TSTP Solution File: NUM518+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM518+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 : n013.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 11:48:20 EDT 2023
% Result : Theorem 22.28s 3.79s
% Output : Proof 115.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.34 % Computer : n013.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Fri Aug 25 14:25:17 EDT 2023
% 0.18/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.62/1.27 Prover 4: Preprocessing ...
% 3.62/1.27 Prover 1: Preprocessing ...
% 4.30/1.30 Prover 0: Preprocessing ...
% 4.30/1.30 Prover 3: Preprocessing ...
% 4.30/1.30 Prover 5: Preprocessing ...
% 4.30/1.30 Prover 6: Preprocessing ...
% 4.30/1.30 Prover 2: Preprocessing ...
% 9.57/2.15 Prover 1: Constructing countermodel ...
% 10.46/2.21 Prover 3: Constructing countermodel ...
% 10.46/2.22 Prover 6: Proving ...
% 11.39/2.30 Prover 5: Constructing countermodel ...
% 12.53/2.49 Prover 2: Proving ...
% 12.53/2.50 Prover 4: Constructing countermodel ...
% 13.67/2.61 Prover 0: Proving ...
% 22.28/3.79 Prover 3: proved (3148ms)
% 22.28/3.79
% 22.28/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.28/3.79
% 22.28/3.80 Prover 5: stopped
% 22.72/3.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.72/3.81 Prover 2: stopped
% 22.72/3.81 Prover 0: stopped
% 22.72/3.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.72/3.81 Prover 6: stopped
% 22.72/3.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.72/3.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 22.72/3.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.83/3.96 Prover 10: Preprocessing ...
% 23.83/3.97 Prover 7: Preprocessing ...
% 23.83/3.98 Prover 8: Preprocessing ...
% 24.15/4.02 Prover 13: Preprocessing ...
% 24.15/4.03 Prover 11: Preprocessing ...
% 25.58/4.22 Prover 10: Constructing countermodel ...
% 26.09/4.29 Prover 7: Constructing countermodel ...
% 26.09/4.30 Prover 8: Warning: ignoring some quantifiers
% 26.09/4.30 Prover 8: Constructing countermodel ...
% 27.86/4.49 Prover 13: Constructing countermodel ...
% 28.87/4.62 Prover 11: Constructing countermodel ...
% 64.69/9.36 Prover 13: stopped
% 65.23/9.37 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 65.65/9.44 Prover 16: Preprocessing ...
% 66.91/9.61 Prover 16: Constructing countermodel ...
% 109.73/15.26 Prover 16: stopped
% 110.16/15.28 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 110.95/15.39 Prover 19: Preprocessing ...
% 112.10/15.55 Prover 19: Warning: ignoring some quantifiers
% 112.10/15.55 Prover 19: Constructing countermodel ...
% 115.17/15.94 Prover 10: Found proof (size 112)
% 115.17/15.94 Prover 10: proved (12118ms)
% 115.17/15.94 Prover 11: stopped
% 115.17/15.94 Prover 4: stopped
% 115.17/15.94 Prover 8: stopped
% 115.17/15.94 Prover 1: stopped
% 115.17/15.94 Prover 7: stopped
% 115.17/15.95 Prover 19: stopped
% 115.17/15.95
% 115.17/15.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 115.17/15.95
% 115.17/15.96 % SZS output start Proof for theBenchmark
% 115.17/15.96 Assumptions after simplification:
% 115.17/15.96 ---------------------------------
% 115.17/15.96
% 115.17/15.96 (mAddAsso)
% 115.36/15.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 115.36/15.99 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 115.36/15.99 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 115.36/15.99 aNaturalNumber0(v0) | ? [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0,
% 115.36/15.99 v5) = v4 & $i(v5) & $i(v4)))
% 115.36/15.99
% 115.36/15.99 (mAddComm)
% 115.36/15.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 115.36/15.99 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 115.36/15.99 (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 115.36/15.99
% 115.36/15.99 (mDefDiv)
% 115.36/15.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~
% 115.36/15.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 115.36/15.99 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0:
% 115.36/15.99 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 115.36/15.99 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0,
% 115.36/15.99 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 115.36/15.99
% 115.36/15.99 (mDefLE)
% 115.36/15.99 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~
% 115.36/15.99 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 115.36/15.99 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 115.36/15.99 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~
% 115.36/15.99 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0,
% 115.36/15.99 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 115.36/15.99
% 115.36/15.99 (mDefPrime)
% 115.36/16.00 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~
% 115.36/16.00 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~
% 115.36/16.00 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 |
% 115.36/16.00 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i]
% 115.36/16.00 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) &
% 115.36/16.00 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & (
% 115.36/16.00 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00))
% 115.36/16.00
% 115.36/16.00 (mDefQuot)
% 115.36/16.00 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 |
% 115.36/16.00 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 115.36/16.00 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 115.36/16.00 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & !
% 115.36/16.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~
% 115.36/16.00 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 115.36/16.00 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~
% 115.36/16.00 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 115.36/16.00 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~
% 115.36/16.00 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 115.36/16.00 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 115.36/16.00
% 115.36/16.00 (mDivTrans)
% 115.36/16.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 115.36/16.00 ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~
% 115.36/16.00 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 115.36/16.00
% 115.36/16.00 (mMulAsso)
% 115.36/16.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 115.36/16.00 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 115.36/16.00 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 115.36/16.00 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0,
% 115.36/16.00 v5) = v4 & $i(v5) & $i(v4)))
% 115.36/16.00
% 115.36/16.00 (mMulComm)
% 115.36/16.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 115.36/16.01 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 115.36/16.01 (sdtasdt0(v1, v0) = v2 & $i(v2)))
% 115.36/16.01
% 115.36/16.01 (mPrimDiv)
% 115.36/16.01 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 115.36/16.01 aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) & doDivides0(v1,
% 115.36/16.01 v0) & aNaturalNumber0(v1)))
% 115.36/16.01
% 115.36/16.01 (mSortsB)
% 115.36/16.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 115.36/16.01 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 115.36/16.01 aNaturalNumber0(v2))
% 115.36/16.01
% 115.36/16.01 (mSortsC_01)
% 115.36/16.01 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 115.36/16.01
% 115.36/16.01 (m__)
% 115.36/16.01 $i(xp) & $i(xm) & $i(xn) & ~ doDivides0(xp, xm) & ~ doDivides0(xp, xn) & !
% 115.36/16.01 [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xm) | ~ $i(v0) | ~ aNaturalNumber0(v0)) &
% 115.36/16.01 ! [v0: $i] : ( ~ (sdtasdt0(xp, v0) = xn) | ~ $i(v0) | ~
% 115.36/16.01 aNaturalNumber0(v0))
% 115.36/16.01
% 115.36/16.01 (m__1837)
% 115.36/16.01 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 115.36/16.01 aNaturalNumber0(xn)
% 115.36/16.01
% 115.36/16.01 (m__1860)
% 115.36/16.01 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : (
% 115.36/16.01 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) =
% 115.36/16.01 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) &
% 115.36/16.01 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~
% 115.36/16.01 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) |
% 115.36/16.01 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) |
% 115.36/16.01 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 115.36/16.01
% 115.36/16.01 (m__2306)
% 115.36/16.01 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 115.36/16.01 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & $i(v0) &
% 115.36/16.01 aNaturalNumber0(xk))
% 115.36/16.01
% 115.36/16.01 (m__2342)
% 115.36/16.01 $i(xr) & $i(xk) & $i(sz10) & $i(sz00) & ? [v0: $i] : ( ~ (xr = sz10) & ~ (xr
% 115.36/16.01 = sz00) & sdtasdt0(xr, v0) = xk & $i(v0) & isPrime0(xr) & doDivides0(xr,
% 115.36/16.01 xk) & aNaturalNumber0(v0) & aNaturalNumber0(xr) & ! [v1: $i] : ! [v2:
% 115.36/16.01 $i] : (v1 = xr | v1 = sz10 | ~ (sdtasdt0(v1, v2) = xr) | ~ $i(v2) | ~
% 115.36/16.01 $i(v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1: $i] :
% 115.36/16.01 (v1 = xr | v1 = sz10 | ~ $i(v1) | ~ doDivides0(v1, xr) | ~
% 115.36/16.01 aNaturalNumber0(v1)))
% 115.36/16.01
% 115.36/16.01 (m__2362)
% 115.36/16.02 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 115.36/16.02 (sdtasdt0(xr, v1) = v0 & sdtasdt0(xn, xm) = v0 & sdtpldt0(xr, v2) = xk &
% 115.36/16.02 $i(v2) & $i(v1) & $i(v0) & doDivides0(xr, v0) & aNaturalNumber0(v2) &
% 115.36/16.02 aNaturalNumber0(v1))
% 115.36/16.02
% 115.36/16.02 (m__2377)
% 115.36/16.02 $i(xk) & $i(xp) & ? [v0: $i] : ( ~ (xk = xp) & sdtpldt0(xk, v0) = xp & $i(v0)
% 115.36/16.02 & sdtlseqdt0(xk, xp) & aNaturalNumber0(v0))
% 115.36/16.02
% 115.36/16.02 (m__2487)
% 115.36/16.02 $i(xr) & $i(xn) & ? [v0: $i] : (sdtasdt0(xr, v0) = xn & $i(v0) &
% 115.36/16.02 doDivides0(xr, xn) & aNaturalNumber0(v0))
% 115.36/16.02
% 115.36/16.02 (m__2504)
% 115.36/16.02 $i(xr) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr)
% 115.36/16.02 = v0 & sdtasdt0(xr, v0) = xn & sdtpldt0(v0, v1) = xn & $i(v1) & $i(v0) &
% 115.36/16.02 sdtlseqdt0(v0, xn) & aNaturalNumber0(v1) & aNaturalNumber0(v0))
% 115.36/16.02
% 115.36/16.02 (m__2529)
% 115.36/16.02 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 115.36/16.02 (sdtsldt0(xn, xr) = v0 & sdtasdt0(v0, xm) = v1 & sdtasdt0(xr, v0) = xn &
% 115.36/16.02 sdtasdt0(xp, v2) = v1 & $i(v2) & $i(v1) & $i(v0) & doDivides0(xp, v1) &
% 115.36/16.02 aNaturalNumber0(v2) & aNaturalNumber0(v0))
% 115.36/16.02
% 115.36/16.02 (m__2645)
% 115.36/16.02 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 115.36/16.02 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v4) & $i(v2) & ((v5 = v0 & v1 =
% 115.36/16.02 xn & sdtsldt0(xn, xr) = v0 & sdtasdt0(xr, v0) = xn & sdtasdt0(xp, v4) =
% 115.36/16.02 v0 & $i(v0) & doDivides0(xp, v0) & aNaturalNumber0(v4) &
% 115.36/16.02 aNaturalNumber0(v0)) | (v3 = xm & sdtasdt0(xp, v2) = xm & doDivides0(xp,
% 115.36/16.02 xm) & aNaturalNumber0(v2))))
% 115.36/16.02
% 115.36/16.02 (function-axioms)
% 115.36/16.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.36/16.02 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 115.36/16.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 115.36/16.02 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 115.36/16.02 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 115.36/16.02 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.36/16.02 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 115.36/16.02
% 115.36/16.02 Further assumptions not needed in the proof:
% 115.36/16.02 --------------------------------------------
% 115.36/16.02 mAMDistr, mAddCanc, mDefDiff, mDivAsso, mDivLE, mDivMin, mDivSum, mIH, mIH_03,
% 115.36/16.02 mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2,
% 115.36/16.02 mMulCanc, mNatSort, mSortsB_02, mSortsC, mZeroAdd, mZeroMul, m_AddZero,
% 115.36/16.02 m_MulUnit, m_MulZero, m__1799, m__1870, m__2075, m__2287, m__2315, m__2327,
% 115.36/16.02 m__2449
% 115.36/16.02
% 115.36/16.02 Those formulas are unsatisfiable:
% 115.36/16.02 ---------------------------------
% 115.36/16.02
% 115.36/16.02 Begin of proof
% 115.36/16.02 |
% 115.36/16.02 | ALPHA: (mSortsC_01) implies:
% 115.36/16.02 | (1) aNaturalNumber0(sz10)
% 115.36/16.02 |
% 115.36/16.02 | ALPHA: (mDefLE) implies:
% 115.36/16.03 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0,
% 115.36/16.03 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 115.36/16.03 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (mDefDiv) implies:
% 115.36/16.03 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 115.36/16.03 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 115.36/16.03 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 115.36/16.03 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) |
% 115.36/16.03 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 115.36/16.03 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (mDefQuot) implies:
% 115.36/16.03 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 =
% 115.36/16.03 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 115.36/16.03 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 115.36/16.03 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~
% 115.36/16.03 | aNaturalNumber0(v0))
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (mDefPrime) implies:
% 115.36/16.03 | (6) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (mPrimDiv) implies:
% 115.36/16.03 | (7) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 115.36/16.03 | aNaturalNumber0(v0) | ? [v1: $i] : ($i(v1) & isPrime0(v1) &
% 115.36/16.03 | doDivides0(v1, v0) & aNaturalNumber0(v1)))
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (m__1837) implies:
% 115.36/16.03 | (8) aNaturalNumber0(xn)
% 115.36/16.03 | (9) aNaturalNumber0(xp)
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (m__1860) implies:
% 115.36/16.03 | (10) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) &
% 115.36/16.03 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) &
% 115.36/16.03 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2:
% 115.36/16.03 | $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) =
% 115.36/16.03 | xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~
% 115.36/16.03 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~
% 115.36/16.03 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2)))
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (m__2306) implies:
% 115.36/16.03 | (11) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 &
% 115.36/16.03 | sdtasdt0(xn, xm) = v0 & $i(v0) & aNaturalNumber0(xk))
% 115.36/16.03 |
% 115.36/16.03 | ALPHA: (m__2342) implies:
% 115.66/16.03 | (12) ? [v0: $i] : ( ~ (xr = sz10) & ~ (xr = sz00) & sdtasdt0(xr, v0) = xk
% 115.66/16.03 | & $i(v0) & isPrime0(xr) & doDivides0(xr, xk) & aNaturalNumber0(v0) &
% 115.66/16.03 | aNaturalNumber0(xr) & ! [v1: $i] : ! [v2: $i] : (v1 = xr | v1 =
% 115.66/16.03 | sz10 | ~ (sdtasdt0(v1, v2) = xr) | ~ $i(v2) | ~ $i(v1) | ~
% 115.66/16.03 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1: $i] : (v1
% 115.66/16.03 | = xr | v1 = sz10 | ~ $i(v1) | ~ doDivides0(v1, xr) | ~
% 115.66/16.03 | aNaturalNumber0(v1)))
% 115.66/16.03 |
% 115.66/16.03 | ALPHA: (m__2362) implies:
% 115.66/16.04 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, v1) = v0 &
% 115.66/16.04 | sdtasdt0(xn, xm) = v0 & sdtpldt0(xr, v2) = xk & $i(v2) & $i(v1) &
% 115.66/16.04 | $i(v0) & doDivides0(xr, v0) & aNaturalNumber0(v2) &
% 115.66/16.04 | aNaturalNumber0(v1))
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (m__2377) implies:
% 115.66/16.04 | (14) $i(xk)
% 115.66/16.04 | (15) ? [v0: $i] : ( ~ (xk = xp) & sdtpldt0(xk, v0) = xp & $i(v0) &
% 115.66/16.04 | sdtlseqdt0(xk, xp) & aNaturalNumber0(v0))
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (m__2487) implies:
% 115.66/16.04 | (16) ? [v0: $i] : (sdtasdt0(xr, v0) = xn & $i(v0) & doDivides0(xr, xn) &
% 115.66/16.04 | aNaturalNumber0(v0))
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (m__2504) implies:
% 115.66/16.04 | (17) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 &
% 115.66/16.04 | sdtasdt0(xr, v0) = xn & sdtpldt0(v0, v1) = xn & $i(v1) & $i(v0) &
% 115.66/16.04 | sdtlseqdt0(v0, xn) & aNaturalNumber0(v1) & aNaturalNumber0(v0))
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (m__2529) implies:
% 115.66/16.04 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtsldt0(xn, xr) = v0 &
% 115.66/16.04 | sdtasdt0(v0, xm) = v1 & sdtasdt0(xr, v0) = xn & sdtasdt0(xp, v2) =
% 115.66/16.04 | v1 & $i(v2) & $i(v1) & $i(v0) & doDivides0(xp, v1) &
% 115.66/16.04 | aNaturalNumber0(v2) & aNaturalNumber0(v0))
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (m__2645) implies:
% 115.66/16.04 | (19) $i(xr)
% 115.66/16.04 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 115.66/16.04 | ? [v5: $i] : ($i(v4) & $i(v2) & ((v5 = v0 & v1 = xn & sdtsldt0(xn, xr)
% 115.66/16.04 | = v0 & sdtasdt0(xr, v0) = xn & sdtasdt0(xp, v4) = v0 & $i(v0) &
% 115.66/16.04 | doDivides0(xp, v0) & aNaturalNumber0(v4) & aNaturalNumber0(v0))
% 115.66/16.04 | | (v3 = xm & sdtasdt0(xp, v2) = xm & doDivides0(xp, xm) &
% 115.66/16.04 | aNaturalNumber0(v2))))
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (m__) implies:
% 115.66/16.04 | (21) ~ doDivides0(xp, xn)
% 115.66/16.04 | (22) ~ doDivides0(xp, xm)
% 115.66/16.04 | (23) $i(xn)
% 115.66/16.04 | (24) $i(xp)
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (function-axioms) implies:
% 115.66/16.04 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 115.66/16.04 | (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 115.66/16.04 |
% 115.66/16.04 | DELTA: instantiating (16) with fresh symbol all_41_0 gives:
% 115.66/16.04 | (26) sdtasdt0(xr, all_41_0) = xn & $i(all_41_0) & doDivides0(xr, xn) &
% 115.66/16.04 | aNaturalNumber0(all_41_0)
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (26) implies:
% 115.66/16.04 | (27) aNaturalNumber0(all_41_0)
% 115.66/16.04 | (28) doDivides0(xr, xn)
% 115.66/16.04 | (29) $i(all_41_0)
% 115.66/16.04 | (30) sdtasdt0(xr, all_41_0) = xn
% 115.66/16.04 |
% 115.66/16.04 | DELTA: instantiating (15) with fresh symbol all_43_0 gives:
% 115.66/16.04 | (31) ~ (xk = xp) & sdtpldt0(xk, all_43_0) = xp & $i(all_43_0) &
% 115.66/16.04 | sdtlseqdt0(xk, xp) & aNaturalNumber0(all_43_0)
% 115.66/16.04 |
% 115.66/16.04 | ALPHA: (31) implies:
% 115.66/16.04 | (32) aNaturalNumber0(all_43_0)
% 115.66/16.04 | (33) sdtlseqdt0(xk, xp)
% 115.66/16.04 | (34) $i(all_43_0)
% 115.66/16.04 | (35) sdtpldt0(xk, all_43_0) = xp
% 115.66/16.04 |
% 115.66/16.04 | DELTA: instantiating (11) with fresh symbol all_45_0 gives:
% 115.66/16.04 | (36) sdtsldt0(all_45_0, xp) = xk & sdtasdt0(xp, xk) = all_45_0 &
% 115.66/16.05 | sdtasdt0(xn, xm) = all_45_0 & $i(all_45_0) & aNaturalNumber0(xk)
% 115.66/16.05 |
% 115.66/16.05 | ALPHA: (36) implies:
% 115.66/16.05 | (37) aNaturalNumber0(xk)
% 115.66/16.05 |
% 115.66/16.05 | DELTA: instantiating (13) with fresh symbols all_47_0, all_47_1, all_47_2
% 115.66/16.05 | gives:
% 115.66/16.05 | (38) sdtasdt0(xr, all_47_1) = all_47_2 & sdtasdt0(xn, xm) = all_47_2 &
% 115.66/16.05 | sdtpldt0(xr, all_47_0) = xk & $i(all_47_0) & $i(all_47_1) &
% 115.66/16.05 | $i(all_47_2) & doDivides0(xr, all_47_2) & aNaturalNumber0(all_47_0) &
% 115.66/16.05 | aNaturalNumber0(all_47_1)
% 115.66/16.05 |
% 115.66/16.05 | ALPHA: (38) implies:
% 115.66/16.05 | (39) aNaturalNumber0(all_47_0)
% 115.66/16.05 | (40) $i(all_47_0)
% 115.66/16.05 | (41) sdtpldt0(xr, all_47_0) = xk
% 115.66/16.05 |
% 115.66/16.05 | DELTA: instantiating (17) with fresh symbols all_49_0, all_49_1 gives:
% 115.66/16.05 | (42) ~ (all_49_1 = xn) & sdtsldt0(xn, xr) = all_49_1 & sdtasdt0(xr,
% 115.66/16.05 | all_49_1) = xn & sdtpldt0(all_49_1, all_49_0) = xn & $i(all_49_0) &
% 115.66/16.05 | $i(all_49_1) & sdtlseqdt0(all_49_1, xn) & aNaturalNumber0(all_49_0) &
% 115.66/16.05 | aNaturalNumber0(all_49_1)
% 115.66/16.05 |
% 115.66/16.05 | ALPHA: (42) implies:
% 115.66/16.05 | (43) sdtsldt0(xn, xr) = all_49_1
% 115.66/16.05 |
% 115.66/16.05 | DELTA: instantiating (18) with fresh symbols all_55_0, all_55_1, all_55_2
% 115.66/16.05 | gives:
% 115.66/16.05 | (44) sdtsldt0(xn, xr) = all_55_2 & sdtasdt0(all_55_2, xm) = all_55_1 &
% 115.66/16.05 | sdtasdt0(xr, all_55_2) = xn & sdtasdt0(xp, all_55_0) = all_55_1 &
% 115.66/16.05 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & doDivides0(xp, all_55_1)
% 115.66/16.05 | & aNaturalNumber0(all_55_0) & aNaturalNumber0(all_55_2)
% 115.66/16.05 |
% 115.66/16.05 | ALPHA: (44) implies:
% 115.66/16.05 | (45) aNaturalNumber0(all_55_2)
% 115.66/16.05 | (46) $i(all_55_2)
% 115.66/16.05 | (47) sdtasdt0(xr, all_55_2) = xn
% 115.66/16.05 | (48) sdtsldt0(xn, xr) = all_55_2
% 115.66/16.05 |
% 115.66/16.05 | DELTA: instantiating (20) with fresh symbols all_57_0, all_57_1, all_57_2,
% 115.66/16.05 | all_57_3, all_57_4, all_57_5 gives:
% 115.66/16.05 | (49) $i(all_57_1) & $i(all_57_3) & ((all_57_0 = all_57_5 & all_57_4 = xn &
% 115.66/16.05 | sdtsldt0(xn, xr) = all_57_5 & sdtasdt0(xr, all_57_5) = xn &
% 115.66/16.05 | sdtasdt0(xp, all_57_1) = all_57_5 & $i(all_57_5) & doDivides0(xp,
% 115.66/16.05 | all_57_5) & aNaturalNumber0(all_57_1) &
% 115.66/16.05 | aNaturalNumber0(all_57_5)) | (all_57_2 = xm & sdtasdt0(xp,
% 115.66/16.05 | all_57_3) = xm & doDivides0(xp, xm) &
% 115.66/16.05 | aNaturalNumber0(all_57_3)))
% 115.66/16.05 |
% 115.66/16.05 | ALPHA: (49) implies:
% 115.66/16.05 | (50) $i(all_57_1)
% 115.66/16.05 | (51) (all_57_0 = all_57_5 & all_57_4 = xn & sdtsldt0(xn, xr) = all_57_5 &
% 115.66/16.05 | sdtasdt0(xr, all_57_5) = xn & sdtasdt0(xp, all_57_1) = all_57_5 &
% 115.66/16.05 | $i(all_57_5) & doDivides0(xp, all_57_5) & aNaturalNumber0(all_57_1)
% 115.66/16.05 | & aNaturalNumber0(all_57_5)) | (all_57_2 = xm & sdtasdt0(xp,
% 115.66/16.05 | all_57_3) = xm & doDivides0(xp, xm) & aNaturalNumber0(all_57_3))
% 115.66/16.05 |
% 115.66/16.05 | DELTA: instantiating (12) with fresh symbol all_59_0 gives:
% 115.66/16.05 | (52) ~ (xr = sz10) & ~ (xr = sz00) & sdtasdt0(xr, all_59_0) = xk &
% 115.66/16.05 | $i(all_59_0) & isPrime0(xr) & doDivides0(xr, xk) &
% 115.66/16.05 | aNaturalNumber0(all_59_0) & aNaturalNumber0(xr) & ! [v0: $i] : !
% 115.66/16.05 | [v1: $i] : (v0 = xr | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xr) | ~
% 115.66/16.05 | $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 115.66/16.05 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xr | v0 = sz10 | ~
% 115.66/16.05 | $i(v0) | ~ doDivides0(v0, xr) | ~ aNaturalNumber0(v0))
% 115.66/16.05 |
% 115.66/16.05 | ALPHA: (52) implies:
% 115.66/16.05 | (53) ~ (xr = sz00)
% 115.66/16.05 | (54) aNaturalNumber0(xr)
% 115.66/16.05 | (55) aNaturalNumber0(all_59_0)
% 115.66/16.05 | (56) $i(all_59_0)
% 115.66/16.05 | (57) sdtasdt0(xr, all_59_0) = xk
% 115.66/16.05 |
% 115.66/16.05 | DELTA: instantiating (10) with fresh symbols all_62_0, all_62_1 gives:
% 115.66/16.06 | (58) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_62_0) = all_62_1 &
% 115.66/16.06 | sdtasdt0(xn, xm) = all_62_1 & $i(all_62_0) & $i(all_62_1) &
% 115.66/16.06 | isPrime0(xp) & doDivides0(xp, all_62_1) & aNaturalNumber0(all_62_0) &
% 115.66/16.06 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1)
% 115.66/16.06 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 115.66/16.06 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~
% 115.66/16.06 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 115.66/16.06 |
% 115.66/16.06 | ALPHA: (58) implies:
% 115.66/16.06 | (59) ~ (xp = sz00)
% 115.66/16.06 | (60) ~ (xp = sz10)
% 115.66/16.06 |
% 115.66/16.06 | BETA: splitting (51) gives:
% 115.66/16.06 |
% 115.66/16.06 | Case 1:
% 115.66/16.06 | |
% 115.66/16.06 | | (61) all_57_0 = all_57_5 & all_57_4 = xn & sdtsldt0(xn, xr) = all_57_5 &
% 115.66/16.06 | | sdtasdt0(xr, all_57_5) = xn & sdtasdt0(xp, all_57_1) = all_57_5 &
% 115.66/16.06 | | $i(all_57_5) & doDivides0(xp, all_57_5) & aNaturalNumber0(all_57_1)
% 115.66/16.06 | | & aNaturalNumber0(all_57_5)
% 115.66/16.06 | |
% 115.66/16.06 | | ALPHA: (61) implies:
% 115.66/16.06 | | (62) aNaturalNumber0(all_57_1)
% 115.66/16.06 | | (63) doDivides0(xp, all_57_5)
% 115.66/16.06 | | (64) sdtasdt0(xp, all_57_1) = all_57_5
% 115.66/16.06 | | (65) sdtsldt0(xn, xr) = all_57_5
% 115.66/16.06 | |
% 115.66/16.06 | | BETA: splitting (6) gives:
% 115.66/16.06 | |
% 115.66/16.06 | | Case 1:
% 115.66/16.06 | | |
% 115.66/16.06 | | | (66) ~ aNaturalNumber0(sz10)
% 115.66/16.06 | | |
% 115.66/16.06 | | | PRED_UNIFY: (1), (66) imply:
% 115.66/16.06 | | | (67) $false
% 115.66/16.06 | | |
% 115.66/16.06 | | | CLOSE: (67) is inconsistent.
% 115.66/16.06 | | |
% 115.66/16.06 | | Case 2:
% 115.66/16.06 | | |
% 115.66/16.06 | | |
% 115.66/16.06 | | | GROUND_INST: instantiating (25) with all_55_2, all_57_5, xr, xn,
% 115.66/16.06 | | | simplifying with (48), (65) gives:
% 115.66/16.06 | | | (68) all_57_5 = all_55_2
% 115.66/16.06 | | |
% 115.66/16.06 | | | GROUND_INST: instantiating (25) with all_49_1, all_57_5, xr, xn,
% 115.66/16.06 | | | simplifying with (43), (65) gives:
% 115.66/16.06 | | | (69) all_57_5 = all_49_1
% 115.66/16.06 | | |
% 115.66/16.06 | | | COMBINE_EQS: (68), (69) imply:
% 115.66/16.06 | | | (70) all_55_2 = all_49_1
% 115.66/16.06 | | |
% 115.66/16.06 | | | REDUCE: (47), (70) imply:
% 115.66/16.06 | | | (71) sdtasdt0(xr, all_49_1) = xn
% 115.66/16.06 | | |
% 115.66/16.06 | | | REDUCE: (64), (69) imply:
% 115.66/16.06 | | | (72) sdtasdt0(xp, all_57_1) = all_49_1
% 115.66/16.06 | | |
% 115.66/16.06 | | | REDUCE: (46), (70) imply:
% 115.66/16.06 | | | (73) $i(all_49_1)
% 115.66/16.06 | | |
% 115.66/16.06 | | | REDUCE: (63), (69) imply:
% 115.66/16.06 | | | (74) doDivides0(xp, all_49_1)
% 115.66/16.06 | | |
% 115.66/16.06 | | | REDUCE: (45), (70) imply:
% 115.66/16.06 | | | (75) aNaturalNumber0(all_49_1)
% 115.66/16.06 | | |
% 115.66/16.06 | | | GROUND_INST: instantiating (7) with xp, simplifying with (9), (24) gives:
% 115.66/16.06 | | | (76) xp = sz10 | xp = sz00 | ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 115.66/16.06 | | | doDivides0(v0, xp) & aNaturalNumber0(v0))
% 115.66/16.06 | | |
% 115.66/16.06 | | | GROUND_INST: instantiating (2) with xk, xp, simplifying with (9), (14),
% 115.66/16.06 | | | (24), (33), (37) gives:
% 115.66/16.07 | | | (77) ? [v0: $i] : (sdtpldt0(xk, v0) = xp & $i(v0) &
% 115.66/16.07 | | | aNaturalNumber0(v0))
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (3) with xp, all_49_1, simplifying with (9),
% 115.66/16.07 | | | (24), (73), (74), (75) gives:
% 115.66/16.07 | | | (78) ? [v0: $i] : (sdtasdt0(xp, v0) = all_49_1 & $i(v0) &
% 115.66/16.07 | | | aNaturalNumber0(v0))
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (3) with xr, xn, simplifying with (8), (19),
% 115.66/16.07 | | | (23), (28), (54) gives:
% 115.66/16.07 | | | (79) ? [v0: $i] : (sdtasdt0(xr, v0) = xn & $i(v0) &
% 115.66/16.07 | | | aNaturalNumber0(v0))
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (mAddComm) with xk, all_43_0, xp, simplifying
% 115.66/16.07 | | | with (14), (32), (34), (35), (37) gives:
% 115.66/16.07 | | | (80) sdtpldt0(all_43_0, xk) = xp & $i(xp)
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (mAddAsso) with xr, all_47_0, all_43_0, xk, xp,
% 115.66/16.07 | | | simplifying with (19), (32), (34), (35), (39), (40), (41),
% 115.66/16.07 | | | (54) gives:
% 115.66/16.07 | | | (81) ? [v0: $i] : (sdtpldt0(all_47_0, all_43_0) = v0 & sdtpldt0(xr,
% 115.66/16.07 | | | v0) = xp & $i(v0) & $i(xp))
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (mMulComm) with xp, all_57_1, all_49_1,
% 115.66/16.07 | | | simplifying with (9), (24), (50), (62), (72) gives:
% 115.66/16.07 | | | (82) sdtasdt0(all_57_1, xp) = all_49_1 & $i(all_49_1)
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (mMulComm) with xr, all_49_1, xn, simplifying
% 115.66/16.07 | | | with (19), (54), (71), (73), (75) gives:
% 115.66/16.07 | | | (83) sdtasdt0(all_49_1, xr) = xn & $i(xn)
% 115.66/16.07 | | |
% 115.66/16.07 | | | ALPHA: (83) implies:
% 115.66/16.07 | | | (84) sdtasdt0(all_49_1, xr) = xn
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (mMulComm) with xr, all_59_0, xk, simplifying
% 115.66/16.07 | | | with (19), (54), (55), (56), (57) gives:
% 115.66/16.07 | | | (85) sdtasdt0(all_59_0, xr) = xk & $i(xk)
% 115.66/16.07 | | |
% 115.66/16.07 | | | GROUND_INST: instantiating (5) with xr, xn, all_49_1, all_41_0,
% 115.66/16.07 | | | simplifying with (8), (19), (23), (27), (28), (29), (30),
% 115.66/16.07 | | | (43), (54) gives:
% 115.66/16.07 | | | (86) all_49_1 = all_41_0 | xr = sz00
% 115.66/16.07 | | |
% 115.66/16.07 | | | DELTA: instantiating (77) with fresh symbol all_90_0 gives:
% 115.66/16.07 | | | (87) sdtpldt0(xk, all_90_0) = xp & $i(all_90_0) &
% 115.66/16.07 | | | aNaturalNumber0(all_90_0)
% 115.66/16.07 | | |
% 115.66/16.07 | | | ALPHA: (87) implies:
% 115.66/16.07 | | | (88) aNaturalNumber0(all_90_0)
% 115.66/16.07 | | | (89) $i(all_90_0)
% 115.66/16.07 | | | (90) sdtpldt0(xk, all_90_0) = xp
% 115.66/16.07 | | |
% 115.66/16.07 | | | DELTA: instantiating (79) with fresh symbol all_94_0 gives:
% 115.66/16.07 | | | (91) sdtasdt0(xr, all_94_0) = xn & $i(all_94_0) &
% 115.66/16.07 | | | aNaturalNumber0(all_94_0)
% 115.66/16.07 | | |
% 115.66/16.07 | | | ALPHA: (91) implies:
% 115.66/16.08 | | | (92) aNaturalNumber0(all_94_0)
% 115.66/16.08 | | | (93) $i(all_94_0)
% 115.66/16.08 | | | (94) sdtasdt0(xr, all_94_0) = xn
% 115.66/16.08 | | |
% 115.66/16.08 | | | DELTA: instantiating (78) with fresh symbol all_100_0 gives:
% 115.66/16.08 | | | (95) sdtasdt0(xp, all_100_0) = all_49_1 & $i(all_100_0) &
% 115.66/16.08 | | | aNaturalNumber0(all_100_0)
% 115.66/16.08 | | |
% 115.66/16.08 | | | ALPHA: (95) implies:
% 115.66/16.08 | | | (96) aNaturalNumber0(all_100_0)
% 115.66/16.08 | | | (97) $i(all_100_0)
% 115.66/16.08 | | | (98) sdtasdt0(xp, all_100_0) = all_49_1
% 115.66/16.08 | | |
% 115.66/16.08 | | | DELTA: instantiating (81) with fresh symbol all_112_0 gives:
% 115.66/16.08 | | | (99) sdtpldt0(all_47_0, all_43_0) = all_112_0 & sdtpldt0(xr, all_112_0)
% 115.66/16.08 | | | = xp & $i(all_112_0) & $i(xp)
% 115.66/16.08 | | |
% 115.66/16.08 | | | ALPHA: (99) implies:
% 115.66/16.08 | | | (100) sdtpldt0(xr, all_112_0) = xp
% 115.66/16.08 | | | (101) sdtpldt0(all_47_0, all_43_0) = all_112_0
% 115.66/16.08 | | |
% 115.66/16.08 | | | BETA: splitting (86) gives:
% 115.66/16.08 | | |
% 115.66/16.08 | | | Case 1:
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | (102) xr = sz00
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | REDUCE: (53), (102) imply:
% 115.66/16.08 | | | | (103) $false
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | CLOSE: (103) is inconsistent.
% 115.66/16.08 | | | |
% 115.66/16.08 | | | Case 2:
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | (104) all_49_1 = all_41_0
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | REDUCE: (84), (104) imply:
% 115.66/16.08 | | | | (105) sdtasdt0(all_41_0, xr) = xn
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | REDUCE: (98), (104) imply:
% 115.66/16.08 | | | | (106) sdtasdt0(xp, all_100_0) = all_41_0
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | REDUCE: (72), (104) imply:
% 115.66/16.08 | | | | (107) sdtasdt0(xp, all_57_1) = all_41_0
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | REDUCE: (74), (104) imply:
% 115.66/16.08 | | | | (108) doDivides0(xp, all_41_0)
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | BETA: splitting (76) gives:
% 115.66/16.08 | | | |
% 115.66/16.08 | | | | Case 1:
% 115.66/16.08 | | | | |
% 115.66/16.08 | | | | | (109) xp = sz00
% 115.66/16.08 | | | | |
% 115.66/16.08 | | | | | REDUCE: (59), (109) imply:
% 115.66/16.08 | | | | | (110) $false
% 115.66/16.08 | | | | |
% 115.66/16.08 | | | | | CLOSE: (110) is inconsistent.
% 115.66/16.08 | | | | |
% 115.66/16.08 | | | | Case 2:
% 115.66/16.08 | | | | |
% 115.66/16.08 | | | | | (111) xp = sz10 | ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 115.66/16.08 | | | | | doDivides0(v0, xp) & aNaturalNumber0(v0))
% 115.66/16.08 | | | | |
% 115.66/16.08 | | | | | BETA: splitting (111) gives:
% 115.66/16.08 | | | | |
% 115.66/16.08 | | | | | Case 1:
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | (112) xp = sz10
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | REDUCE: (60), (112) imply:
% 115.66/16.08 | | | | | | (113) $false
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | CLOSE: (113) is inconsistent.
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | Case 2:
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | GROUND_INST: instantiating (mAddComm) with xk, all_90_0, xp,
% 115.66/16.08 | | | | | | simplifying with (14), (37), (88), (89), (90) gives:
% 115.66/16.08 | | | | | | (114) sdtpldt0(all_90_0, xk) = xp & $i(xp)
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | GROUND_INST: instantiating (mSortsB) with all_47_0, all_43_0,
% 115.66/16.08 | | | | | | all_112_0, simplifying with (32), (34), (39), (40),
% 115.66/16.08 | | | | | | (101) gives:
% 115.66/16.08 | | | | | | (115) aNaturalNumber0(all_112_0)
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | GROUND_INST: instantiating (mAddComm) with all_47_0, all_43_0,
% 115.66/16.08 | | | | | | all_112_0, simplifying with (32), (34), (39), (40),
% 115.66/16.08 | | | | | | (101) gives:
% 115.66/16.08 | | | | | | (116) sdtpldt0(all_43_0, all_47_0) = all_112_0 & $i(all_112_0)
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | ALPHA: (116) implies:
% 115.66/16.08 | | | | | | (117) $i(all_112_0)
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_100_0, all_41_0,
% 115.66/16.08 | | | | | | simplifying with (9), (24), (96), (97), (106) gives:
% 115.66/16.08 | | | | | | (118) sdtasdt0(all_100_0, xp) = all_41_0 & $i(all_41_0)
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | GROUND_INST: instantiating (mMulComm) with xr, all_94_0, xn,
% 115.66/16.08 | | | | | | simplifying with (19), (54), (92), (93), (94) gives:
% 115.66/16.08 | | | | | | (119) sdtasdt0(all_94_0, xr) = xn & $i(xn)
% 115.66/16.08 | | | | | |
% 115.66/16.08 | | | | | | GROUND_INST: instantiating (mMulAsso) with xp, all_57_1, xr,
% 115.66/16.08 | | | | | | all_41_0, xn, simplifying with (9), (19), (24), (50),
% 115.66/16.08 | | | | | | (54), (62), (105), (107) gives:
% 115.66/16.08 | | | | | | (120) ? [v0: $i] : (sdtasdt0(all_57_1, xr) = v0 & sdtasdt0(xp,
% 115.66/16.08 | | | | | | v0) = xn & $i(v0) & $i(xn))
% 115.66/16.08 | | | | | |
% 115.66/16.09 | | | | | | GROUND_INST: instantiating (4) with all_41_0, xn, xr, simplifying
% 115.66/16.09 | | | | | | with (8), (19), (23), (27), (29), (54), (105) gives:
% 115.66/16.09 | | | | | | (121) doDivides0(all_41_0, xn)
% 115.66/16.09 | | | | | |
% 115.66/16.09 | | | | | | DELTA: instantiating (120) with fresh symbol all_342_0 gives:
% 115.66/16.09 | | | | | | (122) sdtasdt0(all_57_1, xr) = all_342_0 & sdtasdt0(xp,
% 115.66/16.09 | | | | | | all_342_0) = xn & $i(all_342_0) & $i(xn)
% 115.66/16.09 | | | | | |
% 115.66/16.09 | | | | | | GROUND_INST: instantiating (mAddComm) with xr, all_112_0, xp,
% 115.66/16.09 | | | | | | simplifying with (19), (54), (100), (115), (117) gives:
% 115.66/16.09 | | | | | | (123) sdtpldt0(all_112_0, xr) = xp & $i(xp)
% 115.66/16.09 | | | | | |
% 115.66/16.09 | | | | | | GROUND_INST: instantiating (mDivTrans) with xp, all_41_0, xn,
% 115.66/16.09 | | | | | | simplifying with (8), (9), (21), (23), (24), (27),
% 115.66/16.09 | | | | | | (29), (108), (121) gives:
% 115.66/16.09 | | | | | | (124) $false
% 115.66/16.09 | | | | | |
% 115.66/16.09 | | | | | | CLOSE: (124) is inconsistent.
% 115.66/16.09 | | | | | |
% 115.66/16.09 | | | | | End of split
% 115.66/16.09 | | | | |
% 115.66/16.09 | | | | End of split
% 115.66/16.09 | | | |
% 115.66/16.09 | | | End of split
% 115.66/16.09 | | |
% 115.66/16.09 | | End of split
% 115.66/16.09 | |
% 115.66/16.09 | Case 2:
% 115.66/16.09 | |
% 115.66/16.09 | | (125) all_57_2 = xm & sdtasdt0(xp, all_57_3) = xm & doDivides0(xp, xm) &
% 115.66/16.09 | | aNaturalNumber0(all_57_3)
% 115.66/16.09 | |
% 115.66/16.09 | | ALPHA: (125) implies:
% 115.66/16.09 | | (126) doDivides0(xp, xm)
% 115.66/16.09 | |
% 115.66/16.09 | | PRED_UNIFY: (22), (126) imply:
% 115.66/16.09 | | (127) $false
% 115.66/16.09 | |
% 115.66/16.09 | | CLOSE: (127) is inconsistent.
% 115.66/16.09 | |
% 115.66/16.09 | End of split
% 115.66/16.09 |
% 115.66/16.09 End of proof
% 115.66/16.09 % SZS output end Proof for theBenchmark
% 115.66/16.09
% 115.66/16.09 15473ms
%------------------------------------------------------------------------------