TSTP Solution File: NUM524+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM524+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 : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:48:22 EDT 2023
% Result : Theorem 18.53s 3.41s
% Output : Proof 36.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.17 % Problem : NUM524+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.18 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.38 % Computer : n022.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Fri Aug 25 10:28:25 EDT 2023
% 0.14/0.38 % CPUTime :
% 0.19/0.65 ________ _____
% 0.19/0.65 ___ __ \_________(_)________________________________
% 0.19/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.65
% 0.19/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.65 (2023-06-19)
% 0.19/0.65
% 0.19/0.65 (c) Philipp Rümmer, 2009-2023
% 0.19/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.65 Amanda Stjerna.
% 0.19/0.65 Free software under BSD-3-Clause.
% 0.19/0.65
% 0.19/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.65
% 0.19/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.66 Running up to 7 provers in parallel.
% 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 3.59/1.28 Prover 4: Preprocessing ...
% 3.59/1.28 Prover 1: Preprocessing ...
% 4.19/1.34 Prover 2: Preprocessing ...
% 4.19/1.34 Prover 3: Preprocessing ...
% 4.19/1.34 Prover 0: Preprocessing ...
% 4.19/1.34 Prover 5: Preprocessing ...
% 4.19/1.35 Prover 6: Preprocessing ...
% 10.82/2.41 Prover 1: Constructing countermodel ...
% 11.83/2.43 Prover 3: Constructing countermodel ...
% 11.83/2.46 Prover 6: Proving ...
% 12.48/2.57 Prover 5: Constructing countermodel ...
% 14.00/2.81 Prover 2: Proving ...
% 15.21/3.07 Prover 4: Constructing countermodel ...
% 17.54/3.24 Prover 0: Proving ...
% 18.53/3.40 Prover 3: proved (2720ms)
% 18.53/3.40
% 18.53/3.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.53/3.41
% 18.53/3.41 Prover 5: stopped
% 18.53/3.42 Prover 2: stopped
% 18.53/3.42 Prover 6: stopped
% 18.53/3.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.53/3.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.53/3.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.53/3.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.53/3.42 Prover 0: stopped
% 18.53/3.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.03/3.58 Prover 11: Preprocessing ...
% 20.03/3.58 Prover 8: Preprocessing ...
% 20.03/3.58 Prover 13: Preprocessing ...
% 20.03/3.61 Prover 7: Preprocessing ...
% 20.03/3.62 Prover 10: Preprocessing ...
% 22.44/3.91 Prover 10: Constructing countermodel ...
% 22.44/3.92 Prover 8: Warning: ignoring some quantifiers
% 22.44/3.94 Prover 8: Constructing countermodel ...
% 22.44/3.94 Prover 7: Constructing countermodel ...
% 22.93/4.03 Prover 13: Constructing countermodel ...
% 25.84/4.38 Prover 11: Constructing countermodel ...
% 35.57/5.68 Prover 10: Found proof (size 118)
% 35.57/5.68 Prover 10: proved (2264ms)
% 35.57/5.68 Prover 11: stopped
% 35.57/5.68 Prover 4: stopped
% 35.57/5.68 Prover 7: stopped
% 35.57/5.68 Prover 13: stopped
% 35.57/5.68 Prover 8: stopped
% 35.57/5.68 Prover 1: stopped
% 35.57/5.69
% 35.57/5.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.57/5.69
% 35.57/5.70 % SZS output start Proof for theBenchmark
% 35.57/5.71 Assumptions after simplification:
% 35.57/5.71 ---------------------------------
% 35.57/5.71
% 35.57/5.71 (mAddComm)
% 35.90/5.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 35.90/5.75 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 35.90/5.75 (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 35.90/5.75
% 35.90/5.75 (mDefDiv)
% 35.90/5.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~
% 35.90/5.76 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 35.90/5.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0:
% 35.90/5.76 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 35.90/5.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0,
% 35.90/5.76 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 35.90/5.76
% 35.90/5.76 (mDefLE)
% 36.08/5.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~
% 36.08/5.76 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 36.08/5.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 36.08/5.76 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~
% 36.08/5.76 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0,
% 36.08/5.76 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 36.08/5.76
% 36.08/5.76 (mDefPrime)
% 36.08/5.77 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~
% 36.08/5.77 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~
% 36.08/5.77 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 |
% 36.08/5.77 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i]
% 36.08/5.77 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) &
% 36.08/5.77 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & (
% 36.08/5.77 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00))
% 36.08/5.77
% 36.08/5.77 (mDefQuot)
% 36.08/5.78 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 |
% 36.08/5.78 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 36.08/5.78 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 36.08/5.78 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & !
% 36.08/5.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~
% 36.08/5.78 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 36.08/5.78 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~
% 36.08/5.78 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 36.08/5.78 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~
% 36.08/5.78 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 36.08/5.78 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 36.08/5.78
% 36.08/5.78 (mDivLE)
% 36.08/5.78 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 36.08/5.78 doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 36.08/5.78 sdtlseqdt0(v0, v1))
% 36.08/5.78
% 36.08/5.78 (mLENTr)
% 36.08/5.78 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 36.08/5.78 aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 36.08/5.78
% 36.08/5.78 (mMulAsso)
% 36.08/5.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 36.08/5.79 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 36.08/5.79 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 36.08/5.79 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0,
% 36.08/5.79 v5) = v4 & $i(v5) & $i(v4)))
% 36.08/5.79
% 36.08/5.79 (mMulCanc)
% 36.08/5.79 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 36.08/5.79 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) =
% 36.08/5.79 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 36.08/5.79 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : (
% 36.08/5.79 ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & $i(v6) &
% 36.08/5.79 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 =
% 36.08/5.79 v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) |
% 36.08/5.79 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 36.08/5.79 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 36.08/5.79
% 36.08/5.79 (mMulComm)
% 36.08/5.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 36.08/5.79 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 36.08/5.79 (sdtasdt0(v1, v0) = v2 & $i(v2)))
% 36.08/5.79
% 36.08/5.79 (mSortsB_02)
% 36.08/5.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 36.08/5.80 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 36.08/5.80 aNaturalNumber0(v2))
% 36.08/5.80
% 36.08/5.80 (mSortsC_01)
% 36.08/5.80 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 36.08/5.80
% 36.08/5.80 (m__)
% 36.08/5.80 $i(xq) & $i(xp) & $i(xm) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 =
% 36.08/5.80 v0) & sdtasdt0(xq, xq) = v1 & sdtasdt0(xp, v1) = v2 & sdtasdt0(xm, xm) =
% 36.08/5.80 v0 & $i(v2) & $i(v1) & $i(v0))
% 36.08/5.80
% 36.08/5.80 (m__2987)
% 36.08/5.80 ~ (xp = sz00) & ~ (xm = sz00) & ~ (xn = sz00) & $i(xp) & $i(xm) & $i(xn) &
% 36.08/5.80 $i(sz00) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & aNaturalNumber0(xn)
% 36.08/5.80
% 36.08/5.80 (m__3014)
% 36.08/5.80 $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1
% 36.08/5.80 & sdtasdt0(xm, xm) = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0))
% 36.08/5.80
% 36.08/5.80 (m__3025)
% 36.08/5.80 ~ (xp = sz10) & $i(xp) & $i(sz10) & isPrime0(xp) & ! [v0: $i] : ! [v1: $i]
% 36.08/5.80 : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xp) | ~ $i(v1) | ~ $i(v0) |
% 36.08/5.80 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp |
% 36.08/5.80 v0 = sz10 | ~ $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0))
% 36.08/5.80
% 36.08/5.80 (m__3046)
% 36.08/5.81 $i(xp) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xp, v2)
% 36.08/5.81 = v0 & sdtasdt0(xp, v1) = xn & sdtasdt0(xn, xn) = v0 & $i(v2) & $i(v1) &
% 36.08/5.81 $i(v0) & doDivides0(xp, v0) & doDivides0(xp, xn) & aNaturalNumber0(v2) &
% 36.08/5.81 aNaturalNumber0(v1))
% 36.08/5.81
% 36.08/5.81 (m__3059)
% 36.08/5.81 sdtsldt0(xn, xp) = xq & sdtasdt0(xp, xq) = xn & $i(xq) & $i(xp) & $i(xn) &
% 36.08/5.81 aNaturalNumber0(xq)
% 36.08/5.81
% 36.08/5.81 (function-axioms)
% 36.08/5.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.08/5.81 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 36.08/5.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 36.08/5.81 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 36.08/5.81 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 36.08/5.81 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.08/5.81 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 36.08/5.81
% 36.08/5.81 Further assumptions not needed in the proof:
% 36.08/5.81 --------------------------------------------
% 36.08/5.81 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDivAsso, mDivMin, mDivSum, mDivTrans,
% 36.08/5.81 mIH, mIH_03, mLEAsym, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2,
% 36.08/5.81 mNatSort, mPDP, mPrimDiv, mSortsB, mSortsC, mZeroAdd, mZeroMul, m_AddZero,
% 36.08/5.81 m_MulUnit, m_MulZero, m__2963
% 36.08/5.81
% 36.08/5.81 Those formulas are unsatisfiable:
% 36.08/5.81 ---------------------------------
% 36.08/5.81
% 36.08/5.81 Begin of proof
% 36.08/5.81 |
% 36.08/5.81 | ALPHA: (mSortsC_01) implies:
% 36.08/5.82 | (1) aNaturalNumber0(sz10)
% 36.08/5.82 |
% 36.08/5.82 | ALPHA: (mMulCanc) implies:
% 36.08/5.82 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 =
% 36.08/5.82 | sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 36.08/5.82 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 36.08/5.82 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 36.08/5.82 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 36.08/5.82 | (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0,
% 36.08/5.82 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 36.08/5.82 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)
% 36.08/5.82 | | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 &
% 36.08/5.82 | sdtasdt0(v1, v0) = v5 & $i(v6) & $i(v5)))
% 36.08/5.82 |
% 36.08/5.82 | ALPHA: (mDefLE) implies:
% 36.08/5.82 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0,
% 36.08/5.82 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 36.08/5.82 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 36.08/5.82 |
% 36.08/5.82 | ALPHA: (mLENTr) implies:
% 36.08/5.82 | (5) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 36.08/5.82 | aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 36.08/5.82 |
% 36.08/5.82 | ALPHA: (mDefDiv) implies:
% 36.08/5.82 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 36.08/5.82 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 36.08/5.82 | : (sdtasdt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 36.08/5.82 |
% 36.08/5.82 | ALPHA: (mDefQuot) implies:
% 36.08/5.83 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 =
% 36.08/5.83 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~
% 36.08/5.83 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 36.08/5.83 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~
% 36.08/5.83 | aNaturalNumber0(v0))
% 36.08/5.83 |
% 36.08/5.83 | ALPHA: (mDivLE) implies:
% 36.08/5.83 | (8) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ $i(v1) | ~ $i(v0) | ~
% 36.08/5.83 | doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)
% 36.08/5.83 | | sdtlseqdt0(v0, v1))
% 36.08/5.83 |
% 36.08/5.83 | ALPHA: (mDefPrime) implies:
% 36.08/5.83 | (9) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)
% 36.08/5.83 |
% 36.08/5.83 | ALPHA: (m__2987) implies:
% 36.08/5.83 | (10) ~ (xn = sz00)
% 36.08/5.83 | (11) ~ (xp = sz00)
% 36.08/5.83 | (12) aNaturalNumber0(xn)
% 36.08/5.83 | (13) aNaturalNumber0(xm)
% 36.08/5.83 | (14) aNaturalNumber0(xp)
% 36.08/5.83 |
% 36.08/5.83 | ALPHA: (m__3014) implies:
% 36.41/5.83 | (15) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xp, v0) = v1 & sdtasdt0(xm, xm)
% 36.41/5.83 | = v0 & sdtasdt0(xn, xn) = v1 & $i(v1) & $i(v0))
% 36.41/5.83 |
% 36.41/5.83 | ALPHA: (m__3025) implies:
% 36.41/5.83 | (16) ~ (xp = sz10)
% 36.41/5.83 | (17) $i(sz10)
% 36.41/5.83 |
% 36.41/5.83 | ALPHA: (m__3046) implies:
% 36.41/5.83 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xp, v2) = v0 &
% 36.41/5.83 | sdtasdt0(xp, v1) = xn & sdtasdt0(xn, xn) = v0 & $i(v2) & $i(v1) &
% 36.41/5.83 | $i(v0) & doDivides0(xp, v0) & doDivides0(xp, xn) &
% 36.41/5.83 | aNaturalNumber0(v2) & aNaturalNumber0(v1))
% 36.41/5.83 |
% 36.41/5.83 | ALPHA: (m__3059) implies:
% 36.41/5.83 | (19) aNaturalNumber0(xq)
% 36.41/5.83 | (20) $i(xn)
% 36.41/5.83 | (21) sdtasdt0(xp, xq) = xn
% 36.41/5.83 | (22) sdtsldt0(xn, xp) = xq
% 36.41/5.83 |
% 36.41/5.83 | ALPHA: (m__) implies:
% 36.41/5.83 | (23) $i(xm)
% 36.41/5.83 | (24) $i(xp)
% 36.41/5.83 | (25) $i(xq)
% 36.41/5.84 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & sdtasdt0(xq,
% 36.41/5.84 | xq) = v1 & sdtasdt0(xp, v1) = v2 & sdtasdt0(xm, xm) = v0 & $i(v2)
% 36.41/5.84 | & $i(v1) & $i(v0))
% 36.41/5.84 |
% 36.41/5.84 | ALPHA: (function-axioms) implies:
% 36.41/5.84 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.41/5.84 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 36.41/5.84 |
% 36.41/5.84 | DELTA: instantiating (15) with fresh symbols all_41_0, all_41_1 gives:
% 36.41/5.84 | (28) sdtasdt0(xp, all_41_1) = all_41_0 & sdtasdt0(xm, xm) = all_41_1 &
% 36.41/5.84 | sdtasdt0(xn, xn) = all_41_0 & $i(all_41_0) & $i(all_41_1)
% 36.41/5.84 |
% 36.41/5.84 | ALPHA: (28) implies:
% 36.41/5.84 | (29) sdtasdt0(xn, xn) = all_41_0
% 36.41/5.84 | (30) sdtasdt0(xm, xm) = all_41_1
% 36.41/5.84 | (31) sdtasdt0(xp, all_41_1) = all_41_0
% 36.41/5.84 |
% 36.41/5.84 | DELTA: instantiating (26) with fresh symbols all_43_0, all_43_1, all_43_2
% 36.41/5.84 | gives:
% 36.41/5.84 | (32) ~ (all_43_0 = all_43_2) & sdtasdt0(xq, xq) = all_43_1 & sdtasdt0(xp,
% 36.41/5.84 | all_43_1) = all_43_0 & sdtasdt0(xm, xm) = all_43_2 & $i(all_43_0) &
% 36.41/5.84 | $i(all_43_1) & $i(all_43_2)
% 36.41/5.84 |
% 36.41/5.84 | ALPHA: (32) implies:
% 36.41/5.84 | (33) ~ (all_43_0 = all_43_2)
% 36.41/5.84 | (34) $i(all_43_2)
% 36.41/5.84 | (35) $i(all_43_1)
% 36.41/5.84 | (36) sdtasdt0(xm, xm) = all_43_2
% 36.41/5.84 | (37) sdtasdt0(xp, all_43_1) = all_43_0
% 36.41/5.84 | (38) sdtasdt0(xq, xq) = all_43_1
% 36.41/5.84 |
% 36.41/5.84 | DELTA: instantiating (18) with fresh symbols all_45_0, all_45_1, all_45_2
% 36.41/5.84 | gives:
% 36.41/5.84 | (39) sdtasdt0(xp, all_45_0) = all_45_2 & sdtasdt0(xp, all_45_1) = xn &
% 36.41/5.84 | sdtasdt0(xn, xn) = all_45_2 & $i(all_45_0) & $i(all_45_1) &
% 36.41/5.84 | $i(all_45_2) & doDivides0(xp, all_45_2) & doDivides0(xp, xn) &
% 36.41/5.84 | aNaturalNumber0(all_45_0) & aNaturalNumber0(all_45_1)
% 36.41/5.84 |
% 36.41/5.84 | ALPHA: (39) implies:
% 36.41/5.84 | (40) aNaturalNumber0(all_45_1)
% 36.41/5.84 | (41) doDivides0(xp, xn)
% 36.41/5.84 | (42) $i(all_45_1)
% 36.41/5.84 | (43) sdtasdt0(xn, xn) = all_45_2
% 36.41/5.85 | (44) sdtasdt0(xp, all_45_1) = xn
% 36.41/5.85 |
% 36.41/5.85 | BETA: splitting (9) gives:
% 36.41/5.85 |
% 36.41/5.85 | Case 1:
% 36.41/5.85 | |
% 36.41/5.85 | | (45) ~ aNaturalNumber0(sz10)
% 36.41/5.85 | |
% 36.41/5.85 | | PRED_UNIFY: (1), (45) imply:
% 36.41/5.85 | | (46) $false
% 36.41/5.85 | |
% 36.41/5.85 | | CLOSE: (46) is inconsistent.
% 36.41/5.85 | |
% 36.41/5.85 | Case 2:
% 36.41/5.85 | |
% 36.41/5.85 | |
% 36.41/5.85 | | GROUND_INST: instantiating (27) with all_41_0, all_45_2, xn, xn, simplifying
% 36.41/5.85 | | with (29), (43) gives:
% 36.41/5.85 | | (47) all_45_2 = all_41_0
% 36.41/5.85 | |
% 36.41/5.85 | | GROUND_INST: instantiating (27) with all_41_1, all_43_2, xm, xm, simplifying
% 36.41/5.85 | | with (30), (36) gives:
% 36.41/5.85 | | (48) all_43_2 = all_41_1
% 36.41/5.85 | |
% 36.41/5.85 | | REDUCE: (33), (48) imply:
% 36.41/5.85 | | (49) ~ (all_43_0 = all_41_1)
% 36.41/5.85 | |
% 36.41/5.85 | | REDUCE: (34), (48) imply:
% 36.41/5.85 | | (50) $i(all_41_1)
% 36.41/5.85 | |
% 36.41/5.85 | | GROUND_INST: instantiating (5) with xp, simplifying with (14), (24) gives:
% 36.41/5.85 | | (51) xp = sz10 | xp = sz00 | sdtlseqdt0(sz10, xp)
% 36.41/5.85 | |
% 36.41/5.85 | | GROUND_INST: instantiating (8) with xp, xn, simplifying with (12), (14),
% 36.41/5.85 | | (20), (24), (41) gives:
% 36.41/5.85 | | (52) xn = sz00 | sdtlseqdt0(xp, xn)
% 36.41/5.85 | |
% 36.41/5.85 | | GROUND_INST: instantiating (6) with xp, xn, simplifying with (12), (14),
% 36.41/5.85 | | (20), (24), (41) gives:
% 36.41/5.85 | | (53) ? [v0: $i] : (sdtasdt0(xp, v0) = xn & $i(v0) & aNaturalNumber0(v0))
% 36.41/5.85 | |
% 36.41/5.86 | | GROUND_INST: instantiating (mSortsB_02) with xm, xm, all_41_1, simplifying
% 36.41/5.86 | | with (13), (23), (30) gives:
% 36.41/5.86 | | (54) aNaturalNumber0(all_41_1)
% 36.41/5.86 | |
% 36.41/5.86 | | GROUND_INST: instantiating (mMulAsso) with xp, xq, xn, xn, all_41_0,
% 36.41/5.86 | | simplifying with (12), (14), (19), (20), (21), (24), (25), (29)
% 36.41/5.86 | | gives:
% 36.41/5.86 | | (55) ? [v0: $i] : (sdtasdt0(xq, xn) = v0 & sdtasdt0(xp, v0) = all_41_0 &
% 36.41/5.86 | | $i(v0) & $i(all_41_0))
% 36.41/5.86 | |
% 36.41/5.86 | | GROUND_INST: instantiating (mMulComm) with xp, xq, xn, simplifying with
% 36.41/5.86 | | (14), (19), (21), (24), (25) gives:
% 36.41/5.86 | | (56) sdtasdt0(xq, xp) = xn & $i(xn)
% 36.41/5.86 | |
% 36.41/5.86 | | GROUND_INST: instantiating (mMulAsso) with xp, all_45_1, xn, xn, all_41_0,
% 36.41/5.86 | | simplifying with (12), (14), (20), (24), (29), (40), (42), (44)
% 36.41/5.86 | | gives:
% 36.41/5.86 | | (57) ? [v0: $i] : (sdtasdt0(all_45_1, xn) = v0 & sdtasdt0(xp, v0) =
% 36.41/5.86 | | all_41_0 & $i(v0) & $i(all_41_0))
% 36.41/5.86 | |
% 36.41/5.86 | | GROUND_INST: instantiating (mMulComm) with xp, all_45_1, xn, simplifying
% 36.41/5.86 | | with (14), (24), (40), (42), (44) gives:
% 36.41/5.86 | | (58) sdtasdt0(all_45_1, xp) = xn & $i(xn)
% 36.41/5.86 | |
% 36.41/5.86 | | GROUND_INST: instantiating (mSortsB_02) with xq, xq, all_43_1, simplifying
% 36.41/5.86 | | with (19), (25), (38) gives:
% 36.41/5.86 | | (59) aNaturalNumber0(all_43_1)
% 36.41/5.86 | |
% 36.41/5.87 | | GROUND_INST: instantiating (7) with xp, xn, xq, all_45_1, simplifying with
% 36.41/5.87 | | (12), (14), (20), (22), (24), (40), (41), (42), (44) gives:
% 36.59/5.87 | | (60) all_45_1 = xq | xp = sz00
% 36.59/5.87 | |
% 36.59/5.87 | | DELTA: instantiating (53) with fresh symbol all_65_0 gives:
% 36.59/5.87 | | (61) sdtasdt0(xp, all_65_0) = xn & $i(all_65_0) &
% 36.59/5.87 | | aNaturalNumber0(all_65_0)
% 36.59/5.87 | |
% 36.59/5.87 | | ALPHA: (61) implies:
% 36.59/5.87 | | (62) aNaturalNumber0(all_65_0)
% 36.59/5.87 | | (63) $i(all_65_0)
% 36.59/5.87 | | (64) sdtasdt0(xp, all_65_0) = xn
% 36.59/5.87 | |
% 36.59/5.87 | | DELTA: instantiating (55) with fresh symbol all_67_0 gives:
% 36.59/5.87 | | (65) sdtasdt0(xq, xn) = all_67_0 & sdtasdt0(xp, all_67_0) = all_41_0 &
% 36.59/5.87 | | $i(all_67_0) & $i(all_41_0)
% 36.59/5.87 | |
% 36.59/5.87 | | ALPHA: (65) implies:
% 36.59/5.87 | | (66) sdtasdt0(xq, xn) = all_67_0
% 36.59/5.87 | |
% 36.59/5.87 | | DELTA: instantiating (57) with fresh symbol all_69_0 gives:
% 36.59/5.87 | | (67) sdtasdt0(all_45_1, xn) = all_69_0 & sdtasdt0(xp, all_69_0) =
% 36.59/5.87 | | all_41_0 & $i(all_69_0) & $i(all_41_0)
% 36.59/5.87 | |
% 36.59/5.87 | | ALPHA: (67) implies:
% 36.59/5.87 | | (68) sdtasdt0(all_45_1, xn) = all_69_0
% 36.59/5.87 | |
% 36.59/5.87 | | BETA: splitting (51) gives:
% 36.59/5.87 | |
% 36.59/5.87 | | Case 1:
% 36.59/5.87 | | |
% 36.59/5.87 | | | (69) sdtlseqdt0(sz10, xp)
% 36.59/5.87 | | |
% 36.59/5.87 | | | BETA: splitting (60) gives:
% 36.59/5.87 | | |
% 36.59/5.87 | | | Case 1:
% 36.59/5.87 | | | |
% 36.59/5.87 | | | | (70) xp = sz00
% 36.59/5.87 | | | |
% 36.59/5.87 | | | | REDUCE: (11), (70) imply:
% 36.59/5.87 | | | | (71) $false
% 36.59/5.87 | | | |
% 36.59/5.87 | | | | CLOSE: (71) is inconsistent.
% 36.59/5.87 | | | |
% 36.59/5.87 | | | Case 2:
% 36.59/5.87 | | | |
% 36.59/5.87 | | | | (72) all_45_1 = xq
% 36.59/5.87 | | | |
% 36.59/5.87 | | | | REDUCE: (68), (72) imply:
% 36.59/5.87 | | | | (73) sdtasdt0(xq, xn) = all_69_0
% 36.59/5.87 | | | |
% 36.59/5.87 | | | | BETA: splitting (52) gives:
% 36.59/5.87 | | | |
% 36.59/5.87 | | | | Case 1:
% 36.59/5.87 | | | | |
% 36.59/5.87 | | | | |
% 36.59/5.87 | | | | | GROUND_INST: instantiating (27) with all_67_0, all_69_0, xn, xq,
% 36.59/5.87 | | | | | simplifying with (66), (73) gives:
% 36.59/5.87 | | | | | (74) all_69_0 = all_67_0
% 36.59/5.87 | | | | |
% 36.59/5.87 | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_43_1, all_43_0,
% 36.59/5.87 | | | | | simplifying with (14), (24), (35), (37), (59) gives:
% 36.59/5.87 | | | | | (75) sdtasdt0(all_43_1, xp) = all_43_0 & $i(all_43_0)
% 36.59/5.87 | | | | |
% 36.59/5.87 | | | | | ALPHA: (75) implies:
% 36.59/5.87 | | | | | (76) sdtasdt0(all_43_1, xp) = all_43_0
% 36.59/5.87 | | | | |
% 36.59/5.87 | | | | | GROUND_INST: instantiating (4) with sz10, xp, simplifying with (1),
% 36.59/5.87 | | | | | (14), (17), (24), (69) gives:
% 36.59/5.87 | | | | | (77) ? [v0: $i] : (sdtpldt0(sz10, v0) = xp & $i(v0) &
% 36.59/5.87 | | | | | aNaturalNumber0(v0))
% 36.59/5.87 | | | | |
% 36.59/5.88 | | | | | GROUND_INST: instantiating (3) with xp, all_65_0, xq, xn, xn,
% 36.59/5.88 | | | | | simplifying with (14), (19), (21), (24), (25), (62),
% 36.59/5.88 | | | | | (63), (64) gives:
% 36.59/5.88 | | | | | (78) all_65_0 = xq | xp = sz00 | ? [v0: $i] : ? [v1: $i] : ( ~
% 36.59/5.88 | | | | | (v1 = v0) & sdtasdt0(all_65_0, xp) = v0 & sdtasdt0(xq, xp) =
% 36.59/5.88 | | | | | v1 & $i(v1) & $i(v0))
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | GROUND_INST: instantiating (2) with xp, all_65_0, xq, xn, simplifying
% 36.59/5.88 | | | | | with (14), (19), (21), (24), (25), (62), (63), (64)
% 36.59/5.88 | | | | | gives:
% 36.59/5.88 | | | | | (79) all_65_0 = xq | xp = sz00
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | GROUND_INST: instantiating (mMulAsso) with xp, all_65_0, xn, xn,
% 36.59/5.88 | | | | | all_41_0, simplifying with (12), (14), (20), (24), (29),
% 36.59/5.88 | | | | | (62), (63), (64) gives:
% 36.59/5.88 | | | | | (80) ? [v0: $i] : (sdtasdt0(all_65_0, xn) = v0 & sdtasdt0(xp, v0)
% 36.59/5.88 | | | | | = all_41_0 & $i(v0) & $i(all_41_0))
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | GROUND_INST: instantiating (mMulComm) with xp, all_65_0, xn,
% 36.59/5.88 | | | | | simplifying with (14), (24), (62), (63), (64) gives:
% 36.59/5.88 | | | | | (81) sdtasdt0(all_65_0, xp) = xn & $i(xn)
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | ALPHA: (81) implies:
% 36.59/5.88 | | | | | (82) sdtasdt0(all_65_0, xp) = xn
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | GROUND_INST: instantiating (mSortsB_02) with xq, xn, all_67_0,
% 36.59/5.88 | | | | | simplifying with (12), (19), (20), (25), (66) gives:
% 36.59/5.88 | | | | | (83) aNaturalNumber0(all_67_0)
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | DELTA: instantiating (77) with fresh symbol all_129_0 gives:
% 36.59/5.88 | | | | | (84) sdtpldt0(sz10, all_129_0) = xp & $i(all_129_0) &
% 36.59/5.88 | | | | | aNaturalNumber0(all_129_0)
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | ALPHA: (84) implies:
% 36.59/5.88 | | | | | (85) aNaturalNumber0(all_129_0)
% 36.59/5.88 | | | | | (86) $i(all_129_0)
% 36.59/5.88 | | | | | (87) sdtpldt0(sz10, all_129_0) = xp
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | DELTA: instantiating (80) with fresh symbol all_135_0 gives:
% 36.59/5.88 | | | | | (88) sdtasdt0(all_65_0, xn) = all_135_0 & sdtasdt0(xp, all_135_0) =
% 36.59/5.88 | | | | | all_41_0 & $i(all_135_0) & $i(all_41_0)
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | ALPHA: (88) implies:
% 36.59/5.88 | | | | | (89) $i(all_135_0)
% 36.59/5.88 | | | | | (90) sdtasdt0(xp, all_135_0) = all_41_0
% 36.59/5.88 | | | | | (91) sdtasdt0(all_65_0, xn) = all_135_0
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | BETA: splitting (78) gives:
% 36.59/5.88 | | | | |
% 36.59/5.88 | | | | | Case 1:
% 36.59/5.88 | | | | | |
% 36.59/5.88 | | | | | | (92) xp = sz00
% 36.59/5.88 | | | | | |
% 36.59/5.88 | | | | | | REDUCE: (11), (92) imply:
% 36.59/5.88 | | | | | | (93) $false
% 36.59/5.88 | | | | | |
% 36.59/5.88 | | | | | | CLOSE: (93) is inconsistent.
% 36.59/5.88 | | | | | |
% 36.59/5.88 | | | | | Case 2:
% 36.59/5.88 | | | | | |
% 36.59/5.88 | | | | | | (94) all_65_0 = xq | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 36.59/5.88 | | | | | | sdtasdt0(all_65_0, xp) = v0 & sdtasdt0(xq, xp) = v1 &
% 36.59/5.88 | | | | | | $i(v1) & $i(v0))
% 36.59/5.88 | | | | | |
% 36.59/5.88 | | | | | | BETA: splitting (94) gives:
% 36.59/5.88 | | | | | |
% 36.59/5.88 | | | | | | Case 1:
% 36.59/5.88 | | | | | | |
% 36.59/5.88 | | | | | | | (95) all_65_0 = xq
% 36.59/5.88 | | | | | | |
% 36.59/5.88 | | | | | | | REDUCE: (82), (95) imply:
% 36.59/5.88 | | | | | | | (96) sdtasdt0(xq, xp) = xn
% 36.59/5.88 | | | | | | |
% 36.59/5.88 | | | | | | | REDUCE: (91), (95) imply:
% 36.59/5.88 | | | | | | | (97) sdtasdt0(xq, xn) = all_135_0
% 36.59/5.88 | | | | | | |
% 36.59/5.88 | | | | | | | GROUND_INST: instantiating (27) with all_67_0, all_135_0, xn, xq,
% 36.59/5.88 | | | | | | | simplifying with (66), (97) gives:
% 36.59/5.89 | | | | | | | (98) all_135_0 = all_67_0
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | REDUCE: (90), (98) imply:
% 36.59/5.89 | | | | | | | (99) sdtasdt0(xp, all_67_0) = all_41_0
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | REDUCE: (89), (98) imply:
% 36.59/5.89 | | | | | | | (100) $i(all_67_0)
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | GROUND_INST: instantiating (2) with xp, all_41_1, all_67_0,
% 36.59/5.89 | | | | | | | all_41_0, simplifying with (14), (24), (31), (50),
% 36.59/5.89 | | | | | | | (54), (83), (99), (100) gives:
% 36.59/5.89 | | | | | | | (101) all_67_0 = all_41_1 | xp = sz00
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | GROUND_INST: instantiating (mAddComm) with sz10, all_129_0, xp,
% 36.59/5.89 | | | | | | | simplifying with (1), (17), (85), (86), (87) gives:
% 36.59/5.89 | | | | | | | (102) sdtpldt0(all_129_0, sz10) = xp & $i(xp)
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | GROUND_INST: instantiating (mMulAsso) with xq, xq, xp, all_43_1,
% 36.59/5.89 | | | | | | | all_43_0, simplifying with (14), (19), (24), (25),
% 36.59/5.89 | | | | | | | (38), (76) gives:
% 36.59/5.89 | | | | | | | (103) ? [v0: $i] : (sdtasdt0(xq, v0) = all_43_0 & sdtasdt0(xq,
% 36.59/5.89 | | | | | | | xp) = v0 & $i(v0) & $i(all_43_0))
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | DELTA: instantiating (103) with fresh symbol all_263_0 gives:
% 36.59/5.89 | | | | | | | (104) sdtasdt0(xq, all_263_0) = all_43_0 & sdtasdt0(xq, xp) =
% 36.59/5.89 | | | | | | | all_263_0 & $i(all_263_0) & $i(all_43_0)
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | ALPHA: (104) implies:
% 36.59/5.89 | | | | | | | (105) sdtasdt0(xq, xp) = all_263_0
% 36.59/5.89 | | | | | | | (106) sdtasdt0(xq, all_263_0) = all_43_0
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | BETA: splitting (101) gives:
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | Case 1:
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | (107) xp = sz00
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | REDUCE: (11), (107) imply:
% 36.59/5.89 | | | | | | | | (108) $false
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | CLOSE: (108) is inconsistent.
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | Case 2:
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | (109) all_67_0 = all_41_1
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | REDUCE: (66), (109) imply:
% 36.59/5.89 | | | | | | | | (110) sdtasdt0(xq, xn) = all_41_1
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | GROUND_INST: instantiating (27) with xn, all_263_0, xp, xq,
% 36.59/5.89 | | | | | | | | simplifying with (96), (105) gives:
% 36.59/5.89 | | | | | | | | (111) all_263_0 = xn
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | REDUCE: (106), (111) imply:
% 36.59/5.89 | | | | | | | | (112) sdtasdt0(xq, xn) = all_43_0
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | GROUND_INST: instantiating (27) with all_41_1, all_43_0, xn, xq,
% 36.59/5.89 | | | | | | | | simplifying with (110), (112) gives:
% 36.59/5.89 | | | | | | | | (113) all_43_0 = all_41_1
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | REDUCE: (49), (113) imply:
% 36.59/5.89 | | | | | | | | (114) $false
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | CLOSE: (114) is inconsistent.
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | End of split
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | Case 2:
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | (115) ~ (all_65_0 = xq)
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | BETA: splitting (79) gives:
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | | Case 1:
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | (116) xp = sz00
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | REDUCE: (11), (116) imply:
% 36.59/5.89 | | | | | | | | (117) $false
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | CLOSE: (117) is inconsistent.
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | Case 2:
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | (118) all_65_0 = xq
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | REDUCE: (115), (118) imply:
% 36.59/5.89 | | | | | | | | (119) $false
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | | CLOSE: (119) is inconsistent.
% 36.59/5.89 | | | | | | | |
% 36.59/5.89 | | | | | | | End of split
% 36.59/5.89 | | | | | | |
% 36.59/5.89 | | | | | | End of split
% 36.59/5.89 | | | | | |
% 36.59/5.89 | | | | | End of split
% 36.59/5.89 | | | | |
% 36.59/5.89 | | | | Case 2:
% 36.59/5.89 | | | | |
% 36.59/5.89 | | | | | (120) xn = sz00
% 36.59/5.89 | | | | |
% 36.59/5.89 | | | | | REDUCE: (10), (120) imply:
% 36.59/5.89 | | | | | (121) $false
% 36.59/5.89 | | | | |
% 36.59/5.89 | | | | | CLOSE: (121) is inconsistent.
% 36.59/5.89 | | | | |
% 36.59/5.89 | | | | End of split
% 36.59/5.89 | | | |
% 36.59/5.89 | | | End of split
% 36.59/5.89 | | |
% 36.59/5.89 | | Case 2:
% 36.59/5.89 | | |
% 36.59/5.89 | | | (122) xp = sz10 | xp = sz00
% 36.59/5.89 | | |
% 36.59/5.89 | | | BETA: splitting (122) gives:
% 36.59/5.89 | | |
% 36.59/5.89 | | | Case 1:
% 36.59/5.89 | | | |
% 36.59/5.89 | | | | (123) xp = sz00
% 36.59/5.89 | | | |
% 36.59/5.89 | | | | REDUCE: (11), (123) imply:
% 36.59/5.89 | | | | (124) $false
% 36.59/5.89 | | | |
% 36.59/5.89 | | | | CLOSE: (124) is inconsistent.
% 36.59/5.89 | | | |
% 36.59/5.89 | | | Case 2:
% 36.59/5.89 | | | |
% 36.59/5.89 | | | | (125) xp = sz10
% 36.59/5.89 | | | |
% 36.59/5.89 | | | | REDUCE: (16), (125) imply:
% 36.59/5.89 | | | | (126) $false
% 36.59/5.89 | | | |
% 36.59/5.89 | | | | CLOSE: (126) is inconsistent.
% 36.59/5.89 | | | |
% 36.59/5.89 | | | End of split
% 36.59/5.89 | | |
% 36.59/5.89 | | End of split
% 36.59/5.89 | |
% 36.59/5.89 | End of split
% 36.59/5.89 |
% 36.59/5.89 End of proof
% 36.59/5.89 % SZS output end Proof for theBenchmark
% 36.59/5.89
% 36.59/5.89 5241ms
%------------------------------------------------------------------------------