TSTP Solution File: NUM458+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM458+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 11:47:52 EDT 2023
% Result : Theorem 9.90s 2.11s
% Output : Proof 12.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM458+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 09:06:55 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
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 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 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 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 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
% 2.34/1.03 Prover 4: Preprocessing ...
% 2.34/1.03 Prover 1: Preprocessing ...
% 3.02/1.08 Prover 3: Preprocessing ...
% 3.02/1.08 Prover 2: Preprocessing ...
% 3.02/1.08 Prover 0: Preprocessing ...
% 3.02/1.08 Prover 5: Preprocessing ...
% 3.02/1.08 Prover 6: Preprocessing ...
% 5.91/1.51 Prover 1: Constructing countermodel ...
% 5.91/1.53 Prover 6: Proving ...
% 5.91/1.53 Prover 3: Constructing countermodel ...
% 6.48/1.60 Prover 5: Constructing countermodel ...
% 7.21/1.70 Prover 3: gave up
% 7.21/1.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.21/1.72 Prover 4: Constructing countermodel ...
% 7.84/1.74 Prover 2: Proving ...
% 8.11/1.78 Prover 7: Preprocessing ...
% 8.11/1.78 Prover 1: gave up
% 8.11/1.78 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.11/1.83 Prover 8: Preprocessing ...
% 8.75/1.86 Prover 0: Proving ...
% 8.75/1.91 Prover 8: Warning: ignoring some quantifiers
% 8.75/1.91 Prover 8: Constructing countermodel ...
% 9.60/2.01 Prover 7: Constructing countermodel ...
% 9.90/2.07 Prover 7: gave up
% 9.90/2.09 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.90/2.11 Prover 0: proved (1481ms)
% 9.90/2.11
% 9.90/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.90/2.11
% 10.52/2.11 Prover 5: stopped
% 10.52/2.11 Prover 6: stopped
% 10.52/2.12 Prover 2: stopped
% 10.52/2.12 Prover 9: Preprocessing ...
% 10.52/2.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.52/2.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.52/2.12 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.52/2.13 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.52/2.15 Prover 8: gave up
% 10.52/2.16 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.52/2.17 Prover 10: Preprocessing ...
% 10.52/2.17 Prover 13: Preprocessing ...
% 11.04/2.18 Prover 16: Preprocessing ...
% 11.04/2.20 Prover 11: Preprocessing ...
% 11.04/2.20 Prover 19: Preprocessing ...
% 11.04/2.22 Prover 4: Found proof (size 38)
% 11.04/2.22 Prover 4: proved (1596ms)
% 11.04/2.23 Prover 13: stopped
% 11.04/2.24 Prover 16: Constructing countermodel ...
% 11.04/2.24 Prover 16: stopped
% 11.04/2.25 Prover 10: Constructing countermodel ...
% 11.04/2.25 Prover 11: stopped
% 11.04/2.26 Prover 10: stopped
% 11.75/2.30 Prover 19: Warning: ignoring some quantifiers
% 11.75/2.30 Prover 19: Constructing countermodel ...
% 11.75/2.31 Prover 19: stopped
% 11.98/2.35 Prover 9: Constructing countermodel ...
% 11.98/2.35 Prover 9: stopped
% 11.98/2.35
% 11.98/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.98/2.35
% 11.98/2.36 % SZS output start Proof for theBenchmark
% 11.98/2.36 Assumptions after simplification:
% 11.98/2.36 ---------------------------------
% 11.98/2.36
% 11.98/2.36 (mAddCanc)
% 11.98/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1
% 11.98/2.40 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ $i(v2) | ~
% 11.98/2.40 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8:
% 11.98/2.40 $i] : ? [v9: $i] : (sdtpldt0(v0, v2) = v9 & sdtpldt0(v0, v1) = v8 &
% 11.98/2.40 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 11.98/2.40 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~
% 11.98/2.40 (v9 = v8) & ~ (v4 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 11.98/2.40 : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~
% 11.98/2.40 (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] :
% 11.98/2.40 ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (sdtpldt0(v1, v0)
% 11.98/2.40 = v9 & sdtpldt0(v0, v2) = v8 & aNaturalNumber0(v2) = v7 &
% 11.98/2.40 aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & $i(v8) & (
% 11.98/2.40 ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v4) & ~ (v8 =
% 11.98/2.40 v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 11.98/2.40 [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3)
% 11.98/2.40 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 11.98/2.40 any] : ? [v8: $i] : ? [v9: $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v0,
% 11.98/2.40 v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 &
% 11.98/2.40 aNaturalNumber0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) |
% 11.98/2.40 ~ (v5 = 0) | ( ~ (v9 = v4) & ~ (v8 = v3))))) & ! [v0: $i] : ! [v1:
% 11.98/2.40 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v0,
% 11.98/2.40 v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.98/2.40 $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 11.98/2.40 $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2)
% 11.98/2.40 = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) &
% 11.98/2.40 $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4
% 11.98/2.40 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 11.98/2.40 (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~
% 11.98/2.40 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] :
% 11.98/2.40 ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v1, v0) = v8 & sdtpldt0(v0, v2) = v7 &
% 11.98/2.40 sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v2) = v5 & aNaturalNumber0(v0) =
% 11.98/2.40 v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ( ~ (v8 = v3)
% 11.98/2.40 & ~ (v7 = v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.98/2.40 $i] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) |
% 11.98/2.40 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 11.98/2.40 $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0) = v8 & sdtpldt0(v0,
% 11.98/2.40 v2) = v7 & sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 &
% 11.98/2.40 aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~
% 11.98/2.40 (v4 = 0) | ( ~ (v8 = v3) & ~ (v7 = v6))))) & ! [v0: $i] : ! [v1: $i]
% 11.98/2.40 : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~
% 11.98/2.40 (aNaturalNumber0(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 11.98/2.40 : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0)
% 11.98/2.40 = v8 & sdtpldt0(v1, v0) = v7 & sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v2)
% 11.98/2.40 = v5 & aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0)
% 11.98/2.40 | ~ (v4 = 0) | ( ~ (v8 = v7) & ~ (v6 = v3))))) & ! [v0: $i] : ! [v1:
% 11.98/2.40 $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (sdtpldt0(v0, v1) = v3) | ~
% 11.98/2.40 (aNaturalNumber0(v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 11.98/2.40 : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0)
% 11.98/2.40 = v8 & sdtpldt0(v1, v0) = v7 & sdtpldt0(v0, v2) = v6 & aNaturalNumber0(v1)
% 11.98/2.40 = v5 & aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0)
% 11.98/2.40 | ~ (v4 = 0) | ( ~ (v8 = v7) & ~ (v6 = v3))))) & ! [v0: $i] : ! [v1:
% 11.98/2.40 $i] : ! [v2: $i] : (v2 = v1 | ~ (aNaturalNumber0(v2) = 0) | ~
% 11.98/2.40 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 11.98/2.40 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 11.98/2.40 ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5
% 11.98/2.40 & sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4)
% 11.98/2.40 & $i(v3)))
% 11.98/2.40
% 11.98/2.40 (mSortsC)
% 11.98/2.41 aNaturalNumber0(sz00) = 0 & $i(sz00)
% 11.98/2.41
% 11.98/2.41 (mSortsC_01)
% 11.98/2.41 ~ (sz10 = sz00) & aNaturalNumber0(sz10) = 0 & $i(sz10) & $i(sz00)
% 11.98/2.41
% 11.98/2.41 (mZeroMul)
% 11.98/2.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | v0 = sz00 | ~
% 11.98/2.41 (sdtasdt0(v0, v1) = sz00) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 11.98/2.41 any] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0)
% 11.98/2.41 | ~ (v2 = 0))))
% 11.98/2.41
% 11.98/2.41 (m_AddZero)
% 12.38/2.41 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~
% 12.38/2.41 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtpldt0(sz00, v0) = v3 &
% 12.38/2.41 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 12.38/2.41 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ?
% 12.38/2.41 [v2: any] : ? [v3: $i] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) =
% 12.38/2.41 v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~
% 12.38/2.41 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtpldt0(v0, sz00) = v0 &
% 12.38/2.41 sdtpldt0(sz00, v0) = v0))
% 12.38/2.41
% 12.38/2.41 (m_MulUnit)
% 12.38/2.41 $i(sz10) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~
% 12.38/2.41 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz10, v0) = v3 &
% 12.38/2.41 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 12.38/2.41 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ?
% 12.38/2.41 [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) =
% 12.38/2.41 v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~
% 12.38/2.41 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz10) = v0 &
% 12.38/2.41 sdtasdt0(sz10, v0) = v0))
% 12.38/2.41
% 12.38/2.41 (m__)
% 12.38/2.41 $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xm) = v0 & ! [v1: $i] :
% 12.38/2.41 ( ~ (sdtpldt0(xm, v1) = xm) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) &
% 12.38/2.41 aNaturalNumber0(v1) = v2)) & ! [v1: $i] : ( ~ (aNaturalNumber0(v1) = 0)
% 12.38/2.41 | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = xm) & sdtpldt0(xm, v1) = v2 &
% 12.38/2.41 $i(v2))))
% 12.38/2.41
% 12.38/2.41 (m__718)
% 12.38/2.41 aNaturalNumber0(xm) = 0 & $i(xm)
% 12.38/2.41
% 12.38/2.41 (function-axioms)
% 12.38/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.38/2.42 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 12.38/2.42 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.38/2.42 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 12.38/2.42 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.38/2.42 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 12.38/2.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 12.38/2.42 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.38/2.42 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 12.38/2.42 | ~ (aNaturalNumber0(v2) = v0))
% 12.38/2.42
% 12.38/2.42 Further assumptions not needed in the proof:
% 12.38/2.42 --------------------------------------------
% 12.38/2.42 mAMDistr, mAddAsso, mAddComm, mDefDiff, mDefLE, mMulAsso, mMulCanc, mMulComm,
% 12.38/2.42 mNatSort, mSortsB, mSortsB_02, mZeroAdd, m_MulZero
% 12.38/2.42
% 12.38/2.42 Those formulas are unsatisfiable:
% 12.38/2.42 ---------------------------------
% 12.38/2.42
% 12.38/2.42 Begin of proof
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (mSortsC) implies:
% 12.38/2.42 | (1) aNaturalNumber0(sz00) = 0
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (mSortsC_01) implies:
% 12.38/2.42 | (2) ~ (sz10 = sz00)
% 12.38/2.42 | (3) aNaturalNumber0(sz10) = 0
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (m_AddZero) implies:
% 12.38/2.42 | (4) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtpldt0(v0,
% 12.38/2.42 | sz00) = v0 & sdtpldt0(sz00, v0) = v0))
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (m_MulUnit) implies:
% 12.38/2.42 | (5) $i(sz10)
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (mAddCanc) implies:
% 12.38/2.42 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 12.38/2.42 | (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~
% 12.38/2.42 | (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.38/2.42 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) &
% 12.38/2.42 | ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 &
% 12.38/2.42 | sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3 & $i(v6) & $i(v5) &
% 12.38/2.42 | $i(v4) & $i(v3)))
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (mZeroMul) implies:
% 12.38/2.42 | (7) $i(sz00)
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (m__718) implies:
% 12.38/2.42 | (8) aNaturalNumber0(xm) = 0
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (m__) implies:
% 12.38/2.42 | (9) $i(xm)
% 12.38/2.42 | (10) ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xm) = v0 & ! [v1: $i] :
% 12.38/2.42 | ( ~ (sdtpldt0(xm, v1) = xm) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 =
% 12.38/2.42 | 0) & aNaturalNumber0(v1) = v2)) & ! [v1: $i] : ( ~
% 12.38/2.42 | (aNaturalNumber0(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 =
% 12.38/2.42 | xm) & sdtpldt0(xm, v1) = v2 & $i(v2))))
% 12.38/2.42 |
% 12.38/2.42 | ALPHA: (function-axioms) implies:
% 12.38/2.42 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.38/2.42 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 12.38/2.42 |
% 12.38/2.43 | DELTA: instantiating (10) with fresh symbol all_20_0 gives:
% 12.38/2.43 | (12) ~ (all_20_0 = 0) & sdtlseqdt0(xm, xm) = all_20_0 & ! [v0: $i] : ( ~
% 12.38/2.43 | (sdtpldt0(xm, v0) = xm) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 12.38/2.43 | aNaturalNumber0(v0) = v1)) & ! [v0: $i] : ( ~
% 12.38/2.43 | (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ( ~ (v1 = xm)
% 12.38/2.43 | & sdtpldt0(xm, v0) = v1 & $i(v1)))
% 12.38/2.43 |
% 12.38/2.43 | ALPHA: (12) implies:
% 12.38/2.43 | (13) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 12.38/2.43 | : ( ~ (v1 = xm) & sdtpldt0(xm, v0) = v1 & $i(v1)))
% 12.38/2.43 |
% 12.38/2.43 | GROUND_INST: instantiating (13) with sz00, simplifying with (1), (7) gives:
% 12.38/2.43 | (14) ? [v0: $i] : ( ~ (v0 = xm) & sdtpldt0(xm, sz00) = v0 & $i(v0))
% 12.38/2.43 |
% 12.38/2.43 | GROUND_INST: instantiating (6) with xm, sz00, sz10, simplifying with (1), (3),
% 12.38/2.43 | (5), (7), (8), (9) gives:
% 12.38/2.43 | (15) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 12.38/2.43 | ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v1 & sdtpldt0(xm,
% 12.38/2.43 | sz00) = v0 & sdtpldt0(sz10, xm) = v3 & sdtpldt0(sz00, xm) = v2 &
% 12.38/2.43 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.38/2.43 |
% 12.38/2.43 | GROUND_INST: instantiating (6) with xm, sz10, sz00, simplifying with (1), (3),
% 12.38/2.43 | (5), (7), (8), (9) gives:
% 12.38/2.43 | (16) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 12.38/2.43 | ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v0 & sdtpldt0(xm,
% 12.38/2.43 | sz00) = v1 & sdtpldt0(sz10, xm) = v2 & sdtpldt0(sz00, xm) = v3 &
% 12.38/2.43 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.38/2.43 |
% 12.38/2.43 | GROUND_INST: instantiating (4) with xm, simplifying with (8), (9) gives:
% 12.38/2.43 | (17) sdtpldt0(xm, sz00) = xm & sdtpldt0(sz00, xm) = xm
% 12.38/2.43 |
% 12.38/2.43 | ALPHA: (17) implies:
% 12.38/2.43 | (18) sdtpldt0(xm, sz00) = xm
% 12.38/2.43 |
% 12.38/2.43 | DELTA: instantiating (14) with fresh symbol all_33_0 gives:
% 12.38/2.43 | (19) ~ (all_33_0 = xm) & sdtpldt0(xm, sz00) = all_33_0 & $i(all_33_0)
% 12.38/2.43 |
% 12.38/2.43 | ALPHA: (19) implies:
% 12.38/2.43 | (20) ~ (all_33_0 = xm)
% 12.38/2.43 | (21) sdtpldt0(xm, sz00) = all_33_0
% 12.38/2.43 |
% 12.38/2.43 | BETA: splitting (15) gives:
% 12.38/2.43 |
% 12.38/2.43 | Case 1:
% 12.38/2.43 | |
% 12.38/2.43 | | (22) sz10 = sz00
% 12.38/2.43 | |
% 12.38/2.43 | | REDUCE: (2), (22) imply:
% 12.38/2.43 | | (23) $false
% 12.38/2.44 | |
% 12.38/2.44 | | CLOSE: (23) is inconsistent.
% 12.38/2.44 | |
% 12.38/2.44 | Case 2:
% 12.38/2.44 | |
% 12.38/2.44 | | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 12.38/2.44 | | v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v1 & sdtpldt0(xm,
% 12.38/2.44 | | sz00) = v0 & sdtpldt0(sz10, xm) = v3 & sdtpldt0(sz00, xm) = v2 &
% 12.38/2.44 | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.38/2.44 | |
% 12.38/2.44 | | DELTA: instantiating (24) with fresh symbols all_49_0, all_49_1, all_49_2,
% 12.38/2.44 | | all_49_3 gives:
% 12.38/2.44 | | (25) ~ (all_49_0 = all_49_1) & ~ (all_49_2 = all_49_3) & sdtpldt0(xm,
% 12.38/2.44 | | sz10) = all_49_2 & sdtpldt0(xm, sz00) = all_49_3 & sdtpldt0(sz10,
% 12.38/2.44 | | xm) = all_49_0 & sdtpldt0(sz00, xm) = all_49_1 & $i(all_49_0) &
% 12.38/2.44 | | $i(all_49_1) & $i(all_49_2) & $i(all_49_3)
% 12.38/2.44 | |
% 12.38/2.44 | | ALPHA: (25) implies:
% 12.38/2.44 | | (26) sdtpldt0(xm, sz00) = all_49_3
% 12.38/2.44 | |
% 12.38/2.44 | | BETA: splitting (16) gives:
% 12.38/2.44 | |
% 12.38/2.44 | | Case 1:
% 12.38/2.44 | | |
% 12.38/2.44 | | | (27) sz10 = sz00
% 12.38/2.44 | | |
% 12.38/2.44 | | | REDUCE: (2), (27) imply:
% 12.38/2.44 | | | (28) $false
% 12.38/2.44 | | |
% 12.38/2.44 | | | CLOSE: (28) is inconsistent.
% 12.38/2.44 | | |
% 12.38/2.44 | | Case 2:
% 12.38/2.44 | | |
% 12.38/2.44 | | | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 12.38/2.44 | | | v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v0 & sdtpldt0(xm,
% 12.38/2.44 | | | sz00) = v1 & sdtpldt0(sz10, xm) = v2 & sdtpldt0(sz00, xm) = v3
% 12.38/2.44 | | | & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 12.38/2.44 | | |
% 12.38/2.44 | | | DELTA: instantiating (29) with fresh symbols all_54_0, all_54_1, all_54_2,
% 12.38/2.44 | | | all_54_3 gives:
% 12.38/2.44 | | | (30) ~ (all_54_0 = all_54_1) & ~ (all_54_2 = all_54_3) & sdtpldt0(xm,
% 12.38/2.44 | | | sz10) = all_54_3 & sdtpldt0(xm, sz00) = all_54_2 &
% 12.38/2.44 | | | sdtpldt0(sz10, xm) = all_54_1 & sdtpldt0(sz00, xm) = all_54_0 &
% 12.38/2.44 | | | $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3)
% 12.38/2.44 | | |
% 12.38/2.44 | | | ALPHA: (30) implies:
% 12.38/2.44 | | | (31) sdtpldt0(xm, sz00) = all_54_2
% 12.38/2.44 | | |
% 12.38/2.44 | | | GROUND_INST: instantiating (11) with all_33_0, all_49_3, sz00, xm,
% 12.38/2.44 | | | simplifying with (21), (26) gives:
% 12.38/2.44 | | | (32) all_49_3 = all_33_0
% 12.38/2.44 | | |
% 12.38/2.44 | | | GROUND_INST: instantiating (11) with all_49_3, all_54_2, sz00, xm,
% 12.38/2.44 | | | simplifying with (26), (31) gives:
% 12.38/2.44 | | | (33) all_54_2 = all_49_3
% 12.38/2.44 | | |
% 12.38/2.44 | | | GROUND_INST: instantiating (11) with xm, all_54_2, sz00, xm, simplifying
% 12.38/2.44 | | | with (18), (31) gives:
% 12.38/2.44 | | | (34) all_54_2 = xm
% 12.38/2.44 | | |
% 12.38/2.44 | | | COMBINE_EQS: (33), (34) imply:
% 12.38/2.44 | | | (35) all_49_3 = xm
% 12.38/2.44 | | |
% 12.38/2.44 | | | SIMP: (35) implies:
% 12.38/2.44 | | | (36) all_49_3 = xm
% 12.38/2.44 | | |
% 12.38/2.44 | | | COMBINE_EQS: (32), (36) imply:
% 12.38/2.44 | | | (37) all_33_0 = xm
% 12.38/2.44 | | |
% 12.38/2.44 | | | SIMP: (37) implies:
% 12.38/2.44 | | | (38) all_33_0 = xm
% 12.38/2.44 | | |
% 12.38/2.44 | | | REDUCE: (20), (38) imply:
% 12.38/2.44 | | | (39) $false
% 12.38/2.44 | | |
% 12.38/2.44 | | | CLOSE: (39) is inconsistent.
% 12.38/2.44 | | |
% 12.38/2.44 | | End of split
% 12.38/2.44 | |
% 12.38/2.44 | End of split
% 12.38/2.44 |
% 12.38/2.44 End of proof
% 12.38/2.44 % SZS output end Proof for theBenchmark
% 12.38/2.44
% 12.38/2.44 1838ms
%------------------------------------------------------------------------------