TSTP Solution File: NUM458+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM458+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 : n001.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 9.60s 2.17s
% Output : Proof 13.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM458+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 09:31:28 EDT 2023
% 0.13/0.33 % 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.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.46/1.04 Prover 4: Preprocessing ...
% 2.46/1.04 Prover 1: Preprocessing ...
% 2.88/1.09 Prover 3: Preprocessing ...
% 2.88/1.09 Prover 5: Preprocessing ...
% 2.88/1.09 Prover 2: Preprocessing ...
% 2.88/1.09 Prover 0: Preprocessing ...
% 2.88/1.09 Prover 6: Preprocessing ...
% 5.30/1.52 Prover 3: Constructing countermodel ...
% 5.30/1.53 Prover 1: Constructing countermodel ...
% 5.30/1.57 Prover 6: Proving ...
% 6.88/1.68 Prover 5: Constructing countermodel ...
% 6.88/1.69 Prover 3: gave up
% 6.88/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.41/1.72 Prover 1: gave up
% 7.41/1.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.41/1.77 Prover 7: Preprocessing ...
% 7.89/1.80 Prover 8: Preprocessing ...
% 7.89/1.80 Prover 2: Proving ...
% 7.89/1.82 Prover 4: Constructing countermodel ...
% 8.78/1.91 Prover 8: Warning: ignoring some quantifiers
% 8.78/1.92 Prover 8: Constructing countermodel ...
% 9.08/1.99 Prover 7: Constructing countermodel ...
% 9.60/2.00 Prover 0: Proving ...
% 9.60/2.05 Prover 7: gave up
% 9.60/2.06 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.60/2.10 Prover 9: Preprocessing ...
% 9.60/2.13 Prover 8: gave up
% 9.60/2.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.60/2.17 Prover 0: proved (1554ms)
% 9.60/2.17
% 9.60/2.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.60/2.17
% 9.60/2.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.60/2.17 Prover 2: stopped
% 9.60/2.18 Prover 5: stopped
% 9.60/2.19 Prover 6: stopped
% 9.60/2.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.60/2.20 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 9.60/2.20 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.60/2.21 Prover 10: Preprocessing ...
% 9.60/2.21 Prover 11: Preprocessing ...
% 10.47/2.24 Prover 19: Preprocessing ...
% 10.47/2.25 Prover 13: Preprocessing ...
% 10.47/2.25 Prover 16: Preprocessing ...
% 10.47/2.29 Prover 16: Constructing countermodel ...
% 10.47/2.30 Prover 10: Constructing countermodel ...
% 11.85/2.33 Prover 10: gave up
% 11.85/2.33 Prover 19: Warning: ignoring some quantifiers
% 11.85/2.33 Prover 13: Constructing countermodel ...
% 11.85/2.34 Prover 19: Constructing countermodel ...
% 12.07/2.40 Prover 19: gave up
% 12.65/2.44 Prover 11: Constructing countermodel ...
% 12.65/2.45 Prover 9: Constructing countermodel ...
% 12.65/2.45 Prover 9: stopped
% 12.65/2.46 Prover 4: Found proof (size 55)
% 12.65/2.46 Prover 4: proved (1837ms)
% 12.65/2.46 Prover 16: stopped
% 12.65/2.46 Prover 11: stopped
% 12.65/2.46 Prover 13: stopped
% 12.65/2.46
% 12.65/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.65/2.46
% 12.65/2.47 % SZS output start Proof for theBenchmark
% 12.65/2.47 Assumptions after simplification:
% 12.65/2.47 ---------------------------------
% 12.65/2.47
% 12.65/2.47 (mAddCanc)
% 12.94/2.51 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1
% 12.94/2.51 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ~ $i(v2) | ~
% 12.94/2.51 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8:
% 12.94/2.51 $i] : ? [v9: $i] : (sdtpldt0(v0, v2) = v9 & sdtpldt0(v0, v1) = v8 &
% 12.94/2.51 aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0)
% 12.94/2.51 = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~
% 12.94/2.51 (v9 = v8) & ~ (v4 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 12.94/2.51 : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~
% 12.94/2.51 (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] :
% 12.94/2.51 ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (sdtpldt0(v1, v0)
% 12.94/2.51 = v9 & sdtpldt0(v0, v2) = v8 & aNaturalNumber0(v2) = v7 &
% 12.94/2.51 aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) & $i(v8) & (
% 12.94/2.51 ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v4) & ~ (v8 =
% 12.94/2.51 v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 12.94/2.51 [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3)
% 12.94/2.51 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7:
% 12.94/2.51 any] : ? [v8: $i] : ? [v9: $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v0,
% 12.94/2.51 v1) = v8 & aNaturalNumber0(v2) = v7 & aNaturalNumber0(v1) = v6 &
% 12.94/2.51 aNaturalNumber0(v0) = v5 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) |
% 12.94/2.51 ~ (v5 = 0) | ( ~ (v9 = v4) & ~ (v8 = v3))))) & ! [v0: $i] : ! [v1:
% 12.94/2.51 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | ~ (sdtpldt0(v0,
% 12.94/2.51 v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 12.94/2.51 $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9:
% 12.94/2.51 $i] : (sdtpldt0(v2, v0) = v9 & sdtpldt0(v1, v0) = v8 & aNaturalNumber0(v2)
% 12.94/2.51 = v7 & aNaturalNumber0(v1) = v6 & aNaturalNumber0(v0) = v5 & $i(v9) &
% 12.94/2.51 $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v9 = v8) & ~ (v4
% 12.94/2.51 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 12.94/2.51 (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~
% 12.94/2.51 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] :
% 12.94/2.51 ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v1, v0) = v8 & sdtpldt0(v0, v2) = v7 &
% 12.94/2.51 sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v2) = v5 & aNaturalNumber0(v0) =
% 12.94/2.51 v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0) | ( ~ (v8 = v3)
% 12.94/2.51 & ~ (v7 = v6))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.94/2.51 $i] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) |
% 12.94/2.51 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 12.94/2.51 $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0) = v8 & sdtpldt0(v0,
% 12.94/2.51 v2) = v7 & sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v1) = v5 &
% 12.94/2.51 aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~
% 12.94/2.51 (v4 = 0) | ( ~ (v8 = v3) & ~ (v7 = v6))))) & ! [v0: $i] : ! [v1: $i]
% 12.94/2.51 : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~
% 12.94/2.51 (aNaturalNumber0(v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 12.94/2.51 : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0)
% 12.94/2.51 = v8 & sdtpldt0(v1, v0) = v7 & sdtpldt0(v0, v1) = v6 & aNaturalNumber0(v2)
% 12.94/2.51 = v5 & aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0)
% 12.94/2.51 | ~ (v4 = 0) | ( ~ (v8 = v7) & ~ (v6 = v3))))) & ! [v0: $i] : ! [v1:
% 12.94/2.52 $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (sdtpldt0(v0, v1) = v3) | ~
% 12.94/2.52 (aNaturalNumber0(v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any]
% 12.94/2.52 : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtpldt0(v2, v0)
% 12.94/2.52 = v8 & sdtpldt0(v1, v0) = v7 & sdtpldt0(v0, v2) = v6 & aNaturalNumber0(v1)
% 12.94/2.52 = v5 & aNaturalNumber0(v0) = v4 & $i(v8) & $i(v7) & $i(v6) & ( ~ (v5 = 0)
% 12.94/2.52 | ~ (v4 = 0) | ( ~ (v8 = v7) & ~ (v6 = v3))))) & ! [v0: $i] : ! [v1:
% 12.94/2.52 $i] : ! [v2: $i] : (v2 = v1 | ~ (aNaturalNumber0(v2) = 0) | ~
% 12.94/2.52 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 12.94/2.52 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 12.94/2.52 ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5
% 12.94/2.52 & sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4)
% 12.94/2.52 & $i(v3)))
% 12.94/2.52
% 12.94/2.52 (mDefLE)
% 12.94/2.52 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 12.94/2.52 (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~
% 12.94/2.52 $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: any] : (( ~ (v4 = 0) &
% 12.94/2.52 aNaturalNumber0(v3) = v4) | (aNaturalNumber0(v1) = v5 &
% 12.94/2.52 aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0: $i]
% 12.94/2.52 : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1)
% 12.94/2.52 = v2) | ~ (aNaturalNumber0(v3) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) |
% 12.94/2.52 ? [v4: any] : ? [v5: any] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4 &
% 12.94/2.52 $i(v4)) | (aNaturalNumber0(v1) = v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5
% 12.94/2.52 = 0) | ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.94/2.52 (sdtlseqdt0(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 12.94/2.52 any] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ($i(v4) & ((v6 = v1 & v5
% 12.94/2.52 = 0 & sdtpldt0(v0, v4) = v1 & aNaturalNumber0(v4) = 0) |
% 12.94/2.52 (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0) | ~
% 12.94/2.52 (v2 = 0))))))
% 12.94/2.52
% 12.94/2.52 (mSortsC)
% 12.94/2.52 aNaturalNumber0(sz00) = 0 & $i(sz00)
% 12.94/2.52
% 12.94/2.52 (mSortsC_01)
% 12.94/2.52 ~ (sz10 = sz00) & aNaturalNumber0(sz10) = 0 & $i(sz10) & $i(sz00)
% 12.94/2.52
% 12.94/2.52 (mZeroMul)
% 12.94/2.52 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | v0 = sz00 | ~
% 12.94/2.52 (sdtasdt0(v0, v1) = sz00) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 12.94/2.52 any] : (aNaturalNumber0(v1) = v3 & aNaturalNumber0(v0) = v2 & ( ~ (v3 = 0)
% 12.94/2.52 | ~ (v2 = 0))))
% 12.94/2.52
% 12.94/2.52 (m_AddZero)
% 12.94/2.52 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~
% 12.94/2.52 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtpldt0(sz00, v0) = v3 &
% 12.94/2.52 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 12.94/2.52 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ $i(v0) | ?
% 12.94/2.52 [v2: any] : ? [v3: $i] : (sdtpldt0(v0, sz00) = v3 & aNaturalNumber0(v0) =
% 12.94/2.52 v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~
% 12.94/2.52 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtpldt0(v0, sz00) = v0 &
% 12.94/2.52 sdtpldt0(sz00, v0) = v0))
% 12.94/2.52
% 12.94/2.52 (m_MulUnit)
% 12.94/2.53 $i(sz10) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~
% 12.94/2.53 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz10, v0) = v3 &
% 12.94/2.53 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 12.94/2.53 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ?
% 12.94/2.53 [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) =
% 12.94/2.53 v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~
% 12.94/2.53 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz10) = v0 &
% 12.94/2.53 sdtasdt0(sz10, v0) = v0))
% 12.94/2.53
% 12.94/2.53 (m__)
% 12.94/2.53 $i(xm) & ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xm) = v0)
% 12.94/2.53
% 12.94/2.53 (m__718)
% 12.94/2.53 aNaturalNumber0(xm) = 0 & $i(xm)
% 12.94/2.53
% 12.94/2.53 (function-axioms)
% 12.94/2.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.94/2.53 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 12.94/2.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.94/2.53 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 12.94/2.53 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.94/2.53 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 12.94/2.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 12.94/2.53 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.94/2.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 12.94/2.53 | ~ (aNaturalNumber0(v2) = v0))
% 12.94/2.53
% 12.94/2.53 Further assumptions not needed in the proof:
% 12.94/2.53 --------------------------------------------
% 12.94/2.53 mAMDistr, mAddAsso, mAddComm, mDefDiff, mMulAsso, mMulCanc, mMulComm, mNatSort,
% 12.94/2.53 mSortsB, mSortsB_02, mZeroAdd, m_MulZero
% 12.94/2.53
% 12.94/2.53 Those formulas are unsatisfiable:
% 12.94/2.53 ---------------------------------
% 12.94/2.53
% 12.94/2.53 Begin of proof
% 12.94/2.53 |
% 12.94/2.53 | ALPHA: (mSortsC) implies:
% 12.94/2.53 | (1) aNaturalNumber0(sz00) = 0
% 12.94/2.53 |
% 12.94/2.53 | ALPHA: (mSortsC_01) implies:
% 12.94/2.53 | (2) ~ (sz10 = sz00)
% 12.94/2.53 | (3) aNaturalNumber0(sz10) = 0
% 12.94/2.53 |
% 12.94/2.53 | ALPHA: (m_AddZero) implies:
% 12.94/2.53 | (4) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtpldt0(v0,
% 12.94/2.53 | sz00) = v0 & sdtpldt0(sz00, v0) = v0))
% 12.94/2.53 |
% 12.94/2.53 | ALPHA: (m_MulUnit) implies:
% 12.94/2.53 | (5) $i(sz10)
% 12.94/2.53 |
% 12.94/2.53 | ALPHA: (mAddCanc) implies:
% 12.94/2.53 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 12.94/2.54 | (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~
% 12.94/2.54 | (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 12.94/2.54 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) &
% 12.94/2.54 | ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 &
% 12.94/2.54 | sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3 & $i(v6) & $i(v5) &
% 12.94/2.54 | $i(v4) & $i(v3)))
% 12.94/2.54 |
% 12.94/2.54 | ALPHA: (mZeroMul) implies:
% 12.94/2.54 | (7) $i(sz00)
% 12.94/2.54 |
% 12.94/2.54 | ALPHA: (mDefLE) implies:
% 12.94/2.54 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~
% 12.94/2.54 | (sdtlseqdt0(v0, v1) = v2) | ~ (aNaturalNumber0(v3) = 0) | ~ $i(v3)
% 12.94/2.54 | | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (( ~ (v4 =
% 12.94/2.54 | v1) & sdtpldt0(v0, v3) = v4 & $i(v4)) | (aNaturalNumber0(v1) =
% 12.94/2.54 | v5 & aNaturalNumber0(v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 12.94/2.54 |
% 12.94/2.54 | ALPHA: (m__718) implies:
% 12.94/2.54 | (9) aNaturalNumber0(xm) = 0
% 12.94/2.54 |
% 12.94/2.54 | ALPHA: (m__) implies:
% 12.94/2.54 | (10) $i(xm)
% 12.94/2.54 | (11) ? [v0: int] : ( ~ (v0 = 0) & sdtlseqdt0(xm, xm) = v0)
% 12.94/2.54 |
% 12.94/2.54 | ALPHA: (function-axioms) implies:
% 12.94/2.54 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.94/2.54 | : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) =
% 12.94/2.54 | v0))
% 12.94/2.54 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.94/2.54 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 12.94/2.54 |
% 12.94/2.54 | DELTA: instantiating (11) with fresh symbol all_20_0 gives:
% 12.94/2.54 | (14) ~ (all_20_0 = 0) & sdtlseqdt0(xm, xm) = all_20_0
% 12.94/2.54 |
% 12.94/2.54 | ALPHA: (14) implies:
% 12.94/2.54 | (15) ~ (all_20_0 = 0)
% 12.94/2.54 | (16) sdtlseqdt0(xm, xm) = all_20_0
% 12.94/2.54 |
% 13.28/2.54 | GROUND_INST: instantiating (6) with xm, sz00, sz10, simplifying with (1), (3),
% 13.28/2.54 | (5), (7), (9), (10) gives:
% 13.28/2.54 | (17) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 13.28/2.54 | ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v1 & sdtpldt0(xm,
% 13.28/2.54 | sz00) = v0 & sdtpldt0(sz10, xm) = v3 & sdtpldt0(sz00, xm) = v2 &
% 13.28/2.54 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.28/2.54 |
% 13.28/2.54 | GROUND_INST: instantiating (6) with xm, sz10, sz00, simplifying with (1), (3),
% 13.28/2.54 | (5), (7), (9), (10) gives:
% 13.28/2.54 | (18) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 13.28/2.54 | ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v0 & sdtpldt0(xm,
% 13.28/2.54 | sz00) = v1 & sdtpldt0(sz10, xm) = v2 & sdtpldt0(sz00, xm) = v3 &
% 13.28/2.54 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.28/2.54 |
% 13.28/2.55 | GROUND_INST: instantiating (4) with xm, simplifying with (9), (10) gives:
% 13.28/2.55 | (19) sdtpldt0(xm, sz00) = xm & sdtpldt0(sz00, xm) = xm
% 13.28/2.55 |
% 13.28/2.55 | ALPHA: (19) implies:
% 13.28/2.55 | (20) sdtpldt0(xm, sz00) = xm
% 13.28/2.55 |
% 13.28/2.55 | GROUND_INST: instantiating (8) with xm, xm, all_20_0, sz00, simplifying with
% 13.28/2.55 | (1), (7), (10), (16) gives:
% 13.28/2.55 | (21) all_20_0 = 0 | ? [v0: any] : ? [v1: any] : (( ~ (v0 = xm) &
% 13.28/2.55 | sdtpldt0(xm, sz00) = v0 & $i(v0)) | (aNaturalNumber0(xm) = v1 &
% 13.28/2.55 | aNaturalNumber0(xm) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 13.28/2.55 |
% 13.28/2.55 | BETA: splitting (21) gives:
% 13.28/2.55 |
% 13.28/2.55 | Case 1:
% 13.28/2.55 | |
% 13.28/2.55 | | (22) all_20_0 = 0
% 13.28/2.55 | |
% 13.28/2.55 | | REDUCE: (15), (22) imply:
% 13.28/2.55 | | (23) $false
% 13.28/2.55 | |
% 13.28/2.55 | | CLOSE: (23) is inconsistent.
% 13.28/2.55 | |
% 13.28/2.55 | Case 2:
% 13.28/2.55 | |
% 13.28/2.55 | | (24) ? [v0: any] : ? [v1: any] : (( ~ (v0 = xm) & sdtpldt0(xm, sz00) =
% 13.28/2.55 | | v0 & $i(v0)) | (aNaturalNumber0(xm) = v1 & aNaturalNumber0(xm) =
% 13.28/2.55 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 13.28/2.55 | |
% 13.28/2.55 | | DELTA: instantiating (24) with fresh symbols all_32_0, all_32_1 gives:
% 13.28/2.55 | | (25) ( ~ (all_32_1 = xm) & sdtpldt0(xm, sz00) = all_32_1 & $i(all_32_1))
% 13.28/2.55 | | | (aNaturalNumber0(xm) = all_32_0 & aNaturalNumber0(xm) = all_32_1 &
% 13.28/2.55 | | ( ~ (all_32_0 = 0) | ~ (all_32_1 = 0)))
% 13.28/2.55 | |
% 13.28/2.55 | | BETA: splitting (25) gives:
% 13.28/2.55 | |
% 13.28/2.55 | | Case 1:
% 13.28/2.55 | | |
% 13.28/2.55 | | | (26) ~ (all_32_1 = xm) & sdtpldt0(xm, sz00) = all_32_1 & $i(all_32_1)
% 13.28/2.55 | | |
% 13.28/2.55 | | | ALPHA: (26) implies:
% 13.28/2.55 | | | (27) ~ (all_32_1 = xm)
% 13.28/2.55 | | | (28) sdtpldt0(xm, sz00) = all_32_1
% 13.28/2.55 | | |
% 13.28/2.55 | | | BETA: splitting (17) gives:
% 13.28/2.55 | | |
% 13.28/2.55 | | | Case 1:
% 13.28/2.55 | | | |
% 13.28/2.55 | | | | (29) sz10 = sz00
% 13.28/2.55 | | | |
% 13.28/2.55 | | | | REDUCE: (2), (29) imply:
% 13.28/2.55 | | | | (30) $false
% 13.28/2.55 | | | |
% 13.28/2.55 | | | | CLOSE: (30) is inconsistent.
% 13.28/2.55 | | | |
% 13.28/2.55 | | | Case 2:
% 13.28/2.55 | | | |
% 13.28/2.55 | | | | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3
% 13.28/2.55 | | | | = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v1 &
% 13.28/2.55 | | | | sdtpldt0(xm, sz00) = v0 & sdtpldt0(sz10, xm) = v3 &
% 13.28/2.55 | | | | sdtpldt0(sz00, xm) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.28/2.55 | | | |
% 13.28/2.55 | | | | DELTA: instantiating (31) with fresh symbols all_66_0, all_66_1,
% 13.28/2.55 | | | | all_66_2, all_66_3 gives:
% 13.28/2.56 | | | | (32) ~ (all_66_0 = all_66_1) & ~ (all_66_2 = all_66_3) &
% 13.28/2.56 | | | | sdtpldt0(xm, sz10) = all_66_2 & sdtpldt0(xm, sz00) = all_66_3 &
% 13.28/2.56 | | | | sdtpldt0(sz10, xm) = all_66_0 & sdtpldt0(sz00, xm) = all_66_1 &
% 13.28/2.56 | | | | $i(all_66_0) & $i(all_66_1) & $i(all_66_2) & $i(all_66_3)
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | ALPHA: (32) implies:
% 13.28/2.56 | | | | (33) sdtpldt0(xm, sz00) = all_66_3
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | BETA: splitting (18) gives:
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | Case 1:
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | (34) sz10 = sz00
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | REDUCE: (2), (34) imply:
% 13.28/2.56 | | | | | (35) $false
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | CLOSE: (35) is inconsistent.
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | Case 2:
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~
% 13.28/2.56 | | | | | (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v0 &
% 13.28/2.56 | | | | | sdtpldt0(xm, sz00) = v1 & sdtpldt0(sz10, xm) = v2 &
% 13.28/2.56 | | | | | sdtpldt0(sz00, xm) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | DELTA: instantiating (36) with fresh symbols all_71_0, all_71_1,
% 13.28/2.56 | | | | | all_71_2, all_71_3 gives:
% 13.28/2.56 | | | | | (37) ~ (all_71_0 = all_71_1) & ~ (all_71_2 = all_71_3) &
% 13.28/2.56 | | | | | sdtpldt0(xm, sz10) = all_71_3 & sdtpldt0(xm, sz00) = all_71_2
% 13.28/2.56 | | | | | & sdtpldt0(sz10, xm) = all_71_1 & sdtpldt0(sz00, xm) =
% 13.28/2.56 | | | | | all_71_0 & $i(all_71_0) & $i(all_71_1) & $i(all_71_2) &
% 13.28/2.56 | | | | | $i(all_71_3)
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | ALPHA: (37) implies:
% 13.28/2.56 | | | | | (38) sdtpldt0(xm, sz00) = all_71_2
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | GROUND_INST: instantiating (13) with all_32_1, all_66_3, sz00, xm,
% 13.28/2.56 | | | | | simplifying with (28), (33) gives:
% 13.28/2.56 | | | | | (39) all_66_3 = all_32_1
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | GROUND_INST: instantiating (13) with all_66_3, all_71_2, sz00, xm,
% 13.28/2.56 | | | | | simplifying with (33), (38) gives:
% 13.28/2.56 | | | | | (40) all_71_2 = all_66_3
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | GROUND_INST: instantiating (13) with xm, all_71_2, sz00, xm,
% 13.28/2.56 | | | | | simplifying with (20), (38) gives:
% 13.28/2.56 | | | | | (41) all_71_2 = xm
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | COMBINE_EQS: (40), (41) imply:
% 13.28/2.56 | | | | | (42) all_66_3 = xm
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | SIMP: (42) implies:
% 13.28/2.56 | | | | | (43) all_66_3 = xm
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | COMBINE_EQS: (39), (43) imply:
% 13.28/2.56 | | | | | (44) all_32_1 = xm
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | REDUCE: (27), (44) imply:
% 13.28/2.56 | | | | | (45) $false
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | | CLOSE: (45) is inconsistent.
% 13.28/2.56 | | | | |
% 13.28/2.56 | | | | End of split
% 13.28/2.56 | | | |
% 13.28/2.56 | | | End of split
% 13.28/2.56 | | |
% 13.28/2.56 | | Case 2:
% 13.28/2.56 | | |
% 13.28/2.56 | | | (46) aNaturalNumber0(xm) = all_32_0 & aNaturalNumber0(xm) = all_32_1 &
% 13.28/2.56 | | | ( ~ (all_32_0 = 0) | ~ (all_32_1 = 0))
% 13.28/2.56 | | |
% 13.28/2.56 | | | ALPHA: (46) implies:
% 13.28/2.56 | | | (47) aNaturalNumber0(xm) = all_32_1
% 13.28/2.56 | | | (48) aNaturalNumber0(xm) = all_32_0
% 13.28/2.56 | | | (49) ~ (all_32_0 = 0) | ~ (all_32_1 = 0)
% 13.28/2.56 | | |
% 13.28/2.56 | | | GROUND_INST: instantiating (12) with 0, all_32_0, xm, simplifying with
% 13.28/2.56 | | | (9), (48) gives:
% 13.28/2.56 | | | (50) all_32_0 = 0
% 13.28/2.56 | | |
% 13.28/2.56 | | | GROUND_INST: instantiating (12) with all_32_1, all_32_0, xm, simplifying
% 13.28/2.56 | | | with (47), (48) gives:
% 13.28/2.56 | | | (51) all_32_0 = all_32_1
% 13.28/2.56 | | |
% 13.28/2.56 | | | COMBINE_EQS: (50), (51) imply:
% 13.28/2.56 | | | (52) all_32_1 = 0
% 13.28/2.56 | | |
% 13.28/2.56 | | | SIMP: (52) implies:
% 13.28/2.56 | | | (53) all_32_1 = 0
% 13.28/2.56 | | |
% 13.28/2.56 | | | BETA: splitting (49) gives:
% 13.28/2.56 | | |
% 13.28/2.56 | | | Case 1:
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | (54) ~ (all_32_0 = 0)
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | REDUCE: (50), (54) imply:
% 13.28/2.56 | | | | (55) $false
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | CLOSE: (55) is inconsistent.
% 13.28/2.56 | | | |
% 13.28/2.56 | | | Case 2:
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | (56) ~ (all_32_1 = 0)
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | REDUCE: (53), (56) imply:
% 13.28/2.56 | | | | (57) $false
% 13.28/2.56 | | | |
% 13.28/2.56 | | | | CLOSE: (57) is inconsistent.
% 13.28/2.56 | | | |
% 13.28/2.56 | | | End of split
% 13.28/2.56 | | |
% 13.28/2.56 | | End of split
% 13.28/2.56 | |
% 13.28/2.56 | End of split
% 13.28/2.56 |
% 13.28/2.56 End of proof
% 13.28/2.56 % SZS output end Proof for theBenchmark
% 13.28/2.56
% 13.28/2.56 1966ms
%------------------------------------------------------------------------------