TSTP Solution File: NUM423+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM423+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 11:47:39 EDT 2023
% Result : Theorem 10.35s 2.14s
% Output : Proof 16.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM423+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n013.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Aug 25 09:58:32 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.20/0.55 ________ _____
% 0.20/0.55 ___ __ \_________(_)________________________________
% 0.20/0.55 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.55 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.55 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.55
% 0.20/0.55 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.55 (2023-06-19)
% 0.20/0.55
% 0.20/0.55 (c) Philipp Rümmer, 2009-2023
% 0.20/0.55 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.55 Amanda Stjerna.
% 0.20/0.55 Free software under BSD-3-Clause.
% 0.20/0.55
% 0.20/0.55 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.55
% 0.20/0.55 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.56 Running up to 7 provers in parallel.
% 0.20/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.59/1.03 Prover 1: Preprocessing ...
% 2.59/1.03 Prover 4: Preprocessing ...
% 2.59/1.08 Prover 3: Preprocessing ...
% 2.59/1.08 Prover 0: Preprocessing ...
% 2.59/1.08 Prover 2: Preprocessing ...
% 2.59/1.08 Prover 6: Preprocessing ...
% 2.59/1.08 Prover 5: Preprocessing ...
% 5.68/1.50 Prover 6: Proving ...
% 5.68/1.50 Prover 3: Constructing countermodel ...
% 5.68/1.51 Prover 1: Constructing countermodel ...
% 6.54/1.57 Prover 4: Constructing countermodel ...
% 6.54/1.57 Prover 5: Constructing countermodel ...
% 6.54/1.62 Prover 2: Proving ...
% 7.32/1.68 Prover 0: Proving ...
% 8.41/1.84 Prover 3: gave up
% 8.41/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.84/1.88 Prover 7: Preprocessing ...
% 9.43/2.11 Prover 7: Constructing countermodel ...
% 10.35/2.14 Prover 0: proved (1573ms)
% 10.35/2.14
% 10.35/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.35/2.14
% 10.35/2.15 Prover 2: stopped
% 10.35/2.15 Prover 6: stopped
% 10.35/2.16 Prover 5: stopped
% 10.81/2.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.81/2.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.81/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.81/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.00/2.19 Prover 8: Preprocessing ...
% 11.00/2.20 Prover 11: Preprocessing ...
% 11.00/2.20 Prover 13: Preprocessing ...
% 11.00/2.20 Prover 10: Preprocessing ...
% 11.00/2.21 Prover 1: gave up
% 11.00/2.21 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.44/2.25 Prover 16: Preprocessing ...
% 11.44/2.29 Prover 8: Warning: ignoring some quantifiers
% 11.44/2.29 Prover 8: Constructing countermodel ...
% 11.44/2.30 Prover 10: Constructing countermodel ...
% 12.04/2.32 Prover 16: Constructing countermodel ...
% 12.04/2.35 Prover 13: Constructing countermodel ...
% 12.51/2.40 Prover 10: gave up
% 12.51/2.42 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.51/2.44 Prover 11: Constructing countermodel ...
% 12.51/2.45 Prover 19: Preprocessing ...
% 13.75/2.61 Prover 8: gave up
% 13.75/2.62 Prover 19: Warning: ignoring some quantifiers
% 13.75/2.62 Prover 19: Constructing countermodel ...
% 15.16/2.80 Prover 4: Found proof (size 52)
% 15.16/2.80 Prover 4: proved (2220ms)
% 15.16/2.80 Prover 16: stopped
% 15.16/2.80 Prover 13: stopped
% 15.16/2.80 Prover 7: stopped
% 15.16/2.80 Prover 19: stopped
% 15.16/2.80 Prover 11: stopped
% 15.16/2.80
% 15.16/2.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.16/2.80
% 15.16/2.81 % SZS output start Proof for theBenchmark
% 15.16/2.81 Assumptions after simplification:
% 15.16/2.81 ---------------------------------
% 15.16/2.81
% 15.16/2.81 (mAddComm)
% 15.71/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~
% 15.71/2.84 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 15.71/2.84 (sdtpldt0(v0, v1) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & $i(v5) &
% 15.71/2.84 ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) & ! [v0: $i] : ! [v1: $i] : !
% 15.71/2.84 [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any]
% 15.71/2.84 : ? [v4: any] : ? [v5: $i] : (sdtpldt0(v1, v0) = v5 & aInteger0(v1) = v4 &
% 15.71/2.84 aInteger0(v0) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 15.71/2.84
% 15.71/2.84 (mAddNeg)
% 15.71/2.84 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ?
% 15.71/2.84 [v2: any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v1, v0) = v4 &
% 15.71/2.84 sdtpldt0(v0, v1) = v3 & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 =
% 15.71/2.84 0) | (v4 = sz00 & v3 = sz00)))) & ! [v0: $i] : ( ~ (aInteger0(v0) =
% 15.71/2.84 0) | ~ $i(v0) | ? [v1: $i] : (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1)
% 15.71/2.84 = sz00 & smndt0(v0) = v1 & $i(v1)))
% 15.71/2.84
% 15.71/2.84 (mIntPlus)
% 15.71/2.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 15.71/2.84 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 15.71/2.84 (aInteger0(v2) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 & ( ~ (v4 = 0)
% 15.71/2.84 | ~ (v3 = 0) | v5 = 0)))
% 15.71/2.84
% 15.71/2.84 (mIntZero)
% 15.71/2.84 aInteger0(sz00) = 0 & $i(sz00)
% 15.71/2.84
% 15.71/2.84 (mMulMinOne)
% 15.71/2.85 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 15.71/2.85 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i]
% 15.71/2.85 : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 & aInteger0(v1) =
% 15.71/2.85 v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1:
% 15.71/2.85 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any]
% 15.71/2.85 : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 &
% 15.71/2.85 aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 =
% 15.71/2.85 v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~
% 15.71/2.85 $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5
% 15.71/2.85 & sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3
% 15.71/2.85 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~ (aInteger0(v1) =
% 15.71/2.85 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1)
% 15.71/2.85 = v2 & smndt0(v1) = v2 & $i(v2))))
% 15.71/2.85
% 15.71/2.85 (mMulZero)
% 15.71/2.85 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~
% 15.71/2.85 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz00, v0) = v3 &
% 15.71/2.85 aInteger0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) &
% 15.71/2.85 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ? [v2:
% 15.71/2.85 any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 & aInteger0(v0) = v2 &
% 15.71/2.85 $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0: $i] : ( ~
% 15.71/2.85 (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00) = sz00 &
% 15.71/2.85 sdtasdt0(sz00, v0) = sz00))
% 15.71/2.85
% 15.71/2.85 (m__)
% 15.71/2.85 $i(xq) & $i(xa) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : (
% 15.71/2.85 ~ (v3 = 0) & ~ (v2 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = v3 &
% 15.71/2.85 aDivisorOf0(xq, v1) = v2 & sdtpldt0(xa, v0) = v1 & smndt0(xa) = v0 & $i(v1)
% 15.71/2.85 & $i(v0) & ! [v4: $i] : ( ~ (sdtasdt0(xq, v4) = v1) | ~ $i(v4) | ? [v5:
% 15.71/2.85 int] : ( ~ (v5 = 0) & aInteger0(v4) = v5)) & ! [v4: $i] : ( ~
% 15.71/2.85 (aInteger0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ( ~ (v5 = v1) &
% 15.71/2.85 sdtasdt0(xq, v4) = v5 & $i(v5))))
% 15.71/2.85
% 15.71/2.85 (m__671)
% 15.71/2.85 ~ (xq = sz00) & aInteger0(xq) = 0 & aInteger0(xa) = 0 & $i(xq) & $i(xa) &
% 15.71/2.85 $i(sz00)
% 15.71/2.85
% 15.71/2.85 (function-axioms)
% 15.71/2.86 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 15.71/2.86 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1)
% 15.71/2.86 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 15.71/2.86 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.71/2.86 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: $i] :
% 15.71/2.86 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 15.71/2.86 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.71/2.86 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 15.71/2.86 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) |
% 15.71/2.86 ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.71/2.86 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~
% 15.71/2.86 (aInteger0(v2) = v0))
% 15.71/2.86
% 15.71/2.86 Further assumptions not needed in the proof:
% 15.71/2.86 --------------------------------------------
% 15.71/2.86 mAddAsso, mAddZero, mDistrib, mDivisor, mEquMod, mIntMult, mIntNeg, mIntOne,
% 15.71/2.86 mIntegers, mMulAsso, mMulComm, mMulOne, mZeroDiv
% 15.71/2.86
% 15.71/2.86 Those formulas are unsatisfiable:
% 15.71/2.86 ---------------------------------
% 15.71/2.86
% 15.71/2.86 Begin of proof
% 15.71/2.86 |
% 15.71/2.86 | ALPHA: (mIntZero) implies:
% 15.71/2.86 | (1) aInteger0(sz00) = 0
% 15.71/2.86 |
% 15.71/2.86 | ALPHA: (mAddComm) implies:
% 15.71/2.86 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 15.71/2.86 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 15.71/2.86 | (sdtpldt0(v1, v0) = v5 & aInteger0(v1) = v4 & aInteger0(v0) = v3 &
% 15.71/2.86 | $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))
% 15.71/2.86 |
% 15.71/2.86 | ALPHA: (mAddNeg) implies:
% 15.71/2.86 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2:
% 15.71/2.86 | any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v1, v0) = v4 &
% 15.71/2.86 | sdtpldt0(v0, v1) = v3 & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~
% 15.71/2.86 | (v2 = 0) | (v4 = sz00 & v3 = sz00))))
% 15.71/2.86 |
% 15.71/2.86 | ALPHA: (mMulZero) implies:
% 15.71/2.86 | (4) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00)
% 15.71/2.86 | = sz00 & sdtasdt0(sz00, v0) = sz00))
% 15.71/2.86 |
% 15.71/2.86 | ALPHA: (mMulMinOne) implies:
% 15.71/2.87 | (5) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 15.71/2.87 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i]
% 15.71/2.87 | : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 &
% 15.71/2.87 | aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 &
% 15.71/2.87 | v4 = v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0,
% 15.71/2.87 | v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 15.71/2.87 | $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & aInteger0(v1) =
% 15.71/2.87 | v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & !
% 15.71/2.87 | [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ? [v3:
% 15.71/2.87 | any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 &
% 15.71/2.87 | sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & (
% 15.71/2.87 | ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~
% 15.71/2.87 | (aInteger0(v1) = 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) =
% 15.71/2.87 | v2 & sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))))
% 15.71/2.87 |
% 15.71/2.87 | ALPHA: (m__671) implies:
% 15.71/2.87 | (6) $i(sz00)
% 15.71/2.87 | (7) aInteger0(xa) = 0
% 15.71/2.87 | (8) aInteger0(xq) = 0
% 15.71/2.87 |
% 15.71/2.87 | ALPHA: (m__) implies:
% 15.71/2.87 | (9) $i(xa)
% 15.71/2.87 | (10) $i(xq)
% 15.71/2.87 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ( ~ (v3 = 0)
% 15.71/2.87 | & ~ (v2 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = v3 &
% 15.71/2.87 | aDivisorOf0(xq, v1) = v2 & sdtpldt0(xa, v0) = v1 & smndt0(xa) = v0 &
% 15.71/2.87 | $i(v1) & $i(v0) & ! [v4: $i] : ( ~ (sdtasdt0(xq, v4) = v1) | ~
% 15.71/2.87 | $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & aInteger0(v4) = v5)) & !
% 15.71/2.87 | [v4: $i] : ( ~ (aInteger0(v4) = 0) | ~ $i(v4) | ? [v5: $i] : ( ~
% 15.71/2.87 | (v5 = v1) & sdtasdt0(xq, v4) = v5 & $i(v5))))
% 15.71/2.87 |
% 15.71/2.87 | ALPHA: (function-axioms) implies:
% 15.71/2.87 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 15.71/2.87 | : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0))
% 15.71/2.87 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.71/2.87 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 15.71/2.87 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.71/2.87 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 15.71/2.87 |
% 15.71/2.87 | DELTA: instantiating (11) with fresh symbols all_19_0, all_19_1, all_19_2,
% 15.71/2.87 | all_19_3 gives:
% 15.71/2.87 | (15) ~ (all_19_0 = 0) & ~ (all_19_1 = 0) & sdteqdtlpzmzozddtrp0(xa, xa,
% 15.71/2.87 | xq) = all_19_0 & aDivisorOf0(xq, all_19_2) = all_19_1 & sdtpldt0(xa,
% 15.71/2.87 | all_19_3) = all_19_2 & smndt0(xa) = all_19_3 & $i(all_19_2) &
% 15.71/2.87 | $i(all_19_3) & ! [v0: $i] : ( ~ (sdtasdt0(xq, v0) = all_19_2) | ~
% 15.71/2.87 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & aInteger0(v0) = v1)) & !
% 15.71/2.87 | [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~
% 15.71/2.87 | (v1 = all_19_2) & sdtasdt0(xq, v0) = v1 & $i(v1)))
% 15.71/2.87 |
% 15.71/2.87 | ALPHA: (15) implies:
% 15.71/2.87 | (16) $i(all_19_3)
% 15.71/2.88 | (17) smndt0(xa) = all_19_3
% 15.71/2.88 | (18) sdtpldt0(xa, all_19_3) = all_19_2
% 15.71/2.88 | (19) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~
% 15.71/2.88 | (v1 = all_19_2) & sdtasdt0(xq, v0) = v1 & $i(v1)))
% 15.71/2.88 |
% 15.71/2.88 | DELTA: instantiating (5) with fresh symbol all_22_0 gives:
% 15.71/2.88 | (20) smndt0(sz10) = all_22_0 & $i(all_22_0) & ! [v0: $i] : ! [v1: $i] : (
% 15.71/2.88 | ~ (sdtasdt0(v0, all_22_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 15.71/2.88 | $i] : ? [v4: $i] : (sdtasdt0(all_22_0, v0) = v3 & smndt0(v0) = v4
% 15.71/2.88 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 &
% 15.71/2.88 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.71/2.88 | (sdtasdt0(all_22_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 15.71/2.88 | $i] : ? [v4: $i] : (sdtasdt0(v0, all_22_0) = v4 & smndt0(v0) = v3
% 15.71/2.88 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 &
% 15.71/2.88 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) =
% 15.71/2.88 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 15.71/2.88 | (sdtasdt0(v0, all_22_0) = v4 & sdtasdt0(all_22_0, v0) = v3 &
% 15.71/2.88 | aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 &
% 15.71/2.88 | v3 = v1)))) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~
% 15.71/2.88 | $i(v0) | ? [v1: $i] : (sdtasdt0(v0, all_22_0) = v1 &
% 15.71/2.88 | sdtasdt0(all_22_0, v0) = v1 & smndt0(v0) = v1 & $i(v1)))
% 15.71/2.88 |
% 15.71/2.88 | ALPHA: (20) implies:
% 15.71/2.88 | (21) ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ?
% 15.71/2.88 | [v2: any] : ? [v3: $i] : ? [v4: $i] : (sdtasdt0(v0, all_22_0) = v4
% 15.71/2.88 | & sdtasdt0(all_22_0, v0) = v3 & aInteger0(v0) = v2 & $i(v4) &
% 15.71/2.88 | $i(v3) & ( ~ (v2 = 0) | (v4 = v1 & v3 = v1))))
% 15.71/2.88 |
% 15.71/2.88 | GROUND_INST: instantiating (19) with sz00, simplifying with (1), (6) gives:
% 15.71/2.88 | (22) ? [v0: any] : ( ~ (v0 = all_19_2) & sdtasdt0(xq, sz00) = v0 & $i(v0))
% 15.71/2.88 |
% 15.71/2.88 | GROUND_INST: instantiating (4) with xq, simplifying with (8), (10) gives:
% 15.71/2.88 | (23) sdtasdt0(xq, sz00) = sz00 & sdtasdt0(sz00, xq) = sz00
% 15.71/2.88 |
% 15.71/2.88 | ALPHA: (23) implies:
% 15.71/2.88 | (24) sdtasdt0(xq, sz00) = sz00
% 15.71/2.88 |
% 15.71/2.88 | GROUND_INST: instantiating (21) with xa, all_19_3, simplifying with (9), (17)
% 15.71/2.88 | gives:
% 15.71/2.88 | (25) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(all_22_0, xa) =
% 15.71/2.88 | v1 & sdtasdt0(xa, all_22_0) = v2 & aInteger0(xa) = v0 & $i(v2) &
% 15.71/2.88 | $i(v1) & ( ~ (v0 = 0) | (v2 = all_19_3 & v1 = all_19_3)))
% 15.71/2.88 |
% 15.71/2.88 | GROUND_INST: instantiating (3) with xa, all_19_3, simplifying with (9), (17)
% 15.71/2.88 | gives:
% 15.71/2.89 | (26) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (sdtpldt0(all_19_3, xa) =
% 15.71/2.89 | v2 & sdtpldt0(xa, all_19_3) = v1 & aInteger0(xa) = v0 & $i(v2) &
% 15.71/2.89 | $i(v1) & ( ~ (v0 = 0) | (v2 = sz00 & v1 = sz00)))
% 15.71/2.89 |
% 15.71/2.89 | GROUND_INST: instantiating (2) with xa, all_19_3, all_19_2, simplifying with
% 15.71/2.89 | (9), (16), (18) gives:
% 15.71/2.89 | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (sdtpldt0(all_19_3, xa) =
% 15.71/2.89 | v2 & aInteger0(all_19_3) = v1 & aInteger0(xa) = v0 & $i(v2) & ( ~
% 15.71/2.89 | (v1 = 0) | ~ (v0 = 0) | v2 = all_19_2))
% 15.71/2.89 |
% 15.71/2.89 | GROUND_INST: instantiating (mIntPlus) with xa, all_19_3, all_19_2, simplifying
% 15.71/2.89 | with (9), (16), (18) gives:
% 15.71/2.89 | (28) ? [v0: any] : ? [v1: any] : ? [v2: any] : (aInteger0(all_19_2) = v2
% 15.71/2.89 | & aInteger0(all_19_3) = v1 & aInteger0(xa) = v0 & ( ~ (v1 = 0) | ~
% 15.71/2.89 | (v0 = 0) | v2 = 0))
% 15.71/2.89 |
% 15.71/2.89 | DELTA: instantiating (22) with fresh symbol all_45_0 gives:
% 15.71/2.89 | (29) ~ (all_45_0 = all_19_2) & sdtasdt0(xq, sz00) = all_45_0 &
% 15.71/2.89 | $i(all_45_0)
% 15.71/2.89 |
% 15.71/2.89 | ALPHA: (29) implies:
% 15.71/2.89 | (30) ~ (all_45_0 = all_19_2)
% 15.71/2.89 | (31) sdtasdt0(xq, sz00) = all_45_0
% 15.71/2.89 |
% 15.71/2.89 | DELTA: instantiating (28) with fresh symbols all_75_0, all_75_1, all_75_2
% 15.71/2.89 | gives:
% 15.71/2.89 | (32) aInteger0(all_19_2) = all_75_0 & aInteger0(all_19_3) = all_75_1 &
% 15.71/2.89 | aInteger0(xa) = all_75_2 & ( ~ (all_75_1 = 0) | ~ (all_75_2 = 0) |
% 15.71/2.89 | all_75_0 = 0)
% 15.71/2.89 |
% 15.71/2.89 | ALPHA: (32) implies:
% 15.71/2.89 | (33) aInteger0(xa) = all_75_2
% 15.71/2.89 |
% 15.71/2.89 | DELTA: instantiating (27) with fresh symbols all_103_0, all_103_1, all_103_2
% 15.71/2.89 | gives:
% 15.71/2.89 | (34) sdtpldt0(all_19_3, xa) = all_103_0 & aInteger0(all_19_3) = all_103_1 &
% 15.71/2.89 | aInteger0(xa) = all_103_2 & $i(all_103_0) & ( ~ (all_103_1 = 0) | ~
% 15.71/2.89 | (all_103_2 = 0) | all_103_0 = all_19_2)
% 15.71/2.89 |
% 15.71/2.89 | ALPHA: (34) implies:
% 15.71/2.89 | (35) aInteger0(xa) = all_103_2
% 15.71/2.89 |
% 15.71/2.89 | DELTA: instantiating (26) with fresh symbols all_115_0, all_115_1, all_115_2
% 15.71/2.89 | gives:
% 15.71/2.89 | (36) sdtpldt0(all_19_3, xa) = all_115_0 & sdtpldt0(xa, all_19_3) =
% 15.71/2.89 | all_115_1 & aInteger0(xa) = all_115_2 & $i(all_115_0) & $i(all_115_1)
% 15.71/2.89 | & ( ~ (all_115_2 = 0) | (all_115_0 = sz00 & all_115_1 = sz00))
% 15.71/2.89 |
% 15.71/2.89 | ALPHA: (36) implies:
% 15.71/2.89 | (37) aInteger0(xa) = all_115_2
% 15.71/2.89 | (38) sdtpldt0(xa, all_19_3) = all_115_1
% 15.71/2.89 | (39) ~ (all_115_2 = 0) | (all_115_0 = sz00 & all_115_1 = sz00)
% 15.71/2.89 |
% 15.71/2.89 | DELTA: instantiating (25) with fresh symbols all_119_0, all_119_1, all_119_2
% 15.71/2.89 | gives:
% 15.71/2.89 | (40) sdtasdt0(all_22_0, xa) = all_119_1 & sdtasdt0(xa, all_22_0) =
% 15.71/2.89 | all_119_0 & aInteger0(xa) = all_119_2 & $i(all_119_0) & $i(all_119_1)
% 15.71/2.89 | & ( ~ (all_119_2 = 0) | (all_119_0 = all_19_3 & all_119_1 = all_19_3))
% 15.71/2.89 |
% 15.71/2.89 | ALPHA: (40) implies:
% 15.71/2.89 | (41) aInteger0(xa) = all_119_2
% 15.71/2.89 |
% 15.71/2.89 | GROUND_INST: instantiating (12) with 0, all_103_2, xa, simplifying with (7),
% 15.71/2.89 | (35) gives:
% 15.71/2.89 | (42) all_103_2 = 0
% 15.71/2.89 |
% 15.71/2.89 | GROUND_INST: instantiating (12) with all_103_2, all_115_2, xa, simplifying
% 15.71/2.89 | with (35), (37) gives:
% 15.71/2.89 | (43) all_115_2 = all_103_2
% 15.71/2.89 |
% 15.71/2.89 | GROUND_INST: instantiating (12) with all_115_2, all_119_2, xa, simplifying
% 15.71/2.89 | with (37), (41) gives:
% 15.71/2.89 | (44) all_119_2 = all_115_2
% 15.71/2.89 |
% 15.71/2.89 | GROUND_INST: instantiating (12) with all_75_2, all_119_2, xa, simplifying with
% 15.71/2.89 | (33), (41) gives:
% 15.71/2.89 | (45) all_119_2 = all_75_2
% 15.71/2.89 |
% 15.71/2.90 | GROUND_INST: instantiating (13) with all_19_2, all_115_1, all_19_3, xa,
% 15.71/2.90 | simplifying with (18), (38) gives:
% 15.71/2.90 | (46) all_115_1 = all_19_2
% 15.71/2.90 |
% 15.71/2.90 | GROUND_INST: instantiating (14) with sz00, all_45_0, sz00, xq, simplifying
% 15.71/2.90 | with (24), (31) gives:
% 15.71/2.90 | (47) all_45_0 = sz00
% 15.71/2.90 |
% 15.71/2.90 | COMBINE_EQS: (44), (45) imply:
% 15.71/2.90 | (48) all_115_2 = all_75_2
% 15.71/2.90 |
% 15.71/2.90 | SIMP: (48) implies:
% 15.71/2.90 | (49) all_115_2 = all_75_2
% 15.71/2.90 |
% 15.71/2.90 | COMBINE_EQS: (43), (49) imply:
% 15.71/2.90 | (50) all_103_2 = all_75_2
% 15.71/2.90 |
% 15.71/2.90 | SIMP: (50) implies:
% 15.71/2.90 | (51) all_103_2 = all_75_2
% 15.71/2.90 |
% 15.71/2.90 | COMBINE_EQS: (42), (51) imply:
% 15.71/2.90 | (52) all_75_2 = 0
% 15.71/2.90 |
% 15.71/2.90 | COMBINE_EQS: (49), (52) imply:
% 15.71/2.90 | (53) all_115_2 = 0
% 15.71/2.90 |
% 15.71/2.90 | REDUCE: (30), (47) imply:
% 15.71/2.90 | (54) ~ (all_19_2 = sz00)
% 15.71/2.90 |
% 15.71/2.90 | SIMP: (54) implies:
% 15.71/2.90 | (55) ~ (all_19_2 = sz00)
% 15.71/2.90 |
% 15.71/2.90 | BETA: splitting (39) gives:
% 15.71/2.90 |
% 15.71/2.90 | Case 1:
% 15.71/2.90 | |
% 15.71/2.90 | | (56) ~ (all_115_2 = 0)
% 15.71/2.90 | |
% 15.71/2.90 | | REDUCE: (53), (56) imply:
% 15.71/2.90 | | (57) $false
% 16.13/2.90 | |
% 16.13/2.90 | | CLOSE: (57) is inconsistent.
% 16.13/2.90 | |
% 16.13/2.90 | Case 2:
% 16.13/2.90 | |
% 16.13/2.90 | | (58) all_115_0 = sz00 & all_115_1 = sz00
% 16.13/2.90 | |
% 16.13/2.90 | | ALPHA: (58) implies:
% 16.13/2.90 | | (59) all_115_1 = sz00
% 16.13/2.90 | |
% 16.13/2.90 | | COMBINE_EQS: (46), (59) imply:
% 16.13/2.90 | | (60) all_19_2 = sz00
% 16.13/2.90 | |
% 16.13/2.90 | | SIMP: (60) implies:
% 16.13/2.90 | | (61) all_19_2 = sz00
% 16.13/2.90 | |
% 16.13/2.90 | | REDUCE: (55), (61) imply:
% 16.13/2.90 | | (62) $false
% 16.13/2.90 | |
% 16.13/2.90 | | CLOSE: (62) is inconsistent.
% 16.13/2.90 | |
% 16.13/2.90 | End of split
% 16.13/2.90 |
% 16.13/2.90 End of proof
% 16.13/2.90 % SZS output end Proof for theBenchmark
% 16.13/2.90
% 16.13/2.90 2347ms
%------------------------------------------------------------------------------