TSTP Solution File: NUM496+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM496+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 11:48:10 EDT 2023
% Result : Theorem 22.81s 4.00s
% Output : Proof 83.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM496+3 : 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 : n017.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 07:52:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.07/1.37 Prover 4: Preprocessing ...
% 4.07/1.38 Prover 1: Preprocessing ...
% 4.76/1.44 Prover 5: Preprocessing ...
% 4.76/1.44 Prover 0: Preprocessing ...
% 4.76/1.44 Prover 6: Preprocessing ...
% 4.76/1.44 Prover 3: Preprocessing ...
% 4.76/1.44 Prover 2: Preprocessing ...
% 12.54/2.55 Prover 3: Constructing countermodel ...
% 12.54/2.57 Prover 1: Constructing countermodel ...
% 12.54/2.57 Prover 6: Proving ...
% 13.12/2.68 Prover 5: Constructing countermodel ...
% 15.95/3.06 Prover 4: Constructing countermodel ...
% 15.95/3.06 Prover 2: Proving ...
% 16.89/3.14 Prover 0: Proving ...
% 22.81/4.00 Prover 3: proved (3346ms)
% 22.81/4.00
% 22.81/4.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.81/4.00
% 22.81/4.00 Prover 5: stopped
% 22.81/4.00 Prover 0: stopped
% 22.81/4.01 Prover 2: stopped
% 22.81/4.02 Prover 6: stopped
% 23.45/4.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.45/4.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.45/4.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.45/4.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.45/4.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.45/4.16 Prover 7: Preprocessing ...
% 23.45/4.16 Prover 8: Preprocessing ...
% 23.45/4.18 Prover 11: Preprocessing ...
% 23.45/4.19 Prover 10: Preprocessing ...
% 24.39/4.25 Prover 13: Preprocessing ...
% 25.62/4.40 Prover 10: Constructing countermodel ...
% 26.42/4.43 Prover 8: Warning: ignoring some quantifiers
% 26.42/4.47 Prover 8: Constructing countermodel ...
% 26.42/4.49 Prover 7: Constructing countermodel ...
% 27.70/4.67 Prover 13: Constructing countermodel ...
% 28.62/4.75 Prover 11: Constructing countermodel ...
% 64.79/9.49 Prover 13: stopped
% 64.79/9.51 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 65.29/9.56 Prover 16: Preprocessing ...
% 66.06/9.68 Prover 16: Constructing countermodel ...
% 81.75/11.78 Prover 10: Found proof (size 117)
% 81.75/11.78 Prover 10: proved (7763ms)
% 81.75/11.78 Prover 11: stopped
% 81.75/11.78 Prover 7: stopped
% 81.75/11.78 Prover 8: stopped
% 81.75/11.78 Prover 16: stopped
% 81.75/11.78 Prover 1: stopped
% 82.21/11.83 Prover 4: stopped
% 82.21/11.83
% 82.21/11.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 82.21/11.83
% 82.21/11.84 % SZS output start Proof for theBenchmark
% 82.21/11.84 Assumptions after simplification:
% 82.21/11.84 ---------------------------------
% 82.21/11.84
% 82.21/11.85 (mAddAsso)
% 82.48/11.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 82.48/11.88 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 82.48/11.88 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 82.48/11.88 aNaturalNumber0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0,
% 82.48/11.88 v5) = v4 & $i(v5) & $i(v4)))
% 82.48/11.88
% 82.48/11.88 (mAddCanc)
% 82.48/11.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1
% 82.48/11.89 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~
% 82.48/11.89 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 82.48/11.89 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) &
% 82.48/11.89 sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & $i(v6) & $i(v5))) & !
% 82.48/11.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 82.48/11.89 (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 82.48/11.89 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 82.48/11.89 aNaturalNumber0(v0))
% 82.48/11.89
% 82.48/11.89 (mAddComm)
% 82.48/11.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 82.48/11.89 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 82.48/11.89 (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 82.48/11.89
% 82.48/11.89 (mDefDiff)
% 82.48/11.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 82.48/11.90 (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ $i(v1)
% 82.48/11.90 | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~
% 82.48/11.90 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] :
% 82.48/11.90 ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~
% 82.48/11.90 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 82.48/11.90 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & !
% 82.48/11.90 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v1, v0) =
% 82.48/11.90 v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 82.48/11.90 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 82.48/11.90 aNaturalNumber0(v2))
% 82.48/11.90
% 82.48/11.90 (mDefDiv)
% 82.48/11.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~
% 82.48/11.90 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 82.48/11.90 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0:
% 82.48/11.90 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 82.48/11.90 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0,
% 82.48/11.90 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 82.48/11.90
% 82.48/11.90 (mDefLE)
% 82.48/11.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~
% 82.48/11.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 82.48/11.91 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~
% 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0,
% 82.48/11.91 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 82.48/11.91
% 82.48/11.91 (mDefPrime)
% 82.48/11.91 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~
% 82.48/11.91 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~
% 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 |
% 82.48/11.91 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i]
% 82.48/11.91 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) &
% 82.48/11.91 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & (
% 82.48/11.91 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00))
% 82.48/11.91
% 82.48/11.91 (mDivSum)
% 82.48/11.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtpldt0(v1, v2)
% 82.48/11.91 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v2) | ~
% 82.48/11.91 doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 82.48/11.91 aNaturalNumber0(v0) | doDivides0(v0, v3))
% 82.48/11.91
% 82.48/11.91 (mDivTrans)
% 82.48/11.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 82.48/11.91 ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~
% 82.48/11.91 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 82.48/11.91
% 82.48/11.91 (mMonAdd)
% 82.48/11.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 82.48/11.92 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 82.48/11.92 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 82.48/11.92 aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 =
% 82.48/11.92 v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 &
% 82.48/11.92 sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & sdtlseqdt0(v4, v5) &
% 82.48/11.92 sdtlseqdt0(v3, v6)))
% 82.48/11.92
% 82.48/11.92 (mPrimDiv)
% 82.48/11.92 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 82.48/11.92 aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & doDivides0(v1,
% 82.48/11.92 v0) & aNaturalNumber0(v1)))
% 82.48/11.92
% 82.48/11.92 (mSortsC_01)
% 82.48/11.92 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 82.48/11.92
% 82.48/11.92 (m__)
% 82.48/11.92 $i(xp) & $i(xm) & $i(xn) & ~ doDivides0(xp, xm) & ~ doDivides0(xp, xn) & !
% 82.48/11.92 [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xm) | ~ $i(v0) | ~ aNaturalNumber0(v0)) &
% 82.48/11.92 ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xn) | ~ $i(v0) | ~
% 82.48/11.92 aNaturalNumber0(v0))
% 82.48/11.92
% 82.48/11.92 (m__1799)
% 82.48/11.95 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] :
% 82.48/11.95 (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm) = v0 & $i(v1) & $i(v0) & ! [v2: $i]
% 82.48/11.95 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 =
% 82.48/11.95 sz00 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4)
% 82.48/11.95 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) |
% 82.48/11.95 doDivides0(v4, v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10:
% 82.48/11.95 $i] : ($i(v9) & $i(v8) & ((v10 = v4 & ~ (v8 = v4) & ~ (v8 = sz10) &
% 82.48/11.95 sdtasdt0(v8, v9) = v4 & doDivides0(v8, v4) & aNaturalNumber0(v9) &
% 82.48/11.95 aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 82.48/11.95 doDivides0(v4, v7) & ! [v11: $i] : ( ~ (sdtasdt0(v4, v11) = v7) |
% 82.48/11.95 ~ $i(v11) | ~ aNaturalNumber0(v11)))))) & ! [v2: $i] : ! [v3:
% 82.48/11.95 $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 |
% 82.48/11.95 ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~
% 82.48/11.95 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | ?
% 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 82.48/11.95 [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & ~
% 82.48/11.95 (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, v4) &
% 82.48/11.95 aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = v2 &
% 82.48/11.95 sdtasdt0(v4, v8) = v2 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v13: $i] : ( ~
% 82.48/11.95 (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~
% 82.48/11.95 aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 82.48/11.95 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 82.48/11.95 (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~
% 82.48/11.95 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ?
% 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ?
% 82.48/11.95 [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) & ~
% 82.48/11.95 (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10, v4) &
% 82.48/11.95 aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 = v3 &
% 82.48/11.95 sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v13: $i] : ( ~
% 82.48/11.95 (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~
% 82.48/11.95 aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 82.48/11.95 $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 82.48/11.95 (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~
% 82.48/11.95 $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] :
% 82.48/11.95 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] :
% 82.48/11.95 ? [v14: $i] : ($i(v13) & $i(v12) & $i(v10) & $i(v8) & ((v14 = v4 & ~ (v12
% 82.48/11.95 = v4) & ~ (v12 = sz10) & sdtasdt0(v12, v13) = v4 &
% 82.48/11.95 doDivides0(v12, v4) & aNaturalNumber0(v13) & aNaturalNumber0(v12)) |
% 82.48/11.95 (v11 = v2 & sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3
% 82.48/11.95 & sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v15: $i] : ( ~
% 82.48/11.95 (sdtasdt0(v4, v15) = v7) | ~ $i(v15) | ~
% 82.48/11.95 aNaturalNumber0(v15)))))) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 82.48/11.95 $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~
% 82.48/11.95 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 82.48/11.95 isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) |
% 82.48/11.95 doDivides0(v4, v2) | ? [v7: $i] : (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 82.48/11.95 doDivides0(v4, v7) & ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) | ~
% 82.48/11.95 $i(v8) | ~ aNaturalNumber0(v8)))) & ! [v2: $i] : ! [v3: $i] : !
% 82.48/11.95 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) | ~
% 82.48/11.95 (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 82.48/11.95 isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3) | ?
% 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v8) & ((v9 = v2 & sdtasdt0(v4,
% 82.48/11.95 v8) = v2 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7)
% 82.48/11.95 & ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) =
% 82.48/11.95 v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2: $i] :
% 82.48/11.95 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4)
% 82.48/11.95 = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 82.48/11.95 ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ?
% 82.48/11.95 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ($i(v8) & ((v9 = v3 & sdtasdt0(v4,
% 82.48/11.95 v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7)
% 82.48/11.95 & ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10) =
% 82.48/11.95 v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & ! [v2: $i] :
% 82.48/11.95 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4)
% 82.48/11.95 = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 82.48/11.95 ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.48/11.95 aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] :
% 82.48/11.95 ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ($i(v10) & $i(v8) & ((v11 = v2
% 82.48/11.95 & sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 &
% 82.48/11.95 sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) =
% 82.48/11.95 v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v12: $i] : ( ~
% 82.48/11.95 (sdtasdt0(v4, v12) = v7) | ~ $i(v12) | ~
% 82.48/11.95 aNaturalNumber0(v12)))))))
% 82.48/11.95
% 82.48/11.95 (m__1837)
% 82.48/11.95 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 82.48/11.95 aNaturalNumber0(xn)
% 82.48/11.95
% 82.48/11.95 (m__1860)
% 82.48/11.95 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (
% 82.48/11.95 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) =
% 82.48/11.95 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) &
% 82.48/11.95 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~
% 82.48/11.95 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) |
% 82.48/11.95 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) |
% 82.48/11.95 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 82.48/11.95
% 82.48/11.95 (m__1870)
% 82.48/11.95 $i(xp) & $i(xn) & ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) &
% 82.48/11.95 sdtlseqdt0(xp, xn) & aNaturalNumber0(v0))
% 82.48/11.95
% 82.48/11.95 (m__1883)
% 82.48/11.96 sdtmndt0(xn, xp) = xr & sdtpldt0(xp, xr) = xn & $i(xr) & $i(xp) & $i(xn) &
% 82.48/11.96 aNaturalNumber0(xr)
% 82.48/11.96
% 82.48/11.96 (m__1894)
% 82.48/11.96 $i(xr) & $i(xn) & ? [v0: $i] : ( ~ (xr = xn) & sdtpldt0(xr, v0) = xn & $i(v0)
% 82.48/11.96 & sdtlseqdt0(xr, xn) & aNaturalNumber0(v0))
% 82.48/11.96
% 82.48/11.96 (m__2027)
% 82.48/11.96 $i(xr) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 82.48/11.96 $i] : ($i(v2) & $i(v0) & ((v3 = xr & sdtasdt0(xp, v2) = xr & doDivides0(xp,
% 82.48/11.96 xr) & aNaturalNumber0(v2)) | (v1 = xm & sdtasdt0(xp, v0) = xm &
% 82.48/11.96 doDivides0(xp, xm) & aNaturalNumber0(v0))))
% 82.48/11.96
% 82.48/11.96 (function-axioms)
% 82.73/11.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 82.73/11.96 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 82.73/11.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 82.73/11.96 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 82.73/11.96 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 82.73/11.96 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 82.73/11.96 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 82.73/11.96
% 82.73/11.96 Further assumptions not needed in the proof:
% 82.73/11.96 --------------------------------------------
% 82.73/11.96 mAMDistr, mDefQuot, mDivAsso, mDivLE, mDivMin, mIH, mIH_03, mLEAsym, mLENTr,
% 82.73/11.96 mLERefl, mLETotal, mLETran, mMonMul, mMonMul2, mMulAsso, mMulCanc, mMulComm,
% 82.73/11.96 mNatSort, mSortsB, mSortsB_02, mSortsC, mZeroAdd, mZeroMul, m_AddZero,
% 82.73/11.96 m_MulUnit, m_MulZero, m__1913
% 82.73/11.96
% 82.73/11.96 Those formulas are unsatisfiable:
% 82.73/11.96 ---------------------------------
% 82.73/11.96
% 82.73/11.96 Begin of proof
% 82.73/11.96 |
% 82.73/11.96 | ALPHA: (mSortsC_01) implies:
% 82.73/11.96 | (1) aNaturalNumber0(sz10)
% 82.73/11.96 |
% 82.73/11.96 | ALPHA: (mAddCanc) implies:
% 82.73/11.96 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 82.73/11.96 | (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~
% 82.73/11.96 | $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)
% 82.73/11.96 | | ~ aNaturalNumber0(v0))
% 82.73/11.97 |
% 82.73/11.97 | ALPHA: (mDefLE) implies:
% 82.73/11.97 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0,
% 82.73/11.97 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 82.73/11.97 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 82.73/11.97 |
% 82.73/11.97 | ALPHA: (mDefDiff) implies:
% 82.73/11.97 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 82.73/11.97 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~
% 82.73/11.97 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) |
% 82.73/11.97 | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 82.73/11.97 |
% 82.73/11.97 | ALPHA: (mDefDiv) implies:
% 82.73/11.97 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 82.73/11.97 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 82.73/11.97 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 82.73/11.97 |
% 82.73/11.97 | ALPHA: (mDefPrime) implies:
% 82.73/11.97 | (6) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)
% 82.73/11.97 |
% 82.73/11.97 | ALPHA: (mPrimDiv) implies:
% 82.73/11.97 | (7) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 82.73/11.97 | aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) &
% 82.73/11.97 | doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 82.73/11.97 |
% 82.73/11.97 | ALPHA: (m__1837) implies:
% 82.73/11.97 | (8) aNaturalNumber0(xn)
% 82.73/11.97 | (9) aNaturalNumber0(xm)
% 82.73/11.97 | (10) aNaturalNumber0(xp)
% 82.73/11.97 |
% 82.73/11.97 | ALPHA: (m__1799) implies:
% 82.73/11.99 | (11) ? [v0: $i] : ? [v1: $i] : (sdtpldt0(v0, xp) = v1 & sdtpldt0(xn, xm)
% 82.73/11.99 | = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 82.73/11.99 | ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~ (sdtpldt0(v5,
% 82.73/11.99 | v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3)
% 82.73/11.99 | | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.73/11.99 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3)
% 82.73/11.99 | | doDivides0(v4, v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 82.73/11.99 | ? [v10: $i] : ($i(v9) & $i(v8) & ((v10 = v4 & ~ (v8 = v4) & ~
% 82.73/11.99 | (v8 = sz10) & sdtasdt0(v8, v9) = v4 & doDivides0(v8, v4) &
% 82.73/11.99 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (sdtasdt0(v2,
% 82.73/11.99 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v11: $i] :
% 82.73/11.99 | ( ~ (sdtasdt0(v4, v11) = v7) | ~ $i(v11) | ~
% 82.73/11.99 | aNaturalNumber0(v11)))))) & ! [v2: $i] : ! [v3: $i] : !
% 82.73/11.99 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 82.73/11.99 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) |
% 82.73/11.99 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4)
% 82.73/11.99 | | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4,
% 82.73/11.99 | v3) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 82.73/11.99 | ? [v11: $i] : ? [v12: $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 =
% 82.73/11.99 | v4 & ~ (v10 = v4) & ~ (v10 = sz10) & sdtasdt0(v10, v11) =
% 82.73/11.99 | v4 & doDivides0(v10, v4) & aNaturalNumber0(v11) &
% 82.73/11.99 | aNaturalNumber0(v10)) | (v9 = v2 & sdtasdt0(v4, v8) = v2 &
% 82.73/11.99 | aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~
% 82.73/11.99 | doDivides0(v4, v7) & ! [v13: $i] : ( ~ (sdtasdt0(v4, v13) =
% 82.73/11.99 | v7) | ~ $i(v13) | ~ aNaturalNumber0(v13)))))) & !
% 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 82.73/11.99 | (v4 = sz10 | v4 = sz00 | ~ (sdtpldt0(v5, v4) = v6) | ~
% 82.73/11.99 | (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 82.73/11.99 | iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) |
% 82.73/11.99 | ~ aNaturalNumber0(v2) | doDivides0(v4, v2) | ? [v7: $i] : ?
% 82.73/11.99 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 82.73/11.99 | $i] : ($i(v11) & $i(v10) & $i(v8) & ((v12 = v4 & ~ (v10 = v4) &
% 82.73/11.99 | ~ (v10 = sz10) & sdtasdt0(v10, v11) = v4 & doDivides0(v10,
% 82.73/11.99 | v4) & aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 =
% 82.73/11.99 | v3 & sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) |
% 82.73/11.99 | (sdtasdt0(v2, v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & !
% 82.73/11.99 | [v13: $i] : ( ~ (sdtasdt0(v4, v13) = v7) | ~ $i(v13) | ~
% 82.73/11.99 | aNaturalNumber0(v13)))))) & ! [v2: $i] : ! [v3: $i] : !
% 82.73/11.99 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v4 = sz10 | v4 = sz00 | ~
% 82.73/11.99 | (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) |
% 82.73/11.99 | ~ $i(v3) | ~ $i(v2) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4)
% 82.73/11.99 | | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ? [v7: $i] :
% 82.73/11.99 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 82.73/11.99 | $i] : ? [v13: $i] : ? [v14: $i] : ($i(v13) & $i(v12) & $i(v10)
% 82.73/11.99 | & $i(v8) & ((v14 = v4 & ~ (v12 = v4) & ~ (v12 = sz10) &
% 82.73/11.99 | sdtasdt0(v12, v13) = v4 & doDivides0(v12, v4) &
% 82.73/11.99 | aNaturalNumber0(v13) & aNaturalNumber0(v12)) | (v11 = v2 &
% 82.73/11.99 | sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 &
% 82.73/11.99 | sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2,
% 82.73/11.99 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v15: $i] :
% 82.73/11.99 | ( ~ (sdtasdt0(v4, v15) = v7) | ~ $i(v15) | ~
% 82.73/11.99 | aNaturalNumber0(v15)))))) & ! [v2: $i] : ! [v3: $i] : !
% 82.73/11.99 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (sdtpldt0(v5, v4) = v6) |
% 82.73/11.99 | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) |
% 82.73/11.99 | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~ aNaturalNumber0(v4) | ~
% 82.73/11.99 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | doDivides0(v4, v3)
% 82.73/11.99 | | doDivides0(v4, v2) | ? [v7: $i] : (sdtasdt0(v2, v3) = v7 &
% 82.73/11.99 | $i(v7) & ~ doDivides0(v4, v7) & ! [v8: $i] : ( ~ (sdtasdt0(v4,
% 82.73/11.99 | v8) = v7) | ~ $i(v8) | ~ aNaturalNumber0(v8)))) & !
% 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 82.73/11.99 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4)
% 82.73/11.99 | | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~
% 82.73/11.99 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~
% 82.73/11.99 | aNaturalNumber0(v2) | doDivides0(v4, v3) | ? [v7: $i] : ? [v8:
% 82.73/11.99 | $i] : ? [v9: $i] : ($i(v8) & ((v9 = v2 & sdtasdt0(v4, v8) = v2
% 82.73/11.99 | & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) &
% 82.73/11.99 | ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10)
% 82.73/11.99 | = v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & !
% 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 82.73/11.99 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4)
% 82.73/11.99 | | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~
% 82.73/11.99 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~
% 82.73/11.99 | aNaturalNumber0(v2) | doDivides0(v4, v2) | ? [v7: $i] : ? [v8:
% 82.73/11.99 | $i] : ? [v9: $i] : ($i(v8) & ((v9 = v3 & sdtasdt0(v4, v8) = v3
% 82.73/11.99 | & aNaturalNumber0(v8)) | (sdtasdt0(v2, v3) = v7 & $i(v7) &
% 82.73/11.99 | ~ doDivides0(v4, v7) & ! [v10: $i] : ( ~ (sdtasdt0(v4, v10)
% 82.73/11.99 | = v7) | ~ $i(v10) | ~ aNaturalNumber0(v10)))))) & !
% 82.73/11.99 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (
% 82.73/11.99 | ~ (sdtpldt0(v5, v4) = v6) | ~ (sdtpldt0(v2, v3) = v5) | ~ $i(v4)
% 82.73/11.99 | | ~ $i(v3) | ~ $i(v2) | ~ isPrime0(v4) | ~ iLess0(v6, v1) | ~
% 82.73/11.99 | aNaturalNumber0(v4) | ~ aNaturalNumber0(v3) | ~
% 82.73/11.99 | aNaturalNumber0(v2) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 82.73/11.99 | [v10: $i] : ? [v11: $i] : ($i(v10) & $i(v8) & ((v11 = v2 &
% 82.73/11.99 | sdtasdt0(v4, v10) = v2 & aNaturalNumber0(v10)) | (v9 = v3 &
% 82.73/11.99 | sdtasdt0(v4, v8) = v3 & aNaturalNumber0(v8)) | (sdtasdt0(v2,
% 82.73/11.99 | v3) = v7 & $i(v7) & ~ doDivides0(v4, v7) & ! [v12: $i] :
% 82.73/11.99 | ( ~ (sdtasdt0(v4, v12) = v7) | ~ $i(v12) | ~
% 82.73/11.99 | aNaturalNumber0(v12)))))))
% 82.73/11.99 |
% 82.73/11.99 | ALPHA: (m__1860) implies:
% 82.73/11.99 | (12) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) &
% 82.73/11.99 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) &
% 82.73/11.99 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2:
% 82.73/11.99 | $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) =
% 82.73/11.99 | xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~
% 82.73/11.99 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~
% 82.73/11.99 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 82.73/11.99 |
% 82.73/11.99 | ALPHA: (m__1870) implies:
% 82.73/12.00 | (13) ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) & sdtlseqdt0(xp, xn) &
% 82.73/12.00 | aNaturalNumber0(v0))
% 82.73/12.00 |
% 82.73/12.00 | ALPHA: (m__1883) implies:
% 82.73/12.00 | (14) aNaturalNumber0(xr)
% 82.73/12.00 | (15) sdtpldt0(xp, xr) = xn
% 82.73/12.00 | (16) sdtmndt0(xn, xp) = xr
% 82.73/12.00 |
% 82.73/12.00 | ALPHA: (m__1894) implies:
% 82.73/12.00 | (17) ? [v0: $i] : ( ~ (xr = xn) & sdtpldt0(xr, v0) = xn & $i(v0) &
% 82.73/12.00 | sdtlseqdt0(xr, xn) & aNaturalNumber0(v0))
% 82.73/12.00 |
% 82.73/12.00 | ALPHA: (m__2027) implies:
% 82.73/12.00 | (18) $i(xr)
% 82.73/12.00 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v2) &
% 82.73/12.00 | $i(v0) & ((v3 = xr & sdtasdt0(xp, v2) = xr & doDivides0(xp, xr) &
% 82.73/12.00 | aNaturalNumber0(v2)) | (v1 = xm & sdtasdt0(xp, v0) = xm &
% 82.73/12.00 | doDivides0(xp, xm) & aNaturalNumber0(v0))))
% 82.73/12.00 |
% 82.73/12.00 | ALPHA: (m__) implies:
% 83.10/12.00 | (20) ~ doDivides0(xp, xn)
% 83.10/12.00 | (21) ~ doDivides0(xp, xm)
% 83.10/12.00 | (22) $i(xn)
% 83.10/12.00 | (23) $i(xm)
% 83.10/12.00 | (24) $i(xp)
% 83.10/12.00 |
% 83.10/12.00 | ALPHA: (function-axioms) implies:
% 83.10/12.00 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 83.10/12.00 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 83.10/12.00 |
% 83.10/12.00 | DELTA: instantiating (13) with fresh symbol all_39_0 gives:
% 83.10/12.00 | (26) sdtpldt0(xp, all_39_0) = xn & $i(all_39_0) & sdtlseqdt0(xp, xn) &
% 83.10/12.00 | aNaturalNumber0(all_39_0)
% 83.10/12.00 |
% 83.10/12.00 | ALPHA: (26) implies:
% 83.10/12.00 | (27) aNaturalNumber0(all_39_0)
% 83.10/12.00 | (28) sdtlseqdt0(xp, xn)
% 83.10/12.00 | (29) $i(all_39_0)
% 83.10/12.00 | (30) sdtpldt0(xp, all_39_0) = xn
% 83.10/12.00 |
% 83.10/12.00 | DELTA: instantiating (17) with fresh symbol all_41_0 gives:
% 83.10/12.00 | (31) ~ (xr = xn) & sdtpldt0(xr, all_41_0) = xn & $i(all_41_0) &
% 83.10/12.00 | sdtlseqdt0(xr, xn) & aNaturalNumber0(all_41_0)
% 83.10/12.00 |
% 83.10/12.00 | ALPHA: (31) implies:
% 83.10/12.00 | (32) ~ (xr = xn)
% 83.10/12.00 | (33) aNaturalNumber0(all_41_0)
% 83.10/12.00 | (34) sdtlseqdt0(xr, xn)
% 83.10/12.00 | (35) $i(all_41_0)
% 83.10/12.00 | (36) sdtpldt0(xr, all_41_0) = xn
% 83.10/12.00 |
% 83.10/12.00 | DELTA: instantiating (19) with fresh symbols all_45_0, all_45_1, all_45_2,
% 83.10/12.00 | all_45_3 gives:
% 83.10/12.00 | (37) $i(all_45_1) & $i(all_45_3) & ((all_45_0 = xr & sdtasdt0(xp, all_45_1)
% 83.10/12.00 | = xr & doDivides0(xp, xr) & aNaturalNumber0(all_45_1)) | (all_45_2
% 83.10/12.00 | = xm & sdtasdt0(xp, all_45_3) = xm & doDivides0(xp, xm) &
% 83.10/12.00 | aNaturalNumber0(all_45_3)))
% 83.10/12.00 |
% 83.10/12.00 | ALPHA: (37) implies:
% 83.10/12.00 | (38) (all_45_0 = xr & sdtasdt0(xp, all_45_1) = xr & doDivides0(xp, xr) &
% 83.10/12.00 | aNaturalNumber0(all_45_1)) | (all_45_2 = xm & sdtasdt0(xp, all_45_3)
% 83.10/12.00 | = xm & doDivides0(xp, xm) & aNaturalNumber0(all_45_3))
% 83.10/12.00 |
% 83.10/12.00 | DELTA: instantiating (12) with fresh symbols all_47_0, all_47_1 gives:
% 83.10/12.00 | (39) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_47_0) = all_47_1 &
% 83.10/12.00 | sdtasdt0(xn, xm) = all_47_1 & $i(all_47_0) & $i(all_47_1) &
% 83.10/12.00 | isPrime0(xp) & doDivides0(xp, all_47_1) & aNaturalNumber0(all_47_0) &
% 83.10/12.00 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1)
% 83.10/12.00 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.00 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 83.10/12.00 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 83.10/12.00 |
% 83.10/12.00 | ALPHA: (39) implies:
% 83.10/12.00 | (40) ~ (xp = sz00)
% 83.10/12.00 | (41) ~ (xp = sz10)
% 83.10/12.00 | (42) ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0,
% 83.10/12.00 | v1) = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.00 | aNaturalNumber0(v0))
% 83.10/12.00 |
% 83.10/12.00 | DELTA: instantiating (11) with fresh symbols all_50_0, all_50_1 gives:
% 83.10/12.01 | (43) sdtpldt0(all_50_1, xp) = all_50_0 & sdtpldt0(xn, xm) = all_50_1 &
% 83.10/12.01 | $i(all_50_0) & $i(all_50_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 83.10/12.01 | : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~
% 83.10/12.01 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 83.10/12.01 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~
% 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v1) | doDivides0(v2, v0) | ?
% 83.10/12.01 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v7) &
% 83.10/12.01 | $i(v6) & ((v8 = v2 & ~ (v6 = v2) & ~ (v6 = sz10) & sdtasdt0(v6,
% 83.10/12.01 | v7) = v2 & doDivides0(v6, v2) & aNaturalNumber0(v7) &
% 83.10/12.01 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~
% 83.10/12.01 | doDivides0(v2, v5) & ! [v9: $i] : ( ~ (sdtasdt0(v2, v9) = v5)
% 83.10/12.01 | | ~ $i(v9) | ~ aNaturalNumber0(v9)))))) & ! [v0: $i] : !
% 83.10/12.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 =
% 83.10/12.01 | sz00 | ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~
% 83.10/12.01 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~
% 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5: $i] : ? [v6: $i]
% 83.10/12.01 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) &
% 83.10/12.01 | $i(v8) & $i(v6) & ((v10 = v2 & ~ (v8 = v2) & ~ (v8 = sz10) &
% 83.10/12.01 | sdtasdt0(v8, v9) = v2 & doDivides0(v8, v2) &
% 83.10/12.01 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (v7 = v0 &
% 83.10/12.01 | sdtasdt0(v2, v6) = v0 & aNaturalNumber0(v6)) | (sdtasdt0(v0,
% 83.10/12.01 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v11: $i] : (
% 83.10/12.01 | ~ (sdtasdt0(v2, v11) = v5) | ~ $i(v11) | ~
% 83.10/12.01 | aNaturalNumber0(v11)))))) & ! [v0: $i] : ! [v1: $i] : !
% 83.10/12.01 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~
% 83.10/12.01 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 83.10/12.01 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~
% 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5: $i] : ? [v6: $i]
% 83.10/12.01 | : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v9) &
% 83.10/12.01 | $i(v8) & $i(v6) & ((v10 = v2 & ~ (v8 = v2) & ~ (v8 = sz10) &
% 83.10/12.01 | sdtasdt0(v8, v9) = v2 & doDivides0(v8, v2) &
% 83.10/12.01 | aNaturalNumber0(v9) & aNaturalNumber0(v8)) | (v7 = v1 &
% 83.10/12.01 | sdtasdt0(v2, v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0,
% 83.10/12.01 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v11: $i] : (
% 83.10/12.01 | ~ (sdtasdt0(v2, v11) = v5) | ~ $i(v11) | ~
% 83.10/12.01 | aNaturalNumber0(v11)))))) & ! [v0: $i] : ! [v1: $i] : !
% 83.10/12.01 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz10 | v2 = sz00 | ~
% 83.10/12.01 | (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) |
% 83.10/12.01 | ~ $i(v1) | ~ $i(v0) | ~ iLess0(v4, all_50_0) | ~
% 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.01 | aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 83.10/12.01 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i]
% 83.10/12.01 | : ($i(v11) & $i(v10) & $i(v8) & $i(v6) & ((v12 = v2 & ~ (v10 = v2)
% 83.10/12.01 | & ~ (v10 = sz10) & sdtasdt0(v10, v11) = v2 & doDivides0(v10,
% 83.10/12.01 | v2) & aNaturalNumber0(v11) & aNaturalNumber0(v10)) | (v9 =
% 83.10/12.01 | v0 & sdtasdt0(v2, v8) = v0 & aNaturalNumber0(v8)) | (v7 = v1 &
% 83.10/12.01 | sdtasdt0(v2, v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0,
% 83.10/12.01 | v1) = v5 & $i(v5) & ~ doDivides0(v2, v5) & ! [v13: $i] : (
% 83.10/12.01 | ~ (sdtasdt0(v2, v13) = v5) | ~ $i(v13) | ~
% 83.10/12.01 | aNaturalNumber0(v13)))))) & ! [v0: $i] : ! [v1: $i] : !
% 83.10/12.01 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3, v2) = v4) |
% 83.10/12.01 | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 83.10/12.01 | isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~ aNaturalNumber0(v2) | ~
% 83.10/12.01 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v2, v1) |
% 83.10/12.01 | doDivides0(v2, v0) | ? [v5: $i] : (sdtasdt0(v0, v1) = v5 & $i(v5) &
% 83.10/12.01 | ~ doDivides0(v2, v5) & ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5)
% 83.10/12.01 | | ~ $i(v6) | ~ aNaturalNumber0(v6)))) & ! [v0: $i] : ! [v1:
% 83.10/12.01 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3,
% 83.10/12.01 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 83.10/12.01 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~
% 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v1) | ? [v5: $i] : ? [v6: $i]
% 83.10/12.01 | : ? [v7: $i] : ($i(v6) & ((v7 = v0 & sdtasdt0(v2, v6) = v0 &
% 83.10/12.01 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~
% 83.10/12.01 | doDivides0(v2, v5) & ! [v8: $i] : ( ~ (sdtasdt0(v2, v8) = v5)
% 83.10/12.01 | | ~ $i(v8) | ~ aNaturalNumber0(v8)))))) & ! [v0: $i] : !
% 83.10/12.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3,
% 83.10/12.01 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 83.10/12.01 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~
% 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.01 | aNaturalNumber0(v0) | doDivides0(v2, v0) | ? [v5: $i] : ? [v6: $i]
% 83.10/12.01 | : ? [v7: $i] : ($i(v6) & ((v7 = v1 & sdtasdt0(v2, v6) = v1 &
% 83.10/12.01 | aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 & $i(v5) & ~
% 83.10/12.01 | doDivides0(v2, v5) & ! [v8: $i] : ( ~ (sdtasdt0(v2, v8) = v5)
% 83.10/12.01 | | ~ $i(v8) | ~ aNaturalNumber0(v8)))))) & ! [v0: $i] : !
% 83.10/12.01 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v3,
% 83.10/12.01 | v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 83.10/12.01 | ~ $i(v0) | ~ isPrime0(v2) | ~ iLess0(v4, all_50_0) | ~
% 83.10/12.01 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 83.10/12.01 | aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 83.10/12.01 | [v8: $i] : ? [v9: $i] : ($i(v8) & $i(v6) & ((v9 = v0 & sdtasdt0(v2,
% 83.10/12.01 | v8) = v0 & aNaturalNumber0(v8)) | (v7 = v1 & sdtasdt0(v2,
% 83.10/12.01 | v6) = v1 & aNaturalNumber0(v6)) | (sdtasdt0(v0, v1) = v5 &
% 83.10/12.01 | $i(v5) & ~ doDivides0(v2, v5) & ! [v10: $i] : ( ~
% 83.10/12.01 | (sdtasdt0(v2, v10) = v5) | ~ $i(v10) | ~
% 83.10/12.01 | aNaturalNumber0(v10))))))
% 83.10/12.01 |
% 83.10/12.01 | ALPHA: (43) implies:
% 83.10/12.01 | (44) sdtpldt0(xn, xm) = all_50_1
% 83.10/12.01 |
% 83.10/12.01 | BETA: splitting (38) gives:
% 83.10/12.01 |
% 83.10/12.01 | Case 1:
% 83.10/12.01 | |
% 83.10/12.01 | | (45) all_45_0 = xr & sdtasdt0(xp, all_45_1) = xr & doDivides0(xp, xr) &
% 83.10/12.01 | | aNaturalNumber0(all_45_1)
% 83.10/12.01 | |
% 83.10/12.01 | | ALPHA: (45) implies:
% 83.10/12.01 | | (46) doDivides0(xp, xr)
% 83.10/12.01 | |
% 83.10/12.01 | | BETA: splitting (6) gives:
% 83.10/12.01 | |
% 83.10/12.01 | | Case 1:
% 83.10/12.01 | | |
% 83.10/12.02 | | | (47) ~ aNaturalNumber0(sz10)
% 83.10/12.02 | | |
% 83.10/12.02 | | | PRED_UNIFY: (1), (47) imply:
% 83.10/12.02 | | | (48) $false
% 83.10/12.02 | | |
% 83.10/12.02 | | | CLOSE: (48) is inconsistent.
% 83.10/12.02 | | |
% 83.10/12.02 | | Case 2:
% 83.10/12.02 | | |
% 83.10/12.02 | | | (49) ~ isPrime0(sz10)
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (7) with xp, simplifying with (10), (24) gives:
% 83.10/12.02 | | | (50) xp = sz10 | xp = sz00 | ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 83.10/12.02 | | | doDivides0(v0, xp) & aNaturalNumber0(v0))
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (3) with xp, xn, simplifying with (8), (10),
% 83.10/12.02 | | | (22), (24), (28) gives:
% 83.10/12.02 | | | (51) ? [v0: $i] : (sdtpldt0(xp, v0) = xn & $i(v0) &
% 83.10/12.02 | | | aNaturalNumber0(v0))
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (3) with xr, xn, simplifying with (8), (14),
% 83.10/12.02 | | | (18), (22), (34) gives:
% 83.10/12.02 | | | (52) ? [v0: $i] : (sdtpldt0(xr, v0) = xn & $i(v0) &
% 83.10/12.02 | | | aNaturalNumber0(v0))
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (mAddAsso) with xp, xr, xm, xn, all_50_1,
% 83.10/12.02 | | | simplifying with (9), (10), (14), (15), (18), (23), (24),
% 83.10/12.02 | | | (44) gives:
% 83.10/12.02 | | | (53) ? [v0: $i] : (sdtpldt0(xr, xm) = v0 & sdtpldt0(xp, v0) = all_50_1
% 83.10/12.02 | | | & $i(v0) & $i(all_50_1))
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (mAddAsso) with xp, all_39_0, xm, xn, all_50_1,
% 83.10/12.02 | | | simplifying with (9), (10), (23), (24), (27), (29), (30),
% 83.10/12.02 | | | (44) gives:
% 83.10/12.02 | | | (54) ? [v0: $i] : (sdtpldt0(all_39_0, xm) = v0 & sdtpldt0(xp, v0) =
% 83.10/12.02 | | | all_50_1 & $i(v0) & $i(all_50_1))
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (mAddComm) with xp, all_39_0, xn, simplifying
% 83.10/12.02 | | | with (10), (24), (27), (29), (30) gives:
% 83.10/12.02 | | | (55) sdtpldt0(all_39_0, xp) = xn & $i(xn)
% 83.10/12.02 | | |
% 83.10/12.02 | | | ALPHA: (55) implies:
% 83.10/12.02 | | | (56) sdtpldt0(all_39_0, xp) = xn
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (mMonAdd) with xr, xn, all_41_0, xn,
% 83.10/12.02 | | | simplifying with (8), (14), (18), (22), (33), (34), (35),
% 83.10/12.02 | | | (36) gives:
% 83.10/12.02 | | | (57) xr = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xn)
% 83.10/12.02 | | | & ~ (v1 = v0) & sdtpldt0(all_41_0, xr) = v0 &
% 83.10/12.02 | | | sdtpldt0(all_41_0, xn) = v1 & sdtpldt0(xn, all_41_0) = v2 &
% 83.10/12.02 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn,
% 83.10/12.02 | | | v2))
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (mAddComm) with xr, all_41_0, xn, simplifying
% 83.10/12.02 | | | with (14), (18), (33), (35), (36) gives:
% 83.10/12.02 | | | (58) sdtpldt0(all_41_0, xr) = xn & $i(xn)
% 83.10/12.02 | | |
% 83.10/12.02 | | | ALPHA: (58) implies:
% 83.10/12.02 | | | (59) sdtpldt0(all_41_0, xr) = xn
% 83.10/12.02 | | |
% 83.10/12.02 | | | GROUND_INST: instantiating (4) with xp, xn, xr, all_39_0, simplifying with
% 83.10/12.02 | | | (8), (10), (16), (22), (24), (27), (28), (29), (30) gives:
% 83.10/12.02 | | | (60) all_39_0 = xr
% 83.10/12.02 | | |
% 83.10/12.02 | | | DELTA: instantiating (52) with fresh symbol all_73_0 gives:
% 83.10/12.02 | | | (61) sdtpldt0(xr, all_73_0) = xn & $i(all_73_0) &
% 83.10/12.02 | | | aNaturalNumber0(all_73_0)
% 83.10/12.02 | | |
% 83.10/12.02 | | | ALPHA: (61) implies:
% 83.10/12.02 | | | (62) aNaturalNumber0(all_73_0)
% 83.10/12.02 | | | (63) $i(all_73_0)
% 83.10/12.02 | | | (64) sdtpldt0(xr, all_73_0) = xn
% 83.10/12.02 | | |
% 83.10/12.02 | | | DELTA: instantiating (51) with fresh symbol all_75_0 gives:
% 83.10/12.02 | | | (65) sdtpldt0(xp, all_75_0) = xn & $i(all_75_0) &
% 83.10/12.02 | | | aNaturalNumber0(all_75_0)
% 83.10/12.02 | | |
% 83.10/12.02 | | | ALPHA: (65) implies:
% 83.10/12.02 | | | (66) aNaturalNumber0(all_75_0)
% 83.10/12.02 | | | (67) $i(all_75_0)
% 83.10/12.02 | | | (68) sdtpldt0(xp, all_75_0) = xn
% 83.10/12.02 | | |
% 83.10/12.02 | | | DELTA: instantiating (53) with fresh symbol all_81_0 gives:
% 83.10/12.02 | | | (69) sdtpldt0(xr, xm) = all_81_0 & sdtpldt0(xp, all_81_0) = all_50_1 &
% 83.10/12.02 | | | $i(all_81_0) & $i(all_50_1)
% 83.10/12.02 | | |
% 83.10/12.02 | | | ALPHA: (69) implies:
% 83.10/12.02 | | | (70) sdtpldt0(xr, xm) = all_81_0
% 83.10/12.02 | | |
% 83.10/12.02 | | | DELTA: instantiating (54) with fresh symbol all_85_0 gives:
% 83.10/12.03 | | | (71) sdtpldt0(all_39_0, xm) = all_85_0 & sdtpldt0(xp, all_85_0) =
% 83.10/12.03 | | | all_50_1 & $i(all_85_0) & $i(all_50_1)
% 83.10/12.03 | | |
% 83.10/12.03 | | | ALPHA: (71) implies:
% 83.10/12.03 | | | (72) sdtpldt0(all_39_0, xm) = all_85_0
% 83.10/12.03 | | |
% 83.10/12.03 | | | REDUCE: (56), (60) imply:
% 83.10/12.03 | | | (73) sdtpldt0(xr, xp) = xn
% 83.10/12.03 | | |
% 83.10/12.03 | | | REDUCE: (60), (72) imply:
% 83.10/12.03 | | | (74) sdtpldt0(xr, xm) = all_85_0
% 83.10/12.03 | | |
% 83.10/12.03 | | | BETA: splitting (50) gives:
% 83.10/12.03 | | |
% 83.10/12.03 | | | Case 1:
% 83.10/12.03 | | | |
% 83.10/12.03 | | | | (75) xp = sz00
% 83.10/12.03 | | | |
% 83.10/12.03 | | | | REDUCE: (40), (75) imply:
% 83.10/12.03 | | | | (76) $false
% 83.10/12.03 | | | |
% 83.10/12.03 | | | | CLOSE: (76) is inconsistent.
% 83.10/12.03 | | | |
% 83.10/12.03 | | | Case 2:
% 83.10/12.03 | | | |
% 83.10/12.03 | | | | (77) xp = sz10 | ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 83.10/12.03 | | | | doDivides0(v0, xp) & aNaturalNumber0(v0))
% 83.10/12.03 | | | |
% 83.10/12.03 | | | | BETA: splitting (57) gives:
% 83.10/12.03 | | | |
% 83.10/12.03 | | | | Case 1:
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | (78) xr = xn
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | REDUCE: (32), (78) imply:
% 83.10/12.03 | | | | | (79) $false
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | CLOSE: (79) is inconsistent.
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | Case 2:
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xn) & ~
% 83.10/12.03 | | | | | (v1 = v0) & sdtpldt0(all_41_0, xr) = v0 & sdtpldt0(all_41_0,
% 83.10/12.03 | | | | | xn) = v1 & sdtpldt0(xn, all_41_0) = v2 & $i(v2) & $i(v1) &
% 83.10/12.03 | | | | | $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xn, v2))
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | DELTA: instantiating (80) with fresh symbols all_102_0, all_102_1,
% 83.10/12.03 | | | | | all_102_2 gives:
% 83.10/12.03 | | | | | (81) ~ (all_102_0 = xn) & ~ (all_102_1 = all_102_2) &
% 83.10/12.03 | | | | | sdtpldt0(all_41_0, xr) = all_102_2 & sdtpldt0(all_41_0, xn) =
% 83.10/12.03 | | | | | all_102_1 & sdtpldt0(xn, all_41_0) = all_102_0 & $i(all_102_0)
% 83.10/12.03 | | | | | & $i(all_102_1) & $i(all_102_2) & sdtlseqdt0(all_102_2,
% 83.10/12.03 | | | | | all_102_1) & sdtlseqdt0(xn, all_102_0)
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | ALPHA: (81) implies:
% 83.10/12.03 | | | | | (82) $i(all_102_2)
% 83.10/12.03 | | | | | (83) sdtpldt0(all_41_0, xr) = all_102_2
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | BETA: splitting (77) gives:
% 83.10/12.03 | | | | |
% 83.10/12.03 | | | | | Case 1:
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | (84) xp = sz10
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | REDUCE: (41), (84) imply:
% 83.10/12.03 | | | | | | (85) $false
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | CLOSE: (85) is inconsistent.
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | Case 2:
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | (86) ? [v0: $i] : ($i(v0) & isPrime0(v0) & doDivides0(v0, xp) &
% 83.10/12.03 | | | | | | aNaturalNumber0(v0))
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | DELTA: instantiating (86) with fresh symbol all_107_0 gives:
% 83.10/12.03 | | | | | | (87) $i(all_107_0) & isPrime0(all_107_0) & doDivides0(all_107_0,
% 83.10/12.03 | | | | | | xp) & aNaturalNumber0(all_107_0)
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | ALPHA: (87) implies:
% 83.10/12.03 | | | | | | (88) aNaturalNumber0(all_107_0)
% 83.10/12.03 | | | | | | (89) doDivides0(all_107_0, xp)
% 83.10/12.03 | | | | | | (90) isPrime0(all_107_0)
% 83.10/12.03 | | | | | | (91) $i(all_107_0)
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | GROUND_INST: instantiating (25) with all_81_0, all_85_0, xm, xr,
% 83.10/12.03 | | | | | | simplifying with (70), (74) gives:
% 83.10/12.03 | | | | | | (92) all_85_0 = all_81_0
% 83.10/12.03 | | | | | |
% 83.10/12.03 | | | | | | GROUND_INST: instantiating (25) with xn, all_102_2, xr, all_41_0,
% 83.10/12.03 | | | | | | simplifying with (59), (83) gives:
% 83.10/12.03 | | | | | | (93) all_102_2 = xn
% 83.10/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (mDivTrans) with all_107_0, xp, xr,
% 83.25/12.03 | | | | | | simplifying with (10), (14), (18), (24), (46), (88),
% 83.25/12.03 | | | | | | (89), (91) gives:
% 83.25/12.03 | | | | | | (94) doDivides0(all_107_0, xr)
% 83.25/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (5) with all_107_0, xp, simplifying with
% 83.25/12.03 | | | | | | (10), (24), (88), (89), (91) gives:
% 83.25/12.03 | | | | | | (95) ? [v0: $i] : (sdtasdt0(all_107_0, v0) = xp & $i(v0) &
% 83.25/12.03 | | | | | | aNaturalNumber0(v0))
% 83.25/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (4) with xp, xn, xr, all_75_0,
% 83.25/12.03 | | | | | | simplifying with (8), (10), (16), (22), (24), (28),
% 83.25/12.03 | | | | | | (66), (67), (68) gives:
% 83.25/12.03 | | | | | | (96) all_75_0 = xr
% 83.25/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (mAddComm) with xp, all_75_0, xn,
% 83.25/12.03 | | | | | | simplifying with (10), (24), (66), (67), (68) gives:
% 83.25/12.03 | | | | | | (97) sdtpldt0(all_75_0, xp) = xn & $i(xn)
% 83.25/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (mMonAdd) with xr, xn, xm, all_81_0,
% 83.25/12.03 | | | | | | simplifying with (8), (9), (14), (18), (22), (23),
% 83.25/12.03 | | | | | | (34), (70) gives:
% 83.25/12.03 | | | | | | (98) xr = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ( ~ (v2
% 83.25/12.03 | | | | | | = all_81_0) & ~ (v1 = v0) & sdtpldt0(xm, xr) = v0 &
% 83.25/12.03 | | | | | | sdtpldt0(xm, xn) = v1 & sdtpldt0(xn, xm) = v2 & $i(v2) &
% 83.25/12.03 | | | | | | $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) &
% 83.25/12.03 | | | | | | sdtlseqdt0(all_81_0, v2))
% 83.25/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (2) with xr, all_73_0, all_41_0, xn,
% 83.25/12.03 | | | | | | simplifying with (14), (18), (33), (35), (36), (62),
% 83.25/12.03 | | | | | | (63), (64) gives:
% 83.25/12.03 | | | | | | (99) all_73_0 = all_41_0
% 83.25/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (2) with xr, all_73_0, xp, xn,
% 83.25/12.03 | | | | | | simplifying with (10), (14), (18), (24), (62), (63),
% 83.25/12.03 | | | | | | (64), (73) gives:
% 83.25/12.03 | | | | | | (100) all_73_0 = xp
% 83.25/12.03 | | | | | |
% 83.25/12.03 | | | | | | GROUND_INST: instantiating (mMonAdd) with xr, xn, all_73_0, xn,
% 83.25/12.03 | | | | | | simplifying with (8), (14), (18), (22), (34), (62),
% 83.25/12.03 | | | | | | (63), (64) gives:
% 83.25/12.04 | | | | | | (101) xr = xn | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2
% 83.25/12.04 | | | | | | = xn) & ~ (v1 = v0) & sdtpldt0(all_73_0, xr) = v0 &
% 83.25/12.04 | | | | | | sdtpldt0(all_73_0, xn) = v1 & sdtpldt0(xn, all_73_0) = v2
% 83.25/12.04 | | | | | | & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) &
% 83.25/12.04 | | | | | | sdtlseqdt0(xn, v2))
% 83.25/12.04 | | | | | |
% 83.25/12.04 | | | | | | COMBINE_EQS: (99), (100) imply:
% 83.25/12.04 | | | | | | (102) all_41_0 = xp
% 83.25/12.04 | | | | | |
% 83.25/12.04 | | | | | | DELTA: instantiating (95) with fresh symbol all_129_0 gives:
% 83.25/12.04 | | | | | | (103) sdtasdt0(all_107_0, all_129_0) = xp & $i(all_129_0) &
% 83.25/12.04 | | | | | | aNaturalNumber0(all_129_0)
% 83.25/12.04 | | | | | |
% 83.25/12.04 | | | | | | ALPHA: (103) implies:
% 83.25/12.04 | | | | | | (104) aNaturalNumber0(all_129_0)
% 83.25/12.04 | | | | | | (105) $i(all_129_0)
% 83.25/12.04 | | | | | | (106) sdtasdt0(all_107_0, all_129_0) = xp
% 83.25/12.04 | | | | | |
% 83.25/12.04 | | | | | | BETA: splitting (101) gives:
% 83.25/12.04 | | | | | |
% 83.25/12.04 | | | | | | Case 1:
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | (107) xr = xn
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | REDUCE: (32), (107) imply:
% 83.25/12.04 | | | | | | | (108) $false
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | CLOSE: (108) is inconsistent.
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | Case 2:
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xn) &
% 83.25/12.04 | | | | | | | ~ (v1 = v0) & sdtpldt0(all_73_0, xr) = v0 &
% 83.25/12.04 | | | | | | | sdtpldt0(all_73_0, xn) = v1 & sdtpldt0(xn, all_73_0) =
% 83.25/12.04 | | | | | | | v2 & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) &
% 83.25/12.04 | | | | | | | sdtlseqdt0(xn, v2))
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | DELTA: instantiating (109) with fresh symbols all_192_0,
% 83.25/12.04 | | | | | | | all_192_1, all_192_2 gives:
% 83.25/12.04 | | | | | | | (110) ~ (all_192_0 = xn) & ~ (all_192_1 = all_192_2) &
% 83.25/12.04 | | | | | | | sdtpldt0(all_73_0, xr) = all_192_2 & sdtpldt0(all_73_0,
% 83.25/12.04 | | | | | | | xn) = all_192_1 & sdtpldt0(xn, all_73_0) = all_192_0 &
% 83.25/12.04 | | | | | | | $i(all_192_0) & $i(all_192_1) & $i(all_192_2) &
% 83.25/12.04 | | | | | | | sdtlseqdt0(all_192_2, all_192_1) & sdtlseqdt0(xn,
% 83.25/12.04 | | | | | | | all_192_0)
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | ALPHA: (110) implies:
% 83.25/12.04 | | | | | | | (111) sdtpldt0(all_73_0, xr) = all_192_2
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | REDUCE: (100), (111) imply:
% 83.25/12.04 | | | | | | | (112) sdtpldt0(xp, xr) = all_192_2
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | BETA: splitting (98) gives:
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | | Case 1:
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | (113) xr = xn
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | REDUCE: (32), (113) imply:
% 83.25/12.04 | | | | | | | | (114) $false
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | CLOSE: (114) is inconsistent.
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | Case 2:
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | GROUND_INST: instantiating (25) with xn, all_192_2, xr, xp,
% 83.25/12.04 | | | | | | | | simplifying with (15), (112) gives:
% 83.25/12.04 | | | | | | | | (115) all_192_2 = xn
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | GROUND_INST: instantiating (mDivSum) with all_107_0, xp, xr, xn,
% 83.25/12.04 | | | | | | | | simplifying with (10), (14), (15), (18), (24),
% 83.25/12.04 | | | | | | | | (88), (89), (91), (94) gives:
% 83.25/12.04 | | | | | | | | (116) doDivides0(all_107_0, xn)
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | GROUND_INST: instantiating (42) with all_107_0, all_129_0,
% 83.25/12.04 | | | | | | | | simplifying with (88), (91), (104), (105), (106)
% 83.25/12.04 | | | | | | | | gives:
% 83.25/12.04 | | | | | | | | (117) all_107_0 = xp | all_107_0 = sz10
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | BETA: splitting (117) gives:
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | | Case 1:
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | (118) all_107_0 = xp
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | REDUCE: (116), (118) imply:
% 83.25/12.04 | | | | | | | | | (119) doDivides0(xp, xn)
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | PRED_UNIFY: (20), (119) imply:
% 83.25/12.04 | | | | | | | | | (120) $false
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | CLOSE: (120) is inconsistent.
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | Case 2:
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | (121) all_107_0 = sz10
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | REDUCE: (90), (121) imply:
% 83.25/12.04 | | | | | | | | | (122) isPrime0(sz10)
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | PRED_UNIFY: (49), (122) imply:
% 83.25/12.04 | | | | | | | | | (123) $false
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | | CLOSE: (123) is inconsistent.
% 83.25/12.04 | | | | | | | | |
% 83.25/12.04 | | | | | | | | End of split
% 83.25/12.04 | | | | | | | |
% 83.25/12.04 | | | | | | | End of split
% 83.25/12.04 | | | | | | |
% 83.25/12.04 | | | | | | End of split
% 83.25/12.04 | | | | | |
% 83.25/12.04 | | | | | End of split
% 83.25/12.04 | | | | |
% 83.25/12.04 | | | | End of split
% 83.25/12.04 | | | |
% 83.25/12.04 | | | End of split
% 83.25/12.04 | | |
% 83.25/12.04 | | End of split
% 83.25/12.04 | |
% 83.25/12.04 | Case 2:
% 83.25/12.04 | |
% 83.25/12.04 | | (124) all_45_2 = xm & sdtasdt0(xp, all_45_3) = xm & doDivides0(xp, xm) &
% 83.25/12.04 | | aNaturalNumber0(all_45_3)
% 83.25/12.04 | |
% 83.25/12.04 | | ALPHA: (124) implies:
% 83.25/12.04 | | (125) doDivides0(xp, xm)
% 83.25/12.04 | |
% 83.25/12.04 | | PRED_UNIFY: (21), (125) imply:
% 83.25/12.04 | | (126) $false
% 83.25/12.04 | |
% 83.25/12.04 | | CLOSE: (126) is inconsistent.
% 83.25/12.04 | |
% 83.25/12.04 | End of split
% 83.25/12.04 |
% 83.25/12.04 End of proof
% 83.25/12.04 % SZS output end Proof for theBenchmark
% 83.25/12.04
% 83.25/12.04 11412ms
%------------------------------------------------------------------------------