TSTP Solution File: NUM423+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 9.59s 2.10s
% Output : Proof 15.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM423+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 09:07:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.07 Prover 4: Preprocessing ...
% 2.58/1.07 Prover 1: Preprocessing ...
% 2.96/1.12 Prover 2: Preprocessing ...
% 2.96/1.12 Prover 6: Preprocessing ...
% 2.96/1.12 Prover 0: Preprocessing ...
% 2.96/1.12 Prover 5: Preprocessing ...
% 2.96/1.12 Prover 3: Preprocessing ...
% 5.66/1.53 Prover 1: Constructing countermodel ...
% 5.66/1.55 Prover 6: Proving ...
% 5.66/1.55 Prover 3: Constructing countermodel ...
% 6.75/1.64 Prover 4: Constructing countermodel ...
% 6.75/1.65 Prover 5: Constructing countermodel ...
% 7.33/1.73 Prover 2: Proving ...
% 7.33/1.74 Prover 0: Proving ...
% 7.33/1.77 Prover 3: gave up
% 7.33/1.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.76/1.80 Prover 7: Preprocessing ...
% 7.76/1.83 Prover 1: gave up
% 7.76/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.43/1.88 Prover 8: Preprocessing ...
% 8.43/1.97 Prover 7: Constructing countermodel ...
% 8.43/2.00 Prover 8: Warning: ignoring some quantifiers
% 8.97/2.03 Prover 8: Constructing countermodel ...
% 9.59/2.10 Prover 0: proved (1487ms)
% 9.59/2.10
% 9.59/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.59/2.10
% 9.59/2.10 Prover 5: stopped
% 9.59/2.10 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.59/2.10 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.59/2.10 Prover 6: stopped
% 9.59/2.11 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.59/2.11 Prover 2: stopped
% 10.20/2.13 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.20/2.15 Prover 10: Preprocessing ...
% 10.20/2.15 Prover 13: Preprocessing ...
% 10.20/2.15 Prover 11: Preprocessing ...
% 10.20/2.16 Prover 16: Preprocessing ...
% 10.67/2.22 Prover 16: Constructing countermodel ...
% 10.67/2.22 Prover 10: Constructing countermodel ...
% 10.67/2.24 Prover 8: gave up
% 10.67/2.25 Prover 13: Constructing countermodel ...
% 10.67/2.26 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.28/2.28 Prover 10: gave up
% 11.28/2.29 Prover 19: Preprocessing ...
% 11.28/2.30 Prover 11: Constructing countermodel ...
% 11.82/2.41 Prover 19: Warning: ignoring some quantifiers
% 11.82/2.41 Prover 19: Constructing countermodel ...
% 13.48/2.57 Prover 19: gave up
% 13.83/2.72 Prover 4: Found proof (size 89)
% 13.83/2.72 Prover 4: proved (2099ms)
% 13.83/2.72 Prover 16: stopped
% 13.83/2.72 Prover 13: stopped
% 13.83/2.72 Prover 11: stopped
% 13.83/2.72 Prover 7: stopped
% 13.83/2.72
% 13.83/2.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.83/2.72
% 14.58/2.73 % SZS output start Proof for theBenchmark
% 14.58/2.73 Assumptions after simplification:
% 14.58/2.73 ---------------------------------
% 14.58/2.73
% 14.58/2.74 (mAddNeg)
% 14.72/2.76 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ?
% 14.72/2.76 [v2: any] : ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v1, v0) = v4 &
% 14.72/2.76 sdtpldt0(v0, v1) = v3 & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 =
% 14.72/2.76 0) | (v4 = sz00 & v3 = sz00)))) & ! [v0: $i] : ( ~ (aInteger0(v0) =
% 14.72/2.76 0) | ~ $i(v0) | ? [v1: $i] : (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1)
% 14.72/2.76 = sz00 & smndt0(v0) = v1 & $i(v1)))
% 14.72/2.76
% 14.72/2.76 (mDivisor)
% 14.72/2.77 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 |
% 14.72/2.77 v1 = sz00 | ~ (aDivisorOf0(v1, v0) = v2) | ~ (sdtasdt0(v1, v3) = v0) | ~
% 14.72/2.77 (aInteger0(v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ((
% 14.72/2.77 ~ (v4 = 0) & aInteger0(v3) = v4) | ( ~ (v4 = 0) & aInteger0(v1) = v4)))
% 14.72/2.77 & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | v1 = sz00
% 14.72/2.77 | ~ (aDivisorOf0(v1, v0) = v2) | ~ (aInteger0(v3) = 0) | ~ (aInteger0(v0)
% 14.72/2.77 = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : (( ~ (v4 = v0) &
% 14.72/2.77 sdtasdt0(v1, v3) = v4 & $i(v4)) | ( ~ (v4 = 0) & aInteger0(v1) = v4))) &
% 14.72/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aInteger0(v1) = v2) |
% 14.72/2.77 ~ (aInteger0(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 14.72/2.77 & aDivisorOf0(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.72/2.77 (v1 = sz00 | ~ (sdtasdt0(v1, v2) = v0) | ~ (aInteger0(v1) = 0) | ~
% 14.72/2.77 (aInteger0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] :
% 14.72/2.77 ((v3 = 0 & aDivisorOf0(v1, v0) = 0) | ( ~ (v3 = 0) & aInteger0(v2) = v3))) &
% 14.72/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ (aInteger0(v2) = 0)
% 14.72/2.77 | ~ (aInteger0(v1) = 0) | ~ (aInteger0(v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 14.72/2.77 ~ $i(v0) | ? [v3: any] : ((v3 = 0 & aDivisorOf0(v1, v0) = 0) | ( ~ (v3 =
% 14.72/2.77 v0) & sdtasdt0(v1, v2) = v3 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] :
% 14.72/2.77 ! [v2: MultipleValueBool] : ( ~ (aInteger0(v1) = v2) | ~ (aInteger0(v0) = 0)
% 14.72/2.77 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ?
% 14.72/2.77 [v6: $i] : ($i(v4) & ((v6 = v0 & v5 = 0 & sdtasdt0(v1, v4) = v0 &
% 14.72/2.77 aInteger0(v4) = 0) | ( ~ (v3 = 0) & aDivisorOf0(v1, v0) = v3)))) & !
% 14.72/2.77 [v0: $i] : ! [v1: $i] : ( ~ (aDivisorOf0(v1, v0) = 0) | ~ (aInteger0(v0) =
% 14.72/2.77 0) | ~ $i(v1) | ~ $i(v0) | aInteger0(v1) = 0) & ! [v0: $i] : ! [v1:
% 14.72/2.77 $i] : ( ~ (aDivisorOf0(v1, v0) = 0) | ~ (aInteger0(v0) = 0) | ~ $i(v1) |
% 14.72/2.77 ~ $i(v0) | ? [v2: $i] : (sdtasdt0(v1, v2) = v0 & aInteger0(v2) = 0 &
% 14.72/2.77 $i(v2))) & ! [v0: $i] : ! [v1: MultipleValueBool] : ( ~ (aInteger0(v0) =
% 14.72/2.77 0) | ~ (aInteger0(sz00) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 14.72/2.77 aDivisorOf0(sz00, v0) = v2)) & ! [v0: $i] : ( ~ (aDivisorOf0(sz00, v0) =
% 14.72/2.77 0) | ~ (aInteger0(v0) = 0) | ~ $i(v0))
% 14.72/2.77
% 14.72/2.77 (mEquMod)
% 14.72/2.77 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 14.72/2.77 : ! [v5: any] : (v2 = sz00 | ~ (aDivisorOf0(v2, v4) = v5) | ~ (sdtpldt0(v0,
% 14.72/2.77 v3) = v4) | ~ (smndt0(v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 14.72/2.77 ? [v6: any] : ? [v7: any] : ? [v8: any] : ? [v9: any] :
% 14.72/2.77 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = v9 & aInteger0(v2) = v8 & aInteger0(v1)
% 14.72/2.77 = v7 & aInteger0(v0) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ((
% 14.72/2.77 ~ (v9 = 0) | v5 = 0) & ( ~ (v5 = 0) | v9 = 0))))) & ! [v0: $i] : !
% 14.72/2.77 [v1: $i] : ! [v2: $i] : ! [v3: any] : (v2 = sz00 | ~
% 14.72/2.77 (sdteqdtlpzmzozddtrp0(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 14.72/2.77 | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] :
% 14.72/2.77 ? [v9: any] : (aDivisorOf0(v2, v8) = v9 & sdtpldt0(v0, v7) = v8 & smndt0(v1)
% 14.72/2.77 = v7 & aInteger0(v2) = v6 & aInteger0(v1) = v5 & aInteger0(v0) = v4 &
% 14.72/2.77 $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v9 = 0)
% 14.72/2.77 | v3 = 0) & ( ~ (v3 = 0) | v9 = 0)))))
% 14.72/2.77
% 14.72/2.77 (mIntNeg)
% 14.72/2.77 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ? [v2: any] :
% 14.72/2.77 ? [v3: any] : (aInteger0(v1) = v3 & aInteger0(v0) = v2 & ( ~ (v2 = 0) | v3
% 14.72/2.77 = 0))) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 14.72/2.77 : (smndt0(v0) = v1 & aInteger0(v1) = 0 & $i(v1)))
% 14.72/2.77
% 14.72/2.77 (mIntZero)
% 14.72/2.77 aInteger0(sz00) = 0 & $i(sz00)
% 14.72/2.77
% 14.72/2.77 (mMulMinOne)
% 14.72/2.78 $i(sz10) & ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 14.72/2.78 $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i]
% 14.72/2.78 : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 & aInteger0(v1) =
% 14.72/2.78 v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1:
% 14.72/2.78 $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ? [v3: any]
% 14.72/2.78 : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 &
% 14.72/2.78 aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 =
% 14.72/2.78 v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~
% 14.72/2.78 $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5
% 14.72/2.78 & sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3
% 14.72/2.78 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~ (aInteger0(v1) =
% 14.72/2.78 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) = v2 & sdtasdt0(v0, v1)
% 14.72/2.78 = v2 & smndt0(v1) = v2 & $i(v2))))
% 14.72/2.78
% 14.72/2.78 (mMulZero)
% 14.72/2.78 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~
% 14.72/2.78 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz00, v0) = v3 &
% 14.72/2.78 aInteger0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) &
% 14.72/2.78 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ? [v2:
% 14.72/2.78 any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 & aInteger0(v0) = v2 &
% 14.72/2.78 $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 = sz00)))) & ! [v0: $i] : ( ~
% 14.72/2.78 (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00) = sz00 &
% 14.72/2.78 sdtasdt0(sz00, v0) = sz00))
% 14.72/2.78
% 14.72/2.78 (m__)
% 14.72/2.78 $i(xq) & $i(xa) & ? [v0: int] : ( ~ (v0 = 0) & sdteqdtlpzmzozddtrp0(xa, xa,
% 14.72/2.78 xq) = v0)
% 14.72/2.78
% 14.72/2.78 (m__671)
% 14.72/2.78 ~ (xq = sz00) & aInteger0(xq) = 0 & aInteger0(xa) = 0 & $i(xq) & $i(xa) &
% 14.72/2.78 $i(sz00)
% 14.72/2.78
% 14.72/2.78 (function-axioms)
% 14.72/2.78 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.72/2.78 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v1)
% 14.72/2.78 | ~ (sdteqdtlpzmzozddtrp0(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 14.72/2.78 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.72/2.78 (aDivisorOf0(v3, v2) = v1) | ~ (aDivisorOf0(v3, v2) = v0)) & ! [v0: $i] :
% 14.72/2.78 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1)
% 14.72/2.78 | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.72/2.78 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 14.72/2.78 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) |
% 14.72/2.78 ~ (smndt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.72/2.78 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~
% 14.72/2.78 (aInteger0(v2) = v0))
% 14.72/2.78
% 14.72/2.78 Further assumptions not needed in the proof:
% 14.72/2.78 --------------------------------------------
% 14.72/2.78 mAddAsso, mAddComm, mAddZero, mDistrib, mIntMult, mIntOne, mIntPlus, mIntegers,
% 14.72/2.78 mMulAsso, mMulComm, mMulOne, mZeroDiv
% 14.72/2.78
% 14.72/2.78 Those formulas are unsatisfiable:
% 14.72/2.78 ---------------------------------
% 14.72/2.78
% 14.72/2.78 Begin of proof
% 14.72/2.78 |
% 14.72/2.78 | ALPHA: (mIntZero) implies:
% 14.72/2.78 | (1) aInteger0(sz00) = 0
% 14.72/2.78 |
% 14.72/2.78 | ALPHA: (mIntNeg) implies:
% 14.72/2.79 | (2) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 14.72/2.79 | (smndt0(v0) = v1 & aInteger0(v1) = 0 & $i(v1)))
% 14.72/2.79 |
% 14.72/2.79 | ALPHA: (mAddNeg) implies:
% 14.72/2.79 | (3) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 14.72/2.79 | (sdtpldt0(v1, v0) = sz00 & sdtpldt0(v0, v1) = sz00 & smndt0(v0) = v1
% 14.72/2.79 | & $i(v1)))
% 14.72/2.79 |
% 14.72/2.79 | ALPHA: (mMulZero) implies:
% 14.72/2.79 | (4) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz00)
% 14.72/2.79 | = sz00 & sdtasdt0(sz00, v0) = sz00))
% 14.72/2.79 |
% 14.72/2.79 | ALPHA: (mMulMinOne) implies:
% 14.72/2.79 | (5) ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 14.72/2.79 | ( ~ (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i]
% 14.72/2.79 | : ? [v5: $i] : (sdtasdt0(v0, v1) = v4 & smndt0(v1) = v5 &
% 14.72/2.79 | aInteger0(v1) = v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 &
% 14.72/2.79 | v4 = v2)))) & ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0,
% 14.72/2.79 | v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 14.72/2.79 | $i] : (sdtasdt0(v1, v0) = v5 & smndt0(v1) = v4 & aInteger0(v1) =
% 14.72/2.79 | v3 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & !
% 14.72/2.79 | [v1: $i] : ! [v2: $i] : ( ~ (smndt0(v1) = v2) | ~ $i(v1) | ? [v3:
% 14.72/2.79 | any] : ? [v4: $i] : ? [v5: $i] : (sdtasdt0(v1, v0) = v5 &
% 14.72/2.79 | sdtasdt0(v0, v1) = v4 & aInteger0(v1) = v3 & $i(v5) & $i(v4) & (
% 14.72/2.79 | ~ (v3 = 0) | (v5 = v2 & v4 = v2)))) & ! [v1: $i] : ( ~
% 14.72/2.79 | (aInteger0(v1) = 0) | ~ $i(v1) | ? [v2: $i] : (sdtasdt0(v1, v0) =
% 14.72/2.79 | v2 & sdtasdt0(v0, v1) = v2 & smndt0(v1) = v2 & $i(v2))))
% 14.72/2.79 |
% 14.72/2.79 | ALPHA: (mDivisor) implies:
% 14.72/2.79 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: MultipleValueBool] : ( ~
% 14.72/2.79 | (aInteger0(v1) = v2) | ~ (aInteger0(v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 14.72/2.79 | | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ($i(v4) &
% 14.72/2.79 | ((v6 = v0 & v5 = 0 & sdtasdt0(v1, v4) = v0 & aInteger0(v4) = 0) | (
% 14.72/2.79 | ~ (v3 = 0) & aDivisorOf0(v1, v0) = v3))))
% 14.72/2.79 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~
% 14.72/2.79 | (aInteger0(v2) = 0) | ~ (aInteger0(v1) = 0) | ~ (aInteger0(v0) = 0)
% 14.72/2.79 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ((v3 = 0 &
% 14.72/2.79 | aDivisorOf0(v1, v0) = 0) | ( ~ (v3 = v0) & sdtasdt0(v1, v2) = v3
% 14.72/2.79 | & $i(v3))))
% 14.72/2.79 |
% 14.72/2.79 | ALPHA: (mEquMod) implies:
% 14.72/2.79 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : (v2 = sz00 |
% 14.72/2.79 | ~ (sdteqdtlpzmzozddtrp0(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 14.72/2.79 | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7: $i] :
% 14.72/2.79 | ? [v8: $i] : ? [v9: any] : (aDivisorOf0(v2, v8) = v9 & sdtpldt0(v0,
% 14.72/2.79 | v7) = v8 & smndt0(v1) = v7 & aInteger0(v2) = v6 & aInteger0(v1) =
% 14.72/2.79 | v5 & aInteger0(v0) = v4 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 =
% 14.72/2.79 | 0) | ~ (v4 = 0) | (( ~ (v9 = 0) | v3 = 0) & ( ~ (v3 = 0) | v9
% 14.72/2.79 | = 0)))))
% 14.72/2.79 |
% 14.72/2.79 | ALPHA: (m__671) implies:
% 14.72/2.79 | (9) ~ (xq = sz00)
% 14.72/2.79 | (10) $i(sz00)
% 14.72/2.79 | (11) aInteger0(xa) = 0
% 14.72/2.79 | (12) aInteger0(xq) = 0
% 14.72/2.79 |
% 14.72/2.79 | ALPHA: (m__) implies:
% 14.72/2.79 | (13) $i(xa)
% 14.72/2.79 | (14) $i(xq)
% 14.72/2.80 | (15) ? [v0: int] : ( ~ (v0 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = v0)
% 14.72/2.80 |
% 14.72/2.80 | ALPHA: (function-axioms) implies:
% 14.72/2.80 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.72/2.80 | : (v1 = v0 | ~ (aInteger0(v2) = v1) | ~ (aInteger0(v2) = v0))
% 14.72/2.80 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 14.72/2.80 | v1) | ~ (smndt0(v2) = v0))
% 14.72/2.80 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.72/2.80 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 14.72/2.80 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.72/2.80 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 14.72/2.80 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.72/2.80 | : ! [v3: $i] : (v1 = v0 | ~ (aDivisorOf0(v3, v2) = v1) | ~
% 14.72/2.80 | (aDivisorOf0(v3, v2) = v0))
% 14.72/2.80 |
% 14.72/2.80 | DELTA: instantiating (15) with fresh symbol all_19_0 gives:
% 14.72/2.80 | (21) ~ (all_19_0 = 0) & sdteqdtlpzmzozddtrp0(xa, xa, xq) = all_19_0
% 14.72/2.80 |
% 14.72/2.80 | ALPHA: (21) implies:
% 14.72/2.80 | (22) ~ (all_19_0 = 0)
% 14.72/2.80 | (23) sdteqdtlpzmzozddtrp0(xa, xa, xq) = all_19_0
% 14.72/2.80 |
% 14.72/2.80 | DELTA: instantiating (5) with fresh symbol all_21_0 gives:
% 14.72/2.80 | (24) smndt0(sz10) = all_21_0 & $i(all_21_0) & ! [v0: $i] : ! [v1: $i] : (
% 14.72/2.80 | ~ (sdtasdt0(v0, all_21_0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 14.72/2.80 | $i] : ? [v4: $i] : (sdtasdt0(all_21_0, v0) = v3 & smndt0(v0) = v4
% 14.72/2.80 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 &
% 14.72/2.80 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 14.72/2.80 | (sdtasdt0(all_21_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 14.72/2.80 | $i] : ? [v4: $i] : (sdtasdt0(v0, all_21_0) = v4 & smndt0(v0) = v3
% 14.72/2.80 | & aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 &
% 14.72/2.80 | v3 = v1)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) =
% 14.72/2.80 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] :
% 14.72/2.80 | (sdtasdt0(v0, all_21_0) = v4 & sdtasdt0(all_21_0, v0) = v3 &
% 14.72/2.80 | aInteger0(v0) = v2 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | (v4 = v1 &
% 14.72/2.80 | v3 = v1)))) & ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~
% 14.72/2.80 | $i(v0) | ? [v1: $i] : (sdtasdt0(v0, all_21_0) = v1 &
% 14.72/2.80 | sdtasdt0(all_21_0, v0) = v1 & smndt0(v0) = v1 & $i(v1)))
% 14.72/2.80 |
% 14.72/2.80 | ALPHA: (24) implies:
% 14.72/2.80 | (25) ! [v0: $i] : ( ~ (aInteger0(v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 14.72/2.80 | (sdtasdt0(v0, all_21_0) = v1 & sdtasdt0(all_21_0, v0) = v1 &
% 14.72/2.80 | smndt0(v0) = v1 & $i(v1)))
% 14.72/2.80 |
% 14.72/2.80 | GROUND_INST: instantiating (25) with xa, simplifying with (11), (13) gives:
% 14.72/2.80 | (26) ? [v0: $i] : (sdtasdt0(all_21_0, xa) = v0 & sdtasdt0(xa, all_21_0) =
% 14.72/2.80 | v0 & smndt0(xa) = v0 & $i(v0))
% 14.72/2.80 |
% 14.72/2.80 | GROUND_INST: instantiating (3) with xa, simplifying with (11), (13) gives:
% 14.72/2.80 | (27) ? [v0: $i] : (sdtpldt0(v0, xa) = sz00 & sdtpldt0(xa, v0) = sz00 &
% 14.72/2.80 | smndt0(xa) = v0 & $i(v0))
% 14.72/2.80 |
% 14.72/2.80 | GROUND_INST: instantiating (2) with xa, simplifying with (11), (13) gives:
% 14.72/2.80 | (28) ? [v0: $i] : (smndt0(xa) = v0 & aInteger0(v0) = 0 & $i(v0))
% 14.72/2.80 |
% 14.72/2.81 | GROUND_INST: instantiating (6) with sz00, xq, 0, simplifying with (1), (10),
% 14.72/2.81 | (12), (14) gives:
% 14.72/2.81 | (29) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ($i(v1) &
% 14.72/2.81 | ((v3 = sz00 & v2 = 0 & sdtasdt0(xq, v1) = sz00 & aInteger0(v1) = 0)
% 14.72/2.81 | | ( ~ (v0 = 0) & aDivisorOf0(xq, sz00) = v0)))
% 14.72/2.81 |
% 14.72/2.81 | GROUND_INST: instantiating (7) with sz00, xq, sz00, simplifying with (1),
% 14.72/2.81 | (10), (12), (14) gives:
% 14.72/2.81 | (30) xq = sz00 | ? [v0: any] : ((v0 = 0 & aDivisorOf0(xq, sz00) = 0) | ( ~
% 14.72/2.81 | (v0 = sz00) & sdtasdt0(xq, sz00) = v0 & $i(v0)))
% 14.72/2.81 |
% 14.72/2.81 | GROUND_INST: instantiating (4) with xq, simplifying with (12), (14) gives:
% 14.72/2.81 | (31) sdtasdt0(xq, sz00) = sz00 & sdtasdt0(sz00, xq) = sz00
% 14.72/2.81 |
% 14.72/2.81 | ALPHA: (31) implies:
% 14.72/2.81 | (32) sdtasdt0(xq, sz00) = sz00
% 14.72/2.81 |
% 14.72/2.81 | GROUND_INST: instantiating (8) with xa, xa, xq, all_19_0, simplifying with
% 14.72/2.81 | (13), (14), (23) gives:
% 14.72/2.81 | (33) xq = sz00 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] :
% 14.72/2.81 | ? [v4: $i] : ? [v5: any] : (aDivisorOf0(xq, v4) = v5 & sdtpldt0(xa,
% 14.72/2.81 | v3) = v4 & smndt0(xa) = v3 & aInteger0(xq) = v2 & aInteger0(xa) =
% 14.72/2.81 | v1 & aInteger0(xa) = v0 & $i(v4) & $i(v3) & ( ~ (v2 = 0) | ~ (v1 =
% 14.72/2.81 | 0) | ~ (v0 = 0) | (( ~ (v5 = 0) | all_19_0 = 0) & ( ~ (all_19_0
% 14.72/2.81 | = 0) | v5 = 0))))
% 14.72/2.81 |
% 14.72/2.81 | DELTA: instantiating (28) with fresh symbol all_44_0 gives:
% 14.72/2.81 | (34) smndt0(xa) = all_44_0 & aInteger0(all_44_0) = 0 & $i(all_44_0)
% 14.72/2.81 |
% 14.72/2.81 | ALPHA: (34) implies:
% 14.72/2.81 | (35) smndt0(xa) = all_44_0
% 14.72/2.81 |
% 14.72/2.81 | DELTA: instantiating (27) with fresh symbol all_52_0 gives:
% 14.72/2.81 | (36) sdtpldt0(all_52_0, xa) = sz00 & sdtpldt0(xa, all_52_0) = sz00 &
% 14.72/2.81 | smndt0(xa) = all_52_0 & $i(all_52_0)
% 14.72/2.81 |
% 14.72/2.81 | ALPHA: (36) implies:
% 14.72/2.81 | (37) smndt0(xa) = all_52_0
% 14.72/2.81 | (38) sdtpldt0(xa, all_52_0) = sz00
% 14.72/2.81 |
% 14.72/2.81 | DELTA: instantiating (26) with fresh symbol all_56_0 gives:
% 14.72/2.81 | (39) sdtasdt0(all_21_0, xa) = all_56_0 & sdtasdt0(xa, all_21_0) = all_56_0
% 14.72/2.81 | & smndt0(xa) = all_56_0 & $i(all_56_0)
% 14.72/2.81 |
% 14.72/2.81 | ALPHA: (39) implies:
% 14.72/2.81 | (40) smndt0(xa) = all_56_0
% 14.72/2.81 |
% 14.72/2.81 | DELTA: instantiating (29) with fresh symbols all_78_0, all_78_1, all_78_2,
% 14.72/2.81 | all_78_3 gives:
% 14.72/2.81 | (41) $i(all_78_2) & ((all_78_0 = sz00 & all_78_1 = 0 & sdtasdt0(xq,
% 14.72/2.81 | all_78_2) = sz00 & aInteger0(all_78_2) = 0) | ( ~ (all_78_3 = 0)
% 14.72/2.81 | & aDivisorOf0(xq, sz00) = all_78_3))
% 14.72/2.81 |
% 14.72/2.81 | ALPHA: (41) implies:
% 14.72/2.81 | (42) (all_78_0 = sz00 & all_78_1 = 0 & sdtasdt0(xq, all_78_2) = sz00 &
% 14.72/2.81 | aInteger0(all_78_2) = 0) | ( ~ (all_78_3 = 0) & aDivisorOf0(xq,
% 14.72/2.81 | sz00) = all_78_3)
% 14.72/2.81 |
% 14.72/2.81 | BETA: splitting (30) gives:
% 14.72/2.81 |
% 14.72/2.81 | Case 1:
% 14.72/2.81 | |
% 14.72/2.81 | | (43) xq = sz00
% 14.72/2.81 | |
% 14.72/2.81 | | REDUCE: (9), (43) imply:
% 14.72/2.81 | | (44) $false
% 14.72/2.81 | |
% 14.72/2.81 | | CLOSE: (44) is inconsistent.
% 14.72/2.81 | |
% 14.72/2.81 | Case 2:
% 14.72/2.81 | |
% 14.72/2.82 | | (45) ? [v0: any] : ((v0 = 0 & aDivisorOf0(xq, sz00) = 0) | ( ~ (v0 =
% 14.72/2.82 | | sz00) & sdtasdt0(xq, sz00) = v0 & $i(v0)))
% 14.72/2.82 | |
% 14.72/2.82 | | DELTA: instantiating (45) with fresh symbol all_125_0 gives:
% 14.72/2.82 | | (46) (all_125_0 = 0 & aDivisorOf0(xq, sz00) = 0) | ( ~ (all_125_0 = sz00)
% 14.72/2.82 | | & sdtasdt0(xq, sz00) = all_125_0 & $i(all_125_0))
% 14.72/2.82 | |
% 14.72/2.82 | | BETA: splitting (46) gives:
% 14.72/2.82 | |
% 14.72/2.82 | | Case 1:
% 14.72/2.82 | | |
% 14.72/2.82 | | | (47) all_125_0 = 0 & aDivisorOf0(xq, sz00) = 0
% 14.72/2.82 | | |
% 14.72/2.82 | | | ALPHA: (47) implies:
% 14.72/2.82 | | | (48) aDivisorOf0(xq, sz00) = 0
% 14.72/2.82 | | |
% 14.72/2.82 | | | BETA: splitting (33) gives:
% 14.72/2.82 | | |
% 14.72/2.82 | | | Case 1:
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | (49) xq = sz00
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | REDUCE: (9), (49) imply:
% 14.72/2.82 | | | | (50) $false
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | CLOSE: (50) is inconsistent.
% 14.72/2.82 | | | |
% 14.72/2.82 | | | Case 2:
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : ?
% 14.72/2.82 | | | | [v4: $i] : ? [v5: any] : (aDivisorOf0(xq, v4) = v5 &
% 14.72/2.82 | | | | sdtpldt0(xa, v3) = v4 & smndt0(xa) = v3 & aInteger0(xq) = v2 &
% 14.72/2.82 | | | | aInteger0(xa) = v1 & aInteger0(xa) = v0 & $i(v4) & $i(v3) & (
% 14.72/2.82 | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v5 = 0) |
% 14.72/2.82 | | | | all_19_0 = 0) & ( ~ (all_19_0 = 0) | v5 = 0))))
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | DELTA: instantiating (51) with fresh symbols all_165_0, all_165_1,
% 14.72/2.82 | | | | all_165_2, all_165_3, all_165_4, all_165_5 gives:
% 14.72/2.82 | | | | (52) aDivisorOf0(xq, all_165_1) = all_165_0 & sdtpldt0(xa, all_165_2)
% 14.72/2.82 | | | | = all_165_1 & smndt0(xa) = all_165_2 & aInteger0(xq) = all_165_3
% 14.72/2.82 | | | | & aInteger0(xa) = all_165_4 & aInteger0(xa) = all_165_5 &
% 14.72/2.82 | | | | $i(all_165_1) & $i(all_165_2) & ( ~ (all_165_3 = 0) | ~
% 14.72/2.82 | | | | (all_165_4 = 0) | ~ (all_165_5 = 0) | (( ~ (all_165_0 = 0) |
% 14.72/2.82 | | | | all_19_0 = 0) & ( ~ (all_19_0 = 0) | all_165_0 = 0)))
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | ALPHA: (52) implies:
% 14.72/2.82 | | | | (53) aInteger0(xa) = all_165_5
% 14.72/2.82 | | | | (54) aInteger0(xa) = all_165_4
% 14.72/2.82 | | | | (55) aInteger0(xq) = all_165_3
% 14.72/2.82 | | | | (56) smndt0(xa) = all_165_2
% 14.72/2.82 | | | | (57) sdtpldt0(xa, all_165_2) = all_165_1
% 14.72/2.82 | | | | (58) aDivisorOf0(xq, all_165_1) = all_165_0
% 14.72/2.82 | | | | (59) ~ (all_165_3 = 0) | ~ (all_165_4 = 0) | ~ (all_165_5 = 0) |
% 14.72/2.82 | | | | (( ~ (all_165_0 = 0) | all_19_0 = 0) & ( ~ (all_19_0 = 0) |
% 14.72/2.82 | | | | all_165_0 = 0))
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | BETA: splitting (42) gives:
% 14.72/2.82 | | | |
% 14.72/2.82 | | | | Case 1:
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | GROUND_INST: instantiating (16) with 0, all_165_4, xa, simplifying
% 14.72/2.82 | | | | | with (11), (54) gives:
% 14.72/2.82 | | | | | (60) all_165_4 = 0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | GROUND_INST: instantiating (16) with all_165_5, all_165_4, xa,
% 14.72/2.82 | | | | | simplifying with (53), (54) gives:
% 14.72/2.82 | | | | | (61) all_165_4 = all_165_5
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | GROUND_INST: instantiating (16) with 0, all_165_3, xq, simplifying
% 14.72/2.82 | | | | | with (12), (55) gives:
% 14.72/2.82 | | | | | (62) all_165_3 = 0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | GROUND_INST: instantiating (17) with all_44_0, all_56_0, xa,
% 14.72/2.82 | | | | | simplifying with (35), (40) gives:
% 14.72/2.82 | | | | | (63) all_56_0 = all_44_0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | GROUND_INST: instantiating (17) with all_56_0, all_165_2, xa,
% 14.72/2.82 | | | | | simplifying with (40), (56) gives:
% 14.72/2.82 | | | | | (64) all_165_2 = all_56_0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | GROUND_INST: instantiating (17) with all_52_0, all_165_2, xa,
% 14.72/2.82 | | | | | simplifying with (37), (56) gives:
% 14.72/2.82 | | | | | (65) all_165_2 = all_52_0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | COMBINE_EQS: (64), (65) imply:
% 14.72/2.82 | | | | | (66) all_56_0 = all_52_0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | SIMP: (66) implies:
% 14.72/2.82 | | | | | (67) all_56_0 = all_52_0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | COMBINE_EQS: (60), (61) imply:
% 14.72/2.82 | | | | | (68) all_165_5 = 0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | COMBINE_EQS: (63), (67) imply:
% 14.72/2.82 | | | | | (69) all_52_0 = all_44_0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | COMBINE_EQS: (65), (69) imply:
% 14.72/2.82 | | | | | (70) all_165_2 = all_44_0
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | REDUCE: (57), (70) imply:
% 14.72/2.82 | | | | | (71) sdtpldt0(xa, all_44_0) = all_165_1
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | REDUCE: (38), (69) imply:
% 14.72/2.82 | | | | | (72) sdtpldt0(xa, all_44_0) = sz00
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | BETA: splitting (59) gives:
% 14.72/2.82 | | | | |
% 14.72/2.82 | | | | | Case 1:
% 14.72/2.82 | | | | | |
% 14.72/2.82 | | | | | | (73) ~ (all_165_3 = 0)
% 14.72/2.82 | | | | | |
% 14.72/2.82 | | | | | | REDUCE: (62), (73) imply:
% 14.72/2.82 | | | | | | (74) $false
% 14.72/2.82 | | | | | |
% 14.72/2.82 | | | | | | CLOSE: (74) is inconsistent.
% 14.72/2.82 | | | | | |
% 14.72/2.82 | | | | | Case 2:
% 14.72/2.82 | | | | | |
% 15.07/2.82 | | | | | | (75) ~ (all_165_4 = 0) | ~ (all_165_5 = 0) | (( ~ (all_165_0 =
% 15.07/2.82 | | | | | | 0) | all_19_0 = 0) & ( ~ (all_19_0 = 0) | all_165_0 =
% 15.07/2.82 | | | | | | 0))
% 15.07/2.82 | | | | | |
% 15.07/2.82 | | | | | | BETA: splitting (75) gives:
% 15.07/2.82 | | | | | |
% 15.07/2.82 | | | | | | Case 1:
% 15.07/2.82 | | | | | | |
% 15.07/2.82 | | | | | | | (76) ~ (all_165_4 = 0)
% 15.07/2.82 | | | | | | |
% 15.07/2.82 | | | | | | | REDUCE: (60), (76) imply:
% 15.07/2.83 | | | | | | | (77) $false
% 15.07/2.83 | | | | | | |
% 15.07/2.83 | | | | | | | CLOSE: (77) is inconsistent.
% 15.07/2.83 | | | | | | |
% 15.07/2.83 | | | | | | Case 2:
% 15.07/2.83 | | | | | | |
% 15.07/2.83 | | | | | | | (78) ~ (all_165_5 = 0) | (( ~ (all_165_0 = 0) | all_19_0 = 0)
% 15.07/2.83 | | | | | | | & ( ~ (all_19_0 = 0) | all_165_0 = 0))
% 15.07/2.83 | | | | | | |
% 15.07/2.83 | | | | | | | BETA: splitting (78) gives:
% 15.07/2.83 | | | | | | |
% 15.07/2.83 | | | | | | | Case 1:
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | | (79) ~ (all_165_5 = 0)
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | | REDUCE: (68), (79) imply:
% 15.07/2.83 | | | | | | | | (80) $false
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | | CLOSE: (80) is inconsistent.
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | Case 2:
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | | (81) ( ~ (all_165_0 = 0) | all_19_0 = 0) & ( ~ (all_19_0 = 0)
% 15.07/2.83 | | | | | | | | | all_165_0 = 0)
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | | ALPHA: (81) implies:
% 15.07/2.83 | | | | | | | | (82) ~ (all_165_0 = 0) | all_19_0 = 0
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | | BETA: splitting (82) gives:
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | | Case 1:
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | (83) ~ (all_165_0 = 0)
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | GROUND_INST: instantiating (18) with sz00, all_165_1, all_44_0,
% 15.07/2.83 | | | | | | | | | xa, simplifying with (71), (72) gives:
% 15.07/2.83 | | | | | | | | | (84) all_165_1 = sz00
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | REDUCE: (58), (84) imply:
% 15.07/2.83 | | | | | | | | | (85) aDivisorOf0(xq, sz00) = all_165_0
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | GROUND_INST: instantiating (20) with 0, all_165_0, sz00, xq,
% 15.07/2.83 | | | | | | | | | simplifying with (48), (85) gives:
% 15.07/2.83 | | | | | | | | | (86) all_165_0 = 0
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | REDUCE: (83), (86) imply:
% 15.07/2.83 | | | | | | | | | (87) $false
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | CLOSE: (87) is inconsistent.
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | Case 2:
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | (88) all_19_0 = 0
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | REDUCE: (22), (88) imply:
% 15.07/2.83 | | | | | | | | | (89) $false
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | | CLOSE: (89) is inconsistent.
% 15.07/2.83 | | | | | | | | |
% 15.07/2.83 | | | | | | | | End of split
% 15.07/2.83 | | | | | | | |
% 15.07/2.83 | | | | | | | End of split
% 15.07/2.83 | | | | | | |
% 15.07/2.83 | | | | | | End of split
% 15.07/2.83 | | | | | |
% 15.07/2.83 | | | | | End of split
% 15.07/2.83 | | | | |
% 15.07/2.83 | | | | Case 2:
% 15.07/2.83 | | | | |
% 15.07/2.83 | | | | | (90) ~ (all_78_3 = 0) & aDivisorOf0(xq, sz00) = all_78_3
% 15.07/2.83 | | | | |
% 15.07/2.83 | | | | | ALPHA: (90) implies:
% 15.07/2.83 | | | | | (91) ~ (all_78_3 = 0)
% 15.07/2.83 | | | | | (92) aDivisorOf0(xq, sz00) = all_78_3
% 15.07/2.83 | | | | |
% 15.07/2.83 | | | | | GROUND_INST: instantiating (20) with 0, all_78_3, sz00, xq,
% 15.07/2.83 | | | | | simplifying with (48), (92) gives:
% 15.07/2.83 | | | | | (93) all_78_3 = 0
% 15.07/2.83 | | | | |
% 15.07/2.83 | | | | | REDUCE: (91), (93) imply:
% 15.07/2.83 | | | | | (94) $false
% 15.07/2.83 | | | | |
% 15.07/2.83 | | | | | CLOSE: (94) is inconsistent.
% 15.07/2.83 | | | | |
% 15.07/2.83 | | | | End of split
% 15.07/2.83 | | | |
% 15.07/2.83 | | | End of split
% 15.07/2.83 | | |
% 15.07/2.83 | | Case 2:
% 15.07/2.83 | | |
% 15.07/2.83 | | | (95) ~ (all_125_0 = sz00) & sdtasdt0(xq, sz00) = all_125_0 &
% 15.07/2.83 | | | $i(all_125_0)
% 15.07/2.83 | | |
% 15.07/2.83 | | | ALPHA: (95) implies:
% 15.07/2.83 | | | (96) ~ (all_125_0 = sz00)
% 15.07/2.83 | | | (97) sdtasdt0(xq, sz00) = all_125_0
% 15.07/2.83 | | |
% 15.07/2.83 | | | GROUND_INST: instantiating (19) with sz00, all_125_0, sz00, xq,
% 15.07/2.83 | | | simplifying with (32), (97) gives:
% 15.07/2.83 | | | (98) all_125_0 = sz00
% 15.07/2.83 | | |
% 15.07/2.83 | | | REDUCE: (96), (98) imply:
% 15.07/2.83 | | | (99) $false
% 15.07/2.83 | | |
% 15.07/2.83 | | | CLOSE: (99) is inconsistent.
% 15.07/2.83 | | |
% 15.07/2.83 | | End of split
% 15.07/2.83 | |
% 15.07/2.83 | End of split
% 15.07/2.83 |
% 15.07/2.83 End of proof
% 15.07/2.83 % SZS output end Proof for theBenchmark
% 15.07/2.83
% 15.07/2.83 2235ms
%------------------------------------------------------------------------------