TSTP Solution File: NUM465+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM465+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 : n005.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 11:47:55 EDT 2023
% Result : Theorem 33.61s 5.26s
% Output : Proof 35.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM465+2 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n005.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 10:54:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.24/1.12 Prover 1: Preprocessing ...
% 3.24/1.12 Prover 4: Preprocessing ...
% 3.24/1.15 Prover 2: Preprocessing ...
% 3.24/1.15 Prover 3: Preprocessing ...
% 3.24/1.15 Prover 5: Preprocessing ...
% 3.24/1.15 Prover 6: Preprocessing ...
% 3.24/1.15 Prover 0: Preprocessing ...
% 7.38/1.75 Prover 1: Constructing countermodel ...
% 7.38/1.75 Prover 3: Constructing countermodel ...
% 7.38/1.76 Prover 6: Proving ...
% 7.97/1.90 Prover 5: Constructing countermodel ...
% 8.65/1.99 Prover 2: Proving ...
% 8.65/2.03 Prover 4: Constructing countermodel ...
% 10.27/2.16 Prover 0: Proving ...
% 12.13/2.37 Prover 3: gave up
% 12.13/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.53/2.44 Prover 7: Preprocessing ...
% 13.38/2.61 Prover 7: Constructing countermodel ...
% 33.61/5.26 Prover 5: proved (4618ms)
% 33.61/5.26
% 33.61/5.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.61/5.26
% 33.61/5.27 Prover 2: stopped
% 33.61/5.27 Prover 6: stopped
% 34.05/5.29 Prover 0: stopped
% 34.05/5.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 34.05/5.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 34.05/5.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 34.05/5.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 34.05/5.31 Prover 7: Found proof (size 60)
% 34.05/5.31 Prover 7: proved (2928ms)
% 34.05/5.31 Prover 4: stopped
% 34.05/5.31 Prover 1: stopped
% 34.05/5.32 Prover 10: Preprocessing ...
% 34.05/5.33 Prover 8: Preprocessing ...
% 34.05/5.34 Prover 13: Preprocessing ...
% 34.05/5.35 Prover 11: Preprocessing ...
% 34.05/5.36 Prover 10: stopped
% 34.74/5.38 Prover 8: Warning: ignoring some quantifiers
% 34.74/5.38 Prover 13: stopped
% 34.74/5.39 Prover 8: Constructing countermodel ...
% 34.74/5.39 Prover 8: stopped
% 34.74/5.39 Prover 11: stopped
% 34.74/5.39
% 34.74/5.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.74/5.39
% 34.74/5.40 % SZS output start Proof for theBenchmark
% 34.74/5.40 Assumptions after simplification:
% 34.74/5.40 ---------------------------------
% 34.74/5.40
% 34.74/5.40 (mAMDistr)
% 35.04/5.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 35.04/5.44 $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~
% 35.04/5.44 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 35.04/5.44 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ?
% 35.04/5.44 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v5
% 35.04/5.44 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 &
% 35.04/5.44 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) &
% 35.04/5.44 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 35.04/5.44 : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0,
% 35.04/5.44 v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 35.04/5.44 $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.44 aNaturalNumber0(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 35.04/5.44 : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 &
% 35.04/5.44 sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 &
% 35.04/5.44 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] :
% 35.04/5.44 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v0) = v4) | ~
% 35.04/5.44 (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 35.04/5.44 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ?
% 35.04/5.44 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 35.04/5.44 (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 &
% 35.04/5.44 sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 &
% 35.04/5.44 sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 35.04/5.44 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 35.04/5.44 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 35.04/5.44 ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.44 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 35.04/5.44 : ? [v9: $i] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 &
% 35.04/5.44 sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 &
% 35.04/5.44 sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) &
% 35.04/5.44 $i(v6) & $i(v5) & $i(v4)))
% 35.04/5.44
% 35.04/5.44 (mAddComm)
% 35.04/5.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~
% 35.04/5.44 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 35.04/5.44 (sdtpldt0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 35.04/5.44 : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1)
% 35.04/5.44 | ~ aNaturalNumber0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 35.04/5.44
% 35.04/5.44 (mDefLE)
% 35.04/5.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~
% 35.04/5.44 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 35.04/5.44 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 35.04/5.44 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~
% 35.04/5.44 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0,
% 35.04/5.44 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 35.04/5.44
% 35.04/5.44 (mLETotal)
% 35.04/5.45 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) |
% 35.04/5.45 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 35.04/5.45 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 35.04/5.45
% 35.04/5.45 (mMonMul)
% 35.04/5.46 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 35.04/5.46 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) =
% 35.04/5.46 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~
% 35.04/5.46 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 35.04/5.46 sdtlseqdt0(v3, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 35.04/5.46 : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~
% 35.04/5.46 (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 35.04/5.46 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.46 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) &
% 35.04/5.46 sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & $i(v6) & $i(v5) &
% 35.04/5.46 sdtlseqdt0(v5, v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 35.04/5.46 $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~
% 35.04/5.46 (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 35.04/5.46 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.46 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & ~ (v5 =
% 35.04/5.46 v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & $i(v6) & $i(v5) &
% 35.04/5.46 sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0: $i] : ! [v1: $i] : !
% 35.04/5.46 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1,
% 35.04/5.46 v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 35.04/5.46 $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~
% 35.04/5.46 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : (
% 35.04/5.46 ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5
% 35.04/5.46 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0:
% 35.04/5.46 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0
% 35.04/5.46 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2)
% 35.04/5.46 | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) |
% 35.04/5.46 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & !
% 35.04/5.46 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 |
% 35.04/5.46 v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 35.04/5.46 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~
% 35.04/5.46 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ?
% 35.04/5.46 [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 &
% 35.04/5.46 sdtasdt0(v1, v0) = v5 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v6))) & ! [v0:
% 35.04/5.46 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~
% 35.04/5.46 (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1)
% 35.04/5.46 | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~
% 35.04/5.46 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] :
% 35.04/5.46 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) |
% 35.04/5.46 ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 35.04/5.46 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.46 aNaturalNumber0(v0))
% 35.04/5.46
% 35.04/5.46 (mSortsC_01)
% 35.04/5.46 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 35.04/5.46
% 35.04/5.46 (m_MulUnit)
% 35.04/5.46 $i(sz10) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1)
% 35.04/5.46 | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0
% 35.04/5.46 | ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & !
% 35.04/5.46 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ $i(v0) | ~
% 35.04/5.46 aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0: $i] : ! [v1: $i] :
% 35.04/5.46 ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 35.04/5.46 sdtasdt0(v0, sz10) = v0)
% 35.04/5.46
% 35.04/5.46 (m_MulZero)
% 35.04/5.46 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) =
% 35.04/5.46 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] :
% 35.04/5.46 (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~
% 35.04/5.46 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) =
% 35.04/5.46 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & !
% 35.04/5.46 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~
% 35.04/5.46 aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 35.04/5.46
% 35.04/5.46 (m__)
% 35.04/5.46 $i(xn) & $i(xm) & $i(sz00) & ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm)
% 35.04/5.46 = v0 & $i(v0) & ~ sdtlseqdt0(xn, v0) & ! [v1: $i] : ( ~ (sdtpldt0(xn, v1)
% 35.04/5.46 = v0) | ~ $i(v1) | ~ aNaturalNumber0(v1)))
% 35.04/5.46
% 35.04/5.46 (m__1007)
% 35.04/5.46 $i(xm) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ($i(v0) & (xm =
% 35.04/5.46 sz00 | (v1 = xm & sdtpldt0(sz10, v0) = xm & sdtlseqdt0(sz10, xm) &
% 35.04/5.46 aNaturalNumber0(v0))))
% 35.04/5.46
% 35.04/5.46 (m__987)
% 35.04/5.46 $i(xn) & $i(xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm)
% 35.04/5.46
% 35.04/5.46 Further assumptions not needed in the proof:
% 35.04/5.46 --------------------------------------------
% 35.04/5.46 mAddAsso, mAddCanc, mDefDiff, mLEAsym, mLENTr, mLERefl, mLETran, mMonAdd,
% 35.04/5.46 mMulAsso, mMulCanc, mMulComm, mNatSort, mSortsB, mSortsB_02, mSortsC, mZeroAdd,
% 35.04/5.46 mZeroMul, m_AddZero
% 35.04/5.46
% 35.04/5.46 Those formulas are unsatisfiable:
% 35.04/5.46 ---------------------------------
% 35.04/5.46
% 35.04/5.46 Begin of proof
% 35.04/5.46 |
% 35.04/5.47 | ALPHA: (mSortsC_01) implies:
% 35.04/5.47 | (1) aNaturalNumber0(sz10)
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (mAddComm) implies:
% 35.04/5.47 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 35.04/5.47 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.47 | aNaturalNumber0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 35.04/5.47 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) |
% 35.04/5.47 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.47 | aNaturalNumber0(v0) | (sdtpldt0(v0, v1) = v2 & $i(v2)))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (m_MulUnit) implies:
% 35.04/5.47 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) |
% 35.04/5.47 | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (m_MulZero) implies:
% 35.04/5.47 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) |
% 35.04/5.47 | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (mAMDistr) implies:
% 35.04/5.47 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 35.04/5.47 | ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 35.04/5.47 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 35.04/5.47 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6:
% 35.04/5.47 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v3, v0) =
% 35.04/5.47 | v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0,
% 35.04/5.47 | v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 &
% 35.04/5.47 | sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 35.04/5.47 | & $i(v4)))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (mDefLE) implies:
% 35.04/5.47 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0,
% 35.04/5.47 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 35.04/5.47 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (mLETotal) implies:
% 35.04/5.47 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 35.04/5.47 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) |
% 35.04/5.47 | sdtlseqdt0(v0, v1))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (mMonMul) implies:
% 35.04/5.47 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 35.04/5.47 | (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0,
% 35.04/5.47 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1,
% 35.04/5.47 | v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 35.04/5.47 | aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (m__987) implies:
% 35.04/5.47 | (10) aNaturalNumber0(xm)
% 35.04/5.47 | (11) aNaturalNumber0(xn)
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (m__1007) implies:
% 35.04/5.47 | (12) $i(sz10)
% 35.04/5.47 | (13) ? [v0: $i] : ? [v1: $i] : ($i(v0) & (xm = sz00 | (v1 = xm &
% 35.04/5.47 | sdtpldt0(sz10, v0) = xm & sdtlseqdt0(sz10, xm) &
% 35.04/5.47 | aNaturalNumber0(v0))))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (m__) implies:
% 35.04/5.47 | (14) $i(xm)
% 35.04/5.47 | (15) $i(xn)
% 35.04/5.47 | (16) ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm) = v0 & $i(v0) & ~
% 35.04/5.47 | sdtlseqdt0(xn, v0) & ! [v1: $i] : ( ~ (sdtpldt0(xn, v1) = v0) | ~
% 35.04/5.47 | $i(v1) | ~ aNaturalNumber0(v1)))
% 35.04/5.47 |
% 35.04/5.47 | DELTA: instantiating (13) with fresh symbols all_27_0, all_27_1 gives:
% 35.04/5.47 | (17) $i(all_27_1) & (xm = sz00 | (all_27_0 = xm & sdtpldt0(sz10, all_27_1)
% 35.04/5.47 | = xm & sdtlseqdt0(sz10, xm) & aNaturalNumber0(all_27_1)))
% 35.04/5.47 |
% 35.04/5.47 | ALPHA: (17) implies:
% 35.04/5.48 | (18) $i(all_27_1)
% 35.04/5.48 | (19) xm = sz00 | (all_27_0 = xm & sdtpldt0(sz10, all_27_1) = xm &
% 35.04/5.48 | sdtlseqdt0(sz10, xm) & aNaturalNumber0(all_27_1))
% 35.04/5.48 |
% 35.04/5.48 | DELTA: instantiating (16) with fresh symbol all_29_0 gives:
% 35.04/5.48 | (20) ~ (xm = sz00) & sdtasdt0(xn, xm) = all_29_0 & $i(all_29_0) & ~
% 35.04/5.48 | sdtlseqdt0(xn, all_29_0) & ! [v0: $i] : ( ~ (sdtpldt0(xn, v0) =
% 35.04/5.48 | all_29_0) | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 35.04/5.48 |
% 35.04/5.48 | ALPHA: (20) implies:
% 35.04/5.48 | (21) ~ (xm = sz00)
% 35.04/5.48 | (22) ~ sdtlseqdt0(xn, all_29_0)
% 35.04/5.48 | (23) sdtasdt0(xn, xm) = all_29_0
% 35.04/5.48 |
% 35.04/5.48 | BETA: splitting (19) gives:
% 35.04/5.48 |
% 35.04/5.48 | Case 1:
% 35.04/5.48 | |
% 35.04/5.48 | | (24) xm = sz00
% 35.04/5.48 | |
% 35.04/5.48 | | REDUCE: (21), (24) imply:
% 35.04/5.48 | | (25) $false
% 35.04/5.48 | |
% 35.04/5.48 | | CLOSE: (25) is inconsistent.
% 35.04/5.48 | |
% 35.04/5.48 | Case 2:
% 35.04/5.48 | |
% 35.04/5.48 | | (26) all_27_0 = xm & sdtpldt0(sz10, all_27_1) = xm & sdtlseqdt0(sz10, xm)
% 35.04/5.48 | | & aNaturalNumber0(all_27_1)
% 35.04/5.48 | |
% 35.04/5.48 | | ALPHA: (26) implies:
% 35.04/5.48 | | (27) aNaturalNumber0(all_27_1)
% 35.04/5.48 | | (28) sdtlseqdt0(sz10, xm)
% 35.04/5.48 | | (29) sdtpldt0(sz10, all_27_1) = xm
% 35.04/5.48 | |
% 35.04/5.48 | | GROUND_INST: instantiating (8) with xn, xn, simplifying with (11), (15)
% 35.04/5.48 | | gives:
% 35.04/5.48 | | (30) sdtlseqdt0(xn, xn)
% 35.04/5.48 | |
% 35.04/5.48 | | GROUND_INST: instantiating (7) with sz10, xm, simplifying with (1), (10),
% 35.04/5.48 | | (12), (14), (28) gives:
% 35.04/5.48 | | (31) ? [v0: $i] : (sdtpldt0(sz10, v0) = xm & $i(v0) &
% 35.04/5.48 | | aNaturalNumber0(v0))
% 35.04/5.48 | |
% 35.04/5.48 | | GROUND_INST: instantiating (2) with sz10, all_27_1, xm, simplifying with
% 35.04/5.48 | | (1), (12), (18), (27), (29) gives:
% 35.04/5.48 | | (32) sdtpldt0(all_27_1, sz10) = xm & $i(xm)
% 35.04/5.48 | |
% 35.04/5.48 | | GROUND_INST: instantiating (6) with xn, sz10, all_27_1, xm, all_29_0,
% 35.04/5.48 | | simplifying with (1), (11), (12), (15), (18), (23), (27), (29)
% 35.04/5.48 | | gives:
% 35.04/5.48 | | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 35.04/5.48 | | : (sdtasdt0(all_27_1, xn) = v4 & sdtasdt0(xn, all_27_1) = v1 &
% 35.04/5.48 | | sdtasdt0(xn, sz10) = v0 & sdtasdt0(xm, xn) = v2 & sdtasdt0(sz10,
% 35.04/5.48 | | xn) = v3 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_29_0 &
% 35.04/5.48 | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_29_0))
% 35.04/5.48 | |
% 35.04/5.48 | | GROUND_INST: instantiating (4) with xn, all_29_0, simplifying with (11),
% 35.04/5.48 | | (15) gives:
% 35.04/5.48 | | (34) all_29_0 = xn | ~ (sdtasdt0(xn, sz10) = all_29_0)
% 35.04/5.48 | |
% 35.04/5.48 | | GROUND_INST: instantiating (5) with xm, all_29_0, simplifying with (10),
% 35.04/5.48 | | (14) gives:
% 35.04/5.48 | | (35) all_29_0 = sz00 | ~ (sdtasdt0(sz00, xm) = all_29_0)
% 35.04/5.48 | |
% 35.04/5.48 | | DELTA: instantiating (31) with fresh symbol all_42_0 gives:
% 35.04/5.48 | | (36) sdtpldt0(sz10, all_42_0) = xm & $i(all_42_0) &
% 35.04/5.48 | | aNaturalNumber0(all_42_0)
% 35.04/5.48 | |
% 35.04/5.48 | | ALPHA: (36) implies:
% 35.04/5.48 | | (37) aNaturalNumber0(all_42_0)
% 35.04/5.48 | | (38) $i(all_42_0)
% 35.04/5.49 | | (39) sdtpldt0(sz10, all_42_0) = xm
% 35.04/5.49 | |
% 35.04/5.49 | | DELTA: instantiating (33) with fresh symbols all_44_0, all_44_1, all_44_2,
% 35.04/5.49 | | all_44_3, all_44_4 gives:
% 35.04/5.49 | | (40) sdtasdt0(all_27_1, xn) = all_44_0 & sdtasdt0(xn, all_27_1) =
% 35.04/5.49 | | all_44_3 & sdtasdt0(xn, sz10) = all_44_4 & sdtasdt0(xm, xn) =
% 35.04/5.49 | | all_44_2 & sdtasdt0(sz10, xn) = all_44_1 & sdtpldt0(all_44_1,
% 35.04/5.49 | | all_44_0) = all_44_2 & sdtpldt0(all_44_4, all_44_3) = all_29_0 &
% 35.04/5.49 | | $i(all_44_0) & $i(all_44_1) & $i(all_44_2) & $i(all_44_3) &
% 35.04/5.49 | | $i(all_44_4) & $i(all_29_0)
% 35.04/5.49 | |
% 35.04/5.49 | | ALPHA: (40) implies:
% 35.04/5.49 | | (41) sdtasdt0(xn, sz10) = all_44_4
% 35.04/5.49 | |
% 35.04/5.49 | | PRED_UNIFY: (22), (30) imply:
% 35.04/5.49 | | (42) ~ (all_29_0 = xn)
% 35.04/5.49 | |
% 35.04/5.49 | | BETA: splitting (34) gives:
% 35.04/5.49 | |
% 35.04/5.49 | | Case 1:
% 35.04/5.49 | | |
% 35.04/5.49 | | | (43) ~ (sdtasdt0(xn, sz10) = all_29_0)
% 35.04/5.49 | | |
% 35.04/5.49 | | | PRED_UNIFY: (23), (43) imply:
% 35.04/5.49 | | | (44) ~ (xm = sz10)
% 35.04/5.49 | | |
% 35.04/5.49 | | | PRED_UNIFY: (41), (43) imply:
% 35.04/5.49 | | | (45) ~ (all_44_4 = all_29_0)
% 35.04/5.49 | | |
% 35.04/5.49 | | | GROUND_INST: instantiating (3) with all_42_0, sz10, xm, simplifying with
% 35.04/5.49 | | | (1), (12), (37), (38), (39) gives:
% 35.04/5.49 | | | (46) sdtpldt0(all_42_0, sz10) = xm & $i(xm)
% 35.04/5.49 | | |
% 35.04/5.49 | | | GROUND_INST: instantiating (9) with xn, sz10, xm, all_44_4, all_29_0,
% 35.04/5.49 | | | simplifying with (1), (10), (11), (12), (14), (15), (23),
% 35.04/5.49 | | | (28), (41) gives:
% 35.04/5.49 | | | (47) xn = sz00 | xm = sz10 | sdtlseqdt0(all_44_4, all_29_0)
% 35.04/5.49 | | |
% 35.04/5.49 | | | GROUND_INST: instantiating (4) with xn, all_44_4, simplifying with (11),
% 35.04/5.49 | | | (15), (41) gives:
% 35.04/5.49 | | | (48) all_44_4 = xn
% 35.04/5.49 | | |
% 35.04/5.49 | | | REDUCE: (45), (48) imply:
% 35.04/5.49 | | | (49) ~ (all_29_0 = xn)
% 35.04/5.49 | | |
% 35.04/5.49 | | | BETA: splitting (47) gives:
% 35.04/5.49 | | |
% 35.04/5.49 | | | Case 1:
% 35.04/5.49 | | | |
% 35.04/5.49 | | | | (50) sdtlseqdt0(all_44_4, all_29_0)
% 35.04/5.49 | | | |
% 35.04/5.49 | | | | REDUCE: (48), (50) imply:
% 35.04/5.49 | | | | (51) sdtlseqdt0(xn, all_29_0)
% 35.04/5.49 | | | |
% 35.04/5.49 | | | | PRED_UNIFY: (22), (51) imply:
% 35.04/5.49 | | | | (52) $false
% 35.04/5.49 | | | |
% 35.04/5.49 | | | | CLOSE: (52) is inconsistent.
% 35.04/5.49 | | | |
% 35.04/5.49 | | | Case 2:
% 35.04/5.49 | | | |
% 35.04/5.49 | | | | (53) xn = sz00 | xm = sz10
% 35.04/5.49 | | | |
% 35.04/5.49 | | | | BETA: splitting (53) gives:
% 35.04/5.49 | | | |
% 35.04/5.49 | | | | Case 1:
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | (54) xn = sz00
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | REDUCE: (42), (54) imply:
% 35.04/5.49 | | | | | (55) ~ (all_29_0 = sz00)
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | REDUCE: (23), (54) imply:
% 35.04/5.49 | | | | | (56) sdtasdt0(sz00, xm) = all_29_0
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | BETA: splitting (35) gives:
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | Case 1:
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | | (57) ~ (sdtasdt0(sz00, xm) = all_29_0)
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | | PRED_UNIFY: (56), (57) imply:
% 35.04/5.49 | | | | | | (58) $false
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | | CLOSE: (58) is inconsistent.
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | Case 2:
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | | (59) all_29_0 = sz00
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | | REDUCE: (55), (59) imply:
% 35.04/5.49 | | | | | | (60) $false
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | | CLOSE: (60) is inconsistent.
% 35.04/5.49 | | | | | |
% 35.04/5.49 | | | | | End of split
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | Case 2:
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | (61) xm = sz10
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | REDUCE: (44), (61) imply:
% 35.04/5.49 | | | | | (62) $false
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | | CLOSE: (62) is inconsistent.
% 35.04/5.49 | | | | |
% 35.04/5.49 | | | | End of split
% 35.04/5.49 | | | |
% 35.04/5.49 | | | End of split
% 35.04/5.49 | | |
% 35.04/5.49 | | Case 2:
% 35.04/5.49 | | |
% 35.04/5.49 | | | (63) all_29_0 = xn
% 35.04/5.49 | | |
% 35.04/5.49 | | | REDUCE: (42), (63) imply:
% 35.04/5.49 | | | (64) $false
% 35.04/5.49 | | |
% 35.04/5.49 | | | CLOSE: (64) is inconsistent.
% 35.04/5.49 | | |
% 35.04/5.49 | | End of split
% 35.04/5.49 | |
% 35.04/5.49 | End of split
% 35.04/5.49 |
% 35.04/5.49 End of proof
% 35.04/5.49 % SZS output end Proof for theBenchmark
% 35.04/5.49
% 35.04/5.49 4876ms
%------------------------------------------------------------------------------