TSTP Solution File: RNG067+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG067+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : 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 13:57:39 EDT 2023
% Result : Theorem 25.03s 4.25s
% Output : Proof 52.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG067+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Aug 27 03:24:48 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.61 ________ _____
% 0.17/0.61 ___ __ \_________(_)________________________________
% 0.17/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.61
% 0.17/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.61 (2023-06-19)
% 0.17/0.61
% 0.17/0.61 (c) Philipp Rümmer, 2009-2023
% 0.17/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.61 Amanda Stjerna.
% 0.17/0.61 Free software under BSD-3-Clause.
% 0.17/0.61
% 0.17/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.61
% 0.17/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.60/0.63 Running up to 7 provers in parallel.
% 0.60/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.60/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.60/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.60/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.60/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.60/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.60/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.70/1.34 Prover 4: Preprocessing ...
% 3.70/1.34 Prover 1: Preprocessing ...
% 4.08/1.39 Prover 3: Preprocessing ...
% 4.08/1.39 Prover 6: Preprocessing ...
% 4.08/1.40 Prover 2: Preprocessing ...
% 4.08/1.40 Prover 5: Preprocessing ...
% 4.08/1.40 Prover 0: Preprocessing ...
% 12.03/2.46 Prover 3: Constructing countermodel ...
% 12.03/2.46 Prover 1: Constructing countermodel ...
% 12.39/2.53 Prover 6: Proving ...
% 14.90/2.89 Prover 5: Constructing countermodel ...
% 16.41/3.21 Prover 4: Constructing countermodel ...
% 18.02/3.27 Prover 2: Proving ...
% 18.02/3.29 Prover 0: Proving ...
% 25.03/4.23 Prover 3: proved (3590ms)
% 25.03/4.23
% 25.03/4.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.03/4.25
% 25.03/4.25 Prover 5: stopped
% 25.03/4.25 Prover 6: stopped
% 25.03/4.25 Prover 2: stopped
% 25.03/4.26 Prover 0: stopped
% 25.48/4.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.48/4.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.48/4.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.48/4.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.48/4.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.46/4.46 Prover 8: Preprocessing ...
% 26.46/4.48 Prover 7: Preprocessing ...
% 26.46/4.49 Prover 13: Preprocessing ...
% 26.46/4.53 Prover 11: Preprocessing ...
% 27.61/4.57 Prover 10: Preprocessing ...
% 28.79/4.73 Prover 8: Warning: ignoring some quantifiers
% 29.03/4.74 Prover 8: Constructing countermodel ...
% 29.03/4.79 Prover 7: Constructing countermodel ...
% 29.76/4.85 Prover 13: Constructing countermodel ...
% 30.24/4.89 Prover 10: Constructing countermodel ...
% 33.38/5.33 Prover 11: Constructing countermodel ...
% 51.44/7.68 Prover 10: Found proof (size 150)
% 51.44/7.69 Prover 10: proved (3432ms)
% 51.44/7.69 Prover 13: stopped
% 51.44/7.69 Prover 4: stopped
% 51.44/7.69 Prover 11: stopped
% 51.44/7.69 Prover 7: stopped
% 51.44/7.69 Prover 1: stopped
% 51.44/7.69 Prover 8: stopped
% 51.44/7.69
% 51.44/7.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.44/7.69
% 51.44/7.73 % SZS output start Proof for theBenchmark
% 51.97/7.74 Assumptions after simplification:
% 51.97/7.74 ---------------------------------
% 51.97/7.74
% 51.97/7.74 (mArith)
% 52.21/7.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 52.21/7.79 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 52.21/7.79 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5:
% 52.21/7.79 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 &
% 52.21/7.79 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 &
% 52.21/7.79 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 &
% 52.21/7.79 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 52.21/7.79 $i(v3)))
% 52.21/7.79
% 52.21/7.79 (mDefInit)
% 52.21/7.79 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 52.21/7.79 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 52.21/7.79 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 52.21/7.79 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 52.21/7.79 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 52.21/7.79 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 52.21/7.79 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 52.21/7.80 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 52.21/7.80 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 52.21/7.80 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 52.21/7.80 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 52.21/7.80 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 52.21/7.80 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 52.21/7.80
% 52.21/7.80 (mDimNat)
% 52.21/7.80 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 52.21/7.80 aVector0(v0) | aNaturalNumber0(v1))
% 52.21/7.80
% 52.21/7.80 (mDistr)
% 52.21/7.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 52.21/7.80 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 52.21/7.80 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 52.21/7.80 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i]
% 52.21/7.80 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 52.21/7.80 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 &
% 52.21/7.80 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 52.21/7.80
% 52.21/7.80 (mLEMon)
% 52.21/7.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 52.21/7.80 $i] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ $i(v3) |
% 52.21/7.81 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~
% 52.21/7.81 sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) |
% 52.21/7.81 ~ aScalar0(v0) | sdtlseqdt0(v4, v5))
% 52.21/7.81
% 52.21/7.81 (mMulSc)
% 52.21/7.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 52.21/7.81 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 52.21/7.81
% 52.21/7.81 (mNatExtr)
% 52.21/7.81 $i(sz00) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | ?
% 52.21/7.81 [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aNaturalNumber0(v1)))
% 52.21/7.81
% 52.21/7.81 (mSumSc)
% 52.21/7.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 52.21/7.81 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 52.21/7.81
% 52.21/7.81 (m__)
% 52.21/7.81 $i(xN) & $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 52.21/7.81 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 52.21/7.81 $i] : (sdtasdt0(xS, xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4
% 52.21/7.81 & sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) = v6 &
% 52.21/7.81 sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0, v0) = v1 &
% 52.21/7.81 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 52.21/7.81 $i(v0) & ~ sdtlseqdt0(v3, v8))
% 52.21/7.81
% 52.21/7.81 (m__1652)
% 52.21/7.82 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 52.21/7.82 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 52.21/7.82 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 52.21/7.82 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 52.21/7.82 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 52.21/7.82 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 52.21/7.82 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 52.21/7.82 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 52.21/7.82
% 52.21/7.82 (m__1678)
% 52.21/7.82 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 52.21/7.82
% 52.21/7.82 (m__1678_01)
% 52.21/7.82 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 52.21/7.82 v0 & $i(v0))
% 52.21/7.82
% 52.21/7.82 (m__1692)
% 52.21/7.82 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 52.21/7.82 $i(v0))
% 52.21/7.82
% 52.21/7.82 (m__1709)
% 52.21/7.82 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp &
% 52.21/7.82 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 &
% 52.21/7.82 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 52.21/7.82 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 52.21/7.82 (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 52.21/7.82
% 52.21/7.82 (m__1726)
% 52.21/7.82 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq &
% 52.21/7.82 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 &
% 52.21/7.82 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 52.21/7.82 (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 52.21/7.82 (sdtlbdtrb0(xq, v2) = v3 & $i(v3))))
% 52.21/7.82
% 52.21/7.82 (m__1746)
% 52.21/7.82 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 52.21/7.82 v0 & $i(v0) & aScalar0(xA))
% 52.21/7.82
% 52.21/7.82 (m__1766)
% 52.21/7.82 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 52.21/7.82 v0 & $i(v0) & aScalar0(xB))
% 52.21/7.82
% 52.21/7.82 (m__1820)
% 52.21/7.83 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE)
% 52.21/7.83
% 52.21/7.83 (m__1873)
% 52.21/7.83 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH)
% 52.21/7.83
% 52.21/7.83 (m__1892)
% 52.21/7.83 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR)
% 52.21/7.83
% 52.21/7.83 (m__1911)
% 52.21/7.83 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP)
% 52.21/7.83
% 52.21/7.83 (m__1930)
% 52.21/7.83 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS)
% 52.21/7.83
% 52.21/7.83 (m__1949)
% 52.21/7.83 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN)
% 52.21/7.83
% 52.21/7.83 (m__1967)
% 52.21/7.83 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0
% 52.21/7.83 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 52.21/7.83
% 52.21/7.83 (m__2004)
% 52.21/7.83 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) &
% 52.21/7.83 sdtlseqdt0(v0, xN))
% 52.21/7.83
% 52.21/7.83 (m__2104)
% 52.21/7.83 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 52.21/7.83 $i] : ? [v4: $i] : (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 &
% 52.21/7.83 sdtasdt0(xR, xR) = v2 & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 &
% 52.21/7.83 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4))
% 52.21/7.83
% 52.21/7.83 (function-axioms)
% 52.21/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 52.21/7.84 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 52.21/7.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 52.21/7.84 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 52.21/7.84 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 52.21/7.84 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 52.21/7.84 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 52.21/7.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 52.21/7.84 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 52.21/7.84 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 52.21/7.84 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 52.21/7.84 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 52.21/7.84 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 52.21/7.84
% 52.21/7.84 Further assumptions not needed in the proof:
% 52.21/7.84 --------------------------------------------
% 52.21/7.84 mDefSPN, mDefSPZ, mDistr2, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, mLEMonM,
% 52.21/7.84 mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mNatSort, mNegSc, mPosMon,
% 52.21/7.84 mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat,
% 52.21/7.84 mVcSort, mZeroNat, m__1783, m__1800, m__1837, m__1854
% 52.21/7.84
% 52.21/7.84 Those formulas are unsatisfiable:
% 52.21/7.84 ---------------------------------
% 52.21/7.84
% 52.21/7.84 Begin of proof
% 52.21/7.84 |
% 52.21/7.84 | ALPHA: (mNatExtr) implies:
% 52.21/7.84 | (1) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | ? [v1:
% 52.21/7.84 | $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aNaturalNumber0(v1)))
% 52.21/7.84 |
% 52.21/7.84 | ALPHA: (mDefInit) implies:
% 52.21/7.85 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 52.21/7.85 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 52.21/7.85 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 52.21/7.85 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 52.21/7.85 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 52.21/7.85 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 52.21/7.85 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 52.21/7.85 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 52.21/7.85 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 52.21/7.85 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 52.21/7.85 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 52.21/7.85 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 52.21/7.85 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 52.21/7.85 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 52.21/7.85 | aVector0(v1))))))
% 52.21/7.85 |
% 52.21/7.85 | ALPHA: (m__1678) implies:
% 52.21/7.85 | (3) aVector0(xs)
% 52.54/7.85 | (4) aVector0(xt)
% 52.54/7.85 |
% 52.54/7.85 | ALPHA: (m__1652) implies:
% 52.54/7.85 | (5) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 52.54/7.85 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 52.54/7.85 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 52.54/7.85 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 52.54/7.85 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 52.54/7.85 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 52.54/7.85 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 52.54/7.85 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 52.54/7.85 | $i(v7)))))))
% 52.54/7.85 |
% 52.54/7.85 | ALPHA: (m__1678_01) implies:
% 52.54/7.85 | (6) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 52.54/7.85 | $i(v0))
% 52.54/7.85 |
% 52.54/7.85 | ALPHA: (m__1692) implies:
% 52.54/7.85 | (7) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 52.54/7.85 |
% 52.54/7.85 | ALPHA: (m__1709) implies:
% 52.54/7.86 | (8) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp)
% 52.54/7.86 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 52.54/7.86 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 52.54/7.86 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 52.54/7.86 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 52.54/7.86 |
% 52.54/7.86 | ALPHA: (m__1726) implies:
% 52.54/7.86 | (9) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq)
% 52.54/7.86 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 52.54/7.86 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 52.54/7.86 | (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 52.54/7.86 | (sdtlbdtrb0(xq, v2) = v3 & $i(v3))))
% 52.54/7.86 |
% 52.54/7.86 | ALPHA: (m__1746) implies:
% 52.54/7.86 | (10) $i(xs)
% 52.54/7.86 | (11) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 52.54/7.86 | $i(v0) & aScalar0(xA))
% 52.54/7.86 |
% 52.54/7.86 | ALPHA: (m__1766) implies:
% 52.54/7.86 | (12) $i(xt)
% 52.54/7.86 | (13) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 &
% 52.54/7.86 | $i(v0) & aScalar0(xB))
% 52.54/7.86 |
% 52.54/7.86 | ALPHA: (m__1820) implies:
% 52.54/7.86 | (14) aScalar0(xE)
% 52.54/7.86 |
% 52.54/7.86 | ALPHA: (m__1873) implies:
% 52.54/7.86 | (15) aScalar0(xH)
% 52.54/7.86 |
% 52.54/7.86 | ALPHA: (m__1892) implies:
% 52.54/7.86 | (16) aScalar0(xR)
% 52.60/7.86 |
% 52.60/7.86 | ALPHA: (m__1911) implies:
% 52.60/7.86 | (17) aScalar0(xP)
% 52.60/7.86 | (18) $i(xH)
% 52.60/7.86 | (19) sdtasdt0(xE, xH) = xP
% 52.60/7.86 |
% 52.60/7.86 | ALPHA: (m__1930) implies:
% 52.60/7.86 | (20) aScalar0(xS)
% 52.60/7.86 |
% 52.60/7.86 | ALPHA: (m__1949) implies:
% 52.60/7.86 | (21) aScalar0(xN)
% 52.60/7.86 |
% 52.60/7.86 | ALPHA: (m__1967) implies:
% 52.60/7.86 | (22) $i(xE)
% 52.60/7.86 |
% 52.60/7.86 | ALPHA: (m__2004) implies:
% 52.60/7.86 | (23) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & sdtlseqdt0(v0, xN))
% 52.60/7.86 |
% 52.60/7.86 | ALPHA: (m__2104) implies:
% 52.60/7.87 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 52.60/7.87 | (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v2
% 52.60/7.87 | & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & $i(v4) & $i(v3) &
% 52.60/7.87 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4))
% 52.60/7.87 |
% 52.60/7.87 | ALPHA: (m__) implies:
% 52.60/7.87 | (25) $i(xR)
% 52.60/7.87 | (26) $i(xP)
% 52.60/7.87 | (27) $i(xS)
% 52.60/7.87 | (28) $i(xN)
% 52.60/7.87 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 52.60/7.87 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xS,
% 52.60/7.87 | xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4 &
% 52.60/7.87 | sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) =
% 52.60/7.87 | v6 & sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0,
% 52.60/7.87 | v0) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 52.60/7.87 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v3, v8))
% 52.60/7.87 |
% 52.60/7.87 | ALPHA: (function-axioms) implies:
% 52.60/7.87 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 52.60/7.87 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 52.60/7.87 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 52.60/7.87 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 52.60/7.87 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 52.60/7.87 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 52.60/7.87 |
% 52.60/7.87 | DELTA: instantiating (6) with fresh symbol all_33_0 gives:
% 52.60/7.87 | (33) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 52.60/7.87 | $i(all_33_0)
% 52.60/7.87 |
% 52.60/7.87 | ALPHA: (33) implies:
% 52.60/7.88 | (34) aDimensionOf0(xs) = all_33_0
% 52.60/7.88 | (35) aDimensionOf0(xt) = all_33_0
% 52.60/7.88 |
% 52.60/7.88 | DELTA: instantiating (7) with fresh symbol all_35_0 gives:
% 52.60/7.88 | (36) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0)
% 52.60/7.88 |
% 52.60/7.88 | ALPHA: (36) implies:
% 52.60/7.88 | (37) ~ (all_35_0 = sz00)
% 52.60/7.88 | (38) aDimensionOf0(xs) = all_35_0
% 52.60/7.88 |
% 52.60/7.88 | DELTA: instantiating (23) with fresh symbol all_37_0 gives:
% 52.60/7.88 | (39) sdtasdt0(xP, xP) = all_37_0 & $i(all_37_0) & sdtlseqdt0(all_37_0, xN)
% 52.60/7.88 |
% 52.60/7.88 | ALPHA: (39) implies:
% 52.60/7.88 | (40) sdtlseqdt0(all_37_0, xN)
% 52.60/7.88 | (41) sdtasdt0(xP, xP) = all_37_0
% 52.60/7.88 |
% 52.60/7.88 | DELTA: instantiating (11) with fresh symbol all_39_0 gives:
% 52.60/7.88 | (42) sdtlbdtrb0(xs, all_39_0) = xA & aDimensionOf0(xs) = all_39_0 &
% 52.60/7.88 | $i(all_39_0) & aScalar0(xA)
% 52.60/7.88 |
% 52.60/7.88 | ALPHA: (42) implies:
% 52.60/7.88 | (43) aDimensionOf0(xs) = all_39_0
% 52.60/7.88 |
% 52.60/7.88 | DELTA: instantiating (13) with fresh symbol all_41_0 gives:
% 52.60/7.88 | (44) sdtlbdtrb0(xt, all_41_0) = xB & aDimensionOf0(xt) = all_41_0 &
% 52.60/7.88 | $i(all_41_0) & aScalar0(xB)
% 52.60/7.88 |
% 52.60/7.88 | ALPHA: (44) implies:
% 52.60/7.88 | (45) aDimensionOf0(xt) = all_41_0
% 52.60/7.88 |
% 52.60/7.88 | DELTA: instantiating (24) with fresh symbols all_45_0, all_45_1, all_45_2,
% 52.60/7.88 | all_45_3, all_45_4 gives:
% 52.60/7.88 | (46) sdtasdt0(xS, xS) = all_45_1 & sdtasdt0(xP, xP) = all_45_4 &
% 52.60/7.88 | sdtasdt0(xR, xR) = all_45_2 & sdtpldt0(all_45_2, all_45_1) = all_45_0
% 52.60/7.88 | & sdtpldt0(all_45_4, all_45_4) = all_45_3 & $i(all_45_0) &
% 52.60/7.88 | $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & $i(all_45_4) &
% 52.60/7.88 | sdtlseqdt0(all_45_3, all_45_0)
% 52.60/7.88 |
% 52.60/7.88 | ALPHA: (46) implies:
% 52.60/7.88 | (47) sdtlseqdt0(all_45_3, all_45_0)
% 52.60/7.88 | (48) sdtpldt0(all_45_4, all_45_4) = all_45_3
% 52.60/7.88 | (49) sdtpldt0(all_45_2, all_45_1) = all_45_0
% 52.60/7.88 | (50) sdtasdt0(xR, xR) = all_45_2
% 52.60/7.88 | (51) sdtasdt0(xP, xP) = all_45_4
% 52.60/7.88 | (52) sdtasdt0(xS, xS) = all_45_1
% 52.60/7.88 |
% 52.60/7.88 | DELTA: instantiating (8) with fresh symbols all_47_0, all_47_1 gives:
% 52.60/7.88 | (53) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_47_1 &
% 52.60/7.88 | aDimensionOf0(xs) = all_47_0 & szszuzczcdt0(all_47_1) = all_47_0 &
% 52.60/7.88 | $i(all_47_0) & $i(all_47_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i]
% 52.60/7.88 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 52.60/7.88 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1)))
% 52.60/7.88 |
% 52.60/7.88 | ALPHA: (53) implies:
% 52.60/7.89 | (54) aDimensionOf0(xs) = all_47_0
% 52.60/7.89 | (55) sziznziztdt0(xs) = xp
% 52.60/7.89 |
% 52.60/7.89 | DELTA: instantiating (9) with fresh symbols all_50_0, all_50_1 gives:
% 52.60/7.89 | (56) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_50_1 &
% 52.60/7.89 | aDimensionOf0(xt) = all_50_0 & szszuzczcdt0(all_50_1) = all_50_0 &
% 52.60/7.89 | $i(all_50_0) & $i(all_50_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i]
% 52.60/7.89 | : ( ~ (sdtlbdtrb0(xt, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 52.60/7.89 | (sdtlbdtrb0(xq, v0) = v1 & $i(v1)))
% 52.60/7.89 |
% 52.60/7.89 | ALPHA: (56) implies:
% 52.60/7.89 | (57) aDimensionOf0(xt) = all_50_0
% 52.60/7.89 | (58) sziznziztdt0(xt) = xq
% 52.60/7.89 |
% 52.60/7.89 | DELTA: instantiating (29) with fresh symbols all_53_0, all_53_1, all_53_2,
% 52.60/7.89 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7, all_53_8 gives:
% 52.60/7.89 | (59) sdtasdt0(xS, xS) = all_53_3 & sdtasdt0(xP, xP) = all_53_8 &
% 52.60/7.89 | sdtasdt0(xR, xR) = all_53_4 & sdtpldt0(all_53_1, xN) = all_53_0 &
% 52.60/7.89 | sdtpldt0(all_53_2, xN) = all_53_1 & sdtpldt0(all_53_4, all_53_3) =
% 52.60/7.89 | all_53_2 & sdtpldt0(all_53_6, all_53_8) = all_53_5 &
% 52.60/7.89 | sdtpldt0(all_53_7, all_53_8) = all_53_6 & sdtpldt0(all_53_8, all_53_8)
% 52.60/7.89 | = all_53_7 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3)
% 52.60/7.89 | & $i(all_53_4) & $i(all_53_5) & $i(all_53_6) & $i(all_53_7) &
% 52.60/7.89 | $i(all_53_8) & ~ sdtlseqdt0(all_53_5, all_53_0)
% 52.60/7.89 |
% 52.60/7.89 | ALPHA: (59) implies:
% 52.60/7.89 | (60) ~ sdtlseqdt0(all_53_5, all_53_0)
% 52.60/7.89 | (61) $i(all_53_4)
% 52.60/7.89 | (62) $i(all_53_3)
% 52.60/7.89 | (63) sdtpldt0(all_53_8, all_53_8) = all_53_7
% 52.60/7.89 | (64) sdtpldt0(all_53_7, all_53_8) = all_53_6
% 52.60/7.89 | (65) sdtpldt0(all_53_6, all_53_8) = all_53_5
% 52.60/7.89 | (66) sdtpldt0(all_53_4, all_53_3) = all_53_2
% 52.60/7.89 | (67) sdtpldt0(all_53_2, xN) = all_53_1
% 52.60/7.89 | (68) sdtpldt0(all_53_1, xN) = all_53_0
% 52.60/7.89 | (69) sdtasdt0(xR, xR) = all_53_4
% 52.60/7.89 | (70) sdtasdt0(xP, xP) = all_53_8
% 52.60/7.89 | (71) sdtasdt0(xS, xS) = all_53_3
% 52.60/7.89 |
% 52.60/7.90 | DELTA: instantiating (5) with fresh symbol all_55_0 gives:
% 52.60/7.90 | (72) aDimensionOf0(xs) = all_55_0 & $i(all_55_0) & ! [v0: $i] : ! [v1:
% 52.60/7.90 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 52.60/7.90 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 52.60/7.90 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 52.60/7.90 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 52.60/7.90 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 52.60/7.90 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 52.60/7.90 | iLess0(v5, all_55_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 52.60/7.90 | & $i(v6))))))
% 52.60/7.90 |
% 52.60/7.90 | ALPHA: (72) implies:
% 52.60/7.90 | (73) aDimensionOf0(xs) = all_55_0
% 52.60/7.90 |
% 52.60/7.90 | GROUND_INST: instantiating (32) with all_45_2, all_53_4, xR, xR, simplifying
% 52.60/7.90 | with (50), (69) gives:
% 52.60/7.90 | (74) all_53_4 = all_45_2
% 52.60/7.90 |
% 52.60/7.90 | GROUND_INST: instantiating (32) with all_45_4, all_53_8, xP, xP, simplifying
% 52.60/7.90 | with (51), (70) gives:
% 52.60/7.90 | (75) all_53_8 = all_45_4
% 52.60/7.90 |
% 52.60/7.90 | GROUND_INST: instantiating (32) with all_37_0, all_53_8, xP, xP, simplifying
% 52.60/7.90 | with (41), (70) gives:
% 52.60/7.90 | (76) all_53_8 = all_37_0
% 52.60/7.90 |
% 52.60/7.90 | GROUND_INST: instantiating (32) with all_45_1, all_53_3, xS, xS, simplifying
% 52.60/7.90 | with (52), (71) gives:
% 52.60/7.90 | (77) all_53_3 = all_45_1
% 52.60/7.90 |
% 52.60/7.90 | GROUND_INST: instantiating (30) with all_39_0, all_47_0, xs, simplifying with
% 52.60/7.90 | (43), (54) gives:
% 52.60/7.90 | (78) all_47_0 = all_39_0
% 52.60/7.90 |
% 52.60/7.90 | GROUND_INST: instantiating (30) with all_35_0, all_47_0, xs, simplifying with
% 52.60/7.90 | (38), (54) gives:
% 52.60/7.90 | (79) all_47_0 = all_35_0
% 52.60/7.90 |
% 52.60/7.91 | GROUND_INST: instantiating (30) with all_47_0, all_55_0, xs, simplifying with
% 52.60/7.91 | (54), (73) gives:
% 52.60/7.91 | (80) all_55_0 = all_47_0
% 52.60/7.91 |
% 52.60/7.91 | GROUND_INST: instantiating (30) with all_33_0, all_55_0, xs, simplifying with
% 52.60/7.91 | (34), (73) gives:
% 52.60/7.91 | (81) all_55_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | GROUND_INST: instantiating (30) with all_41_0, all_50_0, xt, simplifying with
% 52.60/7.91 | (45), (57) gives:
% 52.60/7.91 | (82) all_50_0 = all_41_0
% 52.60/7.91 |
% 52.60/7.91 | GROUND_INST: instantiating (30) with all_33_0, all_50_0, xt, simplifying with
% 52.60/7.91 | (35), (57) gives:
% 52.60/7.91 | (83) all_50_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | COMBINE_EQS: (80), (81) imply:
% 52.60/7.91 | (84) all_47_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | SIMP: (84) implies:
% 52.60/7.91 | (85) all_47_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | COMBINE_EQS: (75), (76) imply:
% 52.60/7.91 | (86) all_45_4 = all_37_0
% 52.60/7.91 |
% 52.60/7.91 | SIMP: (86) implies:
% 52.60/7.91 | (87) all_45_4 = all_37_0
% 52.60/7.91 |
% 52.60/7.91 | COMBINE_EQS: (82), (83) imply:
% 52.60/7.91 | (88) all_41_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | COMBINE_EQS: (78), (85) imply:
% 52.60/7.91 | (89) all_39_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | COMBINE_EQS: (78), (79) imply:
% 52.60/7.91 | (90) all_39_0 = all_35_0
% 52.60/7.91 |
% 52.60/7.91 | COMBINE_EQS: (89), (90) imply:
% 52.60/7.91 | (91) all_35_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | SIMP: (91) implies:
% 52.60/7.91 | (92) all_35_0 = all_33_0
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (37), (92) imply:
% 52.60/7.91 | (93) ~ (all_33_0 = sz00)
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (66), (74), (77) imply:
% 52.60/7.91 | (94) sdtpldt0(all_45_2, all_45_1) = all_53_2
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (65), (76) imply:
% 52.60/7.91 | (95) sdtpldt0(all_53_6, all_37_0) = all_53_5
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (64), (76) imply:
% 52.60/7.91 | (96) sdtpldt0(all_53_7, all_37_0) = all_53_6
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (63), (76) imply:
% 52.60/7.91 | (97) sdtpldt0(all_37_0, all_37_0) = all_53_7
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (48), (87) imply:
% 52.60/7.91 | (98) sdtpldt0(all_37_0, all_37_0) = all_45_3
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (62), (77) imply:
% 52.60/7.91 | (99) $i(all_45_1)
% 52.60/7.91 |
% 52.60/7.91 | REDUCE: (61), (74) imply:
% 52.60/7.91 | (100) $i(all_45_2)
% 52.60/7.91 |
% 52.60/7.91 | GROUND_INST: instantiating (31) with all_45_3, all_53_7, all_37_0, all_37_0,
% 52.60/7.91 | simplifying with (97), (98) gives:
% 52.60/7.92 | (101) all_53_7 = all_45_3
% 52.60/7.92 |
% 52.60/7.92 | GROUND_INST: instantiating (31) with all_45_0, all_53_2, all_45_1, all_45_2,
% 52.60/7.92 | simplifying with (49), (94) gives:
% 52.60/7.92 | (102) all_53_2 = all_45_0
% 52.60/7.92 |
% 52.60/7.92 | REDUCE: (67), (102) imply:
% 52.60/7.92 | (103) sdtpldt0(all_45_0, xN) = all_53_1
% 52.60/7.92 |
% 52.60/7.92 | REDUCE: (96), (101) imply:
% 52.60/7.92 | (104) sdtpldt0(all_45_3, all_37_0) = all_53_6
% 52.60/7.92 |
% 52.60/7.92 | GROUND_INST: instantiating (mMulSc) with xR, xR, all_45_2, simplifying with
% 52.60/7.92 | (16), (25), (50) gives:
% 52.60/7.92 | (105) aScalar0(all_45_2)
% 52.60/7.92 |
% 52.60/7.92 | GROUND_INST: instantiating (mDistr) with xP, xP, xP, all_37_0, all_37_0,
% 52.60/7.92 | all_45_3, simplifying with (17), (26), (41), (98) gives:
% 52.60/7.92 | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1,
% 52.60/7.92 | xP) = v2 & sdtasdt0(xP, v0) = all_45_3 & sdtasdt0(xP, xP) = v3 &
% 52.60/7.92 | sdtpldt0(all_37_0, v3) = v2 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xP,
% 52.60/7.92 | xP) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_45_3))
% 52.60/7.92 |
% 52.60/7.92 | GROUND_INST: instantiating (mMulSc) with xP, xP, all_37_0, simplifying with
% 52.60/7.92 | (17), (26), (41) gives:
% 52.60/7.92 | (107) aScalar0(all_37_0)
% 52.60/7.92 |
% 52.60/7.92 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_45_1, simplifying with
% 52.60/7.92 | (20), (27), (52) gives:
% 52.60/7.92 | (108) aScalar0(all_45_1)
% 52.60/7.92 |
% 52.60/7.92 | GROUND_INST: instantiating (mDimNat) with xt, all_33_0, simplifying with (4),
% 52.60/7.92 | (12), (35) gives:
% 52.60/7.92 | (109) aNaturalNumber0(all_33_0)
% 52.60/7.92 |
% 52.60/7.92 | GROUND_INST: instantiating (2) with xs, xp, simplifying with (3), (10), (55)
% 52.60/7.92 | gives:
% 52.60/7.92 | (110) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( !
% 52.60/7.92 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2)
% 52.60/7.92 | = v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp)
% 52.60/7.92 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 &
% 52.60/7.92 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~
% 52.60/7.92 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ?
% 52.60/7.92 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4)
% 52.60/7.92 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs,
% 52.60/7.92 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | (
% 52.60/7.92 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & !
% 52.60/7.92 | [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) |
% 52.60/7.92 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xp)
% 52.60/7.92 | = v1) | ~ $i(xp) | aVector0(xp)))))
% 52.60/7.92 |
% 52.60/7.93 | GROUND_INST: instantiating (2) with xt, xq, simplifying with (4), (12), (58)
% 52.60/7.93 | gives:
% 52.60/7.93 | (111) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( !
% 52.60/7.93 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2)
% 52.60/7.93 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq)
% 52.60/7.93 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 &
% 52.60/7.93 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~
% 52.60/7.93 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ?
% 52.60/7.93 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4)
% 52.60/7.93 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt,
% 52.60/7.93 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | (
% 52.60/7.93 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & !
% 52.60/7.93 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) |
% 52.60/7.93 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq)
% 52.60/7.93 | = v1) | ~ $i(xq) | aVector0(xq)))))
% 52.60/7.93 |
% 52.60/7.93 | DELTA: instantiating (106) with fresh symbols all_77_0, all_77_1, all_77_2,
% 52.60/7.93 | all_77_3 gives:
% 52.60/7.93 | (112) sdtasdt0(all_77_2, xP) = all_77_1 & sdtasdt0(xP, all_77_3) = all_45_3
% 52.60/7.93 | & sdtasdt0(xP, xP) = all_77_0 & sdtpldt0(all_37_0, all_77_0) =
% 52.60/7.93 | all_77_1 & sdtpldt0(xP, xP) = all_77_2 & sdtpldt0(xP, xP) = all_77_3
% 52.60/7.93 | & $i(all_77_0) & $i(all_77_1) & $i(all_77_2) & $i(all_77_3) &
% 52.60/7.93 | $i(all_45_3)
% 52.60/7.93 |
% 52.60/7.93 | ALPHA: (112) implies:
% 52.60/7.93 | (113) $i(all_77_0)
% 52.60/7.93 | (114) sdtpldt0(xP, xP) = all_77_3
% 52.60/7.93 | (115) sdtpldt0(xP, xP) = all_77_2
% 52.60/7.93 | (116) sdtpldt0(all_37_0, all_77_0) = all_77_1
% 52.60/7.93 | (117) sdtasdt0(xP, xP) = all_77_0
% 52.60/7.93 | (118) sdtasdt0(xP, all_77_3) = all_45_3
% 52.60/7.93 | (119) sdtasdt0(all_77_2, xP) = all_77_1
% 52.60/7.93 |
% 52.60/7.93 | DELTA: instantiating (110) with fresh symbol all_80_0 gives:
% 52.60/7.93 | (120) aDimensionOf0(xs) = all_80_0 & $i(all_80_0) & (all_80_0 = sz00 | ( !
% 52.60/7.93 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) =
% 52.60/7.93 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) |
% 52.60/7.93 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) &
% 52.60/7.93 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1)
% 52.60/7.93 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 52.60/7.93 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 52.60/7.93 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 &
% 52.60/7.93 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 52.60/7.93 | all_80_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 52.60/7.93 | [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) |
% 52.60/7.94 | szszuzczcdt0(v0) = all_80_0) & ! [v0: $i] : ( ~
% 52.60/7.94 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | aVector0(xp))))
% 52.60/7.94 |
% 52.60/7.94 | ALPHA: (120) implies:
% 52.60/7.94 | (121) $i(all_80_0)
% 52.60/7.94 | (122) aDimensionOf0(xs) = all_80_0
% 52.60/7.94 |
% 52.60/7.94 | DELTA: instantiating (111) with fresh symbol all_82_0 gives:
% 52.60/7.94 | (123) aDimensionOf0(xt) = all_82_0 & $i(all_82_0) & (all_82_0 = sz00 | ( !
% 52.60/7.94 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 52.60/7.94 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) |
% 52.60/7.94 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) &
% 52.60/7.94 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1)
% 52.60/7.94 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 52.60/7.94 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 52.60/7.94 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 &
% 52.60/7.94 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 52.60/7.94 | all_82_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 52.60/7.94 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) |
% 52.60/7.94 | szszuzczcdt0(v0) = all_82_0) & ! [v0: $i] : ( ~
% 52.60/7.94 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq))))
% 52.60/7.94 |
% 52.60/7.94 | ALPHA: (123) implies:
% 52.60/7.94 | (124) aDimensionOf0(xt) = all_82_0
% 52.60/7.94 | (125) all_82_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 52.60/7.94 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(xq) = v0) | ~
% 52.60/7.94 | $i(v1) | ~ $i(xq) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1)
% 52.60/7.94 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~
% 52.60/7.94 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 52.60/7.94 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 52.60/7.94 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) =
% 52.60/7.94 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 52.60/7.94 | all_82_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 52.60/7.94 | $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0)
% 52.60/7.94 | = all_82_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~
% 52.60/7.94 | $i(xq) | aVector0(xq)))
% 52.60/7.94 |
% 52.60/7.94 | GROUND_INST: instantiating (31) with all_77_3, all_77_2, xP, xP, simplifying
% 52.60/7.94 | with (114), (115) gives:
% 52.60/7.94 | (126) all_77_2 = all_77_3
% 52.60/7.94 |
% 52.60/7.94 | GROUND_INST: instantiating (32) with all_37_0, all_77_0, xP, xP, simplifying
% 52.60/7.94 | with (41), (117) gives:
% 52.60/7.94 | (127) all_77_0 = all_37_0
% 52.60/7.94 |
% 52.60/7.94 | GROUND_INST: instantiating (30) with all_33_0, all_80_0, xs, simplifying with
% 52.60/7.94 | (34), (122) gives:
% 52.60/7.94 | (128) all_80_0 = all_33_0
% 52.60/7.94 |
% 52.60/7.94 | GROUND_INST: instantiating (30) with all_33_0, all_82_0, xt, simplifying with
% 52.60/7.94 | (35), (124) gives:
% 52.60/7.94 | (129) all_82_0 = all_33_0
% 52.60/7.94 |
% 52.60/7.94 | REDUCE: (119), (126) imply:
% 52.60/7.94 | (130) sdtasdt0(all_77_3, xP) = all_77_1
% 52.60/7.94 |
% 52.60/7.95 | REDUCE: (116), (127) imply:
% 52.60/7.95 | (131) sdtpldt0(all_37_0, all_37_0) = all_77_1
% 52.60/7.95 |
% 52.60/7.95 | REDUCE: (121), (128) imply:
% 52.60/7.95 | (132) $i(all_33_0)
% 52.60/7.95 |
% 52.60/7.95 | REDUCE: (113), (127) imply:
% 52.60/7.95 | (133) $i(all_37_0)
% 52.60/7.95 |
% 52.60/7.95 | BETA: splitting (125) gives:
% 52.60/7.95 |
% 52.60/7.95 | Case 1:
% 52.60/7.95 | |
% 52.60/7.95 | | (134) all_82_0 = sz00
% 52.60/7.95 | |
% 52.60/7.95 | | COMBINE_EQS: (129), (134) imply:
% 52.60/7.95 | | (135) all_33_0 = sz00
% 52.60/7.95 | |
% 52.60/7.95 | | REDUCE: (93), (135) imply:
% 52.60/7.95 | | (136) $false
% 52.60/7.95 | |
% 52.60/7.95 | | CLOSE: (136) is inconsistent.
% 52.60/7.95 | |
% 52.60/7.95 | Case 2:
% 52.60/7.95 | |
% 52.60/7.95 | | (137) ~ (all_82_0 = sz00)
% 52.60/7.95 | |
% 52.60/7.95 | | GROUND_INST: instantiating (31) with all_45_3, all_77_1, all_37_0, all_37_0,
% 52.60/7.95 | | simplifying with (98), (131) gives:
% 52.60/7.95 | | (138) all_77_1 = all_45_3
% 52.60/7.95 | |
% 52.60/7.95 | | REDUCE: (130), (138) imply:
% 52.60/7.95 | | (139) sdtasdt0(all_77_3, xP) = all_45_3
% 52.60/7.95 | |
% 52.60/7.95 | | GROUND_INST: instantiating (1) with all_33_0, simplifying with (109), (132)
% 52.60/7.95 | | gives:
% 52.60/7.95 | | (140) all_33_0 = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = all_33_0 &
% 52.60/7.95 | | $i(v0) & aNaturalNumber0(v0))
% 52.60/7.95 | |
% 52.60/7.95 | | GROUND_INST: instantiating (mArith) with all_37_0, all_37_0, all_37_0,
% 52.60/7.95 | | all_45_3, all_53_6, simplifying with (98), (104), (107), (133)
% 52.60/7.95 | | gives:
% 52.60/7.95 | | (141) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 52.60/7.95 | | (sdtasdt0(v1, all_37_0) = v2 & sdtasdt0(all_37_0, v3) = v2 &
% 52.60/7.95 | | sdtasdt0(all_37_0, all_37_0) = v3 & sdtasdt0(all_37_0, all_37_0)
% 52.60/7.95 | | = v1 & sdtpldt0(all_37_0, v0) = all_53_6 & sdtpldt0(all_37_0,
% 52.60/7.95 | | all_37_0) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 52.60/7.95 | | $i(all_53_6) & $i(all_45_3))
% 52.60/7.95 | |
% 52.60/7.95 | | GROUND_INST: instantiating (mSumSc) with all_37_0, all_37_0, all_45_3,
% 52.60/7.95 | | simplifying with (98), (107), (133) gives:
% 52.60/7.95 | | (142) aScalar0(all_45_3)
% 52.60/7.95 | |
% 52.60/7.96 | | GROUND_INST: instantiating (mArith) with all_45_2, all_45_1, xN, all_45_0,
% 52.60/7.96 | | all_53_1, simplifying with (21), (28), (49), (99), (100),
% 52.60/7.96 | | (103), (105), (108) gives:
% 52.60/7.96 | | (143) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 52.60/7.96 | | (sdtasdt0(v1, xN) = v2 & sdtasdt0(all_45_1, all_45_2) = v1 &
% 52.60/7.96 | | sdtasdt0(all_45_1, xN) = v3 & sdtasdt0(all_45_2, v3) = v2 &
% 52.60/7.96 | | sdtasdt0(all_45_2, all_45_1) = v1 & sdtpldt0(all_45_1, all_45_2)
% 52.60/7.96 | | = all_45_0 & sdtpldt0(all_45_1, xN) = v0 & sdtpldt0(all_45_2, v0)
% 52.60/7.96 | | = all_53_1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_1) &
% 52.60/7.96 | | $i(all_45_0))
% 52.60/7.96 | |
% 52.60/7.96 | | GROUND_INST: instantiating (mSumSc) with all_45_2, all_45_1, all_45_0,
% 52.60/7.96 | | simplifying with (49), (99), (100), (105), (108) gives:
% 52.60/7.96 | | (144) aScalar0(all_45_0)
% 52.60/7.96 | |
% 52.60/7.96 | | GROUND_INST: instantiating (mDistr) with xE, xH, xH, xP, xP, all_77_3,
% 52.60/7.96 | | simplifying with (14), (15), (18), (19), (22), (114) gives:
% 52.60/7.96 | | (145) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 52.60/7.96 | | (sdtasdt0(v1, xH) = v2 & sdtasdt0(xH, xH) = v3 & sdtasdt0(xE, v0) =
% 52.60/7.96 | | all_77_3 & sdtpldt0(xP, v3) = v2 & sdtpldt0(xH, xH) = v0 &
% 52.60/7.96 | | sdtpldt0(xE, xH) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 52.60/7.96 | | $i(all_77_3))
% 52.60/7.96 | |
% 52.60/7.96 | | GROUND_INST: instantiating (mSumSc) with xP, xP, all_77_3, simplifying with
% 52.60/7.96 | | (17), (26), (114) gives:
% 52.60/7.96 | | (146) aScalar0(all_77_3)
% 52.60/7.96 | |
% 52.60/7.96 | | DELTA: instantiating (145) with fresh symbols all_118_0, all_118_1,
% 52.60/7.96 | | all_118_2, all_118_3 gives:
% 52.60/7.96 | | (147) sdtasdt0(all_118_2, xH) = all_118_1 & sdtasdt0(xH, xH) = all_118_0
% 52.60/7.96 | | & sdtasdt0(xE, all_118_3) = all_77_3 & sdtpldt0(xP, all_118_0) =
% 52.60/7.96 | | all_118_1 & sdtpldt0(xH, xH) = all_118_3 & sdtpldt0(xE, xH) =
% 52.60/7.96 | | all_118_2 & $i(all_118_0) & $i(all_118_1) & $i(all_118_2) &
% 52.60/7.96 | | $i(all_118_3) & $i(all_77_3)
% 52.60/7.96 | |
% 52.60/7.96 | | ALPHA: (147) implies:
% 52.60/7.96 | | (148) $i(all_77_3)
% 52.60/7.96 | |
% 52.60/7.96 | | DELTA: instantiating (141) with fresh symbols all_120_0, all_120_1,
% 52.60/7.96 | | all_120_2, all_120_3 gives:
% 52.60/7.96 | | (149) sdtasdt0(all_120_2, all_37_0) = all_120_1 & sdtasdt0(all_37_0,
% 52.60/7.96 | | all_120_0) = all_120_1 & sdtasdt0(all_37_0, all_37_0) = all_120_0
% 52.60/7.96 | | & sdtasdt0(all_37_0, all_37_0) = all_120_2 & sdtpldt0(all_37_0,
% 52.60/7.96 | | all_120_3) = all_53_6 & sdtpldt0(all_37_0, all_37_0) = all_120_3
% 52.60/7.96 | | & $i(all_120_0) & $i(all_120_1) & $i(all_120_2) & $i(all_120_3) &
% 52.60/7.96 | | $i(all_53_6) & $i(all_45_3)
% 52.60/7.96 | |
% 52.60/7.96 | | ALPHA: (149) implies:
% 52.60/7.96 | | (150) $i(all_120_3)
% 52.60/7.96 | | (151) sdtpldt0(all_37_0, all_37_0) = all_120_3
% 52.60/7.96 | | (152) sdtpldt0(all_37_0, all_120_3) = all_53_6
% 52.60/7.96 | |
% 52.60/7.96 | | DELTA: instantiating (143) with fresh symbols all_122_0, all_122_1,
% 52.60/7.96 | | all_122_2, all_122_3 gives:
% 52.60/7.96 | | (153) sdtasdt0(all_122_2, xN) = all_122_1 & sdtasdt0(all_45_1, all_45_2)
% 52.60/7.96 | | = all_122_2 & sdtasdt0(all_45_1, xN) = all_122_0 &
% 52.60/7.96 | | sdtasdt0(all_45_2, all_122_0) = all_122_1 & sdtasdt0(all_45_2,
% 52.60/7.96 | | all_45_1) = all_122_2 & sdtpldt0(all_45_1, all_45_2) = all_45_0 &
% 52.60/7.96 | | sdtpldt0(all_45_1, xN) = all_122_3 & sdtpldt0(all_45_2, all_122_3)
% 52.60/7.96 | | = all_53_1 & $i(all_122_0) & $i(all_122_1) & $i(all_122_2) &
% 52.60/7.96 | | $i(all_122_3) & $i(all_53_1) & $i(all_45_0)
% 52.60/7.96 | |
% 52.60/7.96 | | ALPHA: (153) implies:
% 52.60/7.96 | | (154) $i(all_45_0)
% 52.60/7.96 | | (155) sdtpldt0(all_45_1, all_45_2) = all_45_0
% 52.60/7.96 | |
% 52.60/7.96 | | BETA: splitting (140) gives:
% 52.60/7.96 | |
% 52.60/7.96 | | Case 1:
% 52.60/7.96 | | |
% 52.60/7.96 | | | (156) all_33_0 = sz00
% 52.60/7.97 | | |
% 52.60/7.97 | | | REDUCE: (93), (156) imply:
% 52.60/7.97 | | | (157) $false
% 52.60/7.97 | | |
% 52.60/7.97 | | | CLOSE: (157) is inconsistent.
% 52.60/7.97 | | |
% 52.60/7.97 | | Case 2:
% 52.60/7.97 | | |
% 52.60/7.97 | | |
% 52.60/7.97 | | | GROUND_INST: instantiating (31) with all_45_3, all_120_3, all_37_0,
% 52.60/7.97 | | | all_37_0, simplifying with (98), (151) gives:
% 52.60/7.97 | | | (158) all_120_3 = all_45_3
% 52.60/7.97 | | |
% 52.60/7.97 | | | REDUCE: (152), (158) imply:
% 52.60/7.97 | | | (159) sdtpldt0(all_37_0, all_45_3) = all_53_6
% 52.60/7.97 | | |
% 52.60/7.97 | | | REDUCE: (150), (158) imply:
% 52.60/7.97 | | | (160) $i(all_45_3)
% 52.60/7.97 | | |
% 52.60/7.97 | | | GROUND_INST: instantiating (mArith) with all_45_3, all_37_0, all_37_0,
% 52.60/7.97 | | | all_53_6, all_53_5, simplifying with (95), (104), (107),
% 52.60/7.97 | | | (133), (142), (160) gives:
% 52.60/7.97 | | | (161) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 52.60/7.97 | | | (sdtasdt0(v1, all_37_0) = v2 & sdtasdt0(all_45_3, v3) = v2 &
% 52.60/7.97 | | | sdtasdt0(all_45_3, all_37_0) = v1 & sdtasdt0(all_37_0,
% 52.60/7.97 | | | all_45_3) = v1 & sdtasdt0(all_37_0, all_37_0) = v3 &
% 52.60/7.97 | | | sdtpldt0(all_45_3, v0) = all_53_5 & sdtpldt0(all_37_0,
% 52.60/7.97 | | | all_45_3) = all_53_6 & sdtpldt0(all_37_0, all_37_0) = v0 &
% 52.60/7.97 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_5) &
% 52.60/7.97 | | | $i(all_53_6))
% 52.60/7.97 | | |
% 52.60/7.97 | | | GROUND_INST: instantiating (mLEMon) with all_45_3, all_45_0, all_37_0, xN,
% 52.60/7.97 | | | all_53_6, all_53_1, simplifying with (21), (28), (40), (47),
% 52.60/7.97 | | | (103), (104), (107), (133), (142), (144), (154), (160) gives:
% 52.60/7.97 | | | (162) sdtlseqdt0(all_53_6, all_53_1)
% 52.60/7.97 | | |
% 52.60/7.97 | | | GROUND_INST: instantiating (mSumSc) with all_45_0, xN, all_53_1,
% 52.60/7.97 | | | simplifying with (21), (28), (103), (144), (154) gives:
% 52.60/7.97 | | | (163) aScalar0(all_53_1)
% 52.60/7.97 | | |
% 52.60/7.97 | | | GROUND_INST: instantiating (mDistr) with xP, all_77_3, xP, all_45_3,
% 52.60/7.97 | | | all_37_0, all_53_6, simplifying with (17), (26), (41), (104),
% 52.60/7.97 | | | (118), (146), (148) gives:
% 52.60/7.97 | | | (164) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 52.60/7.97 | | | (sdtasdt0(v1, xP) = v2 & sdtasdt0(all_77_3, xP) = v3 &
% 52.60/7.97 | | | sdtasdt0(xP, v0) = all_53_6 & sdtpldt0(all_77_3, xP) = v0 &
% 52.60/7.97 | | | sdtpldt0(all_37_0, v3) = v2 & sdtpldt0(xP, all_77_3) = v1 &
% 52.60/7.97 | | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_6))
% 52.60/7.97 | | |
% 52.60/7.97 | | | GROUND_INST: instantiating (mSumSc) with all_37_0, all_45_3, all_53_6,
% 52.60/7.97 | | | simplifying with (107), (133), (142), (159), (160) gives:
% 52.60/7.97 | | | (165) aScalar0(all_53_6)
% 52.60/7.97 | | |
% 52.60/7.97 | | | GROUND_INST: instantiating (mArith) with all_45_1, all_45_2, xN, all_45_0,
% 52.60/7.97 | | | all_53_1, simplifying with (21), (28), (99), (100), (103),
% 52.60/7.97 | | | (105), (108), (155) gives:
% 52.60/7.98 | | | (166) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 52.60/7.98 | | | (sdtasdt0(v1, xN) = v2 & sdtasdt0(all_45_1, v3) = v2 &
% 52.60/7.98 | | | sdtasdt0(all_45_1, all_45_2) = v1 & sdtasdt0(all_45_2,
% 52.60/7.98 | | | all_45_1) = v1 & sdtasdt0(all_45_2, xN) = v3 &
% 52.60/7.98 | | | sdtpldt0(all_45_1, v0) = all_53_1 & sdtpldt0(all_45_2,
% 52.60/7.98 | | | all_45_1) = all_45_0 & sdtpldt0(all_45_2, xN) = v0 & $i(v3) &
% 52.60/7.98 | | | $i(v2) & $i(v1) & $i(v0) & $i(all_53_1) & $i(all_45_0))
% 52.60/7.98 | | |
% 52.60/7.98 | | | DELTA: instantiating (164) with fresh symbols all_160_0, all_160_1,
% 52.60/7.98 | | | all_160_2, all_160_3 gives:
% 52.60/7.98 | | | (167) sdtasdt0(all_160_2, xP) = all_160_1 & sdtasdt0(all_77_3, xP) =
% 52.60/7.98 | | | all_160_0 & sdtasdt0(xP, all_160_3) = all_53_6 &
% 52.60/7.98 | | | sdtpldt0(all_77_3, xP) = all_160_3 & sdtpldt0(all_37_0,
% 52.60/7.98 | | | all_160_0) = all_160_1 & sdtpldt0(xP, all_77_3) = all_160_2 &
% 52.60/7.98 | | | $i(all_160_0) & $i(all_160_1) & $i(all_160_2) & $i(all_160_3) &
% 52.60/7.98 | | | $i(all_53_6)
% 52.60/7.98 | | |
% 52.60/7.98 | | | ALPHA: (167) implies:
% 52.60/7.98 | | | (168) $i(all_160_1)
% 52.60/7.98 | | | (169) sdtpldt0(all_37_0, all_160_0) = all_160_1
% 52.60/7.98 | | | (170) sdtasdt0(all_77_3, xP) = all_160_0
% 52.60/7.98 | | |
% 52.60/7.98 | | | DELTA: instantiating (161) with fresh symbols all_164_0, all_164_1,
% 52.60/7.98 | | | all_164_2, all_164_3 gives:
% 52.60/7.98 | | | (171) sdtasdt0(all_164_2, all_37_0) = all_164_1 & sdtasdt0(all_45_3,
% 52.60/7.98 | | | all_164_0) = all_164_1 & sdtasdt0(all_45_3, all_37_0) =
% 52.60/7.98 | | | all_164_2 & sdtasdt0(all_37_0, all_45_3) = all_164_2 &
% 52.60/7.98 | | | sdtasdt0(all_37_0, all_37_0) = all_164_0 & sdtpldt0(all_45_3,
% 52.60/7.98 | | | all_164_3) = all_53_5 & sdtpldt0(all_37_0, all_45_3) = all_53_6
% 52.60/7.98 | | | & sdtpldt0(all_37_0, all_37_0) = all_164_3 & $i(all_164_0) &
% 52.60/7.98 | | | $i(all_164_1) & $i(all_164_2) & $i(all_164_3) & $i(all_53_5) &
% 52.60/7.98 | | | $i(all_53_6)
% 52.60/7.98 | | |
% 52.60/7.98 | | | DELTA: instantiating (166) with fresh symbols all_168_0, all_168_1,
% 52.60/7.98 | | | all_168_2, all_168_3 gives:
% 52.60/7.98 | | | (172) sdtasdt0(all_168_2, xN) = all_168_1 & sdtasdt0(all_45_1,
% 52.60/7.98 | | | all_168_0) = all_168_1 & sdtasdt0(all_45_1, all_45_2) =
% 52.60/7.98 | | | all_168_2 & sdtasdt0(all_45_2, all_45_1) = all_168_2 &
% 52.60/7.98 | | | sdtasdt0(all_45_2, xN) = all_168_0 & sdtpldt0(all_45_1,
% 52.60/7.98 | | | all_168_3) = all_53_1 & sdtpldt0(all_45_2, all_45_1) = all_45_0
% 52.60/7.98 | | | & sdtpldt0(all_45_2, xN) = all_168_3 & $i(all_168_0) &
% 52.60/7.98 | | | $i(all_168_1) & $i(all_168_2) & $i(all_168_3) & $i(all_53_1) &
% 52.60/7.98 | | | $i(all_45_0)
% 52.60/7.98 | | |
% 52.60/7.98 | | | ALPHA: (172) implies:
% 52.60/7.98 | | | (173) $i(all_53_1)
% 52.60/7.98 | | |
% 52.60/7.98 | | | GROUND_INST: instantiating (32) with all_45_3, all_160_0, xP, all_77_3,
% 52.60/7.98 | | | simplifying with (139), (170) gives:
% 52.60/7.98 | | | (174) all_160_0 = all_45_3
% 52.60/7.98 | | |
% 52.60/7.98 | | | REDUCE: (169), (174) imply:
% 52.60/7.98 | | | (175) sdtpldt0(all_37_0, all_45_3) = all_160_1
% 52.60/7.98 | | |
% 52.60/7.98 | | | GROUND_INST: instantiating (31) with all_53_6, all_160_1, all_45_3,
% 52.60/7.98 | | | all_37_0, simplifying with (159), (175) gives:
% 52.60/7.98 | | | (176) all_160_1 = all_53_6
% 52.60/7.98 | | |
% 52.60/7.98 | | | REDUCE: (168), (176) imply:
% 52.60/7.98 | | | (177) $i(all_53_6)
% 52.60/7.98 | | |
% 52.60/7.98 | | | GROUND_INST: instantiating (mLEMon) with all_53_6, all_53_1, all_37_0, xN,
% 52.60/7.98 | | | all_53_5, all_53_0, simplifying with (21), (28), (40), (60),
% 52.60/7.98 | | | (68), (95), (107), (133), (162), (163), (165), (173), (177)
% 52.60/7.98 | | | gives:
% 52.60/7.98 | | | (178) $false
% 52.60/7.98 | | |
% 52.60/7.98 | | | CLOSE: (178) is inconsistent.
% 52.60/7.98 | | |
% 52.60/7.98 | | End of split
% 52.60/7.98 | |
% 52.60/7.98 | End of split
% 52.60/7.98 |
% 52.60/7.98 End of proof
% 52.60/7.99 % SZS output end Proof for theBenchmark
% 52.60/7.99
% 52.60/7.99 7370ms
%------------------------------------------------------------------------------