255) all_90_8 = all_76_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (206), (248) imply:
% 50.51/7.55 | | | | | | | | (256) all_90_8 = all_84_4
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (205), (248) imply:
% 50.51/7.55 | | | | | | | | (257) all_90_8 = all_86_4
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (234), (235) imply:
% 50.51/7.55 | | | | | | | | (258) all_105_2 = all_68_0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (249), (250) imply:
% 50.51/7.55 | | | | | | | | (259) all_100_2 = all_86_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (259) implies:
% 50.51/7.55 | | | | | | | | (260) all_100_2 = all_86_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (222), (223) imply:
% 50.51/7.55 | | | | | | | | (261) all_90_6 = all_84_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (222), (224) imply:
% 50.51/7.55 | | | | | | | | (262) all_90_6 = all_72_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (216), (217) imply:
% 50.51/7.55 | | | | | | | | (263) all_90_7 = all_76_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (263) implies:
% 50.51/7.55 | | | | | | | | (264) all_90_7 = all_76_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (228), (254) imply:
% 50.51/7.55 | | | | | | | | (265) all_88_6 = all_70_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (265) implies:
% 50.51/7.55 | | | | | | | | (266) all_88_6 = all_70_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (227), (260) imply:
% 50.51/7.55 | | | | | | | | (267) all_88_6 = all_86_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (267) implies:
% 50.51/7.55 | | | | | | | | (268) all_88_6 = all_86_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (242), (243) imply:
% 50.51/7.55 | | | | | | | | (269) all_88_4 = all_50_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (261), (262) imply:
% 50.51/7.55 | | | | | | | | (270) all_84_2 = all_72_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (270) implies:
% 50.51/7.55 | | | | | | | | (271) all_84_2 = all_72_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (215), (264) imply:
% 50.51/7.55 | | | | | | | | (272) all_86_3 = all_76_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (272) implies:
% 50.51/7.55 | | | | | | | | (273) all_86_3 = all_76_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (255), (257) imply:
% 50.51/7.55 | | | | | | | | (274) all_86_4 = all_76_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (256), (257) imply:
% 50.51/7.55 | | | | | | | | (275) all_86_4 = all_84_4
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (226), (268) imply:
% 50.51/7.55 | | | | | | | | (276) all_86_2 = all_80_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (225), (268) imply:
% 50.51/7.55 | | | | | | | | (277) all_86_2 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (266), (268) imply:
% 50.51/7.55 | | | | | | | | (278) all_86_2 = all_70_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (212), (213) imply:
% 50.51/7.55 | | | | | | | | (279) all_84_3 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (213), (214) imply:
% 50.51/7.55 | | | | | | | | (280) all_84_3 = all_82_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (203), (204) imply:
% 50.51/7.55 | | | | | | | | (281) all_84_4 = all_68_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (281) implies:
% 50.51/7.55 | | | | | | | | (282) all_84_4 = all_68_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (276), (277) imply:
% 50.51/7.55 | | | | | | | | (283) all_80_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (276), (278) imply:
% 50.51/7.55 | | | | | | | | (284) all_80_1 = all_70_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (210), (273) imply:
% 50.51/7.55 | | | | | | | | (285) all_82_1 = all_76_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (285) implies:
% 50.51/7.55 | | | | | | | | (286) all_82_1 = all_76_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (211), (273) imply:
% 50.51/7.55 | | | | | | | | (287) all_76_1 = all_74_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (274), (275) imply:
% 50.51/7.55 | | | | | | | | (288) all_84_4 = all_76_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (288) implies:
% 50.51/7.55 | | | | | | | | (289) all_84_4 = all_76_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (220), (221) imply:
% 50.51/7.55 | | | | | | | | (290) all_78_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (221), (271) imply:
% 50.51/7.55 | | | | | | | | (291) all_78_1 = all_72_1
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (279), (280) imply:
% 50.51/7.55 | | | | | | | | (292) all_82_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (292) implies:
% 50.51/7.55 | | | | | | | | (293) all_82_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (282), (289) imply:
% 50.51/7.55 | | | | | | | | (294) all_76_2 = all_68_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (202), (289) imply:
% 50.51/7.55 | | | | | | | | (295) all_82_2 = all_76_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (295) implies:
% 50.51/7.55 | | | | | | | | (296) all_82_2 = all_76_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (286), (293) imply:
% 50.51/7.55 | | | | | | | | (297) all_76_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (297) implies:
% 50.51/7.55 | | | | | | | | (298) all_76_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (200), (201) imply:
% 50.51/7.55 | | | | | | | | (299) all_74_2 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (201), (296) imply:
% 50.51/7.55 | | | | | | | | (300) all_76_2 = all_74_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (300) implies:
% 50.51/7.55 | | | | | | | | (301) all_76_2 = all_74_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (283), (284) imply:
% 50.51/7.55 | | | | | | | | (302) all_70_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (236), (239) imply:
% 50.51/7.55 | | | | | | | | (303) all_78_2 = all_70_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (236), (238) imply:
% 50.51/7.55 | | | | | | | | (304) all_78_2 = all_72_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (236), (237) imply:
% 50.51/7.55 | | | | | | | | (305) all_78_2 = all_74_0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (290), (291) imply:
% 50.51/7.55 | | | | | | | | (306) all_72_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (304), (305) imply:
% 50.51/7.55 | | | | | | | | (307) all_74_0 = all_72_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (303), (305) imply:
% 50.51/7.55 | | | | | | | | (308) all_74_0 = all_70_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (287), (298) imply:
% 50.51/7.55 | | | | | | | | (309) all_74_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (309) implies:
% 50.51/7.55 | | | | | | | | (310) all_74_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (294), (301) imply:
% 50.51/7.55 | | | | | | | | (311) all_74_2 = all_68_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (311) implies:
% 50.51/7.55 | | | | | | | | (312) all_74_2 = all_68_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (307), (308) imply:
% 50.51/7.55 | | | | | | | | (313) all_72_2 = all_70_2
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (252), (310) imply:
% 50.51/7.55 | | | | | | | | (314) all_68_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | SIMP: (314) implies:
% 50.51/7.55 | | | | | | | | (315) all_68_1 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (299), (312) imply:
% 50.51/7.55 | | | | | | | | (316) all_68_2 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | COMBINE_EQS: (204), (316) imply:
% 50.51/7.55 | | | | | | | | (317) all_88_8 = 0
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | REDUCE: (156), (242) imply:
% 50.51/7.55 | | | | | | | | (318) sdtpldt0(all_50_2, xp) = all_90_3
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | REDUCE: (144), (269) imply:
% 50.51/7.55 | | | | | | | | (319) sdtpldt0(all_50_2, xr) = all_88_3
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | BETA: splitting (84) gives:
% 50.51/7.55 | | | | | | | |
% 50.51/7.55 | | | | | | | | Case 1:
% 50.51/7.55 | | | | | | | | |
% 50.51/7.55 | | | | | | | | | (320) xp = xn
% 50.51/7.55 | | | | | | | | |
% 50.51/7.55 | | | | | | | | | REDUCE: (10), (320) imply:
% 50.51/7.55 | | | | | | | | | (321) $false
% 50.51/7.55 | | | | | | | | |
% 50.51/7.55 | | | | | | | | | CLOSE: (321) is inconsistent.
% 50.51/7.55 | | | | | | | | |
% 50.51/7.55 | | | | | | | | Case 2:
% 50.51/7.55 | | | | | | | | |
% 50.51/7.55 | | | | | | | | | (322) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xp) =
% 50.51/7.55 | | | | | | | | | v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) | ~
% 50.51/7.55 | | | | | | | | | (v0 = 0))) | ! [v0: $i] : ! [v1: $i] : ! [v2:
% 50.51/7.55 | | | | | | | | | $i] : ! [v3: any] : ( ~ (sdtlseqdt0(v1, v2) = v3)
% 50.51/7.55 | | | | | | | | | | ~ (sdtpldt0(xp, v0) = v2) | ~ (sdtpldt0(xn, v0)
% 50.51/7.55 | | | | | | | | | = v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] :
% 50.51/7.55 | | | | | | | | | ? [v6: $i] : ? [v7: any] : (sdtlseqdt0(v5, v6) =
% 50.51/7.55 | | | | | | | | | v7 & sdtpldt0(v0, xp) = v6 & sdtpldt0(v0, xn) =
% 50.51/7.55 | | | | | | | | | v5 & aNaturalNumber0(v0) = v4 & $i(v6) & $i(v5) &
% 50.51/7.55 | | | | | | | | | ( ~ (v4 = 0) | (v7 = 0 & v3 = 0 & ~ (v6 = v5) &
% 50.51/7.55 | | | | | | | | | ~ (v2 = v1)))))
% 50.51/7.55 | | | | | | | | |
% 50.51/7.55 | | | | | | | | | BETA: splitting (97) gives:
% 50.51/7.55 | | | | | | | | |
% 50.51/7.55 | | | | | | | | | Case 1:
% 50.51/7.55 | | | | | | | | | |
% 50.51/7.55 | | | | | | | | | | (323) ? [v0: int] : ( ~ (v0 = 0) & aNaturalNumber0(xp) =
% 50.51/7.56 | | | | | | | | | | v0)
% 50.51/7.56 | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | BETA: splitting (322) gives:
% 50.51/7.56 | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | Case 1:
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | (324) ? [v0: any] : ? [v1: any] : (aNaturalNumber0(xp)
% 50.51/7.56 | | | | | | | | | | | = v1 & aNaturalNumber0(xn) = v0 & ( ~ (v1 = 0) |
% 50.51/7.56 | | | | | | | | | | | ~ (v0 = 0)))
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | DELTA: instantiating (323) with fresh symbol all_172_0
% 50.51/7.56 | | | | | | | | | | | gives:
% 50.51/7.56 | | | | | | | | | | | (325) ~ (all_172_0 = 0) & aNaturalNumber0(xp) =
% 50.51/7.56 | | | | | | | | | | | all_172_0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | ALPHA: (325) implies:
% 50.51/7.56 | | | | | | | | | | | (326) ~ (all_172_0 = 0)
% 50.51/7.56 | | | | | | | | | | | (327) aNaturalNumber0(xp) = all_172_0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | DELTA: instantiating (324) with fresh symbols all_174_0,
% 50.51/7.56 | | | | | | | | | | | all_174_1 gives:
% 50.51/7.56 | | | | | | | | | | | (328) aNaturalNumber0(xp) = all_174_0 &
% 50.51/7.56 | | | | | | | | | | | aNaturalNumber0(xn) = all_174_1 & ( ~ (all_174_0 =
% 50.51/7.56 | | | | | | | | | | | 0) | ~ (all_174_1 = 0))
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | ALPHA: (328) implies:
% 50.51/7.56 | | | | | | | | | | | (329) aNaturalNumber0(xp) = all_174_0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_174_0, xp,
% 50.51/7.56 | | | | | | | | | | | simplifying with (7), (329) gives:
% 50.51/7.56 | | | | | | | | | | | (330) all_174_0 = 0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | GROUND_INST: instantiating (28) with all_172_0, all_174_0, xp,
% 50.51/7.56 | | | | | | | | | | | simplifying with (327), (329) gives:
% 50.51/7.56 | | | | | | | | | | | (331) all_174_0 = all_172_0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | COMBINE_EQS: (330), (331) imply:
% 50.51/7.56 | | | | | | | | | | | (332) all_172_0 = 0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | REDUCE: (326), (332) imply:
% 50.51/7.56 | | | | | | | | | | | (333) $false
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | CLOSE: (333) is inconsistent.
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | Case 2:
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | DELTA: instantiating (323) with fresh symbol all_173_0
% 50.51/7.56 | | | | | | | | | | | gives:
% 50.51/7.56 | | | | | | | | | | | (334) ~ (all_173_0 = 0) & aNaturalNumber0(xp) =
% 50.51/7.56 | | | | | | | | | | | all_173_0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | ALPHA: (334) implies:
% 50.51/7.56 | | | | | | | | | | | (335) ~ (all_173_0 = 0)
% 50.51/7.56 | | | | | | | | | | | (336) aNaturalNumber0(xp) = all_173_0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_173_0, xp,
% 50.51/7.56 | | | | | | | | | | | simplifying with (7), (336) gives:
% 50.51/7.56 | | | | | | | | | | | (337) all_173_0 = 0
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | REDUCE: (335), (337) imply:
% 50.51/7.56 | | | | | | | | | | | (338) $false
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | | CLOSE: (338) is inconsistent.
% 50.51/7.56 | | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | End of split
% 50.51/7.56 | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | Case 2:
% 50.51/7.56 | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | (339) ~ (xp = sz10) & ~ (xp = sz00) & ! [v0: $i] : (v0
% 50.51/7.56 | | | | | | | | | | = xp | v0 = sz10 | ~ (doDivides0(v0, xp) = 0) |
% 50.51/7.56 | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 50.51/7.56 | | | | | | | | | | aNaturalNumber0(v0) = v1))
% 50.51/7.56 | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | ALPHA: (339) implies:
% 50.51/7.56 | | | | | | | | | | (340) ~ (xp = sz00)
% 50.51/7.56 | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | BETA: splitting (117) gives:
% 50.51/7.56 | | | | | | | | | |
% 50.51/7.56 | | | | | | | | | | Case 1:
% 50.51/7.56 | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | (341) ~ (all_74_1 = 0)
% 50.95/7.56 | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | REDUCE: (310), (341) imply:
% 50.95/7.56 | | | | | | | | | | | (342) $false
% 50.95/7.56 | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | CLOSE: (342) is inconsistent.
% 50.95/7.56 | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | Case 2:
% 50.95/7.56 | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | (343) ~ (all_74_2 = 0) | all_74_0 = 0
% 50.95/7.56 | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | BETA: splitting (102) gives:
% 50.95/7.56 | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | Case 1:
% 50.95/7.56 | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | (344) ~ (all_68_1 = 0)
% 50.95/7.56 | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | REDUCE: (315), (344) imply:
% 50.95/7.56 | | | | | | | | | | | | (345) $false
% 50.95/7.56 | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | CLOSE: (345) is inconsistent.
% 50.95/7.56 | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | Case 2:
% 50.95/7.56 | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | (346) ~ (all_68_2 = 0) | all_68_0 = 0
% 50.95/7.56 | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | BETA: splitting (346) gives:
% 50.95/7.56 | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | Case 1:
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | (347) ~ (all_68_2 = 0)
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | REDUCE: (316), (347) imply:
% 50.95/7.56 | | | | | | | | | | | | | (348) $false
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | CLOSE: (348) is inconsistent.
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | Case 2:
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | (349) all_68_0 = 0
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | REDUCE: (101), (349) imply:
% 50.95/7.56 | | | | | | | | | | | | | (350) aNaturalNumber0(all_42_0) = 0
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | BETA: splitting (89) gives:
% 50.95/7.56 | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | Case 1:
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | (351) ? [v0: any] : ? [v1: any] :
% 50.95/7.56 | | | | | | | | | | | | | | (aNaturalNumber0(all_42_0) = v1 &
% 50.95/7.56 | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v1 = 0) | ~ (v0
% 50.95/7.56 | | | | | | | | | | | | | | = 0)))
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | DELTA: instantiating (351) with fresh symbols all_240_0,
% 50.95/7.56 | | | | | | | | | | | | | | all_240_1 gives:
% 50.95/7.56 | | | | | | | | | | | | | | (352) aNaturalNumber0(all_42_0) = all_240_0 &
% 50.95/7.56 | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_240_1 & ( ~ (all_240_0 =
% 50.95/7.56 | | | | | | | | | | | | | | 0) | ~ (all_240_1 = 0))
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | ALPHA: (352) implies:
% 50.95/7.56 | | | | | | | | | | | | | | (353) aNaturalNumber0(xp) = all_240_1
% 50.95/7.56 | | | | | | | | | | | | | | (354) aNaturalNumber0(all_42_0) = all_240_0
% 50.95/7.56 | | | | | | | | | | | | | | (355) ~ (all_240_0 = 0) | ~ (all_240_1 = 0)
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_240_1, xp,
% 50.95/7.56 | | | | | | | | | | | | | | simplifying with (7), (353) gives:
% 50.95/7.56 | | | | | | | | | | | | | | (356) all_240_1 = 0
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_240_0, all_42_0,
% 50.95/7.56 | | | | | | | | | | | | | | simplifying with (350), (354) gives:
% 50.95/7.56 | | | | | | | | | | | | | | (357) all_240_0 = 0
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | Case 1:
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | (358) ~ (all_240_0 = 0)
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | REDUCE: (357), (358) imply:
% 50.95/7.56 | | | | | | | | | | | | | | | (359) $false
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | CLOSE: (359) is inconsistent.
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | Case 2:
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | (360) ~ (all_240_1 = 0)
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | REDUCE: (356), (360) imply:
% 50.95/7.56 | | | | | | | | | | | | | | | (361) $false
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | CLOSE: (361) is inconsistent.
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | End of split
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | Case 2:
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | (362) ? [v0: $i] : (sdtasdt0(xp, v0) = all_42_0 &
% 50.95/7.56 | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0))
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | DELTA: instantiating (362) with fresh symbol all_240_0
% 50.95/7.56 | | | | | | | | | | | | | | gives:
% 50.95/7.56 | | | | | | | | | | | | | | (363) sdtasdt0(xp, all_240_0) = all_42_0 &
% 50.95/7.56 | | | | | | | | | | | | | | aNaturalNumber0(all_240_0) = 0 & $i(all_240_0)
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | ALPHA: (363) implies:
% 50.95/7.56 | | | | | | | | | | | | | | (364) $i(all_240_0)
% 50.95/7.56 | | | | | | | | | | | | | | (365) aNaturalNumber0(all_240_0) = 0
% 50.95/7.56 | | | | | | | | | | | | | | (366) sdtasdt0(xp, all_240_0) = all_42_0
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 50.95/7.56 | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | Case 1:
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | (367) xp = sz00
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | REDUCE: (340), (367) imply:
% 50.95/7.56 | | | | | | | | | | | | | | | (368) $false
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | | CLOSE: (368) is inconsistent.
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.56 | | | | | | | | | | | | | | Case 2:
% 50.95/7.56 | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | (369) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.95/7.57 | | | | | | | | | | | | | | | (doDivides0(xp, all_42_0) = v2 &
% 50.95/7.57 | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = v1 &
% 50.95/7.57 | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 50.95/7.57 | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0))) | ( ! [v0: $i] : (v0 =
% 50.95/7.57 | | | | | | | | | | | | | | | xk | ~ (sdtasdt0(xp, v0) = all_42_0) | ~
% 50.95/7.57 | | | | | | | | | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 50.95/7.57 | | | | | | | | | | | | | | | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : (
% 50.95/7.57 | | | | | | | | | | | | | | | ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) | (v0 =
% 50.95/7.57 | | | | | | | | | | | | | | | all_42_0 & aNaturalNumber0(xk) = 0)))
% 50.95/7.57 | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 50.95/7.57 | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | (370) ~ (all_88_2 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | (371) ~ (all_74_2 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | REDUCE: (299), (371) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | (372) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | (373) all_74_0 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (308), (373) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | (374) all_70_2 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | SIMP: (374) implies:
% 50.95/7.57 | | | | | | | | | | | | | | | | | (375) all_70_2 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (375) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | (376) all_72_2 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (377) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (doDivides0(xp, all_42_0) = v2 &
% 50.95/7.57 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = v1 &
% 50.95/7.57 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = v0 & ( ~ (v2 = 0) | ~ (v1
% 50.95/7.57 | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0)))
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | DELTA: instantiating (377) with fresh symbols all_282_0,
% 50.95/7.57 | | | | | | | | | | | | | | | | | | all_282_1, all_282_2 gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (378) doDivides0(xp, all_42_0) = all_282_0 &
% 50.95/7.57 | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_42_0) = all_282_1 &
% 50.95/7.57 | | | | | | | | | | | | | | | | | | aNaturalNumber0(xp) = all_282_2 & ( ~ (all_282_0 =
% 50.95/7.57 | | | | | | | | | | | | | | | | | | 0) | ~ (all_282_1 = 0) | ~ (all_282_2 = 0))
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | ALPHA: (378) implies:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (379) aNaturalNumber0(xp) = all_282_2
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (380) aNaturalNumber0(all_42_0) = all_282_1
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (381) doDivides0(xp, all_42_0) = all_282_0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (382) ~ (all_282_0 = 0) | ~ (all_282_1 = 0) | ~
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (all_282_2 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_282_2, xp,
% 50.95/7.57 | | | | | | | | | | | | | | | | | | simplifying with (7), (379) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (383) all_282_2 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_282_1, all_42_0,
% 50.95/7.57 | | | | | | | | | | | | | | | | | | simplifying with (350), (380) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (384) all_282_1 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (33) with 0, all_282_0, all_42_0,
% 50.95/7.57 | | | | | | | | | | | | | | | | | | xp, simplifying with (68), (381) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (385) all_282_0 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | BETA: splitting (382) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | (386) ~ (all_282_0 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | REDUCE: (385), (386) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | (387) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | CLOSE: (387) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | (388) ~ (all_282_1 = 0) | ~ (all_282_2 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | (389) ~ (all_282_1 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (384), (389) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | (390) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | CLOSE: (390) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | (391) ~ (all_282_2 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (391) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | (392) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | CLOSE: (392) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (393) ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 50.95/7.57 | | | | | | | | | | | | | | | | | | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 50.95/7.57 | | | | | | | | | | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1)) & ! [v0:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | $i] : ( ~ (sdtasdt0(xp, xk) = v0) | ~ $i(xk) |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (v0 = all_42_0 & aNaturalNumber0(xk) = 0))
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | ALPHA: (393) implies:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | (394) ! [v0: $i] : (v0 = xk | ~ (sdtasdt0(xp, v0) =
% 50.95/7.57 | | | | | | | | | | | | | | | | | | all_42_0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 50.95/7.57 | | | | | | | | | | | | | | | | | | = 0) & aNaturalNumber0(v0) = v1))
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | (395) ~ (all_72_1 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | REDUCE: (306), (395) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | (396) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | CLOSE: (396) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | (397) ~ (all_72_2 = 0) | all_72_0 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | (398) ~ (all_70_1 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (398) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | (399) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | CLOSE: (399) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | (400) ~ (all_70_2 = 0) | all_70_0 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (397) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | (401) ~ (all_72_2 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (401) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | (402) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | CLOSE: (402) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | (403) all_72_0 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (403) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | (404) aNaturalNumber0(all_50_0) = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (400) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | (405) ~ (all_70_2 = 0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (405) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | (406) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (406) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | (407) all_70_0 = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (407) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | (408) aNaturalNumber0(all_50_1) = 0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (409) all_50_0 = all_50_1
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (409) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (410) $false
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (410) is inconsistent.
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_50_0, all_90_3, xp,
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | all_50_2, simplifying with (54), (318) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (411) all_90_3 = all_50_0
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_50_1, all_88_3, xr,
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | all_50_2, simplifying with (55), (319) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (412) all_88_3 = all_50_1
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (412) imply:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (413) iLess0(all_50_1, all_50_0) = all_88_2
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_240_0, simplifying with
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (364), (365) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (414) all_240_0 = sz10 | all_240_0 = sz00 | ? [v0: $i]
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | : (isPrime0(v0) = 0 & doDivides0(v0, all_240_0) =
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | 0 & aNaturalNumber0(v0) = 0 & $i(v0))
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (394) with all_240_0, simplifying
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | with (364), (366) gives:
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | (415) all_240_0 = xk | ? [v0: int] : ( ~ (v0 = 0) &
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_240_0) = v0)
% 50.95/7.57 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (mIH_03) with all_50_1, all_50_0,
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | all_88_2, simplifying with (52), (73), (413)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | (416) all_88_2 = 0 | all_50_0 = all_50_1 | ? [v0: any]
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | : ? [v1: any] : ? [v2: any] :
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | (sdtlseqdt0(all_50_1, all_50_0) = v2 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_0) = v1 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_1) = v0 & ( ~ (v2 = 0) |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | (417) all_240_0 = xk
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (416) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_88_2 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (418) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | (419) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (419) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | (420) all_50_0 = all_50_1 | ? [v0: any] : ? [v1: any]
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | : ? [v2: any] : (sdtlseqdt0(all_50_1, all_50_0) =
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | v2 & aNaturalNumber0(all_50_0) = v1 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_1) = v0 & ( ~ (v2 = 0) |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_240_0 = sz00
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (421) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (422) xk = sz00
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (422) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (423) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (423) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_240_0 = sz10 | ? [v0: $i] : (isPrime0(v0) = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & doDivides0(v0, all_240_0) = 0 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(v0) = 0 & $i(v0))
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) all_50_0 = all_50_1
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (425) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (426) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (sdtlseqdt0(all_50_1, all_50_0) = v2 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_0) = v1 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_1) = v0 & ( ~ (v2 = 0) |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (427) with fresh symbols all_592_0,
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_592_1, all_592_2 gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) sdtlseqdt0(all_50_1, all_50_0) = all_592_0 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_0) = all_592_1 &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_50_1) = all_592_2 & ( ~
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_592_0 = 0) | ~ (all_592_1 = 0) | ~
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_592_2 = 0))
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (428) implies:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) aNaturalNumber0(all_50_1) = all_592_2
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) aNaturalNumber0(all_50_0) = all_592_1
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) sdtlseqdt0(all_50_1, all_50_0) = all_592_0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) ~ (all_592_0 = 0) | ~ (all_592_1 = 0) | ~
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_592_2 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (424) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_240_0 = sz10
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (417), (433) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) xk = sz10
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (434) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (435) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_592_2, all_50_1,
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (408), (429) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_592_2 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_592_1, all_50_0,
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (404), (430) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) all_592_1 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with 0, all_592_0, all_50_0,
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_50_1, simplifying with (56), (431) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_592_0 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) ~ (all_592_0 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (438), (439) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (440) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) ~ (all_592_1 = 0) | ~ (all_592_2 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) ~ (all_592_1 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (442) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (443) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) ~ (all_592_2 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (436), (444) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (445) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | (446) ? [v0: int] : ( ~ (v0 = 0) &
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | aNaturalNumber0(all_240_0) = v0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (446) with fresh symbol all_460_0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | (447) ~ (all_460_0 = 0) & aNaturalNumber0(all_240_0) =
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | all_460_0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | (448) ~ (all_460_0 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | (449) aNaturalNumber0(all_240_0) = all_460_0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_460_0, all_240_0,
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (365), (449) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | (450) all_460_0 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (448), (450) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | (451) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (451) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | End of split
% 50.95/7.58 | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | (452) ~ (all_88_5 = 0) | ~ (all_88_6 = 0) | ~
% 50.95/7.58 | | | | | | | | | | | | | | | | (all_88_7 = 0) | ~ (all_88_8 = 0) | all_88_0 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | all_88_1 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | BETA: splitting (452) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | (453) ~ (all_88_5 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | REDUCE: (246), (453) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | (454) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | CLOSE: (454) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | (455) ~ (all_88_6 = 0) | ~ (all_88_7 = 0) | ~
% 50.95/7.58 | | | | | | | | | | | | | | | | | (all_88_8 = 0) | all_88_0 = 0 | all_88_1 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | (456) ~ (all_88_6 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | REDUCE: (225), (456) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | (457) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | CLOSE: (457) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | (458) ~ (all_88_7 = 0) | ~ (all_88_8 = 0) | all_88_0 =
% 50.95/7.58 | | | | | | | | | | | | | | | | | | 0 | all_88_1 = 0
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives:
% 50.95/7.58 | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | (459) ~ (all_88_7 = 0)
% 50.95/7.58 | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | REDUCE: (212), (459) imply:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | (460) $false
% 50.95/7.58 | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | | CLOSE: (460) is inconsistent.
% 50.95/7.58 | | | | | | | | | | | | | | | | | | |
% 50.95/7.58 | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.58 | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | (461) ~ (all_88_8 = 0) | all_88_0 = 0 | all_88_1 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | (462) ~ (all_88_8 = 0)
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (317), (462) imply:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | (463) $false
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | CLOSE: (463) is inconsistent.
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | (464) all_88_0 = 0 | all_88_1 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (464) gives:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (465) all_88_0 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (465) imply:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (466) all_48_0 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | SIMP: (466) implies:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (467) all_48_0 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (467) imply:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (468) $false
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (468) is inconsistent.
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (469) all_88_1 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (469) imply:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (470) all_48_1 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | SIMP: (470) implies:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (471) all_48_1 = 0
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | REDUCE: (46), (471) imply:
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | (472) $false
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | | CLOSE: (472) is inconsistent.
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | | |
% 50.95/7.59 | | | | | | | | | End of split
% 50.95/7.59 | | | | | | | | |
% 50.95/7.59 | | | | | | | | End of split
% 50.95/7.59 | | | | | | | |
% 50.95/7.59 | | | | | | | End of split
% 50.95/7.59 | | | | | | |
% 50.95/7.59 | | | | | | End of split
% 50.95/7.59 | | | | | |
% 50.95/7.59 | | | | | End of split
% 50.95/7.59 | | | | |
% 50.95/7.59 | | | | End of split
% 50.95/7.59 | | | |
% 50.95/7.59 | | | End of split
% 50.95/7.59 | | |
% 50.95/7.59 | | End of split
% 50.95/7.59 | |
% 50.95/7.59 | End of split
% 50.95/7.59 |
% 50.95/7.59 End of proof
% 50.95/7.59 % SZS output end Proof for theBenchmark
% 50.95/7.59
% 50.95/7.59 6978ms
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