TSTP Solution File: NUM463+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM463+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 : n002.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 11:47:54 EDT 2023
% Result : Theorem 127.01s 17.45s
% Output : Proof 128.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM463+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:56:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 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
% 2.99/1.09 Prover 1: Preprocessing ...
% 2.99/1.09 Prover 4: Preprocessing ...
% 3.32/1.14 Prover 5: Preprocessing ...
% 3.32/1.14 Prover 3: Preprocessing ...
% 3.32/1.14 Prover 6: Preprocessing ...
% 3.32/1.14 Prover 2: Preprocessing ...
% 3.32/1.14 Prover 0: Preprocessing ...
% 7.20/1.65 Prover 1: Constructing countermodel ...
% 7.78/1.73 Prover 3: Constructing countermodel ...
% 7.78/1.74 Prover 6: Proving ...
% 7.91/1.80 Prover 5: Constructing countermodel ...
% 8.76/1.93 Prover 2: Proving ...
% 8.76/1.99 Prover 4: Constructing countermodel ...
% 10.02/2.07 Prover 3: gave up
% 10.02/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.68/2.16 Prover 0: Proving ...
% 10.68/2.16 Prover 7: Preprocessing ...
% 11.42/2.28 Prover 1: gave up
% 11.82/2.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.82/2.35 Prover 8: Preprocessing ...
% 12.29/2.40 Prover 7: Constructing countermodel ...
% 13.03/2.48 Prover 8: Warning: ignoring some quantifiers
% 13.03/2.48 Prover 8: Constructing countermodel ...
% 15.01/2.72 Prover 8: gave up
% 15.01/2.73 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 15.01/2.78 Prover 9: Preprocessing ...
% 18.71/3.19 Prover 9: Constructing countermodel ...
% 63.96/9.05 Prover 2: stopped
% 64.00/9.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 64.34/9.13 Prover 10: Preprocessing ...
% 64.66/9.19 Prover 10: Constructing countermodel ...
% 100.46/13.96 Prover 5: stopped
% 100.46/13.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 101.29/14.04 Prover 11: Preprocessing ...
% 102.85/14.28 Prover 11: Constructing countermodel ...
% 127.01/17.45 Prover 7: Found proof (size 170)
% 127.01/17.45 Prover 7: proved (15240ms)
% 127.01/17.45 Prover 0: stopped
% 127.01/17.45 Prover 6: stopped
% 127.01/17.45 Prover 9: stopped
% 127.01/17.45 Prover 11: stopped
% 127.01/17.45 Prover 10: stopped
% 127.01/17.45 Prover 4: stopped
% 127.01/17.45
% 127.01/17.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 127.01/17.45
% 127.29/17.47 % SZS output start Proof for theBenchmark
% 127.29/17.47 Assumptions after simplification:
% 127.29/17.47 ---------------------------------
% 127.29/17.47
% 127.29/17.47 (mAMDistr)
% 127.29/17.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 127.29/17.52 $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~
% 127.29/17.52 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.29/17.52 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ?
% 127.29/17.52 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v5
% 127.29/17.52 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 &
% 127.29/17.52 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) &
% 127.29/17.52 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 127.29/17.52 : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0,
% 127.29/17.52 v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 127.29/17.52 $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 127.29/17.52 aNaturalNumber0(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 127.29/17.52 : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 &
% 127.29/17.52 sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 &
% 127.29/17.52 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] :
% 127.29/17.52 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v0) = v4) | ~
% 127.29/17.52 (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.29/17.52 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ?
% 127.29/17.52 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 127.29/17.52 (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 &
% 127.29/17.52 sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 &
% 127.29/17.52 sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 127.29/17.52 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 127.29/17.52 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 127.29/17.52 ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 127.29/17.52 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 127.29/17.52 : ? [v9: $i] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 &
% 127.29/17.52 sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 &
% 127.29/17.52 sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) &
% 127.29/17.52 $i(v6) & $i(v5) & $i(v4)))
% 127.29/17.52
% 127.29/17.52 (mAddComm)
% 127.29/17.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~
% 127.29/17.52 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 127.29/17.52 (sdtpldt0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.29/17.52 : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1)
% 127.29/17.52 | ~ aNaturalNumber0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2)))
% 127.29/17.52
% 127.29/17.52 (mDefLE)
% 127.29/17.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~
% 127.29/17.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 127.29/17.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 127.29/17.53 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~
% 127.29/17.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0,
% 127.29/17.53 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 127.29/17.53
% 127.29/17.53 (mLENTr)
% 127.29/17.53 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 127.29/17.53 aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 127.29/17.53
% 127.29/17.53 (mLETotal)
% 127.29/17.53 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) |
% 127.29/17.53 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 127.29/17.53 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 127.29/17.53
% 127.29/17.53 (mMonAdd)
% 127.66/17.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.66/17.54 (sdtpldt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.54 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 127.66/17.54 aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 =
% 127.66/17.54 v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 &
% 127.66/17.54 sdtpldt0(v0, v2) = v5 & $i(v6) & $i(v5) & $i(v4) & sdtlseqdt0(v5, v6) &
% 127.66/17.54 sdtlseqdt0(v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 127.66/17.54 $i] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 127.66/17.54 $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~
% 127.66/17.54 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] :
% 127.66/17.54 ? [v6: $i] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 &
% 127.66/17.54 sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & $i(v6) & $i(v5) & $i(v4) &
% 127.66/17.54 sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0: $i] : ! [v1: $i] : !
% 127.66/17.54 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 127.66/17.54 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~
% 127.66/17.54 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] :
% 127.66/17.54 ? [v6: $i] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 &
% 127.66/17.54 sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & $i(v6) & $i(v5) & $i(v4) &
% 127.66/17.54 sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0: $i] : ! [v1: $i] : !
% 127.66/17.54 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) |
% 127.66/17.54 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~
% 127.66/17.54 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] :
% 127.66/17.54 ? [v6: $i] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 &
% 127.66/17.54 sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) &
% 127.66/17.54 sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 127.66/17.54
% 127.66/17.54 (mMonMul)
% 127.66/17.55 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 127.66/17.55 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) =
% 127.66/17.55 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~
% 127.66/17.55 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 127.66/17.55 sdtlseqdt0(v3, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 127.66/17.55 : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~
% 127.66/17.55 (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.55 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 127.66/17.55 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) &
% 127.66/17.55 sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & $i(v6) & $i(v5) &
% 127.66/17.55 sdtlseqdt0(v5, v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 127.66/17.55 $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~
% 127.66/17.55 (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.55 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 127.66/17.55 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & ~ (v5 =
% 127.66/17.55 v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & $i(v6) & $i(v5) &
% 127.66/17.55 sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0: $i] : ! [v1: $i] : !
% 127.66/17.55 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1,
% 127.66/17.55 v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 127.66/17.55 $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~
% 127.66/17.55 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : (
% 127.66/17.55 ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5
% 127.66/17.55 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0:
% 127.66/17.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0
% 127.66/17.55 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2)
% 127.66/17.55 | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) |
% 127.66/17.55 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & !
% 127.66/17.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 |
% 127.66/17.55 v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 127.66/17.55 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~
% 127.66/17.55 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ?
% 127.66/17.55 [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 &
% 127.66/17.55 sdtasdt0(v1, v0) = v5 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v6))) & ! [v0:
% 127.66/17.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~
% 127.66/17.55 (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1)
% 127.66/17.55 | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~
% 127.66/17.55 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] :
% 127.66/17.55 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) |
% 127.66/17.55 ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.55 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~
% 127.66/17.55 aNaturalNumber0(v0))
% 127.66/17.55
% 127.66/17.55 (mMulComm)
% 127.66/17.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~
% 127.66/17.55 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 127.66/17.55 (sdtasdt0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 127.66/17.55 : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1)
% 127.66/17.55 | ~ aNaturalNumber0(v0) | (sdtasdt0(v1, v0) = v2 & $i(v2)))
% 127.66/17.55
% 127.66/17.55 (mSortsB_02)
% 127.66/17.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 127.66/17.55 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 127.66/17.55 aNaturalNumber0(v2))
% 127.66/17.55
% 127.66/17.55 (mSortsC_01)
% 127.66/17.55 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10)
% 127.66/17.55
% 127.66/17.55 (m_MulUnit)
% 127.66/17.56 $i(sz10) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1)
% 127.66/17.56 | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0
% 127.66/17.56 | ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & !
% 127.66/17.56 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ $i(v0) | ~
% 127.66/17.56 aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0: $i] : ! [v1: $i] :
% 127.66/17.56 ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 127.66/17.56 sdtasdt0(v0, sz10) = v0)
% 127.66/17.56
% 127.66/17.56 (m_MulZero)
% 127.66/17.56 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) =
% 127.66/17.56 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] :
% 127.66/17.56 (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~
% 127.66/17.56 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) =
% 127.66/17.56 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & !
% 127.66/17.56 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~
% 127.66/17.56 aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 127.66/17.56
% 127.66/17.56 (m__)
% 127.66/17.56 $i(xn) & $i(xm) & $i(sz00) & ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm)
% 127.66/17.56 = v0 & $i(v0) & ~ sdtlseqdt0(xn, v0))
% 127.66/17.56
% 127.66/17.56 (m__987)
% 127.66/17.56 $i(xn) & $i(xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm)
% 127.66/17.56
% 127.66/17.56 (function-axioms)
% 127.66/17.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.66/17.56 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 127.66/17.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) |
% 127.66/17.56 ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 127.66/17.56 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 127.66/17.56
% 127.66/17.56 Further assumptions not needed in the proof:
% 127.66/17.56 --------------------------------------------
% 127.66/17.56 mAddAsso, mAddCanc, mDefDiff, mLEAsym, mLERefl, mLETran, mMulAsso, mMulCanc,
% 127.66/17.56 mNatSort, mSortsB, mSortsC, mZeroAdd, mZeroMul, m_AddZero
% 127.66/17.56
% 127.66/17.56 Those formulas are unsatisfiable:
% 127.66/17.56 ---------------------------------
% 127.66/17.56
% 127.66/17.56 Begin of proof
% 127.66/17.56 |
% 127.66/17.56 | ALPHA: (mSortsC_01) implies:
% 127.66/17.56 | (1) aNaturalNumber0(sz10)
% 127.66/17.56 |
% 127.66/17.56 | ALPHA: (mAddComm) implies:
% 127.66/17.56 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) |
% 127.66/17.56 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 127.66/17.56 | aNaturalNumber0(v0) | (sdtpldt0(v0, v1) = v2 & $i(v2)))
% 127.66/17.56 |
% 127.66/17.56 | ALPHA: (mMulComm) implies:
% 127.66/17.56 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) |
% 127.66/17.56 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~
% 127.66/17.56 | aNaturalNumber0(v0) | (sdtasdt0(v0, v1) = v2 & $i(v2)))
% 127.66/17.56 |
% 127.66/17.56 | ALPHA: (m_MulUnit) implies:
% 127.66/17.56 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) |
% 127.66/17.56 | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 127.66/17.57 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) |
% 127.66/17.57 | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 127.66/17.57 |
% 127.66/17.57 | ALPHA: (m_MulZero) implies:
% 127.66/17.57 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) |
% 127.66/17.57 | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 127.66/17.57 |
% 127.66/17.57 | ALPHA: (mAMDistr) implies:
% 127.66/17.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 127.66/17.57 | ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 127.66/17.57 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 127.66/17.57 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6:
% 127.66/17.57 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v3, v0) =
% 127.66/17.57 | v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0,
% 127.66/17.57 | v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 &
% 127.66/17.57 | sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 127.66/17.57 | & $i(v4)))
% 127.66/17.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 127.66/17.57 | ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) |
% 127.66/17.57 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 127.66/17.57 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6:
% 127.66/17.57 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v2, v0) =
% 127.66/17.57 | v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0,
% 127.66/17.57 | v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 &
% 127.66/17.57 | sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)
% 127.66/17.57 | & $i(v4)))
% 127.66/17.57 |
% 127.66/17.57 | ALPHA: (mDefLE) implies:
% 127.66/17.57 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0,
% 127.66/17.57 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i]
% 127.66/17.57 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 127.66/17.57 |
% 127.66/17.57 | ALPHA: (mLETotal) implies:
% 127.66/17.57 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.57 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) |
% 127.66/17.57 | sdtlseqdt0(v0, v1))
% 127.66/17.57 |
% 127.66/17.57 | ALPHA: (mMonAdd) implies:
% 127.66/17.57 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.66/17.57 | (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.57 | sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)
% 127.66/17.57 | | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 127.66/17.57 | ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2,
% 127.66/17.57 | v0) = v4 & sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) &
% 127.66/17.57 | sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 127.66/17.57 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.66/17.57 | (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.57 | sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)
% 127.66/17.57 | | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 127.66/17.57 | ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2,
% 127.66/17.57 | v0) = v4 & sdtpldt0(v0, v2) = v6 & $i(v6) & $i(v5) & $i(v4) &
% 127.66/17.57 | sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5)))
% 127.66/17.57 |
% 127.66/17.57 | ALPHA: (mMonMul) implies:
% 127.66/17.57 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 127.66/17.57 | (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1,
% 127.66/17.57 | v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 127.66/17.57 | sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)
% 127.66/17.57 | | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 127.66/17.57 |
% 127.66/17.57 | ALPHA: (mLENTr) implies:
% 127.66/17.57 | (14) $i(sz10)
% 127.66/17.58 | (15) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~
% 127.66/17.58 | aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 127.66/17.58 |
% 127.66/17.58 | ALPHA: (m__987) implies:
% 127.66/17.58 | (16) aNaturalNumber0(xm)
% 127.66/17.58 | (17) aNaturalNumber0(xn)
% 127.66/17.58 |
% 127.66/17.58 | ALPHA: (m__) implies:
% 127.86/17.58 | (18) $i(xm)
% 127.86/17.58 | (19) $i(xn)
% 127.86/17.58 | (20) ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm) = v0 & $i(v0) & ~
% 127.86/17.58 | sdtlseqdt0(xn, v0))
% 127.86/17.58 |
% 127.86/17.58 | ALPHA: (function-axioms) implies:
% 127.86/17.58 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.86/17.58 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 127.86/17.58 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 127.86/17.58 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 127.86/17.58 |
% 127.86/17.58 | DELTA: instantiating (20) with fresh symbol all_27_0 gives:
% 127.86/17.58 | (23) ~ (xm = sz00) & sdtasdt0(xn, xm) = all_27_0 & $i(all_27_0) & ~
% 127.86/17.58 | sdtlseqdt0(xn, all_27_0)
% 127.86/17.58 |
% 127.86/17.58 | ALPHA: (23) implies:
% 127.86/17.58 | (24) ~ (xm = sz00)
% 127.86/17.58 | (25) ~ sdtlseqdt0(xn, all_27_0)
% 127.86/17.58 | (26) sdtasdt0(xn, xm) = all_27_0
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (10) with sz10, sz10, simplifying with (1), (14)
% 127.86/17.58 | gives:
% 127.86/17.58 | (27) sdtlseqdt0(sz10, sz10)
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (10) with xm, xm, simplifying with (16), (18)
% 127.86/17.58 | gives:
% 127.86/17.58 | (28) sdtlseqdt0(xm, xm)
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (15) with xm, simplifying with (16), (18) gives:
% 127.86/17.58 | (29) xm = sz10 | xm = sz00 | sdtlseqdt0(sz10, xm)
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (10) with xn, xn, simplifying with (17), (19)
% 127.86/17.58 | gives:
% 127.86/17.58 | (30) sdtlseqdt0(xn, xn)
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (3) with xm, xn, all_27_0, simplifying with (16),
% 127.86/17.58 | (17), (18), (19), (26) gives:
% 127.86/17.58 | (31) sdtasdt0(xm, xn) = all_27_0 & $i(all_27_0)
% 127.86/17.58 |
% 127.86/17.58 | ALPHA: (31) implies:
% 127.86/17.58 | (32) $i(all_27_0)
% 127.86/17.58 | (33) sdtasdt0(xm, xn) = all_27_0
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_27_0, simplifying
% 127.86/17.58 | with (16), (17), (18), (19), (26) gives:
% 127.86/17.58 | (34) aNaturalNumber0(all_27_0)
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (5) with xn, all_27_0, simplifying with (17), (19)
% 127.86/17.58 | gives:
% 127.86/17.58 | (35) all_27_0 = xn | ~ (sdtasdt0(xn, sz10) = all_27_0)
% 127.86/17.58 |
% 127.86/17.58 | GROUND_INST: instantiating (6) with xm, all_27_0, simplifying with (16), (18)
% 127.86/17.58 | gives:
% 127.86/17.58 | (36) all_27_0 = sz00 | ~ (sdtasdt0(sz00, xm) = all_27_0)
% 127.86/17.58 |
% 127.86/17.58 | PRED_UNIFY: (25), (30) imply:
% 127.86/17.58 | (37) ~ (all_27_0 = xn)
% 127.86/17.58 |
% 127.86/17.58 | BETA: splitting (35) gives:
% 127.86/17.58 |
% 127.86/17.58 | Case 1:
% 127.86/17.58 | |
% 127.86/17.58 | | (38) ~ (sdtasdt0(xn, sz10) = all_27_0)
% 127.86/17.58 | |
% 127.86/17.58 | | PRED_UNIFY: (26), (38) imply:
% 127.86/17.58 | | (39) ~ (xm = sz10)
% 127.86/17.58 | |
% 127.86/17.58 | | BETA: splitting (29) gives:
% 127.86/17.58 | |
% 127.86/17.59 | | Case 1:
% 127.86/17.59 | | |
% 127.86/17.59 | | | (40) sdtlseqdt0(sz10, xm)
% 127.86/17.59 | | |
% 127.86/17.59 | | | GROUND_INST: instantiating (10) with xn, all_27_0, simplifying with (17),
% 127.86/17.59 | | | (19), (25), (32), (34) gives:
% 127.86/17.59 | | | (41) sdtlseqdt0(all_27_0, xn)
% 127.86/17.59 | | |
% 127.86/17.59 | | | GROUND_INST: instantiating (9) with sz10, sz10, simplifying with (1),
% 127.86/17.59 | | | (14), (27) gives:
% 127.86/17.59 | | | (42) ? [v0: $i] : (sdtpldt0(sz10, v0) = sz10 & $i(v0) &
% 127.86/17.59 | | | aNaturalNumber0(v0))
% 127.86/17.59 | | |
% 127.86/17.59 | | | GROUND_INST: instantiating (9) with sz10, xm, simplifying with (1), (14),
% 127.86/17.59 | | | (16), (18), (40) gives:
% 127.86/17.59 | | | (43) ? [v0: $i] : (sdtpldt0(sz10, v0) = xm & $i(v0) &
% 127.86/17.59 | | | aNaturalNumber0(v0))
% 127.86/17.59 | | |
% 127.86/17.59 | | | GROUND_INST: instantiating (9) with xm, xm, simplifying with (16), (18),
% 127.86/17.59 | | | (28) gives:
% 127.86/17.59 | | | (44) ? [v0: $i] : (sdtpldt0(xm, v0) = xm & $i(v0) &
% 127.86/17.59 | | | aNaturalNumber0(v0))
% 127.86/17.59 | | |
% 127.86/17.59 | | | GROUND_INST: instantiating (9) with xn, xn, simplifying with (17), (19),
% 127.86/17.59 | | | (30) gives:
% 127.86/17.59 | | | (45) ? [v0: $i] : (sdtpldt0(xn, v0) = xn & $i(v0) &
% 127.86/17.59 | | | aNaturalNumber0(v0))
% 127.86/17.59 | | |
% 127.86/17.59 | | | DELTA: instantiating (45) with fresh symbol all_57_0 gives:
% 127.86/17.59 | | | (46) sdtpldt0(xn, all_57_0) = xn & $i(all_57_0) &
% 127.86/17.59 | | | aNaturalNumber0(all_57_0)
% 127.86/17.59 | | |
% 127.86/17.59 | | | ALPHA: (46) implies:
% 127.86/17.59 | | | (47) aNaturalNumber0(all_57_0)
% 127.86/17.59 | | | (48) $i(all_57_0)
% 127.86/17.59 | | | (49) sdtpldt0(xn, all_57_0) = xn
% 127.86/17.59 | | |
% 127.86/17.59 | | | DELTA: instantiating (44) with fresh symbol all_59_0 gives:
% 127.86/17.59 | | | (50) sdtpldt0(xm, all_59_0) = xm & $i(all_59_0) &
% 127.86/17.59 | | | aNaturalNumber0(all_59_0)
% 127.86/17.59 | | |
% 127.86/17.59 | | | ALPHA: (50) implies:
% 127.86/17.59 | | | (51) aNaturalNumber0(all_59_0)
% 127.86/17.59 | | | (52) $i(all_59_0)
% 127.86/17.59 | | | (53) sdtpldt0(xm, all_59_0) = xm
% 127.86/17.59 | | |
% 127.86/17.59 | | | DELTA: instantiating (42) with fresh symbol all_61_0 gives:
% 127.86/17.59 | | | (54) sdtpldt0(sz10, all_61_0) = sz10 & $i(all_61_0) &
% 127.86/17.59 | | | aNaturalNumber0(all_61_0)
% 127.86/17.59 | | |
% 127.86/17.59 | | | ALPHA: (54) implies:
% 127.86/17.59 | | | (55) aNaturalNumber0(all_61_0)
% 127.86/17.59 | | | (56) $i(all_61_0)
% 127.86/17.59 | | | (57) sdtpldt0(sz10, all_61_0) = sz10
% 127.86/17.59 | | |
% 127.86/17.59 | | | DELTA: instantiating (43) with fresh symbol all_65_0 gives:
% 127.86/17.59 | | | (58) sdtpldt0(sz10, all_65_0) = xm & $i(all_65_0) &
% 127.86/17.59 | | | aNaturalNumber0(all_65_0)
% 127.86/17.59 | | |
% 127.86/17.59 | | | ALPHA: (58) implies:
% 127.86/17.59 | | | (59) aNaturalNumber0(all_65_0)
% 127.86/17.59 | | | (60) $i(all_65_0)
% 127.86/17.59 | | | (61) sdtpldt0(sz10, all_65_0) = xm
% 127.86/17.59 | | |
% 127.86/17.59 | | | GROUND_INST: instantiating (9) with all_27_0, xn, simplifying with (17),
% 127.86/17.59 | | | (19), (32), (34), (41) gives:
% 127.86/17.59 | | | (62) ? [v0: $i] : (sdtpldt0(all_27_0, v0) = xn & $i(v0) &
% 127.86/17.59 | | | aNaturalNumber0(v0))
% 127.86/17.59 | | |
% 127.86/17.59 | | | GROUND_INST: instantiating (11) with sz10, xm, all_61_0, sz10, simplifying
% 127.86/17.59 | | | with (1), (14), (16), (18), (40), (55), (56), (57) gives:
% 127.86/17.59 | | | (63) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 =
% 127.86/17.59 | | | sz10) & ~ (v1 = v0) & sdtpldt0(all_61_0, xm) = v1 &
% 127.86/17.59 | | | sdtpldt0(all_61_0, sz10) = v0 & sdtpldt0(xm, all_61_0) = v2 &
% 127.86/17.59 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10,
% 127.86/17.59 | | | v2))
% 127.86/17.59 | | |
% 127.86/17.60 | | | GROUND_INST: instantiating (2) with all_61_0, sz10, sz10, simplifying with
% 127.86/17.60 | | | (1), (14), (55), (56), (57) gives:
% 127.86/17.60 | | | (64) sdtpldt0(all_61_0, sz10) = sz10
% 127.86/17.60 | | |
% 127.86/17.60 | | | GROUND_INST: instantiating (7) with xn, sz10, all_65_0, xm, all_27_0,
% 127.86/17.60 | | | simplifying with (1), (14), (17), (19), (26), (59), (60),
% 127.86/17.60 | | | (61) gives:
% 127.86/17.60 | | | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 127.86/17.60 | | | $i] : (sdtasdt0(all_65_0, xn) = v4 & sdtasdt0(xn, all_65_0) = v1
% 127.86/17.60 | | | & sdtasdt0(xn, sz10) = v0 & sdtasdt0(xm, xn) = v2 &
% 127.86/17.60 | | | sdtasdt0(sz10, xn) = v3 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0,
% 127.86/17.60 | | | v1) = all_27_0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 127.86/17.60 | | | $i(all_27_0))
% 127.86/17.60 | | |
% 127.86/17.60 | | | GROUND_INST: instantiating (8) with xn, sz10, all_65_0, xm, all_27_0,
% 127.86/17.60 | | | simplifying with (1), (14), (17), (19), (33), (59), (60),
% 127.86/17.60 | | | (61) gives:
% 127.86/17.60 | | | (66) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 127.86/17.60 | | | $i] : (sdtasdt0(all_65_0, xn) = v4 & sdtasdt0(xn, all_65_0) = v2
% 127.86/17.60 | | | & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz10) = v1 &
% 127.86/17.60 | | | sdtasdt0(sz10, xn) = v3 & sdtpldt0(v3, v4) = all_27_0 &
% 127.86/17.60 | | | sdtpldt0(v1, v2) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 127.86/17.60 | | | $i(v0) & $i(all_27_0))
% 127.86/17.60 | | |
% 127.86/17.60 | | | GROUND_INST: instantiating (11) with sz10, xm, all_65_0, xm, simplifying
% 127.86/17.60 | | | with (1), (14), (16), (18), (40), (59), (60), (61) gives:
% 127.86/17.60 | | | (67) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 =
% 127.86/17.60 | | | xm) & ~ (v1 = v0) & sdtpldt0(all_65_0, xm) = v1 &
% 127.86/17.60 | | | sdtpldt0(all_65_0, sz10) = v0 & sdtpldt0(xm, all_65_0) = v2 &
% 127.86/17.60 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm,
% 127.86/17.60 | | | v2))
% 127.86/17.60 | | |
% 127.86/17.60 | | | GROUND_INST: instantiating (2) with all_65_0, sz10, xm, simplifying with
% 127.86/17.60 | | | (1), (14), (59), (60), (61) gives:
% 127.86/17.60 | | | (68) sdtpldt0(all_65_0, sz10) = xm & $i(xm)
% 127.86/17.60 | | |
% 127.86/17.60 | | | GROUND_INST: instantiating (7) with xn, xm, all_59_0, xm, all_27_0,
% 127.86/17.60 | | | simplifying with (16), (17), (18), (19), (26), (51), (52),
% 127.86/17.60 | | | (53) gives:
% 127.86/17.60 | | | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 127.86/17.60 | | | $i] : (sdtasdt0(all_59_0, xn) = v4 & sdtasdt0(xn, all_59_0) = v1
% 127.86/17.60 | | | & sdtasdt0(xn, xm) = v0 & sdtasdt0(xm, xn) = v3 & sdtasdt0(xm,
% 127.86/17.60 | | | xn) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_27_0
% 127.86/17.60 | | | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_27_0))
% 127.86/17.60 | | |
% 127.86/17.61 | | | GROUND_INST: instantiating (8) with xn, xm, all_59_0, xm, all_27_0,
% 127.86/17.61 | | | simplifying with (16), (17), (18), (19), (33), (51), (52),
% 127.86/17.61 | | | (53) gives:
% 127.86/17.61 | | | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 127.86/17.61 | | | $i] : (sdtasdt0(all_59_0, xn) = v4 & sdtasdt0(xn, all_59_0) = v2
% 127.86/17.61 | | | & sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtasdt0(xm,
% 127.86/17.61 | | | xn) = v3 & sdtpldt0(v3, v4) = all_27_0 & sdtpldt0(v1, v2) = v0
% 127.86/17.61 | | | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_27_0))
% 127.86/17.61 | | |
% 127.86/17.61 | | | GROUND_INST: instantiating (12) with sz10, xm, all_59_0, xm, simplifying
% 127.86/17.61 | | | with (1), (14), (16), (18), (40), (51), (52), (53) gives:
% 127.86/17.61 | | | (71) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 =
% 127.86/17.61 | | | xm) & ~ (v1 = v0) & sdtpldt0(all_59_0, xm) = v1 &
% 127.86/17.61 | | | sdtpldt0(all_59_0, sz10) = v0 & sdtpldt0(sz10, all_59_0) = v2 &
% 127.86/17.61 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v2, xm) & sdtlseqdt0(v0,
% 127.86/17.61 | | | v1))
% 127.86/17.61 | | |
% 127.86/17.61 | | | GROUND_INST: instantiating (2) with all_59_0, xm, xm, simplifying with
% 127.86/17.61 | | | (16), (18), (51), (52), (53) gives:
% 127.86/17.61 | | | (72) sdtpldt0(all_59_0, xm) = xm
% 127.86/17.61 | | |
% 127.86/17.61 | | | GROUND_INST: instantiating (8) with xm, xn, all_57_0, xn, all_27_0,
% 127.86/17.61 | | | simplifying with (16), (17), (18), (19), (26), (47), (48),
% 127.86/17.61 | | | (49) gives:
% 127.86/17.61 | | | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 127.86/17.61 | | | $i] : (sdtasdt0(all_57_0, xm) = v4 & sdtasdt0(xn, xm) = v3 &
% 127.86/17.61 | | | sdtasdt0(xm, all_57_0) = v2 & sdtasdt0(xm, xn) = v1 &
% 127.86/17.61 | | | sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = all_27_0 &
% 127.86/17.61 | | | sdtpldt0(v1, v2) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 127.86/17.61 | | | $i(v0) & $i(all_27_0))
% 127.86/17.61 | | |
% 127.86/17.61 | | | GROUND_INST: instantiating (7) with xm, xn, all_57_0, xn, all_27_0,
% 127.86/17.61 | | | simplifying with (16), (17), (18), (19), (33), (47), (48),
% 127.86/17.61 | | | (49) gives:
% 127.86/17.61 | | | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 127.86/17.61 | | | $i] : (sdtasdt0(all_57_0, xm) = v4 & sdtasdt0(xn, xm) = v3 &
% 127.86/17.61 | | | sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, all_57_0) = v1 &
% 127.86/17.61 | | | sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1)
% 127.86/17.61 | | | = all_27_0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 127.86/17.61 | | | $i(all_27_0))
% 127.86/17.61 | | |
% 127.86/17.61 | | | DELTA: instantiating (62) with fresh symbol all_77_0 gives:
% 127.86/17.61 | | | (75) sdtpldt0(all_27_0, all_77_0) = xn & $i(all_77_0) &
% 127.86/17.61 | | | aNaturalNumber0(all_77_0)
% 127.86/17.61 | | |
% 127.86/17.61 | | | ALPHA: (75) implies:
% 127.86/17.62 | | | (76) aNaturalNumber0(all_77_0)
% 127.86/17.62 | | | (77) $i(all_77_0)
% 127.86/17.62 | | | (78) sdtpldt0(all_27_0, all_77_0) = xn
% 127.86/17.62 | | |
% 127.86/17.62 | | | DELTA: instantiating (74) with fresh symbols all_89_0, all_89_1, all_89_2,
% 127.86/17.62 | | | all_89_3, all_89_4 gives:
% 127.86/17.62 | | | (79) sdtasdt0(all_57_0, xm) = all_89_0 & sdtasdt0(xn, xm) = all_89_1 &
% 127.86/17.62 | | | sdtasdt0(xn, xm) = all_89_2 & sdtasdt0(xm, all_57_0) = all_89_3 &
% 127.86/17.62 | | | sdtasdt0(xm, xn) = all_89_4 & sdtpldt0(all_89_1, all_89_0) =
% 127.86/17.62 | | | all_89_2 & sdtpldt0(all_89_4, all_89_3) = all_27_0 & $i(all_89_0)
% 127.86/17.62 | | | & $i(all_89_1) & $i(all_89_2) & $i(all_89_3) & $i(all_89_4) &
% 127.86/17.62 | | | $i(all_27_0)
% 127.86/17.62 | | |
% 127.86/17.62 | | | ALPHA: (79) implies:
% 127.86/17.62 | | | (80) $i(all_89_4)
% 127.86/17.62 | | | (81) sdtasdt0(xm, xn) = all_89_4
% 127.86/17.62 | | | (82) sdtasdt0(xn, xm) = all_89_2
% 127.86/17.62 | | | (83) sdtasdt0(xn, xm) = all_89_1
% 127.86/17.62 | | |
% 127.86/17.62 | | | DELTA: instantiating (73) with fresh symbols all_91_0, all_91_1, all_91_2,
% 127.86/17.62 | | | all_91_3, all_91_4 gives:
% 127.86/17.62 | | | (84) sdtasdt0(all_57_0, xm) = all_91_0 & sdtasdt0(xn, xm) = all_91_1 &
% 127.86/17.62 | | | sdtasdt0(xm, all_57_0) = all_91_2 & sdtasdt0(xm, xn) = all_91_3 &
% 127.86/17.62 | | | sdtasdt0(xm, xn) = all_91_4 & sdtpldt0(all_91_1, all_91_0) =
% 127.86/17.62 | | | all_27_0 & sdtpldt0(all_91_3, all_91_2) = all_91_4 & $i(all_91_0)
% 127.86/17.62 | | | & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & $i(all_91_4) &
% 127.86/17.62 | | | $i(all_27_0)
% 127.86/17.62 | | |
% 127.86/17.62 | | | ALPHA: (84) implies:
% 127.86/17.62 | | | (85) sdtasdt0(xm, xn) = all_91_4
% 127.86/17.62 | | | (86) sdtasdt0(xm, xn) = all_91_3
% 127.86/17.62 | | | (87) sdtasdt0(xn, xm) = all_91_1
% 127.86/17.62 | | |
% 127.86/17.62 | | | DELTA: instantiating (66) with fresh symbols all_93_0, all_93_1, all_93_2,
% 127.86/17.62 | | | all_93_3, all_93_4 gives:
% 127.86/17.62 | | | (88) sdtasdt0(all_65_0, xn) = all_93_0 & sdtasdt0(xn, all_65_0) =
% 127.86/17.62 | | | all_93_2 & sdtasdt0(xn, xm) = all_93_4 & sdtasdt0(xn, sz10) =
% 127.86/17.62 | | | all_93_3 & sdtasdt0(sz10, xn) = all_93_1 & sdtpldt0(all_93_1,
% 127.86/17.62 | | | all_93_0) = all_27_0 & sdtpldt0(all_93_3, all_93_2) = all_93_4 &
% 127.86/17.62 | | | $i(all_93_0) & $i(all_93_1) & $i(all_93_2) & $i(all_93_3) &
% 127.86/17.62 | | | $i(all_93_4) & $i(all_27_0)
% 127.86/17.62 | | |
% 127.86/17.62 | | | ALPHA: (88) implies:
% 127.86/17.62 | | | (89) sdtasdt0(sz10, xn) = all_93_1
% 127.86/17.62 | | | (90) sdtasdt0(xn, sz10) = all_93_3
% 127.86/17.62 | | | (91) sdtasdt0(xn, xm) = all_93_4
% 127.86/17.62 | | |
% 127.86/17.62 | | | DELTA: instantiating (65) with fresh symbols all_95_0, all_95_1, all_95_2,
% 127.86/17.62 | | | all_95_3, all_95_4 gives:
% 127.86/17.62 | | | (92) sdtasdt0(all_65_0, xn) = all_95_0 & sdtasdt0(xn, all_65_0) =
% 127.86/17.62 | | | all_95_3 & sdtasdt0(xn, sz10) = all_95_4 & sdtasdt0(xm, xn) =
% 127.86/17.62 | | | all_95_2 & sdtasdt0(sz10, xn) = all_95_1 & sdtpldt0(all_95_1,
% 127.86/17.62 | | | all_95_0) = all_95_2 & sdtpldt0(all_95_4, all_95_3) = all_27_0 &
% 127.86/17.62 | | | $i(all_95_0) & $i(all_95_1) & $i(all_95_2) & $i(all_95_3) &
% 127.86/17.62 | | | $i(all_95_4) & $i(all_27_0)
% 127.86/17.62 | | |
% 127.86/17.62 | | | ALPHA: (92) implies:
% 127.86/17.62 | | | (93) sdtasdt0(sz10, xn) = all_95_1
% 127.86/17.62 | | | (94) sdtasdt0(xm, xn) = all_95_2
% 127.86/17.62 | | | (95) sdtasdt0(xn, sz10) = all_95_4
% 127.86/17.62 | | |
% 127.86/17.62 | | | DELTA: instantiating (70) with fresh symbols all_97_0, all_97_1, all_97_2,
% 127.86/17.62 | | | all_97_3, all_97_4 gives:
% 127.86/17.62 | | | (96) sdtasdt0(all_59_0, xn) = all_97_0 & sdtasdt0(xn, all_59_0) =
% 127.86/17.62 | | | all_97_2 & sdtasdt0(xn, xm) = all_97_3 & sdtasdt0(xn, xm) =
% 127.86/17.62 | | | all_97_4 & sdtasdt0(xm, xn) = all_97_1 & sdtpldt0(all_97_1,
% 127.86/17.62 | | | all_97_0) = all_27_0 & sdtpldt0(all_97_3, all_97_2) = all_97_4 &
% 127.86/17.62 | | | $i(all_97_0) & $i(all_97_1) & $i(all_97_2) & $i(all_97_3) &
% 127.86/17.62 | | | $i(all_97_4) & $i(all_27_0)
% 127.86/17.62 | | |
% 127.86/17.62 | | | ALPHA: (96) implies:
% 127.86/17.62 | | | (97) sdtasdt0(xm, xn) = all_97_1
% 127.86/17.62 | | | (98) sdtasdt0(xn, xm) = all_97_4
% 127.86/17.62 | | | (99) sdtasdt0(xn, xm) = all_97_3
% 127.86/17.62 | | |
% 127.86/17.62 | | | DELTA: instantiating (69) with fresh symbols all_99_0, all_99_1, all_99_2,
% 127.86/17.62 | | | all_99_3, all_99_4 gives:
% 127.86/17.62 | | | (100) sdtasdt0(all_59_0, xn) = all_99_0 & sdtasdt0(xn, all_59_0) =
% 127.86/17.62 | | | all_99_3 & sdtasdt0(xn, xm) = all_99_4 & sdtasdt0(xm, xn) =
% 127.86/17.62 | | | all_99_1 & sdtasdt0(xm, xn) = all_99_2 & sdtpldt0(all_99_1,
% 127.86/17.62 | | | all_99_0) = all_99_2 & sdtpldt0(all_99_4, all_99_3) = all_27_0
% 127.86/17.62 | | | & $i(all_99_0) & $i(all_99_1) & $i(all_99_2) & $i(all_99_3) &
% 127.86/17.62 | | | $i(all_99_4) & $i(all_27_0)
% 127.86/17.62 | | |
% 127.86/17.62 | | | ALPHA: (100) implies:
% 127.86/17.62 | | | (101) sdtasdt0(xm, xn) = all_99_2
% 127.86/17.62 | | | (102) sdtasdt0(xm, xn) = all_99_1
% 127.86/17.62 | | | (103) sdtasdt0(xn, xm) = all_99_4
% 127.86/17.62 | | |
% 127.86/17.62 | | | BETA: splitting (71) gives:
% 127.86/17.62 | | |
% 127.86/17.62 | | | Case 1:
% 127.86/17.62 | | | |
% 127.86/17.62 | | | | (104) xm = sz10
% 127.86/17.62 | | | |
% 127.86/17.62 | | | | REDUCE: (39), (104) imply:
% 127.86/17.62 | | | | (105) $false
% 127.86/17.62 | | | |
% 127.86/17.62 | | | | CLOSE: (105) is inconsistent.
% 127.86/17.62 | | | |
% 127.86/17.63 | | | Case 2:
% 127.86/17.63 | | | |
% 127.86/17.63 | | | | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xm) & ~
% 127.86/17.63 | | | | (v1 = v0) & sdtpldt0(all_59_0, xm) = v1 & sdtpldt0(all_59_0,
% 127.86/17.63 | | | | sz10) = v0 & sdtpldt0(sz10, all_59_0) = v2 & $i(v2) &
% 127.86/17.63 | | | | $i(v1) & $i(v0) & sdtlseqdt0(v2, xm) & sdtlseqdt0(v0, v1))
% 127.86/17.63 | | | |
% 127.86/17.63 | | | | DELTA: instantiating (106) with fresh symbols all_108_0, all_108_1,
% 127.86/17.63 | | | | all_108_2 gives:
% 127.86/17.63 | | | | (107) ~ (all_108_0 = xm) & ~ (all_108_1 = all_108_2) &
% 127.86/17.63 | | | | sdtpldt0(all_59_0, xm) = all_108_1 & sdtpldt0(all_59_0, sz10) =
% 127.86/17.63 | | | | all_108_2 & sdtpldt0(sz10, all_59_0) = all_108_0 &
% 127.86/17.63 | | | | $i(all_108_0) & $i(all_108_1) & $i(all_108_2) &
% 127.86/17.63 | | | | sdtlseqdt0(all_108_0, xm) & sdtlseqdt0(all_108_2, all_108_1)
% 127.86/17.63 | | | |
% 127.86/17.63 | | | | ALPHA: (107) implies:
% 127.86/17.63 | | | | (108) $i(all_108_1)
% 127.86/17.63 | | | | (109) sdtpldt0(all_59_0, xm) = all_108_1
% 127.86/17.63 | | | |
% 127.86/17.63 | | | | BETA: splitting (63) gives:
% 127.86/17.63 | | | |
% 127.86/17.63 | | | | Case 1:
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | (110) xm = sz10
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | REDUCE: (39), (110) imply:
% 127.86/17.63 | | | | | (111) $false
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | CLOSE: (111) is inconsistent.
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | Case 2:
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | (112) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = sz10) &
% 127.86/17.63 | | | | | ~ (v1 = v0) & sdtpldt0(all_61_0, xm) = v1 &
% 127.86/17.63 | | | | | sdtpldt0(all_61_0, sz10) = v0 & sdtpldt0(xm, all_61_0) = v2
% 127.86/17.63 | | | | | & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) &
% 127.86/17.63 | | | | | sdtlseqdt0(sz10, v2))
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | DELTA: instantiating (112) with fresh symbols all_123_0, all_123_1,
% 127.86/17.63 | | | | | all_123_2 gives:
% 127.86/17.63 | | | | | (113) ~ (all_123_0 = sz10) & ~ (all_123_1 = all_123_2) &
% 127.86/17.63 | | | | | sdtpldt0(all_61_0, xm) = all_123_1 & sdtpldt0(all_61_0, sz10)
% 127.86/17.63 | | | | | = all_123_2 & sdtpldt0(xm, all_61_0) = all_123_0 &
% 127.86/17.63 | | | | | $i(all_123_0) & $i(all_123_1) & $i(all_123_2) &
% 127.86/17.63 | | | | | sdtlseqdt0(all_123_2, all_123_1) & sdtlseqdt0(sz10,
% 127.86/17.63 | | | | | all_123_0)
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | ALPHA: (113) implies:
% 127.86/17.63 | | | | | (114) $i(all_123_2)
% 127.86/17.63 | | | | | (115) sdtpldt0(all_61_0, sz10) = all_123_2
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | BETA: splitting (67) gives:
% 127.86/17.63 | | | | |
% 127.86/17.63 | | | | | Case 1:
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | (116) xm = sz10
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | REDUCE: (39), (116) imply:
% 127.86/17.63 | | | | | | (117) $false
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | CLOSE: (117) is inconsistent.
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | Case 2:
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (21) with xm, all_108_1, xm, all_59_0,
% 127.86/17.63 | | | | | | simplifying with (72), (109) gives:
% 127.86/17.63 | | | | | | (118) all_108_1 = xm
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (21) with sz10, all_123_2, sz10,
% 127.86/17.63 | | | | | | all_61_0, simplifying with (64), (115) gives:
% 127.86/17.63 | | | | | | (119) all_123_2 = sz10
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_93_1, all_95_1, xn, sz10,
% 127.86/17.63 | | | | | | simplifying with (89), (93) gives:
% 127.86/17.63 | | | | | | (120) all_95_1 = all_93_1
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_89_4, all_91_3, xn, xm,
% 127.86/17.63 | | | | | | simplifying with (81), (86) gives:
% 127.86/17.63 | | | | | | (121) all_91_3 = all_89_4
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_27_0, all_99_2, xn, xm,
% 127.86/17.63 | | | | | | simplifying with (33), (101) gives:
% 127.86/17.63 | | | | | | (122) all_99_2 = all_27_0
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_97_1, all_99_2, xn, xm,
% 127.86/17.63 | | | | | | simplifying with (97), (101) gives:
% 127.86/17.63 | | | | | | (123) all_99_2 = all_97_1
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_91_3, all_99_2, xn, xm,
% 127.86/17.63 | | | | | | simplifying with (86), (101) gives:
% 127.86/17.63 | | | | | | (124) all_99_2 = all_91_3
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_91_4, all_99_2, xn, xm,
% 127.86/17.63 | | | | | | simplifying with (85), (101) gives:
% 127.86/17.63 | | | | | | (125) all_99_2 = all_91_4
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_99_2, all_99_1, xn, xm,
% 127.86/17.63 | | | | | | simplifying with (101), (102) gives:
% 127.86/17.63 | | | | | | (126) all_99_1 = all_99_2
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_95_2, all_99_1, xn, xm,
% 127.86/17.63 | | | | | | simplifying with (94), (102) gives:
% 127.86/17.63 | | | | | | (127) all_99_1 = all_95_2
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_93_3, all_95_4, sz10, xn,
% 127.86/17.63 | | | | | | simplifying with (90), (95) gives:
% 127.86/17.63 | | | | | | (128) all_95_4 = all_93_3
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | PRED_UNIFY: (38), (95) imply:
% 127.86/17.63 | | | | | | (129) ~ (all_95_4 = all_27_0)
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_89_1, all_91_1, xm, xn,
% 127.86/17.63 | | | | | | simplifying with (83), (87) gives:
% 127.86/17.63 | | | | | | (130) all_91_1 = all_89_1
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_27_0, all_93_4, xm, xn,
% 127.86/17.63 | | | | | | simplifying with (26), (91) gives:
% 127.86/17.63 | | | | | | (131) all_93_4 = all_27_0
% 127.86/17.63 | | | | | |
% 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_91_1, all_93_4, xm, xn,
% 127.86/17.63 | | | | | | simplifying with (87), (91) gives:
% 127.86/17.63 | | | | | | (132) all_93_4 = all_91_1
% 127.86/17.63 | | | | | |
% 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_89_1, all_97_4, xm, xn,
% 127.86/17.64 | | | | | | simplifying with (83), (98) gives:
% 127.86/17.64 | | | | | | (133) all_97_4 = all_89_1
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_97_3, all_99_4, xm, xn,
% 127.86/17.64 | | | | | | simplifying with (99), (103) gives:
% 127.86/17.64 | | | | | | (134) all_99_4 = all_97_3
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_97_4, all_99_4, xm, xn,
% 127.86/17.64 | | | | | | simplifying with (98), (103) gives:
% 127.86/17.64 | | | | | | (135) all_99_4 = all_97_4
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_89_2, all_99_4, xm, xn,
% 127.86/17.64 | | | | | | simplifying with (82), (103) gives:
% 127.86/17.64 | | | | | | (136) all_99_4 = all_89_2
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (126), (127) imply:
% 127.86/17.64 | | | | | | (137) all_99_2 = all_95_2
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | SIMP: (137) implies:
% 127.86/17.64 | | | | | | (138) all_99_2 = all_95_2
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (123), (124) imply:
% 127.86/17.64 | | | | | | (139) all_97_1 = all_91_3
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (122), (123) imply:
% 127.86/17.64 | | | | | | (140) all_97_1 = all_27_0
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (123), (125) imply:
% 127.86/17.64 | | | | | | (141) all_97_1 = all_91_4
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (123), (138) imply:
% 127.86/17.64 | | | | | | (142) all_97_1 = all_95_2
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (134), (135) imply:
% 127.86/17.64 | | | | | | (143) all_97_3 = all_97_4
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (134), (136) imply:
% 127.86/17.64 | | | | | | (144) all_97_3 = all_89_2
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (141), (142) imply:
% 127.86/17.64 | | | | | | (145) all_95_2 = all_91_4
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (139), (142) imply:
% 127.86/17.64 | | | | | | (146) all_95_2 = all_91_3
% 127.86/17.64 | | | | | |
% 127.86/17.64 | | | | | | COMBINE_EQS: (140), (142) imply:
% 128.17/17.64 | | | | | | (147) all_95_2 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (143), (144) imply:
% 128.17/17.64 | | | | | | (148) all_97_4 = all_89_2
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | SIMP: (148) implies:
% 128.17/17.64 | | | | | | (149) all_97_4 = all_89_2
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (133), (149) imply:
% 128.17/17.64 | | | | | | (150) all_89_1 = all_89_2
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | SIMP: (150) implies:
% 128.17/17.64 | | | | | | (151) all_89_1 = all_89_2
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (145), (147) imply:
% 128.17/17.64 | | | | | | (152) all_91_4 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (145), (146) imply:
% 128.17/17.64 | | | | | | (153) all_91_3 = all_91_4
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | SIMP: (153) implies:
% 128.17/17.64 | | | | | | (154) all_91_3 = all_91_4
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (131), (132) imply:
% 128.17/17.64 | | | | | | (155) all_91_1 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | SIMP: (155) implies:
% 128.17/17.64 | | | | | | (156) all_91_1 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (130), (156) imply:
% 128.17/17.64 | | | | | | (157) all_89_1 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | SIMP: (157) implies:
% 128.17/17.64 | | | | | | (158) all_89_1 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (121), (154) imply:
% 128.17/17.64 | | | | | | (159) all_91_4 = all_89_4
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | SIMP: (159) implies:
% 128.17/17.64 | | | | | | (160) all_91_4 = all_89_4
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (152), (160) imply:
% 128.17/17.64 | | | | | | (161) all_89_4 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | COMBINE_EQS: (151), (158) imply:
% 128.17/17.64 | | | | | | (162) all_89_2 = all_27_0
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | REDUCE: (128), (129) imply:
% 128.17/17.64 | | | | | | (163) ~ (all_93_3 = all_27_0)
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | GROUND_INST: instantiating (2) with all_77_0, all_27_0, xn,
% 128.17/17.64 | | | | | | simplifying with (32), (34), (76), (77), (78) gives:
% 128.17/17.64 | | | | | | (164) sdtpldt0(all_77_0, all_27_0) = xn & $i(xn)
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | GROUND_INST: instantiating (13) with xn, sz10, xm, all_93_1,
% 128.17/17.64 | | | | | | all_27_0, simplifying with (1), (14), (16), (17), (18),
% 128.17/17.64 | | | | | | (19), (33), (40), (89) gives:
% 128.17/17.64 | | | | | | (165) xn = sz00 | xm = sz10 | sdtlseqdt0(all_93_1, all_27_0)
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | GROUND_INST: instantiating (4) with xn, all_93_1, simplifying with
% 128.17/17.64 | | | | | | (17), (19), (89) gives:
% 128.17/17.64 | | | | | | (166) all_93_1 = xn
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | GROUND_INST: instantiating (5) with xn, all_93_3, simplifying with
% 128.17/17.64 | | | | | | (17), (19), (90) gives:
% 128.17/17.64 | | | | | | (167) all_93_3 = xn
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | REDUCE: (163), (167) imply:
% 128.17/17.64 | | | | | | (168) ~ (all_27_0 = xn)
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | BETA: splitting (165) gives:
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | | Case 1:
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | | (169) sdtlseqdt0(all_93_1, all_27_0)
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | | REDUCE: (166), (169) imply:
% 128.17/17.64 | | | | | | | (170) sdtlseqdt0(xn, all_27_0)
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | | PRED_UNIFY: (25), (170) imply:
% 128.17/17.64 | | | | | | | (171) $false
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | | CLOSE: (171) is inconsistent.
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | Case 2:
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | | (172) xn = sz00 | xm = sz10
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | | BETA: splitting (172) gives:
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | | Case 1:
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | (173) xn = sz00
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | REDUCE: (37), (173) imply:
% 128.17/17.64 | | | | | | | | (174) ~ (all_27_0 = sz00)
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | REDUCE: (26), (173) imply:
% 128.17/17.64 | | | | | | | | (175) sdtasdt0(sz00, xm) = all_27_0
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | BETA: splitting (36) gives:
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | Case 1:
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | | (176) ~ (sdtasdt0(sz00, xm) = all_27_0)
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | | PRED_UNIFY: (175), (176) imply:
% 128.17/17.64 | | | | | | | | | (177) $false
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | | CLOSE: (177) is inconsistent.
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | Case 2:
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | | (178) all_27_0 = sz00
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | | REDUCE: (174), (178) imply:
% 128.17/17.64 | | | | | | | | | (179) $false
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | | CLOSE: (179) is inconsistent.
% 128.17/17.64 | | | | | | | | |
% 128.17/17.64 | | | | | | | | End of split
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | Case 2:
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | (180) xm = sz10
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | REDUCE: (39), (180) imply:
% 128.17/17.64 | | | | | | | | (181) $false
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | | CLOSE: (181) is inconsistent.
% 128.17/17.64 | | | | | | | |
% 128.17/17.64 | | | | | | | End of split
% 128.17/17.64 | | | | | | |
% 128.17/17.64 | | | | | | End of split
% 128.17/17.64 | | | | | |
% 128.17/17.64 | | | | | End of split
% 128.17/17.64 | | | | |
% 128.17/17.65 | | | | End of split
% 128.17/17.65 | | | |
% 128.17/17.65 | | | End of split
% 128.17/17.65 | | |
% 128.17/17.65 | | Case 2:
% 128.17/17.65 | | |
% 128.17/17.65 | | | (182) xm = sz10 | xm = sz00
% 128.17/17.65 | | |
% 128.17/17.65 | | | BETA: splitting (182) gives:
% 128.17/17.65 | | |
% 128.17/17.65 | | | Case 1:
% 128.17/17.65 | | | |
% 128.17/17.65 | | | | (183) xm = sz00
% 128.17/17.65 | | | |
% 128.17/17.65 | | | | REDUCE: (24), (183) imply:
% 128.17/17.65 | | | | (184) $false
% 128.17/17.65 | | | |
% 128.17/17.65 | | | | CLOSE: (184) is inconsistent.
% 128.17/17.65 | | | |
% 128.17/17.65 | | | Case 2:
% 128.17/17.65 | | | |
% 128.17/17.65 | | | | (185) xm = sz10
% 128.17/17.65 | | | |
% 128.17/17.65 | | | | REDUCE: (39), (185) imply:
% 128.17/17.65 | | | | (186) $false
% 128.17/17.65 | | | |
% 128.17/17.65 | | | | CLOSE: (186) is inconsistent.
% 128.17/17.65 | | | |
% 128.17/17.65 | | | End of split
% 128.17/17.65 | | |
% 128.17/17.65 | | End of split
% 128.17/17.65 | |
% 128.17/17.65 | Case 2:
% 128.17/17.65 | |
% 128.17/17.65 | | (187) all_27_0 = xn
% 128.17/17.65 | |
% 128.17/17.65 | | REDUCE: (37), (187) imply:
% 128.17/17.65 | | (188) $false
% 128.17/17.65 | |
% 128.17/17.65 | | CLOSE: (188) is inconsistent.
% 128.17/17.65 | |
% 128.17/17.65 | End of split
% 128.17/17.65 |
% 128.17/17.65 End of proof
% 128.17/17.65 % SZS output end Proof for theBenchmark
% 128.17/17.65
% 128.17/17.65 17051ms
%------------------------------------------------------------------------------