TSTP Solution File: RNG048+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG048+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 : n021.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 13:57:32 EDT 2023
% Result : Theorem 24.36s 4.02s
% Output : Proof 24.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG048+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 03:08:57 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.29/1.14 Prover 4: Preprocessing ...
% 3.29/1.14 Prover 1: Preprocessing ...
% 3.29/1.18 Prover 6: Preprocessing ...
% 3.29/1.18 Prover 2: Preprocessing ...
% 3.29/1.19 Prover 5: Preprocessing ...
% 3.29/1.19 Prover 0: Preprocessing ...
% 3.29/1.19 Prover 3: Preprocessing ...
% 8.26/1.84 Prover 1: Constructing countermodel ...
% 8.75/1.92 Prover 3: Constructing countermodel ...
% 8.75/1.96 Prover 6: Proving ...
% 10.54/2.18 Prover 3: gave up
% 10.54/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.54/2.20 Prover 5: Constructing countermodel ...
% 11.03/2.27 Prover 7: Preprocessing ...
% 11.03/2.30 Prover 2: Proving ...
% 11.03/2.32 Prover 1: gave up
% 11.77/2.34 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.77/2.39 Prover 4: Constructing countermodel ...
% 12.25/2.40 Prover 8: Preprocessing ...
% 12.79/2.49 Prover 0: Proving ...
% 13.05/2.51 Prover 7: Constructing countermodel ...
% 13.05/2.53 Prover 8: Warning: ignoring some quantifiers
% 13.31/2.54 Prover 8: Constructing countermodel ...
% 18.88/3.31 Prover 8: gave up
% 19.15/3.33 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 19.28/3.41 Prover 9: Preprocessing ...
% 24.15/3.98 Prover 7: Found proof (size 152)
% 24.15/3.98 Prover 7: proved (1808ms)
% 24.15/3.99 Prover 5: stopped
% 24.15/3.99 Prover 4: stopped
% 24.15/3.99 Prover 0: stopped
% 24.15/3.99 Prover 6: stopped
% 24.15/3.99 Prover 2: stopped
% 24.15/4.01 Prover 9: Constructing countermodel ...
% 24.15/4.01 Prover 9: stopped
% 24.15/4.01
% 24.36/4.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.36/4.02
% 24.36/4.03 % SZS output start Proof for theBenchmark
% 24.36/4.03 Assumptions after simplification:
% 24.36/4.03 ---------------------------------
% 24.36/4.03
% 24.36/4.03 (mDefInit)
% 24.44/4.07 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (aDimensionOf0(v0) =
% 24.44/4.07 v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2: $i] : (sziznziztdt0(v0) = v2 &
% 24.44/4.07 $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v2, v4)
% 24.44/4.07 = v5) | ~ (aDimensionOf0(v2) = v3) | ~ $i(v4) | ~
% 24.44/4.07 aNaturalNumber0(v4) | (sdtlbdtrb0(v0, v4) = v5 & $i(v5))) & ! [v3: $i]
% 24.44/4.07 : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0, v4) = v5) | ~
% 24.44/4.07 (aDimensionOf0(v2) = v3) | ~ $i(v4) | ~ aNaturalNumber0(v4) |
% 24.44/4.07 (sdtlbdtrb0(v2, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 24.44/4.07 v2 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ? [v5:
% 24.44/4.07 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & (( ~ (v8 =
% 24.44/4.07 v7) & sdtlbdtrb0(v3, v6) = v7 & sdtlbdtrb0(v0, v6) = v8 & $i(v8)
% 24.44/4.07 & $i(v7) & aNaturalNumber0(v6)) | ( ~ (v5 = v1) & szszuzczcdt0(v4)
% 24.44/4.07 = v5 & $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v2) = v3) |
% 24.44/4.07 aVector0(v2)) & ! [v3: $i] : ( ~ (aDimensionOf0(v2) = v3) |
% 24.44/4.07 (szszuzczcdt0(v3) = v1 & $i(v1))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 24.44/4.07 (sziznziztdt0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2: $i] :
% 24.44/4.07 (aDimensionOf0(v0) = v2 & $i(v2) & (v2 = sz00 | ( ! [v3: $i] : ! [v4: $i] :
% 24.44/4.07 ! [v5: $i] : ( ~ (sdtlbdtrb0(v1, v4) = v5) | ~ (aDimensionOf0(v1) =
% 24.44/4.07 v3) | ~ $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) |
% 24.44/4.07 (sdtlbdtrb0(v0, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : !
% 24.44/4.07 [v5: $i] : ( ~ (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3)
% 24.44/4.07 | ~ $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 24.44/4.07 v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = v1 | ~
% 24.44/4.07 (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ? [v5: $i]
% 24.44/4.07 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7)
% 24.44/4.07 & sdtlbdtrb0(v3, v6) = v7 & sdtlbdtrb0(v0, v6) = v8 & $i(v8) &
% 24.44/4.07 $i(v7) & aNaturalNumber0(v6)) | ( ~ (v5 = v2) &
% 24.44/4.07 szszuzczcdt0(v4) = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 24.44/4.07 (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2) & !
% 24.44/4.07 [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 24.44/4.07 aVector0(v1))))))
% 24.44/4.07
% 24.44/4.07 (mDefSPN)
% 24.44/4.07 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 24.44/4.07 : ! [v5: $i] : (v2 = sz00 | ~ (sdtlbdtrb0(v1, v2) = v4) | ~ (sdtlbdtrb0(v0,
% 24.44/4.07 v2) = v3) | ~ (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) |
% 24.44/4.07 ~ (sdtasdt0(v3, v4) = v5) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~
% 24.44/4.07 aVector0(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 24.44/4.07 (sdtasasdt0(v7, v8) = v9 & sdtasasdt0(v0, v1) = v6 & sziznziztdt0(v1) = v8 &
% 24.44/4.07 sziznziztdt0(v0) = v7 & sdtpldt0(v9, v5) = v6 & $i(v9) & $i(v8) & $i(v7) &
% 24.44/4.07 $i(v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 24.44/4.07 $i] : ( ~ (sdtasasdt0(v2, v3) = v4) | ~ (sziznziztdt0(v1) = v3) | ~
% 24.44/4.07 (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~
% 24.44/4.07 aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 24.44/4.07 [v9: $i] : ? [v10: $i] : ? [v11: $i] : (aDimensionOf0(v1) = v6 & $i(v6) &
% 24.44/4.07 (v6 = sz00 | (v11 = v7 & sdtasasdt0(v0, v1) = v7 & sdtlbdtrb0(v1, v6) = v9
% 24.44/4.07 & sdtlbdtrb0(v0, v5) = v8 & aDimensionOf0(v0) = v5 & sdtasdt0(v8, v9)
% 24.44/4.07 = v10 & sdtpldt0(v4, v10) = v7 & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 24.44/4.07 $i(v5)) | ( ~ (v6 = v5) & aDimensionOf0(v0) = v5 & $i(v5))))) & !
% 24.44/4.07 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~
% 24.44/4.07 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3: $i] : ?
% 24.44/4.07 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 24.44/4.07 $i] : ? [v10: $i] : ? [v11: $i] : (aDimensionOf0(v1) = v4 & $i(v4) & (v4
% 24.44/4.07 = sz00 | (v11 = v2 & sdtasasdt0(v5, v6) = v7 & sziznziztdt0(v1) = v6 &
% 24.44/4.07 sziznziztdt0(v0) = v5 & sdtlbdtrb0(v1, v4) = v9 & sdtlbdtrb0(v0, v3) =
% 24.44/4.07 v8 & aDimensionOf0(v0) = v3 & sdtasdt0(v8, v9) = v10 & sdtpldt0(v7,
% 24.44/4.07 v10) = v2 & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 24.44/4.07 $i(v3) & $i(v2)) | ( ~ (v4 = v3) & aDimensionOf0(v0) = v3 & $i(v3)))))
% 24.44/4.07
% 24.44/4.07 (mDefSPZ)
% 24.44/4.08 $i(sz0z00) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00
% 24.44/4.08 | ~ (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) |
% 24.44/4.08 ~ aVector0(v0) | ? [v3: $i] : ? [v4: $i] : (aDimensionOf0(v1) = v4 &
% 24.44/4.08 $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) = v3 &
% 24.44/4.08 $i(v3)))))
% 24.44/4.08
% 24.44/4.08 (mDimNat)
% 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 24.44/4.08 aVector0(v0) | aNaturalNumber0(v1))
% 24.44/4.08
% 24.44/4.08 (mElmSc)
% 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aVector0(v0) | ~ aNaturalNumber0(v1) |
% 24.44/4.08 aScalar0(v2))
% 24.44/4.08
% 24.44/4.08 (mEqInit)
% 24.44/4.08 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 24.44/4.08 : ! [v5: $i] : (v5 = v3 | ~ (sziznziztdt0(v1) = v4) | ~ (sziznziztdt0(v0) =
% 24.44/4.08 v2) | ~ (aDimensionOf0(v4) = v5) | ~ (aDimensionOf0(v2) = v3) | ~
% 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v6: $i] : ?
% 24.44/4.08 [v7: $i] : (aDimensionOf0(v1) = v7 & $i(v7) & (v7 = sz00 | ( ~ (v7 = v6) &
% 24.44/4.08 aDimensionOf0(v0) = v6 & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : !
% 24.44/4.08 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = sz00 | ~ (sziznziztdt0(v0) = v3)
% 24.44/4.08 | ~ (aDimensionOf0(v3) = v4) | ~ (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~
% 24.44/4.08 $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ?
% 24.44/4.08 [v7: $i] : ((v7 = v4 & sziznziztdt0(v1) = v6 & aDimensionOf0(v6) = v4 &
% 24.44/4.08 $i(v6) & $i(v4)) | ( ~ (v5 = v2) & aDimensionOf0(v0) = v5 & $i(v5)))) &
% 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 24.44/4.08 (sziznziztdt0(v1) = v3) | ~ (aDimensionOf0(v3) = v4) | ~
% 24.44/4.08 (aDimensionOf0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~
% 24.44/4.08 aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v4 &
% 24.44/4.08 sziznziztdt0(v0) = v6 & aDimensionOf0(v6) = v4 & $i(v6) & $i(v4)) |
% 24.44/4.08 (aDimensionOf0(v1) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 = sz00)))) & ! [v0:
% 24.44/4.08 $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~ (aDimensionOf0(v1) = v2) |
% 24.44/4.08 ~ (aDimensionOf0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~
% 24.44/4.08 aVector0(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sziznziztdt0(v1) =
% 24.44/4.08 v5 & sziznziztdt0(v0) = v3 & aDimensionOf0(v5) = v4 & aDimensionOf0(v3) =
% 24.44/4.08 v4 & $i(v5) & $i(v4) & $i(v3)))
% 24.44/4.08
% 24.44/4.08 (mIH)
% 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~
% 24.44/4.08 aNaturalNumber0(v0) | iLess0(v0, v1))
% 24.44/4.08
% 24.44/4.08 (mLETot)
% 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~
% 24.44/4.08 aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 24.44/4.08
% 24.44/4.08 (mMDNeg)
% 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 24.44/4.08 (smndt0(v1) = v3) | ~ (smndt0(v0) = v2) | ~ (sdtasdt0(v2, v3) = v4) | ~
% 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | (sdtasdt0(v0, v1) =
% 24.44/4.08 v4 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.44/4.08 (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~
% 24.44/4.08 aScalar0(v0) | ? [v3: $i] : ? [v4: $i] : (smndt0(v1) = v4 & smndt0(v0) =
% 24.44/4.08 v3 & sdtasdt0(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2)))
% 24.44/4.08
% 24.44/4.08 (mMulSc)
% 24.44/4.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 24.44/4.08 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 24.44/4.08
% 24.44/4.08 (mPosMon)
% 24.44/4.09 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) =
% 24.44/4.09 v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~
% 24.44/4.09 sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) |
% 24.44/4.09 sdtlseqdt0(sz0z00, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.44/4.09 (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1)
% 24.44/4.09 | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v3:
% 24.44/4.09 $i] : (sdtpldt0(v0, v1) = v3 & $i(v3) & sdtlseqdt0(sz0z00, v3))) & ! [v0:
% 24.44/4.09 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) |
% 24.44/4.09 ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~
% 24.44/4.09 aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v2)) & ! [v0: $i] : !
% 24.44/4.09 [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 24.44/4.09 ~ sdtlseqdt0(sz0z00, v1) | ~ sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~
% 24.44/4.09 aScalar0(v0) | ? [v3: $i] : (sdtasdt0(v0, v1) = v3 & $i(v3) &
% 24.44/4.09 sdtlseqdt0(sz0z00, v3)))
% 24.44/4.09
% 24.44/4.09 (mSZeroSc)
% 24.44/4.09 $i(sz0z00) & aScalar0(sz0z00)
% 24.44/4.09
% 24.44/4.09 (mScPr)
% 24.44/4.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~
% 24.44/4.09 $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | aScalar0(v2) | ?
% 24.44/4.09 [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & aDimensionOf0(v1) = v4 &
% 24.44/4.09 aDimensionOf0(v0) = v3 & $i(v4) & $i(v3)))
% 24.44/4.09
% 24.44/4.09 (mSqPos)
% 24.44/4.09 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~
% 24.44/4.09 $i(v0) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1))
% 24.44/4.09
% 24.44/4.09 (m__)
% 24.44/4.09 $i(sz0z00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasasdt0(v0, v0) =
% 24.44/4.09 v2 & aDimensionOf0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & aVector0(v0) & ~
% 24.44/4.09 sdtlseqdt0(sz0z00, v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v3, v3)
% 24.44/4.09 = v4) | ~ $i(v3) | ~ aVector0(v3) | sdtlseqdt0(sz0z00, v4) | ? [v5:
% 24.44/4.09 $i] : (aDimensionOf0(v3) = v5 & $i(v5) & ~ iLess0(v5, v1))) & ! [v3:
% 24.44/4.09 $i] : ! [v4: $i] : ( ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 24.44/4.09 aVector0(v3) | ~ iLess0(v4, v1) | ? [v5: $i] : (sdtasasdt0(v3, v3) = v5
% 24.44/4.09 & $i(v5) & sdtlseqdt0(sz0z00, v5))))
% 24.44/4.09
% 24.44/4.09 (function-axioms)
% 24.44/4.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.44/4.09 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 24.44/4.09 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 24.44/4.09 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.44/4.09 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 24.44/4.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 24.44/4.09 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 24.44/4.09 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 24.44/4.09 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 24.44/4.09 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 24.44/4.09 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 24.44/4.09 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.44/4.09 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 24.44/4.09
% 24.44/4.09 Further assumptions not needed in the proof:
% 24.44/4.09 --------------------------------------------
% 24.44/4.09 mArith, mDistr, mDistr2, mIHOrd, mLEASm, mLEMon, mLEMonM, mLERef, mLETrn, mLess,
% 24.44/4.09 mMNeg, mNatExtr, mNatSort, mNegSc, mScSort, mScZero, mSqrt, mSuccEqu, mSuccNat,
% 24.44/4.09 mSumSc, mVcSort, mZeroNat
% 24.44/4.09
% 24.44/4.09 Those formulas are unsatisfiable:
% 24.44/4.09 ---------------------------------
% 24.44/4.09
% 24.44/4.09 Begin of proof
% 24.44/4.09 |
% 24.44/4.09 | ALPHA: (mSZeroSc) implies:
% 24.44/4.09 | (1) aScalar0(sz0z00)
% 24.44/4.09 |
% 24.44/4.09 | ALPHA: (mMDNeg) implies:
% 24.44/4.09 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) |
% 24.44/4.09 | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v3:
% 24.44/4.09 | $i] : ? [v4: $i] : (smndt0(v1) = v4 & smndt0(v0) = v3 &
% 24.44/4.09 | sdtasdt0(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2)))
% 24.44/4.09 |
% 24.44/4.09 | ALPHA: (mPosMon) implies:
% 24.44/4.10 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 24.44/4.10 | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(sz0z00, v1) | ~
% 24.44/4.10 | sdtlseqdt0(sz0z00, v0) | ~ aScalar0(v1) | ~ aScalar0(v0) |
% 24.44/4.10 | sdtlseqdt0(sz0z00, v2))
% 24.44/4.10 |
% 24.44/4.10 | ALPHA: (mSqPos) implies:
% 24.44/4.10 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ $i(v0) |
% 24.44/4.10 | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1))
% 24.44/4.10 |
% 24.44/4.10 | ALPHA: (mDefInit) implies:
% 24.44/4.10 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (aDimensionOf0(v0) = v1) |
% 24.44/4.10 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: $i] : (sziznziztdt0(v0) = v2 &
% 24.44/4.10 | $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 24.44/4.10 | (sdtlbdtrb0(v2, v4) = v5) | ~ (aDimensionOf0(v2) = v3) | ~
% 24.44/4.10 | $i(v4) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v0, v4) = v5 &
% 24.44/4.10 | $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 24.44/4.10 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v2) = v3) | ~
% 24.44/4.10 | $i(v4) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v2, v4) = v5 &
% 24.44/4.10 | $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 = v2 | ~
% 24.44/4.10 | (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ? [v5:
% 24.44/4.10 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ($i(v6) & (( ~
% 24.44/4.10 | (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 & sdtlbdtrb0(v0, v6) =
% 24.44/4.10 | v8 & $i(v8) & $i(v7) & aNaturalNumber0(v6)) | ( ~ (v5 = v1)
% 24.44/4.10 | & szszuzczcdt0(v4) = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 24.44/4.10 | (aDimensionOf0(v2) = v3) | aVector0(v2)) & ! [v3: $i] : ( ~
% 24.44/4.10 | (aDimensionOf0(v2) = v3) | (szszuzczcdt0(v3) = v1 & $i(v1)))))
% 24.44/4.10 |
% 24.44/4.10 | ALPHA: (mEqInit) implies:
% 24.44/4.10 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz00 | ~
% 24.44/4.10 | (aDimensionOf0(v1) = v2) | ~ (aDimensionOf0(v0) = v2) | ~ $i(v1) |
% 24.44/4.10 | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3: $i] : ? [v4:
% 24.44/4.10 | $i] : ? [v5: $i] : (sziznziztdt0(v1) = v5 & sziznziztdt0(v0) = v3
% 24.44/4.10 | & aDimensionOf0(v5) = v4 & aDimensionOf0(v3) = v4 & $i(v5) & $i(v4)
% 24.44/4.10 | & $i(v3)))
% 24.44/4.10 |
% 24.44/4.10 | ALPHA: (mDefSPZ) implies:
% 24.44/4.10 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = sz0z00 | ~
% 24.44/4.10 | (sdtasasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) |
% 24.44/4.10 | ~ aVector0(v0) | ? [v3: $i] : ? [v4: $i] : (aDimensionOf0(v1) = v4
% 24.44/4.10 | & $i(v4) & ( ~ (v4 = sz00) | ( ~ (v3 = sz00) & aDimensionOf0(v0) =
% 24.44/4.10 | v3 & $i(v3)))))
% 24.44/4.10 |
% 24.44/4.10 | ALPHA: (mDefSPN) implies:
% 24.44/4.10 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasasdt0(v0, v1) = v2)
% 24.44/4.10 | | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v3:
% 24.44/4.10 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 24.44/4.10 | [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 24.44/4.10 | (aDimensionOf0(v1) = v4 & $i(v4) & (v4 = sz00 | (v11 = v2 &
% 24.44/4.10 | sdtasasdt0(v5, v6) = v7 & sziznziztdt0(v1) = v6 &
% 24.44/4.10 | sziznziztdt0(v0) = v5 & sdtlbdtrb0(v1, v4) = v9 &
% 24.44/4.10 | sdtlbdtrb0(v0, v3) = v8 & aDimensionOf0(v0) = v3 & sdtasdt0(v8,
% 24.44/4.10 | v9) = v10 & sdtpldt0(v7, v10) = v2 & $i(v10) & $i(v9) &
% 24.44/4.10 | $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v3) & $i(v2)) | ( ~ (v4
% 24.44/4.10 | = v3) & aDimensionOf0(v0) = v3 & $i(v3)))))
% 24.44/4.10 |
% 24.44/4.10 | ALPHA: (m__) implies:
% 24.44/4.10 | (9) $i(sz0z00)
% 24.44/4.10 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasasdt0(v0, v0) = v2 &
% 24.44/4.10 | aDimensionOf0(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & aVector0(v0) &
% 24.44/4.11 | ~ sdtlseqdt0(sz0z00, v2) & ! [v3: $i] : ! [v4: $i] : ( ~
% 24.44/4.11 | (sdtasasdt0(v3, v3) = v4) | ~ $i(v3) | ~ aVector0(v3) |
% 24.44/4.11 | sdtlseqdt0(sz0z00, v4) | ? [v5: $i] : (aDimensionOf0(v3) = v5 &
% 24.44/4.11 | $i(v5) & ~ iLess0(v5, v1))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 24.44/4.11 | (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~ aVector0(v3) | ~
% 24.44/4.11 | iLess0(v4, v1) | ? [v5: $i] : (sdtasasdt0(v3, v3) = v5 & $i(v5) &
% 24.44/4.11 | sdtlseqdt0(sz0z00, v5))))
% 24.44/4.11 |
% 24.44/4.11 | ALPHA: (function-axioms) implies:
% 24.44/4.11 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.44/4.11 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 24.44/4.11 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.44/4.11 | (sziznziztdt0(v2) = v1) | ~ (sziznziztdt0(v2) = v0))
% 24.44/4.11 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.44/4.11 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 24.44/4.11 |
% 24.44/4.11 | DELTA: instantiating (10) with fresh symbols all_32_0, all_32_1, all_32_2
% 24.44/4.11 | gives:
% 24.44/4.11 | (14) sdtasasdt0(all_32_2, all_32_2) = all_32_0 & aDimensionOf0(all_32_2) =
% 24.44/4.11 | all_32_1 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) &
% 24.44/4.11 | aVector0(all_32_2) & ~ sdtlseqdt0(sz0z00, all_32_0) & ! [v0: $i] :
% 24.44/4.11 | ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0) | ~
% 24.44/4.11 | aVector0(v0) | sdtlseqdt0(sz0z00, v1) | ? [v2: $i] :
% 24.44/4.11 | (aDimensionOf0(v0) = v2 & $i(v2) & ~ iLess0(v2, all_32_1))) & !
% 24.44/4.11 | [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 24.44/4.11 | aVector0(v0) | ~ iLess0(v1, all_32_1) | ? [v2: $i] :
% 24.44/4.11 | (sdtasasdt0(v0, v0) = v2 & $i(v2) & sdtlseqdt0(sz0z00, v2)))
% 24.44/4.11 |
% 24.44/4.11 | ALPHA: (14) implies:
% 24.44/4.11 | (15) ~ sdtlseqdt0(sz0z00, all_32_0)
% 24.44/4.11 | (16) aVector0(all_32_2)
% 24.44/4.11 | (17) $i(all_32_2)
% 24.44/4.11 | (18) aDimensionOf0(all_32_2) = all_32_1
% 24.44/4.11 | (19) sdtasasdt0(all_32_2, all_32_2) = all_32_0
% 24.44/4.11 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasasdt0(v0, v0) = v1) | ~ $i(v0)
% 24.44/4.11 | | ~ aVector0(v0) | sdtlseqdt0(sz0z00, v1) | ? [v2: $i] :
% 24.44/4.11 | (aDimensionOf0(v0) = v2 & $i(v2) & ~ iLess0(v2, all_32_1)))
% 24.44/4.11 |
% 24.44/4.11 | GROUND_INST: instantiating (mLETot) with sz0z00, sz0z00, simplifying with (1),
% 24.44/4.11 | (9) gives:
% 24.44/4.11 | (21) sdtlseqdt0(sz0z00, sz0z00)
% 24.44/4.11 |
% 24.44/4.11 | GROUND_INST: instantiating (6) with all_32_2, all_32_2, all_32_1, simplifying
% 24.44/4.11 | with (16), (17), (18) gives:
% 24.44/4.11 | (22) all_32_1 = sz00 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 24.44/4.11 | (sziznziztdt0(all_32_2) = v2 & sziznziztdt0(all_32_2) = v0 &
% 24.44/4.11 | aDimensionOf0(v2) = v1 & aDimensionOf0(v0) = v1 & $i(v2) & $i(v1) &
% 24.44/4.11 | $i(v0))
% 24.44/4.11 |
% 24.44/4.11 | GROUND_INST: instantiating (5) with all_32_2, all_32_1, simplifying with (16),
% 24.44/4.11 | (17), (18) gives:
% 24.44/4.12 | (23) all_32_1 = sz00 | ? [v0: $i] : (sziznziztdt0(all_32_2) = v0 & $i(v0)
% 24.44/4.12 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(v0, v2)
% 24.44/4.12 | = v3) | ~ (aDimensionOf0(v0) = v1) | ~ $i(v2) | ~
% 24.44/4.12 | aNaturalNumber0(v2) | (sdtlbdtrb0(all_32_2, v2) = v3 & $i(v3))) &
% 24.44/4.12 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(all_32_2,
% 24.44/4.12 | v2) = v3) | ~ (aDimensionOf0(v0) = v1) | ~ $i(v2) | ~
% 24.44/4.12 | aNaturalNumber0(v2) | (sdtlbdtrb0(v0, v2) = v3 & $i(v3))) & !
% 24.44/4.12 | [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (aDimensionOf0(v1) = v2) | ~
% 24.44/4.12 | $i(v1) | ~ aVector0(v1) | ? [v3: any] : ? [v4: $i] : ? [v5:
% 24.44/4.12 | $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) & sdtlbdtrb0(v1,
% 24.44/4.12 | v4) = v5 & sdtlbdtrb0(all_32_2, v4) = v6 & $i(v6) & $i(v5)
% 24.44/4.12 | & aNaturalNumber0(v4)) | ( ~ (v3 = all_32_1) &
% 24.44/4.12 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 24.44/4.12 | (aDimensionOf0(v0) = v1) | aVector0(v0)) & ! [v1: $i] : ( ~
% 24.44/4.12 | (aDimensionOf0(v0) = v1) | (szszuzczcdt0(v1) = all_32_1 &
% 24.44/4.12 | $i(all_32_1))))
% 24.44/4.12 |
% 24.44/4.12 | GROUND_INST: instantiating (mDimNat) with all_32_2, all_32_1, simplifying with
% 24.44/4.12 | (16), (17), (18) gives:
% 24.44/4.12 | (24) aNaturalNumber0(all_32_1)
% 24.44/4.12 |
% 24.85/4.12 | GROUND_INST: instantiating (7) with all_32_2, all_32_2, all_32_0, simplifying
% 24.85/4.12 | with (16), (17), (19) gives:
% 24.85/4.12 | (25) all_32_0 = sz0z00 | ? [v0: $i] : ? [v1: $i] :
% 24.85/4.12 | (aDimensionOf0(all_32_2) = v1 & $i(v1) & ( ~ (v1 = sz00) | ( ~ (v0 =
% 24.85/4.12 | sz00) & aDimensionOf0(all_32_2) = v0 & $i(v0))))
% 24.85/4.12 |
% 24.85/4.12 | GROUND_INST: instantiating (8) with all_32_2, all_32_2, all_32_0, simplifying
% 24.85/4.12 | with (16), (17), (19) gives:
% 24.85/4.12 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 24.85/4.12 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 24.85/4.12 | (aDimensionOf0(all_32_2) = v1 & $i(v1) & (v1 = sz00 | (v8 = all_32_0 &
% 24.85/4.12 | sdtasasdt0(v2, v3) = v4 & sziznziztdt0(all_32_2) = v3 &
% 24.85/4.12 | sziznziztdt0(all_32_2) = v2 & sdtlbdtrb0(all_32_2, v1) = v6 &
% 24.85/4.12 | sdtlbdtrb0(all_32_2, v0) = v5 & aDimensionOf0(all_32_2) = v0 &
% 24.85/4.12 | sdtasdt0(v5, v6) = v7 & sdtpldt0(v4, v7) = all_32_0 & $i(v7) &
% 24.85/4.12 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v0) &
% 24.85/4.12 | $i(all_32_0)) | ( ~ (v1 = v0) & aDimensionOf0(all_32_2) = v0 &
% 24.85/4.12 | $i(v0))))
% 24.85/4.12 |
% 24.85/4.12 | GROUND_INST: instantiating (20) with all_32_2, all_32_0, simplifying with
% 24.85/4.12 | (15), (16), (17), (19) gives:
% 24.85/4.12 | (27) ? [v0: $i] : (aDimensionOf0(all_32_2) = v0 & $i(v0) & ~ iLess0(v0,
% 24.85/4.12 | all_32_1))
% 24.85/4.12 |
% 24.85/4.12 | DELTA: instantiating (27) with fresh symbol all_44_0 gives:
% 24.85/4.12 | (28) aDimensionOf0(all_32_2) = all_44_0 & $i(all_44_0) & ~
% 24.85/4.12 | iLess0(all_44_0, all_32_1)
% 24.85/4.12 |
% 24.85/4.12 | ALPHA: (28) implies:
% 24.85/4.12 | (29) aDimensionOf0(all_32_2) = all_44_0
% 24.85/4.12 |
% 24.85/4.12 | DELTA: instantiating (26) with fresh symbols all_46_0, all_46_1, all_46_2,
% 24.85/4.12 | all_46_3, all_46_4, all_46_5, all_46_6, all_46_7, all_46_8 gives:
% 24.85/4.12 | (30) aDimensionOf0(all_32_2) = all_46_7 & $i(all_46_7) & (all_46_7 = sz00 |
% 24.85/4.12 | (all_46_0 = all_32_0 & sdtasasdt0(all_46_6, all_46_5) = all_46_4 &
% 24.85/4.12 | sziznziztdt0(all_32_2) = all_46_5 & sziznziztdt0(all_32_2) =
% 24.85/4.12 | all_46_6 & sdtlbdtrb0(all_32_2, all_46_7) = all_46_2 &
% 24.85/4.12 | sdtlbdtrb0(all_32_2, all_46_8) = all_46_3 &
% 24.85/4.12 | aDimensionOf0(all_32_2) = all_46_8 & sdtasdt0(all_46_3, all_46_2)
% 24.85/4.12 | = all_46_1 & sdtpldt0(all_46_4, all_46_1) = all_32_0 &
% 24.85/4.12 | $i(all_46_1) & $i(all_46_2) & $i(all_46_3) & $i(all_46_4) &
% 24.85/4.12 | $i(all_46_5) & $i(all_46_6) & $i(all_46_8) & $i(all_32_0)) | ( ~
% 24.85/4.12 | (all_46_7 = all_46_8) & aDimensionOf0(all_32_2) = all_46_8 &
% 24.85/4.12 | $i(all_46_8)))
% 24.85/4.12 |
% 24.85/4.12 | ALPHA: (30) implies:
% 24.85/4.12 | (31) aDimensionOf0(all_32_2) = all_46_7
% 24.85/4.12 | (32) all_46_7 = sz00 | (all_46_0 = all_32_0 & sdtasasdt0(all_46_6,
% 24.85/4.12 | all_46_5) = all_46_4 & sziznziztdt0(all_32_2) = all_46_5 &
% 24.85/4.12 | sziznziztdt0(all_32_2) = all_46_6 & sdtlbdtrb0(all_32_2, all_46_7) =
% 24.85/4.12 | all_46_2 & sdtlbdtrb0(all_32_2, all_46_8) = all_46_3 &
% 24.85/4.12 | aDimensionOf0(all_32_2) = all_46_8 & sdtasdt0(all_46_3, all_46_2) =
% 24.85/4.12 | all_46_1 & sdtpldt0(all_46_4, all_46_1) = all_32_0 & $i(all_46_1) &
% 24.85/4.12 | $i(all_46_2) & $i(all_46_3) & $i(all_46_4) & $i(all_46_5) &
% 24.85/4.12 | $i(all_46_6) & $i(all_46_8) & $i(all_32_0)) | ( ~ (all_46_7 =
% 24.85/4.12 | all_46_8) & aDimensionOf0(all_32_2) = all_46_8 & $i(all_46_8))
% 24.85/4.12 |
% 24.85/4.12 | PRED_UNIFY: (15), (21) imply:
% 24.85/4.12 | (33) ~ (all_32_0 = sz0z00)
% 24.85/4.12 |
% 24.85/4.12 | GROUND_INST: instantiating (11) with all_32_1, all_46_7, all_32_2, simplifying
% 24.85/4.12 | with (18), (31) gives:
% 24.85/4.12 | (34) all_46_7 = all_32_1
% 24.85/4.12 |
% 24.85/4.12 | GROUND_INST: instantiating (11) with all_44_0, all_46_7, all_32_2, simplifying
% 24.85/4.12 | with (29), (31) gives:
% 24.85/4.12 | (35) all_46_7 = all_44_0
% 24.85/4.12 |
% 24.85/4.12 | COMBINE_EQS: (34), (35) imply:
% 24.85/4.12 | (36) all_44_0 = all_32_1
% 24.85/4.12 |
% 24.85/4.12 | BETA: splitting (25) gives:
% 24.85/4.12 |
% 24.85/4.12 | Case 1:
% 24.85/4.12 | |
% 24.85/4.12 | | (37) all_32_0 = sz0z00
% 24.85/4.12 | |
% 24.85/4.12 | | REDUCE: (33), (37) imply:
% 24.85/4.12 | | (38) $false
% 24.85/4.13 | |
% 24.85/4.13 | | CLOSE: (38) is inconsistent.
% 24.85/4.13 | |
% 24.85/4.13 | Case 2:
% 24.85/4.13 | |
% 24.85/4.13 | | (39) ? [v0: $i] : ? [v1: $i] : (aDimensionOf0(all_32_2) = v1 & $i(v1) &
% 24.85/4.13 | | ( ~ (v1 = sz00) | ( ~ (v0 = sz00) & aDimensionOf0(all_32_2) = v0 &
% 24.85/4.13 | | $i(v0))))
% 24.85/4.13 | |
% 24.85/4.13 | | DELTA: instantiating (39) with fresh symbols all_60_0, all_60_1 gives:
% 24.85/4.13 | | (40) aDimensionOf0(all_32_2) = all_60_0 & $i(all_60_0) & ( ~ (all_60_0 =
% 24.85/4.13 | | sz00) | ( ~ (all_60_1 = sz00) & aDimensionOf0(all_32_2) =
% 24.85/4.13 | | all_60_1 & $i(all_60_1)))
% 24.85/4.13 | |
% 24.85/4.13 | | ALPHA: (40) implies:
% 24.85/4.13 | | (41) aDimensionOf0(all_32_2) = all_60_0
% 24.85/4.13 | | (42) ~ (all_60_0 = sz00) | ( ~ (all_60_1 = sz00) &
% 24.85/4.13 | | aDimensionOf0(all_32_2) = all_60_1 & $i(all_60_1))
% 24.85/4.13 | |
% 24.85/4.13 | | BETA: splitting (42) gives:
% 24.85/4.13 | |
% 24.85/4.13 | | Case 1:
% 24.85/4.13 | | |
% 24.85/4.13 | | | (43) ~ (all_60_0 = sz00)
% 24.85/4.13 | | |
% 24.85/4.13 | | | GROUND_INST: instantiating (11) with all_32_1, all_60_0, all_32_2,
% 24.85/4.13 | | | simplifying with (18), (41) gives:
% 24.85/4.13 | | | (44) all_60_0 = all_32_1
% 24.85/4.13 | | |
% 24.85/4.13 | | | REDUCE: (43), (44) imply:
% 24.85/4.13 | | | (45) ~ (all_32_1 = sz00)
% 24.85/4.13 | | |
% 24.85/4.13 | | | BETA: splitting (32) gives:
% 24.85/4.13 | | |
% 24.85/4.13 | | | Case 1:
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | (46) all_46_7 = sz00
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | COMBINE_EQS: (34), (46) imply:
% 24.85/4.13 | | | | (47) all_32_1 = sz00
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | SIMP: (47) implies:
% 24.85/4.13 | | | | (48) all_32_1 = sz00
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | REDUCE: (45), (48) imply:
% 24.85/4.13 | | | | (49) $false
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | CLOSE: (49) is inconsistent.
% 24.85/4.13 | | | |
% 24.85/4.13 | | | Case 2:
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | (50) ~ (all_46_7 = sz00)
% 24.85/4.13 | | | | (51) (all_46_0 = all_32_0 & sdtasasdt0(all_46_6, all_46_5) = all_46_4
% 24.85/4.13 | | | | & sziznziztdt0(all_32_2) = all_46_5 & sziznziztdt0(all_32_2) =
% 24.85/4.13 | | | | all_46_6 & sdtlbdtrb0(all_32_2, all_46_7) = all_46_2 &
% 24.85/4.13 | | | | sdtlbdtrb0(all_32_2, all_46_8) = all_46_3 &
% 24.85/4.13 | | | | aDimensionOf0(all_32_2) = all_46_8 & sdtasdt0(all_46_3,
% 24.85/4.13 | | | | all_46_2) = all_46_1 & sdtpldt0(all_46_4, all_46_1) =
% 24.85/4.13 | | | | all_32_0 & $i(all_46_1) & $i(all_46_2) & $i(all_46_3) &
% 24.85/4.13 | | | | $i(all_46_4) & $i(all_46_5) & $i(all_46_6) & $i(all_46_8) &
% 24.85/4.13 | | | | $i(all_32_0)) | ( ~ (all_46_7 = all_46_8) &
% 24.85/4.13 | | | | aDimensionOf0(all_32_2) = all_46_8 & $i(all_46_8))
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | BETA: splitting (22) gives:
% 24.85/4.13 | | | |
% 24.85/4.13 | | | | Case 1:
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | (52) all_32_1 = sz00
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | REDUCE: (45), (52) imply:
% 24.85/4.13 | | | | | (53) $false
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | CLOSE: (53) is inconsistent.
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | Case 2:
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 24.85/4.13 | | | | | (sziznziztdt0(all_32_2) = v2 & sziznziztdt0(all_32_2) = v0 &
% 24.85/4.13 | | | | | aDimensionOf0(v2) = v1 & aDimensionOf0(v0) = v1 & $i(v2) &
% 24.85/4.13 | | | | | $i(v1) & $i(v0))
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | DELTA: instantiating (54) with fresh symbols all_77_0, all_77_1,
% 24.85/4.13 | | | | | all_77_2 gives:
% 24.85/4.13 | | | | | (55) sziznziztdt0(all_32_2) = all_77_0 & sziznziztdt0(all_32_2) =
% 24.85/4.13 | | | | | all_77_2 & aDimensionOf0(all_77_0) = all_77_1 &
% 24.85/4.13 | | | | | aDimensionOf0(all_77_2) = all_77_1 & $i(all_77_0) &
% 24.85/4.13 | | | | | $i(all_77_1) & $i(all_77_2)
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | ALPHA: (55) implies:
% 24.85/4.13 | | | | | (56) $i(all_77_1)
% 24.85/4.13 | | | | | (57) aDimensionOf0(all_77_2) = all_77_1
% 24.85/4.13 | | | | | (58) sziznziztdt0(all_32_2) = all_77_2
% 24.85/4.13 | | | | | (59) sziznziztdt0(all_32_2) = all_77_0
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | BETA: splitting (23) gives:
% 24.85/4.13 | | | | |
% 24.85/4.13 | | | | | Case 1:
% 24.85/4.13 | | | | | |
% 24.85/4.13 | | | | | | (60) all_32_1 = sz00
% 24.85/4.13 | | | | | |
% 24.85/4.13 | | | | | | REDUCE: (45), (60) imply:
% 24.85/4.13 | | | | | | (61) $false
% 24.85/4.13 | | | | | |
% 24.85/4.13 | | | | | | CLOSE: (61) is inconsistent.
% 24.85/4.13 | | | | | |
% 24.85/4.13 | | | | | Case 2:
% 24.85/4.13 | | | | | |
% 24.85/4.13 | | | | | | (62) ? [v0: $i] : (sziznziztdt0(all_32_2) = v0 & $i(v0) & !
% 24.85/4.13 | | | | | | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(v0,
% 24.85/4.13 | | | | | | v2) = v3) | ~ (aDimensionOf0(v0) = v1) | ~ $i(v2)
% 24.85/4.13 | | | | | | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(all_32_2, v2) =
% 24.85/4.13 | | | | | | v3 & $i(v3))) & ! [v1: $i] : ! [v2: $i] : ! [v3:
% 24.85/4.13 | | | | | | $i] : ( ~ (sdtlbdtrb0(all_32_2, v2) = v3) | ~
% 24.85/4.13 | | | | | | (aDimensionOf0(v0) = v1) | ~ $i(v2) | ~
% 24.85/4.13 | | | | | | aNaturalNumber0(v2) | (sdtlbdtrb0(v0, v2) = v3 &
% 24.85/4.13 | | | | | | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.85/4.13 | | | | | | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) |
% 24.85/4.13 | | | | | | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 24.85/4.13 | | | | | | ($i(v4) & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 &
% 24.85/4.13 | | | | | | sdtlbdtrb0(all_32_2, v4) = v6 & $i(v6) & $i(v5) &
% 24.85/4.13 | | | | | | aNaturalNumber0(v4)) | ( ~ (v3 = all_32_1) &
% 24.85/4.13 | | | | | | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] :
% 24.85/4.13 | | | | | | ( ~ (aDimensionOf0(v0) = v1) | aVector0(v0)) & ! [v1: $i]
% 24.85/4.13 | | | | | | : ( ~ (aDimensionOf0(v0) = v1) | (szszuzczcdt0(v1) =
% 24.85/4.13 | | | | | | all_32_1 & $i(all_32_1))))
% 24.85/4.13 | | | | | |
% 24.85/4.13 | | | | | | DELTA: instantiating (62) with fresh symbol all_82_0 gives:
% 24.85/4.13 | | | | | | (63) sziznziztdt0(all_32_2) = all_82_0 & $i(all_82_0) & ! [v0:
% 24.85/4.14 | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.85/4.14 | | | | | | (sdtlbdtrb0(all_82_0, v1) = v2) | ~
% 24.85/4.14 | | | | | | (aDimensionOf0(all_82_0) = v0) | ~ $i(v1) | ~
% 24.85/4.14 | | | | | | aNaturalNumber0(v1) | (sdtlbdtrb0(all_32_2, v1) = v2 &
% 24.85/4.14 | | | | | | $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 24.85/4.14 | | | | | | (sdtlbdtrb0(all_32_2, v1) = v2) | ~
% 24.85/4.14 | | | | | | (aDimensionOf0(all_82_0) = v0) | ~ $i(v1) | ~
% 24.85/4.14 | | | | | | aNaturalNumber0(v1) | (sdtlbdtrb0(all_82_0, v1) = v2 &
% 24.85/4.14 | | | | | | $i(v2))) & ! [v0: any] : ! [v1: $i] : (v0 = all_82_0 |
% 24.85/4.14 | | | | | | ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0)
% 24.85/4.14 | | | | | | | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 24.85/4.14 | | | | | | ($i(v3) & (( ~ (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 &
% 24.85/4.14 | | | | | | sdtlbdtrb0(all_32_2, v3) = v5 & $i(v5) & $i(v4) &
% 24.85/4.14 | | | | | | aNaturalNumber0(v3)) | ( ~ (v2 = all_32_1) &
% 24.85/4.14 | | | | | | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : (
% 24.85/4.14 | | | | | | ~ (aDimensionOf0(all_82_0) = v0) | aVector0(all_82_0)) &
% 24.85/4.14 | | | | | | ! [v0: $i] : ( ~ (aDimensionOf0(all_82_0) = v0) |
% 24.85/4.14 | | | | | | (szszuzczcdt0(v0) = all_32_1 & $i(all_32_1)))
% 24.85/4.14 | | | | | |
% 24.85/4.14 | | | | | | ALPHA: (63) implies:
% 24.85/4.14 | | | | | | (64) sziznziztdt0(all_32_2) = all_82_0
% 24.85/4.14 | | | | | | (65) ! [v0: $i] : ( ~ (aDimensionOf0(all_82_0) = v0) |
% 24.85/4.14 | | | | | | (szszuzczcdt0(v0) = all_32_1 & $i(all_32_1)))
% 24.85/4.14 | | | | | | (66) ! [v0: $i] : ( ~ (aDimensionOf0(all_82_0) = v0) |
% 24.85/4.14 | | | | | | aVector0(all_82_0))
% 24.85/4.14 | | | | | |
% 24.85/4.14 | | | | | | BETA: splitting (51) gives:
% 24.85/4.14 | | | | | |
% 24.85/4.14 | | | | | | Case 1:
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | (67) all_46_0 = all_32_0 & sdtasasdt0(all_46_6, all_46_5) =
% 24.85/4.14 | | | | | | | all_46_4 & sziznziztdt0(all_32_2) = all_46_5 &
% 24.85/4.14 | | | | | | | sziznziztdt0(all_32_2) = all_46_6 & sdtlbdtrb0(all_32_2,
% 24.85/4.14 | | | | | | | all_46_7) = all_46_2 & sdtlbdtrb0(all_32_2, all_46_8) =
% 24.85/4.14 | | | | | | | all_46_3 & aDimensionOf0(all_32_2) = all_46_8 &
% 24.85/4.14 | | | | | | | sdtasdt0(all_46_3, all_46_2) = all_46_1 &
% 24.85/4.14 | | | | | | | sdtpldt0(all_46_4, all_46_1) = all_32_0 & $i(all_46_1) &
% 24.85/4.14 | | | | | | | $i(all_46_2) & $i(all_46_3) & $i(all_46_4) & $i(all_46_5)
% 24.85/4.14 | | | | | | | & $i(all_46_6) & $i(all_46_8) & $i(all_32_0)
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | ALPHA: (67) implies:
% 24.85/4.14 | | | | | | | (68) $i(all_46_8)
% 24.85/4.14 | | | | | | | (69) $i(all_46_5)
% 24.85/4.14 | | | | | | | (70) $i(all_46_4)
% 24.85/4.14 | | | | | | | (71) $i(all_46_2)
% 24.85/4.14 | | | | | | | (72) sdtpldt0(all_46_4, all_46_1) = all_32_0
% 24.85/4.14 | | | | | | | (73) sdtasdt0(all_46_3, all_46_2) = all_46_1
% 24.85/4.14 | | | | | | | (74) aDimensionOf0(all_32_2) = all_46_8
% 24.85/4.14 | | | | | | | (75) sdtlbdtrb0(all_32_2, all_46_8) = all_46_3
% 24.85/4.14 | | | | | | | (76) sdtlbdtrb0(all_32_2, all_46_7) = all_46_2
% 24.85/4.14 | | | | | | | (77) sziznziztdt0(all_32_2) = all_46_6
% 24.85/4.14 | | | | | | | (78) sziznziztdt0(all_32_2) = all_46_5
% 24.85/4.14 | | | | | | | (79) sdtasasdt0(all_46_6, all_46_5) = all_46_4
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | REDUCE: (34), (76) imply:
% 24.85/4.14 | | | | | | | (80) sdtlbdtrb0(all_32_2, all_32_1) = all_46_2
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | GROUND_INST: instantiating (11) with all_32_1, all_46_8, all_32_2,
% 24.85/4.14 | | | | | | | simplifying with (18), (74) gives:
% 24.85/4.14 | | | | | | | (81) all_46_8 = all_32_1
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | GROUND_INST: instantiating (13) with all_46_2, all_46_3, all_32_1,
% 24.85/4.14 | | | | | | | all_32_2, simplifying with (80) gives:
% 24.85/4.14 | | | | | | | (82) all_46_2 = all_46_3 | ~ (sdtlbdtrb0(all_32_2, all_32_1) =
% 24.85/4.14 | | | | | | | all_46_3)
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_77_2, all_77_0, all_32_2,
% 24.85/4.14 | | | | | | | simplifying with (58), (59) gives:
% 24.85/4.14 | | | | | | | (83) all_77_0 = all_77_2
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_46_5, all_77_0, all_32_2,
% 24.85/4.14 | | | | | | | simplifying with (59), (78) gives:
% 24.85/4.14 | | | | | | | (84) all_77_0 = all_46_5
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_77_0, all_82_0, all_32_2,
% 24.85/4.14 | | | | | | | simplifying with (59), (64) gives:
% 24.85/4.14 | | | | | | | (85) all_82_0 = all_77_0
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | GROUND_INST: instantiating (12) with all_46_6, all_82_0, all_32_2,
% 24.85/4.14 | | | | | | | simplifying with (64), (77) gives:
% 24.85/4.14 | | | | | | | (86) all_82_0 = all_46_6
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | COMBINE_EQS: (85), (86) imply:
% 24.85/4.14 | | | | | | | (87) all_77_0 = all_46_6
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | SIMP: (87) implies:
% 24.85/4.14 | | | | | | | (88) all_77_0 = all_46_6
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | COMBINE_EQS: (83), (88) imply:
% 24.85/4.14 | | | | | | | (89) all_77_2 = all_46_6
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | COMBINE_EQS: (83), (84) imply:
% 24.85/4.14 | | | | | | | (90) all_77_2 = all_46_5
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | COMBINE_EQS: (89), (90) imply:
% 24.85/4.14 | | | | | | | (91) all_46_5 = all_46_6
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | SIMP: (91) implies:
% 24.85/4.14 | | | | | | | (92) all_46_5 = all_46_6
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | REDUCE: (79), (92) imply:
% 24.85/4.14 | | | | | | | (93) sdtasasdt0(all_46_6, all_46_6) = all_46_4
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | REDUCE: (75), (81) imply:
% 24.85/4.14 | | | | | | | (94) sdtlbdtrb0(all_32_2, all_32_1) = all_46_3
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | REDUCE: (57), (89) imply:
% 24.85/4.14 | | | | | | | (95) aDimensionOf0(all_46_6) = all_77_1
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | REDUCE: (69), (92) imply:
% 24.85/4.14 | | | | | | | (96) $i(all_46_6)
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | REDUCE: (68), (81) imply:
% 24.85/4.14 | | | | | | | (97) $i(all_32_1)
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | BETA: splitting (82) gives:
% 24.85/4.14 | | | | | | |
% 24.85/4.14 | | | | | | | Case 1:
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | (98) ~ (sdtlbdtrb0(all_32_2, all_32_1) = all_46_3)
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | PRED_UNIFY: (94), (98) imply:
% 24.85/4.14 | | | | | | | | (99) $false
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | CLOSE: (99) is inconsistent.
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | Case 2:
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | (100) all_46_2 = all_46_3
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | REDUCE: (73), (100) imply:
% 24.85/4.14 | | | | | | | | (101) sdtasdt0(all_46_3, all_46_3) = all_46_1
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | REDUCE: (71), (100) imply:
% 24.85/4.14 | | | | | | | | (102) $i(all_46_3)
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | GROUND_INST: instantiating (66) with all_77_1 gives:
% 24.85/4.14 | | | | | | | | (103) ~ (aDimensionOf0(all_82_0) = all_77_1) |
% 24.85/4.14 | | | | | | | | aVector0(all_82_0)
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | GROUND_INST: instantiating (65) with all_77_1 gives:
% 24.85/4.14 | | | | | | | | (104) ~ (aDimensionOf0(all_82_0) = all_77_1) |
% 24.85/4.14 | | | | | | | | (szszuzczcdt0(all_77_1) = all_32_1 & $i(all_32_1))
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | GROUND_INST: instantiating (mElmSc) with all_32_2, all_32_1,
% 24.85/4.14 | | | | | | | | all_46_3, simplifying with (16), (17), (24), (94),
% 24.85/4.14 | | | | | | | | (97) gives:
% 24.85/4.14 | | | | | | | | (105) aScalar0(all_46_3)
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | BETA: splitting (103) gives:
% 24.85/4.14 | | | | | | | |
% 24.85/4.14 | | | | | | | | Case 1:
% 24.85/4.14 | | | | | | | | |
% 24.85/4.14 | | | | | | | | | (106) ~ (aDimensionOf0(all_82_0) = all_77_1)
% 24.85/4.14 | | | | | | | | |
% 24.85/4.14 | | | | | | | | | REDUCE: (86), (106) imply:
% 24.85/4.14 | | | | | | | | | (107) ~ (aDimensionOf0(all_46_6) = all_77_1)
% 24.85/4.14 | | | | | | | | |
% 24.85/4.15 | | | | | | | | | PRED_UNIFY: (95), (107) imply:
% 24.85/4.15 | | | | | | | | | (108) $false
% 24.85/4.15 | | | | | | | | |
% 24.85/4.15 | | | | | | | | | CLOSE: (108) is inconsistent.
% 24.85/4.15 | | | | | | | | |
% 24.85/4.15 | | | | | | | | Case 2:
% 24.85/4.15 | | | | | | | | |
% 24.85/4.15 | | | | | | | | | (109) aVector0(all_82_0)
% 24.85/4.15 | | | | | | | | | (110) aDimensionOf0(all_82_0) = all_77_1
% 24.85/4.15 | | | | | | | | |
% 24.85/4.15 | | | | | | | | | REDUCE: (86), (109) imply:
% 24.85/4.15 | | | | | | | | | (111) aVector0(all_46_6)
% 24.85/4.15 | | | | | | | | |
% 24.85/4.15 | | | | | | | | | BETA: splitting (104) gives:
% 24.85/4.15 | | | | | | | | |
% 24.85/4.15 | | | | | | | | | Case 1:
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | (112) ~ (aDimensionOf0(all_82_0) = all_77_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | REDUCE: (86), (112) imply:
% 24.85/4.15 | | | | | | | | | | (113) ~ (aDimensionOf0(all_46_6) = all_77_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | PRED_UNIFY: (95), (113) imply:
% 24.85/4.15 | | | | | | | | | | (114) $false
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | CLOSE: (114) is inconsistent.
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | Case 2:
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | (115) szszuzczcdt0(all_77_1) = all_32_1 & $i(all_32_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | ALPHA: (115) implies:
% 24.85/4.15 | | | | | | | | | | (116) szszuzczcdt0(all_77_1) = all_32_1
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mMulSc) with all_46_3, all_46_3,
% 24.85/4.15 | | | | | | | | | | all_46_1, simplifying with (101), (102), (105)
% 24.85/4.15 | | | | | | | | | | gives:
% 24.85/4.15 | | | | | | | | | | (117) aScalar0(all_46_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (2) with all_46_3, all_46_3,
% 24.85/4.15 | | | | | | | | | | all_46_1, simplifying with (101), (102), (105)
% 24.85/4.15 | | | | | | | | | | gives:
% 24.85/4.15 | | | | | | | | | | (118) ? [v0: $i] : ? [v1: $i] : (smndt0(all_46_3) = v1
% 24.85/4.15 | | | | | | | | | | & smndt0(all_46_3) = v0 & sdtasdt0(v0, v1) =
% 24.85/4.15 | | | | | | | | | | all_46_1 & $i(v1) & $i(v0) & $i(all_46_1))
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (4) with all_46_3, all_46_1,
% 24.85/4.15 | | | | | | | | | | simplifying with (101), (102), (105) gives:
% 24.85/4.15 | | | | | | | | | | (119) sdtlseqdt0(sz0z00, all_46_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mScPr) with all_46_6, all_46_6,
% 24.85/4.15 | | | | | | | | | | all_46_4, simplifying with (93), (96), (111)
% 24.85/4.15 | | | | | | | | | | gives:
% 24.85/4.15 | | | | | | | | | | (120) aScalar0(all_46_4) | ? [v0: $i] : ? [v1: $i] : (
% 24.85/4.15 | | | | | | | | | | ~ (v1 = v0) & aDimensionOf0(all_46_6) = v1 &
% 24.85/4.15 | | | | | | | | | | aDimensionOf0(all_46_6) = v0 & $i(v1) & $i(v0))
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (8) with all_46_6, all_46_6,
% 24.85/4.15 | | | | | | | | | | all_46_4, simplifying with (93), (96), (111)
% 24.85/4.15 | | | | | | | | | | gives:
% 24.85/4.15 | | | | | | | | | | (121) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 24.85/4.15 | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] :
% 24.85/4.15 | | | | | | | | | | ? [v7: $i] : ? [v8: int] :
% 24.85/4.15 | | | | | | | | | | (aDimensionOf0(all_46_6) = v1 & $i(v1) & (v1 = sz00
% 24.85/4.15 | | | | | | | | | | | (v8 = all_46_4 & sdtasasdt0(v2, v3) = v4 &
% 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = v3 &
% 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = v2 &
% 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, v1) = v6 &
% 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, v0) = v5 &
% 24.85/4.15 | | | | | | | | | | aDimensionOf0(all_46_6) = v0 & sdtasdt0(v5,
% 24.85/4.15 | | | | | | | | | | v6) = v7 & sdtpldt0(v4, v7) = all_46_4 &
% 24.85/4.15 | | | | | | | | | | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 24.85/4.15 | | | | | | | | | | $i(v2) & $i(v0) & $i(all_46_4)) | ( ~ (v1 =
% 24.85/4.15 | | | | | | | | | | v0) & aDimensionOf0(all_46_6) = v0 &
% 24.85/4.15 | | | | | | | | | | $i(v0))))
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (20) with all_46_6, all_46_4,
% 24.85/4.15 | | | | | | | | | | simplifying with (93), (96), (111) gives:
% 24.85/4.15 | | | | | | | | | | (122) sdtlseqdt0(sz0z00, all_46_4) | ? [v0: $i] :
% 24.85/4.15 | | | | | | | | | | (aDimensionOf0(all_46_6) = v0 & $i(v0) & ~
% 24.85/4.15 | | | | | | | | | | iLess0(v0, all_32_1))
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mDimNat) with all_46_6, all_77_1,
% 24.85/4.15 | | | | | | | | | | simplifying with (95), (96), (111) gives:
% 24.85/4.15 | | | | | | | | | | (123) aNaturalNumber0(all_77_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | GROUND_INST: instantiating (mIH) with all_77_1, all_32_1,
% 24.85/4.15 | | | | | | | | | | simplifying with (56), (116) gives:
% 24.85/4.15 | | | | | | | | | | (124) ~ aNaturalNumber0(all_77_1) | iLess0(all_77_1,
% 24.85/4.15 | | | | | | | | | | all_32_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | DELTA: instantiating (118) with fresh symbols all_137_0,
% 24.85/4.15 | | | | | | | | | | all_137_1 gives:
% 24.85/4.15 | | | | | | | | | | (125) smndt0(all_46_3) = all_137_0 & smndt0(all_46_3) =
% 24.85/4.15 | | | | | | | | | | all_137_1 & sdtasdt0(all_137_1, all_137_0) =
% 24.85/4.15 | | | | | | | | | | all_46_1 & $i(all_137_0) & $i(all_137_1) &
% 24.85/4.15 | | | | | | | | | | $i(all_46_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | ALPHA: (125) implies:
% 24.85/4.15 | | | | | | | | | | (126) $i(all_46_1)
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | DELTA: instantiating (121) with fresh symbols all_142_0,
% 24.85/4.15 | | | | | | | | | | all_142_1, all_142_2, all_142_3, all_142_4,
% 24.85/4.15 | | | | | | | | | | all_142_5, all_142_6, all_142_7, all_142_8 gives:
% 24.85/4.15 | | | | | | | | | | (127) aDimensionOf0(all_46_6) = all_142_7 & $i(all_142_7)
% 24.85/4.15 | | | | | | | | | | & (all_142_7 = sz00 | (all_142_0 = all_46_4 &
% 24.85/4.15 | | | | | | | | | | sdtasasdt0(all_142_6, all_142_5) = all_142_4 &
% 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = all_142_5 &
% 24.85/4.15 | | | | | | | | | | sziznziztdt0(all_46_6) = all_142_6 &
% 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, all_142_7) = all_142_2 &
% 24.85/4.15 | | | | | | | | | | sdtlbdtrb0(all_46_6, all_142_8) = all_142_3 &
% 24.85/4.15 | | | | | | | | | | aDimensionOf0(all_46_6) = all_142_8 &
% 24.85/4.15 | | | | | | | | | | sdtasdt0(all_142_3, all_142_2) = all_142_1 &
% 24.85/4.15 | | | | | | | | | | sdtpldt0(all_142_4, all_142_1) = all_46_4 &
% 24.85/4.15 | | | | | | | | | | $i(all_142_1) & $i(all_142_2) & $i(all_142_3) &
% 24.85/4.15 | | | | | | | | | | $i(all_142_4) & $i(all_142_5) & $i(all_142_6) &
% 24.85/4.15 | | | | | | | | | | $i(all_142_8) & $i(all_46_4)) | ( ~ (all_142_7
% 24.85/4.15 | | | | | | | | | | = all_142_8) & aDimensionOf0(all_46_6) =
% 24.85/4.15 | | | | | | | | | | all_142_8 & $i(all_142_8)))
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | ALPHA: (127) implies:
% 24.85/4.15 | | | | | | | | | | (128) aDimensionOf0(all_46_6) = all_142_7
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | BETA: splitting (124) gives:
% 24.85/4.15 | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | Case 1:
% 24.85/4.15 | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | (129) ~ aNaturalNumber0(all_77_1)
% 24.85/4.15 | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | PRED_UNIFY: (123), (129) imply:
% 24.85/4.15 | | | | | | | | | | | (130) $false
% 24.85/4.15 | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | CLOSE: (130) is inconsistent.
% 24.85/4.15 | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | Case 2:
% 24.85/4.15 | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | (131) iLess0(all_77_1, all_32_1)
% 24.85/4.15 | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | BETA: splitting (120) gives:
% 24.85/4.15 | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | Case 1:
% 24.85/4.15 | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | (132) aScalar0(all_46_4)
% 24.85/4.15 | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_77_1, all_142_7,
% 24.85/4.15 | | | | | | | | | | | | all_46_6, simplifying with (95), (128) gives:
% 24.85/4.15 | | | | | | | | | | | | (133) all_142_7 = all_77_1
% 24.85/4.15 | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | BETA: splitting (122) gives:
% 24.85/4.15 | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | Case 1:
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | | (134) sdtlseqdt0(sz0z00, all_46_4)
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_46_4, all_46_1,
% 24.85/4.15 | | | | | | | | | | | | | all_32_0, simplifying with (15), (70), (72),
% 24.85/4.15 | | | | | | | | | | | | | (117), (119), (126), (132), (134) gives:
% 24.85/4.15 | | | | | | | | | | | | | (135) $false
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | Case 2:
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | | (136) ? [v0: $i] : (aDimensionOf0(all_46_6) = v0 &
% 24.85/4.15 | | | | | | | | | | | | | $i(v0) & ~ iLess0(v0, all_32_1))
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | | DELTA: instantiating (136) with fresh symbol all_172_0
% 24.85/4.15 | | | | | | | | | | | | | gives:
% 24.85/4.15 | | | | | | | | | | | | | (137) aDimensionOf0(all_46_6) = all_172_0 &
% 24.85/4.15 | | | | | | | | | | | | | $i(all_172_0) & ~ iLess0(all_172_0, all_32_1)
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.15 | | | | | | | | | | | | | ALPHA: (137) implies:
% 24.85/4.15 | | | | | | | | | | | | | (138) ~ iLess0(all_172_0, all_32_1)
% 24.85/4.15 | | | | | | | | | | | | | (139) aDimensionOf0(all_46_6) = all_172_0
% 24.85/4.15 | | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_77_1, all_172_0,
% 24.85/4.16 | | | | | | | | | | | | | all_46_6, simplifying with (95), (139) gives:
% 24.85/4.16 | | | | | | | | | | | | | (140) all_172_0 = all_77_1
% 24.85/4.16 | | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | | PRED_UNIFY: (131), (138) imply:
% 24.85/4.16 | | | | | | | | | | | | | (141) ~ (all_172_0 = all_77_1)
% 24.85/4.16 | | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | | REDUCE: (140), (141) imply:
% 24.85/4.16 | | | | | | | | | | | | | (142) $false
% 24.85/4.16 | | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | | CLOSE: (142) is inconsistent.
% 24.85/4.16 | | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | End of split
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | Case 2:
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | (143) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = v1 &
% 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = v0 & $i(v1) & $i(v0))
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | DELTA: instantiating (143) with fresh symbols all_164_0,
% 24.85/4.16 | | | | | | | | | | | | all_164_1 gives:
% 24.85/4.16 | | | | | | | | | | | | (144) ~ (all_164_0 = all_164_1) &
% 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = all_164_0 &
% 24.85/4.16 | | | | | | | | | | | | aDimensionOf0(all_46_6) = all_164_1 &
% 24.85/4.16 | | | | | | | | | | | | $i(all_164_0) & $i(all_164_1)
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | ALPHA: (144) implies:
% 24.85/4.16 | | | | | | | | | | | | (145) ~ (all_164_0 = all_164_1)
% 24.85/4.16 | | | | | | | | | | | | (146) aDimensionOf0(all_46_6) = all_164_1
% 24.85/4.16 | | | | | | | | | | | | (147) aDimensionOf0(all_46_6) = all_164_0
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_77_1, all_164_1,
% 24.85/4.16 | | | | | | | | | | | | all_46_6, simplifying with (95), (146) gives:
% 24.85/4.16 | | | | | | | | | | | | (148) all_164_1 = all_77_1
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_164_1, all_164_0,
% 24.85/4.16 | | | | | | | | | | | | all_46_6, simplifying with (146), (147) gives:
% 24.85/4.16 | | | | | | | | | | | | (149) all_164_0 = all_164_1
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_142_7, all_164_0,
% 24.85/4.16 | | | | | | | | | | | | all_46_6, simplifying with (128), (147) gives:
% 24.85/4.16 | | | | | | | | | | | | (150) all_164_0 = all_142_7
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | COMBINE_EQS: (149), (150) imply:
% 24.85/4.16 | | | | | | | | | | | | (151) all_164_1 = all_142_7
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | SIMP: (151) implies:
% 24.85/4.16 | | | | | | | | | | | | (152) all_164_1 = all_142_7
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | COMBINE_EQS: (148), (152) imply:
% 24.85/4.16 | | | | | | | | | | | | (153) all_142_7 = all_77_1
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | COMBINE_EQS: (150), (153) imply:
% 24.85/4.16 | | | | | | | | | | | | (154) all_164_0 = all_77_1
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | REDUCE: (145), (148), (154) imply:
% 24.85/4.16 | | | | | | | | | | | | (155) $false
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 24.85/4.16 | | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | | End of split
% 24.85/4.16 | | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | | End of split
% 24.85/4.16 | | | | | | | | | |
% 24.85/4.16 | | | | | | | | | End of split
% 24.85/4.16 | | | | | | | | |
% 24.85/4.16 | | | | | | | | End of split
% 24.85/4.16 | | | | | | | |
% 24.85/4.16 | | | | | | | End of split
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | Case 2:
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | | (156) ~ (all_46_7 = all_46_8) & aDimensionOf0(all_32_2) =
% 24.85/4.16 | | | | | | | all_46_8 & $i(all_46_8)
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | | ALPHA: (156) implies:
% 24.85/4.16 | | | | | | | (157) ~ (all_46_7 = all_46_8)
% 24.85/4.16 | | | | | | | (158) aDimensionOf0(all_32_2) = all_46_8
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | | REDUCE: (34), (157) imply:
% 24.85/4.16 | | | | | | | (159) ~ (all_46_8 = all_32_1)
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | | SIMP: (159) implies:
% 24.85/4.16 | | | | | | | (160) ~ (all_46_8 = all_32_1)
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | | GROUND_INST: instantiating (11) with all_32_1, all_46_8, all_32_2,
% 24.85/4.16 | | | | | | | simplifying with (18), (158) gives:
% 24.85/4.16 | | | | | | | (161) all_46_8 = all_32_1
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | | REDUCE: (160), (161) imply:
% 24.85/4.16 | | | | | | | (162) $false
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | | CLOSE: (162) is inconsistent.
% 24.85/4.16 | | | | | | |
% 24.85/4.16 | | | | | | End of split
% 24.85/4.16 | | | | | |
% 24.85/4.16 | | | | | End of split
% 24.85/4.16 | | | | |
% 24.85/4.16 | | | | End of split
% 24.85/4.16 | | | |
% 24.85/4.16 | | | End of split
% 24.85/4.16 | | |
% 24.85/4.16 | | Case 2:
% 24.85/4.16 | | |
% 24.85/4.16 | | | (163) all_60_0 = sz00
% 24.85/4.16 | | | (164) ~ (all_60_1 = sz00) & aDimensionOf0(all_32_2) = all_60_1 &
% 24.85/4.16 | | | $i(all_60_1)
% 24.85/4.16 | | |
% 24.85/4.16 | | | ALPHA: (164) implies:
% 24.85/4.16 | | | (165) ~ (all_60_1 = sz00)
% 24.85/4.16 | | | (166) aDimensionOf0(all_32_2) = all_60_1
% 24.85/4.16 | | |
% 24.85/4.16 | | | REDUCE: (41), (163) imply:
% 24.85/4.16 | | | (167) aDimensionOf0(all_32_2) = sz00
% 24.85/4.16 | | |
% 24.85/4.16 | | | GROUND_INST: instantiating (11) with sz00, all_60_1, all_32_2, simplifying
% 24.85/4.16 | | | with (166), (167) gives:
% 24.85/4.16 | | | (168) all_60_1 = sz00
% 24.85/4.16 | | |
% 24.85/4.16 | | | REDUCE: (165), (168) imply:
% 24.85/4.16 | | | (169) $false
% 24.85/4.16 | | |
% 24.85/4.16 | | | CLOSE: (169) is inconsistent.
% 24.85/4.16 | | |
% 24.85/4.16 | | End of split
% 24.85/4.16 | |
% 24.85/4.16 | End of split
% 24.85/4.16 |
% 24.85/4.16 End of proof
% 24.85/4.16 % SZS output end Proof for theBenchmark
% 24.85/4.16
% 24.85/4.16 3568ms
%------------------------------------------------------------------------------