TSTP Solution File: NUM457+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM457+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 : n018.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 11.31s 2.26s
% Output : Proof 17.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM457+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n018.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 11:44:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 2.54/1.01 Prover 4: Preprocessing ...
% 2.54/1.02 Prover 1: Preprocessing ...
% 2.54/1.05 Prover 2: Preprocessing ...
% 2.54/1.05 Prover 5: Preprocessing ...
% 2.54/1.05 Prover 3: Preprocessing ...
% 2.54/1.05 Prover 0: Preprocessing ...
% 2.54/1.05 Prover 6: Preprocessing ...
% 4.05/1.41 Prover 1: Constructing countermodel ...
% 4.05/1.44 Prover 3: Constructing countermodel ...
% 5.45/1.49 Prover 6: Proving ...
% 6.10/1.54 Prover 5: Constructing countermodel ...
% 6.77/1.63 Prover 3: gave up
% 6.77/1.64 Prover 2: Proving ...
% 6.77/1.64 Prover 4: Constructing countermodel ...
% 6.77/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.77/1.68 Prover 7: Preprocessing ...
% 7.38/1.73 Prover 1: gave up
% 7.38/1.73 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.38/1.74 Prover 0: Proving ...
% 7.38/1.76 Prover 8: Preprocessing ...
% 8.36/1.84 Prover 8: Warning: ignoring some quantifiers
% 8.36/1.86 Prover 8: Constructing countermodel ...
% 8.36/1.88 Prover 7: Constructing countermodel ...
% 9.05/1.98 Prover 8: gave up
% 9.64/2.00 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 9.64/2.03 Prover 9: Preprocessing ...
% 10.24/2.10 Prover 7: gave up
% 10.24/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.24/2.15 Prover 10: Preprocessing ...
% 11.31/2.26 Prover 0: proved (1628ms)
% 11.31/2.26
% 11.31/2.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.31/2.26
% 11.31/2.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.31/2.26 Prover 10: Constructing countermodel ...
% 11.31/2.26 Prover 6: stopped
% 11.31/2.27 Prover 2: stopped
% 11.31/2.27 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.31/2.27 Prover 5: stopped
% 11.31/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.31/2.28 Prover 11: Preprocessing ...
% 11.31/2.29 Prover 10: gave up
% 11.31/2.29 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.31/2.29 Prover 16: Preprocessing ...
% 11.31/2.31 Prover 19: Preprocessing ...
% 11.31/2.31 Prover 13: Preprocessing ...
% 11.92/2.33 Prover 16: Constructing countermodel ...
% 11.92/2.36 Prover 19: Warning: ignoring some quantifiers
% 11.92/2.36 Prover 19: Constructing countermodel ...
% 12.44/2.39 Prover 9: Constructing countermodel ...
% 12.44/2.39 Prover 9: stopped
% 12.44/2.41 Prover 13: Constructing countermodel ...
% 12.44/2.42 Prover 19: gave up
% 12.44/2.44 Prover 11: Constructing countermodel ...
% 17.45/3.09 Prover 4: Found proof (size 76)
% 17.45/3.09 Prover 4: proved (2455ms)
% 17.45/3.09 Prover 11: stopped
% 17.45/3.09 Prover 13: stopped
% 17.45/3.09 Prover 16: stopped
% 17.45/3.09
% 17.45/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.45/3.09
% 17.45/3.10 % SZS output start Proof for theBenchmark
% 17.45/3.10 Assumptions after simplification:
% 17.45/3.10 ---------------------------------
% 17.45/3.10
% 17.45/3.10 (mMulCanc)
% 17.45/3.15 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 17.45/3.15 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) =
% 17.45/3.15 v3) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 17.45/3.15 ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v0, v2) =
% 17.45/3.15 v8 & sdtasdt0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 &
% 17.45/3.15 aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) |
% 17.45/3.15 ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.45/3.15 $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2,
% 17.45/3.15 v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) |
% 17.45/3.15 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i]
% 17.45/3.15 : ? [v8: $i] : (sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v7 &
% 17.45/3.15 aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & (
% 17.45/3.15 ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v4) & ~ (v7 = v3))))) & ! [v0:
% 17.45/3.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0
% 17.45/3.15 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~
% 17.45/3.15 (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any]
% 17.45/3.15 : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v2, v0) = v8 &
% 17.45/3.15 sdtasdt0(v0, v1) = v7 & aNaturalNumber0(v2) = v6 & aNaturalNumber0(v1) =
% 17.45/3.15 v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | ( ~ (v8 = v4) & ~ (v7
% 17.45/3.15 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 17.45/3.15 ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~
% 17.45/3.15 (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 17.45/3.15 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i]
% 17.45/3.15 : (sdtasdt0(v2, v0) = v8 & sdtasdt0(v1, v0) = v7 & aNaturalNumber0(v2) = v6
% 17.45/3.15 & aNaturalNumber0(v1) = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0)
% 17.45/3.15 | ( ~ (v8 = v7) & ~ (v4 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.45/3.15 $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~
% 17.45/3.15 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 17.45/3.15 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 17.45/3.15 : (sdtasdt0(v1, v0) = v7 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 &
% 17.45/3.15 aNaturalNumber0(v2) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~
% 17.45/3.15 (v7 = v3) & ~ (v6 = v5))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.45/3.15 : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v3) | ~
% 17.45/3.15 (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 17.45/3.15 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 17.45/3.15 : (sdtasdt0(v2, v0) = v7 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 &
% 17.45/3.15 aNaturalNumber0(v1) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~
% 17.45/3.15 (v7 = v3) & ~ (v6 = v5))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.45/3.15 : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~
% 17.45/3.15 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 17.45/3.15 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 17.45/3.15 : (sdtasdt0(v2, v0) = v7 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v1) = v5 &
% 17.45/3.15 aNaturalNumber0(v2) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~
% 17.45/3.15 (v7 = v6) & ~ (v5 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.45/3.15 : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = v3) | ~
% 17.45/3.15 (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 17.45/3.15 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 17.45/3.15 : (sdtasdt0(v2, v0) = v7 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 &
% 17.45/3.15 aNaturalNumber0(v1) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | ( ~
% 17.45/3.15 (v7 = v6) & ~ (v5 = v3))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 17.45/3.15 : (v2 = v1 | v0 = sz00 | ~ (aNaturalNumber0(v2) = 0) | ~
% 17.45/3.15 (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~
% 17.45/3.15 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 17.45/3.15 ( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5
% 17.45/3.15 & sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3 & $i(v6) & $i(v5) & $i(v4)
% 17.45/3.15 & $i(v3)))
% 17.45/3.15
% 17.45/3.15 (mSortsC)
% 17.45/3.15 aNaturalNumber0(sz00) = 0 & $i(sz00)
% 17.45/3.15
% 17.45/3.15 (mSortsC_01)
% 17.45/3.15 ~ (sz10 = sz00) & aNaturalNumber0(sz10) = 0 & $i(sz10) & $i(sz00)
% 17.45/3.15
% 17.45/3.15 (m_MulUnit)
% 17.45/3.16 $i(sz10) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~
% 17.45/3.16 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz10, v0) = v3 &
% 17.45/3.16 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0))))
% 17.45/3.16 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ?
% 17.45/3.16 [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz10) = v3 & aNaturalNumber0(v0) =
% 17.45/3.16 v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = v0 & v1 = v0)))) & ! [v0: $i] : ( ~
% 17.45/3.16 (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0, sz10) = v0 &
% 17.45/3.16 sdtasdt0(sz10, v0) = v0))
% 17.45/3.16
% 17.45/3.16 (m_MulZero)
% 17.45/3.16 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~
% 17.45/3.16 $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(sz00, v0) = v3 &
% 17.45/3.16 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 =
% 17.45/3.16 sz00)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) |
% 17.45/3.16 ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (sdtasdt0(v0, sz00) = v3 &
% 17.45/3.16 aNaturalNumber0(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (v3 = sz00 & v1 =
% 17.45/3.16 sz00)))) & ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) |
% 17.45/3.16 (sdtasdt0(v0, sz00) = sz00 & sdtasdt0(sz00, v0) = sz00))
% 17.45/3.16
% 17.45/3.16 (m__)
% 17.45/3.16 ~ (xn = sz00) & ~ (xm = sz00) & sdtasdt0(xm, xn) = sz00 & $i(xn) & $i(xm) &
% 17.45/3.16 $i(sz00)
% 17.45/3.16
% 17.45/3.16 (m__624)
% 17.45/3.16 aNaturalNumber0(xn) = 0 & aNaturalNumber0(xm) = 0 & $i(xn) & $i(xm)
% 17.45/3.16
% 17.45/3.16 (function-axioms)
% 17.45/3.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.45/3.16 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 17.45/3.16 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 17.45/3.16 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.45/3.16 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 17.45/3.16 | ~ (aNaturalNumber0(v2) = v0))
% 17.45/3.16
% 17.45/3.16 Further assumptions not needed in the proof:
% 17.45/3.16 --------------------------------------------
% 17.45/3.16 mAMDistr, mAddAsso, mAddCanc, mAddComm, mMulAsso, mMulComm, mNatSort, mSortsB,
% 17.45/3.16 mSortsB_02, mZeroAdd, m_AddZero
% 17.45/3.16
% 17.45/3.16 Those formulas are unsatisfiable:
% 17.45/3.16 ---------------------------------
% 17.45/3.16
% 17.45/3.16 Begin of proof
% 17.45/3.16 |
% 17.45/3.16 | ALPHA: (mSortsC) implies:
% 17.45/3.16 | (1) aNaturalNumber0(sz00) = 0
% 17.45/3.16 |
% 17.45/3.16 | ALPHA: (mSortsC_01) implies:
% 17.45/3.16 | (2) ~ (sz10 = sz00)
% 17.45/3.16 | (3) aNaturalNumber0(sz10) = 0
% 17.45/3.16 |
% 17.45/3.16 | ALPHA: (m_MulUnit) implies:
% 17.45/3.16 | (4) $i(sz10)
% 17.45/3.16 |
% 17.45/3.16 | ALPHA: (m_MulZero) implies:
% 17.45/3.16 | (5) ! [v0: $i] : ( ~ (aNaturalNumber0(v0) = 0) | ~ $i(v0) | (sdtasdt0(v0,
% 17.45/3.16 | sz00) = sz00 & sdtasdt0(sz00, v0) = sz00))
% 17.45/3.16 |
% 17.45/3.16 | ALPHA: (mMulCanc) implies:
% 17.89/3.16 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | v0 = sz00 | ~
% 17.89/3.16 | (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~
% 17.89/3.16 | (aNaturalNumber0(v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 17.89/3.16 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) &
% 17.89/3.16 | ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 &
% 17.89/3.16 | sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3 & $i(v6) & $i(v5) &
% 17.89/3.16 | $i(v4) & $i(v3)))
% 17.89/3.16 |
% 17.89/3.16 | ALPHA: (m__624) implies:
% 17.89/3.16 | (7) aNaturalNumber0(xm) = 0
% 17.89/3.17 | (8) aNaturalNumber0(xn) = 0
% 17.89/3.17 |
% 17.89/3.17 | ALPHA: (m__) implies:
% 17.89/3.17 | (9) ~ (xm = sz00)
% 17.89/3.17 | (10) ~ (xn = sz00)
% 17.89/3.17 | (11) $i(sz00)
% 17.89/3.17 | (12) $i(xm)
% 17.89/3.17 | (13) $i(xn)
% 17.89/3.17 | (14) sdtasdt0(xm, xn) = sz00
% 17.89/3.17 |
% 17.89/3.17 | ALPHA: (function-axioms) implies:
% 17.89/3.17 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.89/3.17 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 17.89/3.17 |
% 17.89/3.17 | GROUND_INST: instantiating (6) with xn, sz00, xm, simplifying with (1), (7),
% 17.89/3.17 | (8), (11), (12), (13) gives:
% 17.89/3.17 | (16) xn = sz00 | xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 17.89/3.17 | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v1 &
% 17.89/3.17 | sdtasdt0(xn, sz00) = v0 & sdtasdt0(xm, xn) = v3 & sdtasdt0(sz00, xn)
% 17.89/3.17 | = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.17 |
% 17.89/3.17 | GROUND_INST: instantiating (6) with xn, sz00, sz10, simplifying with (1), (3),
% 17.89/3.17 | (4), (8), (11), (13) gives:
% 17.89/3.17 | (17) xn = sz00 | sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 17.89/3.17 | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, sz10) = v1 &
% 17.89/3.17 | sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz10, xn) = v3 & sdtasdt0(sz00,
% 17.89/3.17 | xn) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.17 |
% 17.89/3.17 | GROUND_INST: instantiating (6) with xm, sz00, xn, simplifying with (1), (7),
% 17.89/3.17 | (8), (11), (12), (13) gives:
% 17.89/3.17 | (18) xn = sz00 | xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 17.89/3.17 | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v3 &
% 17.89/3.17 | sdtasdt0(xm, xn) = v1 & sdtasdt0(xm, sz00) = v0 & sdtasdt0(sz00, xm)
% 17.89/3.17 | = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.17 |
% 17.89/3.17 | GROUND_INST: instantiating (6) with xm, xn, sz00, simplifying with (1), (7),
% 17.89/3.17 | (8), (11), (12), (13) gives:
% 17.89/3.17 | (19) xn = sz00 | xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 17.89/3.17 | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v2 &
% 17.89/3.17 | sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, sz00) = v1 & sdtasdt0(sz00, xm)
% 17.89/3.17 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.17 |
% 17.89/3.17 | GROUND_INST: instantiating (6) with xn, xm, sz00, simplifying with (1), (7),
% 17.89/3.17 | (8), (11), (12), (13) gives:
% 17.89/3.18 | (20) xn = sz00 | xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 17.89/3.18 | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 &
% 17.89/3.18 | sdtasdt0(xn, sz00) = v1 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz00, xn)
% 17.89/3.18 | = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.18 |
% 17.89/3.18 | GROUND_INST: instantiating (5) with xn, simplifying with (8), (13) gives:
% 17.89/3.18 | (21) sdtasdt0(xn, sz00) = sz00 & sdtasdt0(sz00, xn) = sz00
% 17.89/3.18 |
% 17.89/3.18 | ALPHA: (21) implies:
% 17.89/3.18 | (22) sdtasdt0(sz00, xn) = sz00
% 17.89/3.18 |
% 17.89/3.18 | BETA: splitting (20) gives:
% 17.89/3.18 |
% 17.89/3.18 | Case 1:
% 17.89/3.18 | |
% 17.89/3.18 | | (23) xn = sz00
% 17.89/3.18 | |
% 17.89/3.18 | | REDUCE: (10), (23) imply:
% 17.89/3.18 | | (24) $false
% 17.89/3.18 | |
% 17.89/3.18 | | CLOSE: (24) is inconsistent.
% 17.89/3.18 | |
% 17.89/3.18 | Case 2:
% 17.89/3.18 | |
% 17.89/3.18 | | (25) xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.89/3.18 | | ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn,
% 17.89/3.18 | | sz00) = v1 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz00, xn) = v3 &
% 17.89/3.18 | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.18 | |
% 17.89/3.18 | | BETA: splitting (25) gives:
% 17.89/3.18 | |
% 17.89/3.18 | | Case 1:
% 17.89/3.18 | | |
% 17.89/3.18 | | | (26) xm = sz00
% 17.89/3.18 | | |
% 17.89/3.18 | | | REDUCE: (9), (26) imply:
% 17.89/3.18 | | | (27) $false
% 17.89/3.18 | | |
% 17.89/3.18 | | | CLOSE: (27) is inconsistent.
% 17.89/3.18 | | |
% 17.89/3.18 | | Case 2:
% 17.89/3.18 | | |
% 17.89/3.18 | | | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 17.89/3.18 | | | v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn,
% 17.89/3.18 | | | sz00) = v1 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz00, xn) = v3 &
% 17.89/3.18 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.18 | | |
% 17.89/3.18 | | | DELTA: instantiating (28) with fresh symbols all_201_0, all_201_1,
% 17.89/3.18 | | | all_201_2, all_201_3 gives:
% 17.89/3.18 | | | (29) ~ (all_201_0 = all_201_1) & ~ (all_201_2 = all_201_3) &
% 17.89/3.18 | | | sdtasdt0(xn, xm) = all_201_3 & sdtasdt0(xn, sz00) = all_201_2 &
% 17.89/3.18 | | | sdtasdt0(xm, xn) = all_201_1 & sdtasdt0(sz00, xn) = all_201_0 &
% 17.89/3.18 | | | $i(all_201_0) & $i(all_201_1) & $i(all_201_2) & $i(all_201_3)
% 17.89/3.18 | | |
% 17.89/3.18 | | | ALPHA: (29) implies:
% 17.89/3.18 | | | (30) ~ (all_201_0 = all_201_1)
% 17.89/3.18 | | | (31) sdtasdt0(sz00, xn) = all_201_0
% 17.89/3.18 | | | (32) sdtasdt0(xm, xn) = all_201_1
% 17.89/3.18 | | |
% 17.89/3.18 | | | BETA: splitting (17) gives:
% 17.89/3.18 | | |
% 17.89/3.18 | | | Case 1:
% 17.89/3.18 | | | |
% 17.89/3.18 | | | | (33) xn = sz00
% 17.89/3.18 | | | |
% 17.89/3.18 | | | | REDUCE: (10), (33) imply:
% 17.89/3.18 | | | | (34) $false
% 17.89/3.18 | | | |
% 17.89/3.18 | | | | CLOSE: (34) is inconsistent.
% 17.89/3.18 | | | |
% 17.89/3.18 | | | Case 2:
% 17.89/3.18 | | | |
% 17.89/3.18 | | | | (35) sz10 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 17.89/3.18 | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, sz10) = v1 &
% 17.89/3.18 | | | | sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz10, xn) = v3 &
% 17.89/3.18 | | | | sdtasdt0(sz00, xn) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.89/3.18 | | | |
% 17.89/3.18 | | | | BETA: splitting (19) gives:
% 17.89/3.18 | | | |
% 17.89/3.18 | | | | Case 1:
% 17.89/3.18 | | | | |
% 17.89/3.18 | | | | | (36) xn = sz00
% 17.89/3.18 | | | | |
% 17.98/3.18 | | | | | REDUCE: (10), (36) imply:
% 17.98/3.18 | | | | | (37) $false
% 17.98/3.18 | | | | |
% 17.98/3.18 | | | | | CLOSE: (37) is inconsistent.
% 17.98/3.18 | | | | |
% 17.98/3.18 | | | | Case 2:
% 17.98/3.18 | | | | |
% 17.98/3.18 | | | | | (38) xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 17.98/3.18 | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v2 &
% 17.98/3.18 | | | | | sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, sz00) = v1 &
% 17.98/3.18 | | | | | sdtasdt0(sz00, xm) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.98/3.18 | | | | |
% 17.98/3.18 | | | | | BETA: splitting (38) gives:
% 17.98/3.18 | | | | |
% 17.98/3.18 | | | | | Case 1:
% 17.98/3.18 | | | | | |
% 17.98/3.18 | | | | | | (39) xm = sz00
% 17.98/3.18 | | | | | |
% 17.98/3.18 | | | | | | REDUCE: (9), (39) imply:
% 17.98/3.18 | | | | | | (40) $false
% 17.98/3.18 | | | | | |
% 17.98/3.18 | | | | | | CLOSE: (40) is inconsistent.
% 17.98/3.18 | | | | | |
% 17.98/3.18 | | | | | Case 2:
% 17.98/3.18 | | | | | |
% 17.98/3.18 | | | | | | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~
% 17.98/3.18 | | | | | | (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, xm) = v2 &
% 17.98/3.18 | | | | | | sdtasdt0(xm, xn) = v0 & sdtasdt0(xm, sz00) = v1 &
% 17.98/3.18 | | | | | | sdtasdt0(sz00, xm) = v3 & $i(v3) & $i(v2) & $i(v1) &
% 17.98/3.18 | | | | | | $i(v0))
% 17.98/3.18 | | | | | |
% 17.98/3.18 | | | | | | DELTA: instantiating (41) with fresh symbols all_221_0, all_221_1,
% 17.98/3.18 | | | | | | all_221_2, all_221_3 gives:
% 17.98/3.19 | | | | | | (42) ~ (all_221_0 = all_221_1) & ~ (all_221_2 = all_221_3) &
% 17.98/3.19 | | | | | | sdtasdt0(xn, xm) = all_221_1 & sdtasdt0(xm, xn) = all_221_3
% 17.98/3.19 | | | | | | & sdtasdt0(xm, sz00) = all_221_2 & sdtasdt0(sz00, xm) =
% 17.98/3.19 | | | | | | all_221_0 & $i(all_221_0) & $i(all_221_1) & $i(all_221_2) &
% 17.98/3.19 | | | | | | $i(all_221_3)
% 17.98/3.19 | | | | | |
% 17.98/3.19 | | | | | | ALPHA: (42) implies:
% 17.98/3.19 | | | | | | (43) sdtasdt0(xm, xn) = all_221_3
% 17.98/3.19 | | | | | |
% 17.98/3.19 | | | | | | BETA: splitting (35) gives:
% 17.98/3.19 | | | | | |
% 17.98/3.19 | | | | | | Case 1:
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | (44) sz10 = sz00
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | REDUCE: (2), (44) imply:
% 17.98/3.19 | | | | | | | (45) $false
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | CLOSE: (45) is inconsistent.
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | Case 2:
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (
% 17.98/3.19 | | | | | | | ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn, sz10) = v1 &
% 17.98/3.19 | | | | | | | sdtasdt0(xn, sz00) = v0 & sdtasdt0(sz10, xn) = v3 &
% 17.98/3.19 | | | | | | | sdtasdt0(sz00, xn) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 17.98/3.19 | | | | | | | $i(v0))
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | DELTA: instantiating (46) with fresh symbols all_233_0, all_233_1,
% 17.98/3.19 | | | | | | | all_233_2, all_233_3 gives:
% 17.98/3.19 | | | | | | | (47) ~ (all_233_0 = all_233_1) & ~ (all_233_2 = all_233_3) &
% 17.98/3.19 | | | | | | | sdtasdt0(xn, sz10) = all_233_2 & sdtasdt0(xn, sz00) =
% 17.98/3.19 | | | | | | | all_233_3 & sdtasdt0(sz10, xn) = all_233_0 &
% 17.98/3.19 | | | | | | | sdtasdt0(sz00, xn) = all_233_1 & $i(all_233_0) &
% 17.98/3.19 | | | | | | | $i(all_233_1) & $i(all_233_2) & $i(all_233_3)
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | ALPHA: (47) implies:
% 17.98/3.19 | | | | | | | (48) sdtasdt0(sz00, xn) = all_233_1
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | BETA: splitting (18) gives:
% 17.98/3.19 | | | | | | |
% 17.98/3.19 | | | | | | | Case 1:
% 17.98/3.19 | | | | | | | |
% 17.98/3.19 | | | | | | | | (49) xn = sz00
% 17.98/3.19 | | | | | | | |
% 17.98/3.19 | | | | | | | | REDUCE: (10), (49) imply:
% 17.98/3.19 | | | | | | | | (50) $false
% 17.98/3.19 | | | | | | | |
% 17.98/3.19 | | | | | | | | CLOSE: (50) is inconsistent.
% 17.98/3.19 | | | | | | | |
% 17.98/3.19 | | | | | | | Case 2:
% 17.98/3.19 | | | | | | | |
% 17.98/3.19 | | | | | | | | (51) xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 17.98/3.19 | | | | | | | | [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn,
% 17.98/3.19 | | | | | | | | xm) = v3 & sdtasdt0(xm, xn) = v1 & sdtasdt0(xm,
% 17.98/3.19 | | | | | | | | sz00) = v0 & sdtasdt0(sz00, xm) = v2 & $i(v3) &
% 17.98/3.19 | | | | | | | | $i(v2) & $i(v1) & $i(v0))
% 17.98/3.19 | | | | | | | |
% 17.98/3.19 | | | | | | | | BETA: splitting (16) gives:
% 17.98/3.19 | | | | | | | |
% 17.98/3.19 | | | | | | | | Case 1:
% 17.98/3.19 | | | | | | | | |
% 17.98/3.19 | | | | | | | | | (52) xn = sz00
% 17.98/3.19 | | | | | | | | |
% 17.98/3.19 | | | | | | | | | REDUCE: (10), (52) imply:
% 17.98/3.19 | | | | | | | | | (53) $false
% 17.98/3.19 | | | | | | | | |
% 17.98/3.19 | | | | | | | | | CLOSE: (53) is inconsistent.
% 17.98/3.19 | | | | | | | | |
% 17.98/3.19 | | | | | | | | Case 2:
% 17.98/3.19 | | | | | | | | |
% 17.98/3.19 | | | | | | | | | (54) xm = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 17.98/3.19 | | | | | | | | | ? [v3: $i] : ( ~ (v3 = v2) & ~ (v1 = v0) &
% 17.98/3.19 | | | | | | | | | sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, sz00) = v0 &
% 17.98/3.19 | | | | | | | | | sdtasdt0(xm, xn) = v3 & sdtasdt0(sz00, xn) = v2 &
% 17.98/3.19 | | | | | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.98/3.19 | | | | | | | | |
% 17.98/3.19 | | | | | | | | | BETA: splitting (51) gives:
% 17.98/3.19 | | | | | | | | |
% 17.98/3.19 | | | | | | | | | Case 1:
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | (55) xm = sz00
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | REDUCE: (9), (55) imply:
% 17.98/3.19 | | | | | | | | | | (56) $false
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | CLOSE: (56) is inconsistent.
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | Case 2:
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 17.98/3.19 | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtasdt0(xn,
% 17.98/3.19 | | | | | | | | | | xm) = v3 & sdtasdt0(xm, xn) = v1 & sdtasdt0(xm,
% 17.98/3.19 | | | | | | | | | | sz00) = v0 & sdtasdt0(sz00, xm) = v2 & $i(v3) &
% 17.98/3.19 | | | | | | | | | | $i(v2) & $i(v1) & $i(v0))
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | DELTA: instantiating (57) with fresh symbols all_247_0,
% 17.98/3.19 | | | | | | | | | | all_247_1, all_247_2, all_247_3 gives:
% 17.98/3.19 | | | | | | | | | | (58) ~ (all_247_0 = all_247_1) & ~ (all_247_2 =
% 17.98/3.19 | | | | | | | | | | all_247_3) & sdtasdt0(xn, xm) = all_247_0 &
% 17.98/3.19 | | | | | | | | | | sdtasdt0(xm, xn) = all_247_2 & sdtasdt0(xm, sz00) =
% 17.98/3.19 | | | | | | | | | | all_247_3 & sdtasdt0(sz00, xm) = all_247_1 &
% 17.98/3.19 | | | | | | | | | | $i(all_247_0) & $i(all_247_1) & $i(all_247_2) &
% 17.98/3.19 | | | | | | | | | | $i(all_247_3)
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | ALPHA: (58) implies:
% 17.98/3.19 | | | | | | | | | | (59) sdtasdt0(xm, xn) = all_247_2
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | BETA: splitting (54) gives:
% 17.98/3.19 | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | Case 1:
% 17.98/3.19 | | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | | (60) xm = sz00
% 17.98/3.19 | | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | | REDUCE: (9), (60) imply:
% 17.98/3.19 | | | | | | | | | | | (61) $false
% 17.98/3.19 | | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | | CLOSE: (61) is inconsistent.
% 17.98/3.19 | | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | Case 2:
% 17.98/3.19 | | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 17.98/3.19 | | | | | | | | | | | $i] : ( ~ (v3 = v2) & ~ (v1 = v0) &
% 17.98/3.19 | | | | | | | | | | | sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, sz00) = v0
% 17.98/3.19 | | | | | | | | | | | & sdtasdt0(xm, xn) = v3 & sdtasdt0(sz00, xn) =
% 17.98/3.19 | | | | | | | | | | | v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.98/3.19 | | | | | | | | | | |
% 17.98/3.19 | | | | | | | | | | | DELTA: instantiating (62) with fresh symbols all_253_0,
% 17.98/3.19 | | | | | | | | | | | all_253_1, all_253_2, all_253_3 gives:
% 17.98/3.19 | | | | | | | | | | | (63) ~ (all_253_0 = all_253_1) & ~ (all_253_2 =
% 17.98/3.19 | | | | | | | | | | | all_253_3) & sdtasdt0(xn, xm) = all_253_2 &
% 17.98/3.19 | | | | | | | | | | | sdtasdt0(xn, sz00) = all_253_3 & sdtasdt0(xm, xn)
% 17.98/3.19 | | | | | | | | | | | = all_253_0 & sdtasdt0(sz00, xn) = all_253_1 &
% 17.98/3.19 | | | | | | | | | | | $i(all_253_0) & $i(all_253_1) & $i(all_253_2) &
% 17.98/3.19 | | | | | | | | | | | $i(all_253_3)
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | ALPHA: (63) implies:
% 17.98/3.20 | | | | | | | | | | | (64) sdtasdt0(sz00, xn) = all_253_1
% 17.98/3.20 | | | | | | | | | | | (65) sdtasdt0(xm, xn) = all_253_0
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_201_0, all_233_1, xn,
% 17.98/3.20 | | | | | | | | | | | sz00, simplifying with (31), (48) gives:
% 17.98/3.20 | | | | | | | | | | | (66) all_233_1 = all_201_0
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_233_1, all_253_1, xn,
% 17.98/3.20 | | | | | | | | | | | sz00, simplifying with (48), (64) gives:
% 17.98/3.20 | | | | | | | | | | | (67) all_253_1 = all_233_1
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | GROUND_INST: instantiating (15) with sz00, all_253_1, xn, sz00,
% 17.98/3.20 | | | | | | | | | | | simplifying with (22), (64) gives:
% 17.98/3.20 | | | | | | | | | | | (68) all_253_1 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | GROUND_INST: instantiating (15) with sz00, all_247_2, xn, xm,
% 17.98/3.20 | | | | | | | | | | | simplifying with (14), (59) gives:
% 17.98/3.20 | | | | | | | | | | | (69) all_247_2 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_247_2, all_253_0, xn,
% 17.98/3.20 | | | | | | | | | | | xm, simplifying with (59), (65) gives:
% 17.98/3.20 | | | | | | | | | | | (70) all_253_0 = all_247_2
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_221_3, all_253_0, xn,
% 17.98/3.20 | | | | | | | | | | | xm, simplifying with (43), (65) gives:
% 17.98/3.20 | | | | | | | | | | | (71) all_253_0 = all_221_3
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_201_1, all_253_0, xn,
% 17.98/3.20 | | | | | | | | | | | xm, simplifying with (32), (65) gives:
% 17.98/3.20 | | | | | | | | | | | (72) all_253_0 = all_201_1
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | COMBINE_EQS: (71), (72) imply:
% 17.98/3.20 | | | | | | | | | | | (73) all_221_3 = all_201_1
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | COMBINE_EQS: (70), (71) imply:
% 17.98/3.20 | | | | | | | | | | | (74) all_247_2 = all_221_3
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | SIMP: (74) implies:
% 17.98/3.20 | | | | | | | | | | | (75) all_247_2 = all_221_3
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | COMBINE_EQS: (67), (68) imply:
% 17.98/3.20 | | | | | | | | | | | (76) all_233_1 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | SIMP: (76) implies:
% 17.98/3.20 | | | | | | | | | | | (77) all_233_1 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | COMBINE_EQS: (69), (75) imply:
% 17.98/3.20 | | | | | | | | | | | (78) all_221_3 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | SIMP: (78) implies:
% 17.98/3.20 | | | | | | | | | | | (79) all_221_3 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | COMBINE_EQS: (66), (77) imply:
% 17.98/3.20 | | | | | | | | | | | (80) all_201_0 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | COMBINE_EQS: (73), (79) imply:
% 17.98/3.20 | | | | | | | | | | | (81) all_201_1 = sz00
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | REDUCE: (30), (80), (81) imply:
% 17.98/3.20 | | | | | | | | | | | (82) $false
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | | CLOSE: (82) is inconsistent.
% 17.98/3.20 | | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | | End of split
% 17.98/3.20 | | | | | | | | | |
% 17.98/3.20 | | | | | | | | | End of split
% 17.98/3.20 | | | | | | | | |
% 17.98/3.20 | | | | | | | | End of split
% 17.98/3.20 | | | | | | | |
% 17.98/3.20 | | | | | | | End of split
% 17.98/3.20 | | | | | | |
% 17.98/3.20 | | | | | | End of split
% 17.98/3.20 | | | | | |
% 17.98/3.20 | | | | | End of split
% 17.98/3.20 | | | | |
% 17.98/3.20 | | | | End of split
% 17.98/3.20 | | | |
% 17.98/3.20 | | | End of split
% 17.98/3.20 | | |
% 17.98/3.20 | | End of split
% 17.98/3.20 | |
% 17.98/3.20 | End of split
% 17.98/3.20 |
% 17.98/3.20 End of proof
% 17.98/3.20 % SZS output end Proof for theBenchmark
% 17.98/3.20
% 17.98/3.20 2592ms
%------------------------------------------------------------------------------