TSTP Solution File: RNG067+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG067+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 : n029.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 18.21s 3.20s
% Output : Proof 32.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG067+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 02:44:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.43/1.19 Prover 1: Preprocessing ...
% 3.43/1.19 Prover 4: Preprocessing ...
% 3.43/1.25 Prover 0: Preprocessing ...
% 3.43/1.25 Prover 6: Preprocessing ...
% 3.43/1.25 Prover 3: Preprocessing ...
% 3.43/1.25 Prover 2: Preprocessing ...
% 3.43/1.25 Prover 5: Preprocessing ...
% 9.75/2.06 Prover 1: Constructing countermodel ...
% 9.75/2.06 Prover 3: Constructing countermodel ...
% 9.75/2.11 Prover 6: Proving ...
% 9.75/2.16 Prover 5: Constructing countermodel ...
% 11.68/2.35 Prover 2: Proving ...
% 11.68/2.38 Prover 4: Constructing countermodel ...
% 13.00/2.50 Prover 0: Proving ...
% 18.21/3.20 Prover 3: proved (2568ms)
% 18.21/3.20
% 18.21/3.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.21/3.20
% 18.21/3.20 Prover 5: stopped
% 18.21/3.20 Prover 0: stopped
% 18.21/3.21 Prover 6: stopped
% 18.21/3.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.21/3.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.21/3.22 Prover 2: stopped
% 18.21/3.23 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.21/3.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.21/3.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.01/3.30 Prover 8: Preprocessing ...
% 19.01/3.30 Prover 7: Preprocessing ...
% 19.24/3.32 Prover 11: Preprocessing ...
% 19.35/3.34 Prover 13: Preprocessing ...
% 19.35/3.35 Prover 10: Preprocessing ...
% 19.93/3.46 Prover 8: Warning: ignoring some quantifiers
% 19.93/3.47 Prover 8: Constructing countermodel ...
% 20.41/3.53 Prover 10: Constructing countermodel ...
% 20.41/3.55 Prover 7: Constructing countermodel ...
% 20.41/3.56 Prover 13: Constructing countermodel ...
% 20.41/3.74 Prover 11: Constructing countermodel ...
% 31.89/5.01 Prover 10: Found proof (size 122)
% 31.89/5.02 Prover 10: proved (1792ms)
% 31.89/5.02 Prover 4: stopped
% 31.89/5.02 Prover 7: stopped
% 31.89/5.02 Prover 11: stopped
% 31.89/5.02 Prover 8: stopped
% 31.89/5.02 Prover 13: stopped
% 31.89/5.02 Prover 1: stopped
% 31.89/5.02
% 31.89/5.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.89/5.02
% 31.89/5.04 % SZS output start Proof for theBenchmark
% 31.89/5.04 Assumptions after simplification:
% 31.89/5.04 ---------------------------------
% 31.89/5.04
% 31.89/5.04 (mArith)
% 31.89/5.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 31.89/5.07 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 31.89/5.07 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5:
% 31.89/5.07 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 &
% 31.89/5.07 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 &
% 31.89/5.07 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 &
% 31.89/5.07 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 31.89/5.07 $i(v3)))
% 31.89/5.07
% 31.89/5.07 (mDefInit)
% 31.89/5.08 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 31.89/5.08 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 31.89/5.08 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 31.89/5.08 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 31.89/5.08 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 31.89/5.08 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 31.89/5.08 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 31.89/5.08 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 31.89/5.08 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 31.89/5.08 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 31.89/5.08 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 31.89/5.08 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 31.89/5.08 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 31.89/5.08
% 31.89/5.08 (mDistr)
% 31.89/5.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 31.89/5.08 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 31.89/5.08 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 31.89/5.08 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i]
% 31.89/5.08 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 31.89/5.08 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 &
% 31.89/5.08 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 31.89/5.08
% 31.89/5.08 (mLEMon)
% 31.89/5.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 31.89/5.08 $i] : ( ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v0, v2) = v4) | ~ $i(v3) |
% 31.89/5.08 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~
% 31.89/5.08 sdtlseqdt0(v0, v1) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~ aScalar0(v1) |
% 31.89/5.08 ~ aScalar0(v0) | sdtlseqdt0(v4, v5))
% 31.89/5.08
% 31.89/5.08 (mMulSc)
% 31.89/5.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 31.89/5.09 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 31.89/5.09
% 31.89/5.09 (mSumSc)
% 31.89/5.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 31.89/5.09 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 31.89/5.09
% 31.89/5.09 (m__)
% 31.89/5.09 $i(xN) & $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 31.89/5.09 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 31.89/5.09 $i] : (sdtasdt0(xS, xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4
% 31.89/5.09 & sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) = v6 &
% 31.89/5.09 sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0, v0) = v1 &
% 31.89/5.09 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 31.89/5.09 $i(v0) & ~ sdtlseqdt0(v3, v8))
% 31.89/5.09
% 31.89/5.09 (m__1652)
% 31.89/5.09 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 31.89/5.09 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 31.89/5.10 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 31.89/5.10 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 31.89/5.10 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 31.89/5.10 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 31.89/5.10 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 31.89/5.10 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 31.89/5.10
% 31.89/5.10 (m__1678)
% 31.89/5.10 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 31.89/5.10
% 31.89/5.10 (m__1678_01)
% 31.89/5.10 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 31.89/5.10 v0 & $i(v0))
% 31.89/5.10
% 31.89/5.10 (m__1692)
% 31.89/5.10 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 31.89/5.10 $i(v0))
% 31.89/5.10
% 31.89/5.10 (m__1709)
% 31.89/5.10 sziznziztdt0(xs) = xp & $i(xp) & $i(xs) & aVector0(xp)
% 31.89/5.10
% 31.89/5.10 (m__1746)
% 31.89/5.10 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 31.89/5.10 v0 & $i(v0) & aScalar0(xA))
% 31.89/5.10
% 31.89/5.10 (m__1820)
% 31.89/5.10 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE)
% 31.89/5.10
% 31.89/5.10 (m__1873)
% 31.89/5.10 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH)
% 31.89/5.10
% 31.89/5.10 (m__1892)
% 31.89/5.10 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR)
% 31.89/5.10
% 31.89/5.10 (m__1911)
% 31.89/5.10 sdtasdt0(xE, xH) = xP & $i(xP) & $i(xH) & $i(xE) & aScalar0(xP)
% 31.89/5.10
% 31.89/5.10 (m__1930)
% 31.89/5.10 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS)
% 31.89/5.10
% 31.89/5.10 (m__1949)
% 31.89/5.10 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN)
% 31.89/5.10
% 31.89/5.10 (m__1967)
% 31.89/5.11 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0
% 31.89/5.11 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 31.89/5.11
% 31.89/5.11 (m__2004)
% 31.89/5.11 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) &
% 31.89/5.11 sdtlseqdt0(v0, xN))
% 31.89/5.11
% 31.89/5.11 (m__2104)
% 31.89/5.11 $i(xS) & $i(xP) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 31.89/5.11 $i] : ? [v4: $i] : (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 &
% 31.89/5.11 sdtasdt0(xR, xR) = v2 & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 &
% 31.89/5.11 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4))
% 31.89/5.11
% 31.89/5.11 (function-axioms)
% 31.89/5.11 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.89/5.11 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 31.89/5.11 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 31.89/5.11 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 31.89/5.11 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 31.89/5.11 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 31.89/5.11 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 31.89/5.11 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 31.89/5.11 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 31.89/5.11 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 31.89/5.11 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 31.89/5.11 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 31.89/5.12 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 31.89/5.12
% 31.89/5.12 Further assumptions not needed in the proof:
% 31.89/5.12 --------------------------------------------
% 31.89/5.12 mDefSPN, mDefSPZ, mDimNat, mDistr2, mElmSc, mEqInit, mIH, mIHOrd, mLEASm,
% 31.89/5.12 mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mNatExtr, mNatSort,
% 31.89/5.12 mNegSc, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, mSqrt,
% 31.89/5.12 mSuccEqu, mSuccNat, mVcSort, mZeroNat, m__1726, m__1766, m__1783, m__1800,
% 31.89/5.12 m__1837, m__1854
% 31.89/5.12
% 31.89/5.12 Those formulas are unsatisfiable:
% 31.89/5.12 ---------------------------------
% 31.89/5.12
% 31.89/5.12 Begin of proof
% 31.89/5.12 |
% 31.89/5.12 | ALPHA: (mDefInit) implies:
% 31.89/5.12 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 31.89/5.12 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 31.89/5.12 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 31.89/5.12 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 31.89/5.12 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 31.89/5.12 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 31.89/5.12 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 31.89/5.12 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 31.89/5.12 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 31.89/5.12 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 31.89/5.12 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 31.89/5.12 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 31.89/5.12 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 31.89/5.12 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 31.89/5.12 | aVector0(v1))))))
% 31.89/5.12 |
% 31.89/5.12 | ALPHA: (m__1678) implies:
% 31.89/5.12 | (2) aVector0(xs)
% 31.89/5.12 |
% 31.89/5.12 | ALPHA: (m__1652) implies:
% 31.89/5.13 | (3) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 31.89/5.13 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 31.89/5.13 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 31.89/5.13 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 31.89/5.13 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 31.89/5.13 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 31.89/5.13 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 31.89/5.13 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 31.89/5.13 | $i(v7)))))))
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1678_01) implies:
% 31.89/5.13 | (4) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 31.89/5.13 | $i(v0))
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1692) implies:
% 31.89/5.13 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1709) implies:
% 31.89/5.13 | (6) sziznziztdt0(xs) = xp
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1746) implies:
% 31.89/5.13 | (7) $i(xs)
% 31.89/5.13 | (8) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 31.89/5.13 | $i(v0) & aScalar0(xA))
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1820) implies:
% 31.89/5.13 | (9) aScalar0(xE)
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1873) implies:
% 31.89/5.13 | (10) aScalar0(xH)
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1892) implies:
% 31.89/5.13 | (11) aScalar0(xR)
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1911) implies:
% 31.89/5.13 | (12) aScalar0(xP)
% 31.89/5.13 | (13) $i(xH)
% 31.89/5.13 | (14) sdtasdt0(xE, xH) = xP
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1930) implies:
% 31.89/5.13 | (15) aScalar0(xS)
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1949) implies:
% 31.89/5.13 | (16) aScalar0(xN)
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__1967) implies:
% 31.89/5.13 | (17) $i(xE)
% 31.89/5.13 |
% 31.89/5.13 | ALPHA: (m__2004) implies:
% 31.89/5.14 | (18) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & sdtlseqdt0(v0, xN))
% 31.89/5.14 |
% 31.89/5.14 | ALPHA: (m__2104) implies:
% 31.89/5.14 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 31.89/5.14 | (sdtasdt0(xS, xS) = v3 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v2
% 31.89/5.14 | & sdtpldt0(v2, v3) = v4 & sdtpldt0(v0, v0) = v1 & $i(v4) & $i(v3) &
% 31.89/5.14 | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v1, v4))
% 31.89/5.14 |
% 31.89/5.14 | ALPHA: (m__) implies:
% 31.89/5.14 | (20) $i(xR)
% 31.89/5.14 | (21) $i(xP)
% 31.89/5.14 | (22) $i(xS)
% 31.89/5.14 | (23) $i(xN)
% 31.89/5.14 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 31.89/5.14 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(xS,
% 31.89/5.14 | xS) = v5 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xR, xR) = v4 &
% 31.89/5.14 | sdtpldt0(v7, xN) = v8 & sdtpldt0(v6, xN) = v7 & sdtpldt0(v4, v5) =
% 31.89/5.14 | v6 & sdtpldt0(v2, v0) = v3 & sdtpldt0(v1, v0) = v2 & sdtpldt0(v0,
% 31.89/5.14 | v0) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 31.89/5.14 | $i(v2) & $i(v1) & $i(v0) & ~ sdtlseqdt0(v3, v8))
% 31.89/5.14 |
% 31.89/5.14 | ALPHA: (function-axioms) implies:
% 31.89/5.14 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 31.89/5.14 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 31.89/5.14 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.89/5.14 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 31.89/5.14 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.89/5.14 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 31.89/5.14 |
% 31.89/5.14 | DELTA: instantiating (4) with fresh symbol all_33_0 gives:
% 31.89/5.15 | (28) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 31.89/5.15 | $i(all_33_0)
% 31.89/5.15 |
% 31.89/5.15 | ALPHA: (28) implies:
% 31.89/5.15 | (29) aDimensionOf0(xs) = all_33_0
% 31.89/5.15 |
% 31.89/5.15 | DELTA: instantiating (18) with fresh symbol all_35_0 gives:
% 31.89/5.15 | (30) sdtasdt0(xP, xP) = all_35_0 & $i(all_35_0) & sdtlseqdt0(all_35_0, xN)
% 31.89/5.15 |
% 31.89/5.15 | ALPHA: (30) implies:
% 31.89/5.15 | (31) sdtlseqdt0(all_35_0, xN)
% 31.89/5.15 | (32) sdtasdt0(xP, xP) = all_35_0
% 31.89/5.15 |
% 31.89/5.15 | DELTA: instantiating (5) with fresh symbol all_37_0 gives:
% 31.89/5.15 | (33) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0)
% 31.89/5.15 |
% 31.89/5.15 | ALPHA: (33) implies:
% 31.89/5.15 | (34) ~ (all_37_0 = sz00)
% 31.89/5.15 | (35) aDimensionOf0(xs) = all_37_0
% 31.89/5.15 |
% 31.89/5.15 | DELTA: instantiating (8) with fresh symbol all_41_0 gives:
% 31.89/5.15 | (36) sdtlbdtrb0(xs, all_41_0) = xA & aDimensionOf0(xs) = all_41_0 &
% 31.89/5.15 | $i(all_41_0) & aScalar0(xA)
% 31.89/5.15 |
% 31.89/5.15 | ALPHA: (36) implies:
% 31.89/5.15 | (37) aDimensionOf0(xs) = all_41_0
% 31.89/5.15 |
% 31.89/5.15 | DELTA: instantiating (19) with fresh symbols all_45_0, all_45_1, all_45_2,
% 31.89/5.15 | all_45_3, all_45_4 gives:
% 31.89/5.15 | (38) sdtasdt0(xS, xS) = all_45_1 & sdtasdt0(xP, xP) = all_45_4 &
% 31.89/5.15 | sdtasdt0(xR, xR) = all_45_2 & sdtpldt0(all_45_2, all_45_1) = all_45_0
% 31.89/5.15 | & sdtpldt0(all_45_4, all_45_4) = all_45_3 & $i(all_45_0) &
% 31.89/5.15 | $i(all_45_1) & $i(all_45_2) & $i(all_45_3) & $i(all_45_4) &
% 31.89/5.15 | sdtlseqdt0(all_45_3, all_45_0)
% 31.89/5.15 |
% 31.89/5.15 | ALPHA: (38) implies:
% 31.89/5.15 | (39) sdtlseqdt0(all_45_3, all_45_0)
% 31.89/5.15 | (40) sdtpldt0(all_45_4, all_45_4) = all_45_3
% 31.89/5.15 | (41) sdtpldt0(all_45_2, all_45_1) = all_45_0
% 31.89/5.15 | (42) sdtasdt0(xR, xR) = all_45_2
% 31.89/5.15 | (43) sdtasdt0(xP, xP) = all_45_4
% 31.89/5.15 | (44) sdtasdt0(xS, xS) = all_45_1
% 31.89/5.15 |
% 31.89/5.15 | DELTA: instantiating (24) with fresh symbols all_47_0, all_47_1, all_47_2,
% 31.89/5.15 | all_47_3, all_47_4, all_47_5, all_47_6, all_47_7, all_47_8 gives:
% 31.89/5.15 | (45) sdtasdt0(xS, xS) = all_47_3 & sdtasdt0(xP, xP) = all_47_8 &
% 31.89/5.15 | sdtasdt0(xR, xR) = all_47_4 & sdtpldt0(all_47_1, xN) = all_47_0 &
% 31.89/5.15 | sdtpldt0(all_47_2, xN) = all_47_1 & sdtpldt0(all_47_4, all_47_3) =
% 31.89/5.15 | all_47_2 & sdtpldt0(all_47_6, all_47_8) = all_47_5 &
% 31.89/5.15 | sdtpldt0(all_47_7, all_47_8) = all_47_6 & sdtpldt0(all_47_8, all_47_8)
% 31.89/5.15 | = all_47_7 & $i(all_47_0) & $i(all_47_1) & $i(all_47_2) & $i(all_47_3)
% 31.89/5.15 | & $i(all_47_4) & $i(all_47_5) & $i(all_47_6) & $i(all_47_7) &
% 31.89/5.15 | $i(all_47_8) & ~ sdtlseqdt0(all_47_5, all_47_0)
% 31.89/5.15 |
% 31.89/5.15 | ALPHA: (45) implies:
% 31.89/5.15 | (46) ~ sdtlseqdt0(all_47_5, all_47_0)
% 31.89/5.15 | (47) $i(all_47_4)
% 31.89/5.15 | (48) $i(all_47_3)
% 31.89/5.15 | (49) sdtpldt0(all_47_8, all_47_8) = all_47_7
% 31.89/5.15 | (50) sdtpldt0(all_47_7, all_47_8) = all_47_6
% 31.89/5.15 | (51) sdtpldt0(all_47_6, all_47_8) = all_47_5
% 31.89/5.15 | (52) sdtpldt0(all_47_4, all_47_3) = all_47_2
% 31.89/5.15 | (53) sdtpldt0(all_47_2, xN) = all_47_1
% 31.89/5.15 | (54) sdtpldt0(all_47_1, xN) = all_47_0
% 31.89/5.15 | (55) sdtasdt0(xR, xR) = all_47_4
% 31.89/5.15 | (56) sdtasdt0(xP, xP) = all_47_8
% 31.89/5.15 | (57) sdtasdt0(xS, xS) = all_47_3
% 31.89/5.15 |
% 31.89/5.15 | DELTA: instantiating (3) with fresh symbol all_49_0 gives:
% 31.89/5.15 | (58) aDimensionOf0(xs) = all_49_0 & $i(all_49_0) & ! [v0: $i] : ! [v1:
% 31.89/5.15 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 31.89/5.15 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 31.89/5.15 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 31.89/5.15 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 31.89/5.15 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 31.89/5.15 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 31.89/5.15 | iLess0(v5, all_49_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 31.89/5.15 | & $i(v6))))))
% 31.89/5.15 |
% 31.89/5.15 | ALPHA: (58) implies:
% 31.89/5.16 | (59) aDimensionOf0(xs) = all_49_0
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (27) with all_45_2, all_47_4, xR, xR, simplifying
% 31.89/5.16 | with (42), (55) gives:
% 31.89/5.16 | (60) all_47_4 = all_45_2
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (27) with all_45_4, all_47_8, xP, xP, simplifying
% 31.89/5.16 | with (43), (56) gives:
% 31.89/5.16 | (61) all_47_8 = all_45_4
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (27) with all_35_0, all_47_8, xP, xP, simplifying
% 31.89/5.16 | with (32), (56) gives:
% 31.89/5.16 | (62) all_47_8 = all_35_0
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (27) with all_45_1, all_47_3, xS, xS, simplifying
% 31.89/5.16 | with (44), (57) gives:
% 31.89/5.16 | (63) all_47_3 = all_45_1
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (25) with all_37_0, all_41_0, xs, simplifying with
% 31.89/5.16 | (35), (37) gives:
% 31.89/5.16 | (64) all_41_0 = all_37_0
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (25) with all_41_0, all_49_0, xs, simplifying with
% 31.89/5.16 | (37), (59) gives:
% 31.89/5.16 | (65) all_49_0 = all_41_0
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (25) with all_33_0, all_49_0, xs, simplifying with
% 31.89/5.16 | (29), (59) gives:
% 31.89/5.16 | (66) all_49_0 = all_33_0
% 31.89/5.16 |
% 31.89/5.16 | COMBINE_EQS: (65), (66) imply:
% 31.89/5.16 | (67) all_41_0 = all_33_0
% 31.89/5.16 |
% 31.89/5.16 | SIMP: (67) implies:
% 31.89/5.16 | (68) all_41_0 = all_33_0
% 31.89/5.16 |
% 31.89/5.16 | COMBINE_EQS: (61), (62) imply:
% 31.89/5.16 | (69) all_45_4 = all_35_0
% 31.89/5.16 |
% 31.89/5.16 | COMBINE_EQS: (64), (68) imply:
% 31.89/5.16 | (70) all_37_0 = all_33_0
% 31.89/5.16 |
% 31.89/5.16 | SIMP: (70) implies:
% 31.89/5.16 | (71) all_37_0 = all_33_0
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (34), (71) imply:
% 31.89/5.16 | (72) ~ (all_33_0 = sz00)
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (52), (60), (63) imply:
% 31.89/5.16 | (73) sdtpldt0(all_45_2, all_45_1) = all_47_2
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (51), (62) imply:
% 31.89/5.16 | (74) sdtpldt0(all_47_6, all_35_0) = all_47_5
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (50), (62) imply:
% 31.89/5.16 | (75) sdtpldt0(all_47_7, all_35_0) = all_47_6
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (49), (62) imply:
% 31.89/5.16 | (76) sdtpldt0(all_35_0, all_35_0) = all_47_7
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (40), (69) imply:
% 31.89/5.16 | (77) sdtpldt0(all_35_0, all_35_0) = all_45_3
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (48), (63) imply:
% 31.89/5.16 | (78) $i(all_45_1)
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (47), (60) imply:
% 31.89/5.16 | (79) $i(all_45_2)
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (26) with all_45_3, all_47_7, all_35_0, all_35_0,
% 31.89/5.16 | simplifying with (76), (77) gives:
% 31.89/5.16 | (80) all_47_7 = all_45_3
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (26) with all_45_0, all_47_2, all_45_1, all_45_2,
% 31.89/5.16 | simplifying with (41), (73) gives:
% 31.89/5.16 | (81) all_47_2 = all_45_0
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (53), (81) imply:
% 31.89/5.16 | (82) sdtpldt0(all_45_0, xN) = all_47_1
% 31.89/5.16 |
% 31.89/5.16 | REDUCE: (75), (80) imply:
% 31.89/5.16 | (83) sdtpldt0(all_45_3, all_35_0) = all_47_6
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (mMulSc) with xR, xR, all_45_2, simplifying with
% 31.89/5.16 | (11), (20), (42) gives:
% 31.89/5.16 | (84) aScalar0(all_45_2)
% 31.89/5.16 |
% 31.89/5.16 | GROUND_INST: instantiating (mDistr) with xP, xP, xP, all_35_0, all_35_0,
% 31.89/5.16 | all_45_3, simplifying with (12), (21), (32), (77) gives:
% 31.89/5.16 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtasdt0(v1,
% 31.89/5.16 | xP) = v2 & sdtasdt0(xP, v0) = all_45_3 & sdtasdt0(xP, xP) = v3 &
% 31.89/5.16 | sdtpldt0(all_35_0, v3) = v2 & sdtpldt0(xP, xP) = v1 & sdtpldt0(xP,
% 31.89/5.16 | xP) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_45_3))
% 31.89/5.16 |
% 31.89/5.17 | GROUND_INST: instantiating (mMulSc) with xP, xP, all_35_0, simplifying with
% 31.89/5.17 | (12), (21), (32) gives:
% 31.89/5.17 | (86) aScalar0(all_35_0)
% 31.89/5.17 |
% 31.89/5.17 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_45_1, simplifying with
% 31.89/5.17 | (15), (22), (44) gives:
% 31.89/5.17 | (87) aScalar0(all_45_1)
% 31.89/5.17 |
% 31.89/5.17 | GROUND_INST: instantiating (1) with xs, xp, simplifying with (2), (6), (7)
% 31.89/5.17 | gives:
% 31.89/5.17 | (88) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1:
% 31.89/5.17 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2) =
% 31.89/5.17 | v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp) |
% 31.89/5.17 | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 & $i(v3))) &
% 31.89/5.17 | ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~ (aDimensionOf0(v1) =
% 31.89/5.17 | v2) | ~ $i(v1) | ~ aVector0(v1) | ? [v3: $i] : ? [v4:
% 31.89/5.17 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) &
% 31.89/5.17 | sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs, v4) = v6 &
% 31.89/5.17 | $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( ~ (v3 = v0) &
% 31.89/5.17 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 31.89/5.17 | (aDimensionOf0(xp) = v1) | ~ $i(xp) | szszuzczcdt0(v1) = v0)
% 31.89/5.17 | & ! [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) |
% 31.89/5.17 | aVector0(xp)))))
% 31.89/5.17 |
% 31.89/5.17 | DELTA: instantiating (85) with fresh symbols all_73_0, all_73_1, all_73_2,
% 31.89/5.17 | all_73_3 gives:
% 31.89/5.17 | (89) sdtasdt0(all_73_2, xP) = all_73_1 & sdtasdt0(xP, all_73_3) = all_45_3
% 31.89/5.17 | & sdtasdt0(xP, xP) = all_73_0 & sdtpldt0(all_35_0, all_73_0) =
% 31.89/5.17 | all_73_1 & sdtpldt0(xP, xP) = all_73_2 & sdtpldt0(xP, xP) = all_73_3 &
% 31.89/5.17 | $i(all_73_0) & $i(all_73_1) & $i(all_73_2) & $i(all_73_3) &
% 31.89/5.17 | $i(all_45_3)
% 31.89/5.17 |
% 31.89/5.17 | ALPHA: (89) implies:
% 31.89/5.17 | (90) $i(all_73_0)
% 31.89/5.17 | (91) sdtpldt0(xP, xP) = all_73_3
% 31.89/5.17 | (92) sdtpldt0(xP, xP) = all_73_2
% 31.89/5.17 | (93) sdtpldt0(all_35_0, all_73_0) = all_73_1
% 31.89/5.17 | (94) sdtasdt0(xP, xP) = all_73_0
% 31.89/5.17 | (95) sdtasdt0(xP, all_73_3) = all_45_3
% 31.89/5.17 | (96) sdtasdt0(all_73_2, xP) = all_73_1
% 31.89/5.17 |
% 31.89/5.17 | DELTA: instantiating (88) with fresh symbol all_78_0 gives:
% 31.89/5.17 | (97) aDimensionOf0(xs) = all_78_0 & $i(all_78_0) & (all_78_0 = sz00 | ( !
% 31.89/5.17 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) =
% 31.89/5.17 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) | ~
% 31.89/5.17 | aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) & !
% 31.89/5.17 | [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1) |
% 31.89/5.17 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 31.89/5.17 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 31.89/5.17 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 & $i(v5)
% 31.89/5.17 | & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = all_78_0) &
% 31.89/5.17 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 31.89/5.17 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | szszuzczcdt0(v0) =
% 31.89/5.17 | all_78_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~
% 31.89/5.17 | $i(xp) | aVector0(xp))))
% 31.89/5.17 |
% 31.89/5.17 | ALPHA: (97) implies:
% 31.89/5.17 | (98) aDimensionOf0(xs) = all_78_0
% 31.89/5.18 | (99) all_78_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 31.89/5.18 | (sdtlbdtrb0(xs, v1) = v2) | ~ (aDimensionOf0(xp) = v0) | ~
% 31.89/5.18 | $i(v1) | ~ $i(xp) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1)
% 31.89/5.18 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~
% 31.89/5.18 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 31.89/5.18 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 31.89/5.18 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) =
% 31.89/5.18 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 31.89/5.18 | all_78_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 31.89/5.18 | $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) | szszuzczcdt0(v0)
% 31.89/5.18 | = all_78_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~
% 31.89/5.18 | $i(xp) | aVector0(xp)))
% 31.89/5.18 |
% 31.89/5.18 | GROUND_INST: instantiating (26) with all_73_3, all_73_2, xP, xP, simplifying
% 31.89/5.18 | with (91), (92) gives:
% 31.89/5.18 | (100) all_73_2 = all_73_3
% 31.89/5.18 |
% 31.89/5.18 | GROUND_INST: instantiating (27) with all_35_0, all_73_0, xP, xP, simplifying
% 31.89/5.18 | with (32), (94) gives:
% 31.89/5.18 | (101) all_73_0 = all_35_0
% 31.89/5.18 |
% 31.89/5.18 | GROUND_INST: instantiating (25) with all_33_0, all_78_0, xs, simplifying with
% 31.89/5.18 | (29), (98) gives:
% 31.89/5.18 | (102) all_78_0 = all_33_0
% 31.89/5.18 |
% 31.89/5.18 | REDUCE: (96), (100) imply:
% 31.89/5.18 | (103) sdtasdt0(all_73_3, xP) = all_73_1
% 31.89/5.18 |
% 31.89/5.18 | REDUCE: (93), (101) imply:
% 31.89/5.18 | (104) sdtpldt0(all_35_0, all_35_0) = all_73_1
% 31.89/5.18 |
% 31.89/5.18 | REDUCE: (90), (101) imply:
% 31.89/5.18 | (105) $i(all_35_0)
% 31.89/5.18 |
% 31.89/5.18 | BETA: splitting (99) gives:
% 31.89/5.18 |
% 31.89/5.18 | Case 1:
% 31.89/5.18 | |
% 31.89/5.18 | | (106) all_78_0 = sz00
% 31.89/5.18 | |
% 31.89/5.18 | | COMBINE_EQS: (102), (106) imply:
% 31.89/5.18 | | (107) all_33_0 = sz00
% 31.89/5.18 | |
% 31.89/5.18 | | REDUCE: (72), (107) imply:
% 31.89/5.18 | | (108) $false
% 31.89/5.18 | |
% 31.89/5.18 | | CLOSE: (108) is inconsistent.
% 31.89/5.18 | |
% 31.89/5.18 | Case 2:
% 31.89/5.18 | |
% 31.89/5.18 | |
% 31.89/5.18 | | GROUND_INST: instantiating (26) with all_45_3, all_73_1, all_35_0, all_35_0,
% 31.89/5.18 | | simplifying with (77), (104) gives:
% 31.89/5.18 | | (109) all_73_1 = all_45_3
% 31.89/5.18 | |
% 31.89/5.18 | | REDUCE: (103), (109) imply:
% 31.89/5.18 | | (110) sdtasdt0(all_73_3, xP) = all_45_3
% 31.89/5.18 | |
% 31.89/5.18 | | GROUND_INST: instantiating (mArith) with all_35_0, all_35_0, all_35_0,
% 31.89/5.18 | | all_45_3, all_47_6, simplifying with (77), (83), (86), (105)
% 31.89/5.18 | | gives:
% 31.89/5.18 | | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 31.89/5.18 | | (sdtasdt0(v1, all_35_0) = v2 & sdtasdt0(all_35_0, v3) = v2 &
% 31.89/5.18 | | sdtasdt0(all_35_0, all_35_0) = v3 & sdtasdt0(all_35_0, all_35_0)
% 31.89/5.18 | | = v1 & sdtpldt0(all_35_0, v0) = all_47_6 & sdtpldt0(all_35_0,
% 31.89/5.18 | | all_35_0) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 31.89/5.18 | | $i(all_47_6) & $i(all_45_3))
% 31.89/5.18 | |
% 31.89/5.18 | | GROUND_INST: instantiating (mSumSc) with all_35_0, all_35_0, all_45_3,
% 31.89/5.18 | | simplifying with (77), (86), (105) gives:
% 31.89/5.18 | | (112) aScalar0(all_45_3)
% 31.89/5.18 | |
% 31.89/5.18 | | GROUND_INST: instantiating (mArith) with all_45_2, all_45_1, xN, all_45_0,
% 31.89/5.18 | | all_47_1, simplifying with (16), (23), (41), (78), (79), (82),
% 31.89/5.18 | | (84), (87) gives:
% 31.89/5.18 | | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 31.89/5.18 | | (sdtasdt0(v1, xN) = v2 & sdtasdt0(all_45_1, all_45_2) = v1 &
% 31.89/5.18 | | sdtasdt0(all_45_1, xN) = v3 & sdtasdt0(all_45_2, v3) = v2 &
% 31.89/5.19 | | sdtasdt0(all_45_2, all_45_1) = v1 & sdtpldt0(all_45_1, all_45_2)
% 31.89/5.19 | | = all_45_0 & sdtpldt0(all_45_1, xN) = v0 & sdtpldt0(all_45_2, v0)
% 31.89/5.19 | | = all_47_1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_1) &
% 31.89/5.19 | | $i(all_45_0))
% 31.89/5.19 | |
% 31.89/5.19 | | GROUND_INST: instantiating (mSumSc) with all_45_2, all_45_1, all_45_0,
% 31.89/5.19 | | simplifying with (41), (78), (79), (84), (87) gives:
% 31.89/5.19 | | (114) aScalar0(all_45_0)
% 31.89/5.19 | |
% 31.89/5.19 | | GROUND_INST: instantiating (mDistr) with xE, xH, xH, xP, xP, all_73_3,
% 31.89/5.19 | | simplifying with (9), (10), (13), (14), (17), (91) gives:
% 31.89/5.19 | | (115) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 31.89/5.19 | | (sdtasdt0(v1, xH) = v2 & sdtasdt0(xH, xH) = v3 & sdtasdt0(xE, v0) =
% 31.89/5.19 | | all_73_3 & sdtpldt0(xP, v3) = v2 & sdtpldt0(xH, xH) = v0 &
% 31.89/5.19 | | sdtpldt0(xE, xH) = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 31.89/5.19 | | $i(all_73_3))
% 31.89/5.19 | |
% 31.89/5.19 | | GROUND_INST: instantiating (mSumSc) with xP, xP, all_73_3, simplifying with
% 31.89/5.19 | | (12), (21), (91) gives:
% 31.89/5.19 | | (116) aScalar0(all_73_3)
% 31.89/5.19 | |
% 31.89/5.19 | | DELTA: instantiating (115) with fresh symbols all_123_0, all_123_1,
% 31.89/5.19 | | all_123_2, all_123_3 gives:
% 31.89/5.19 | | (117) sdtasdt0(all_123_2, xH) = all_123_1 & sdtasdt0(xH, xH) = all_123_0
% 31.89/5.19 | | & sdtasdt0(xE, all_123_3) = all_73_3 & sdtpldt0(xP, all_123_0) =
% 31.89/5.19 | | all_123_1 & sdtpldt0(xH, xH) = all_123_3 & sdtpldt0(xE, xH) =
% 31.89/5.19 | | all_123_2 & $i(all_123_0) & $i(all_123_1) & $i(all_123_2) &
% 31.89/5.19 | | $i(all_123_3) & $i(all_73_3)
% 31.89/5.19 | |
% 31.89/5.19 | | ALPHA: (117) implies:
% 31.89/5.19 | | (118) $i(all_73_3)
% 31.89/5.19 | |
% 31.89/5.19 | | DELTA: instantiating (111) with fresh symbols all_125_0, all_125_1,
% 31.89/5.19 | | all_125_2, all_125_3 gives:
% 31.89/5.19 | | (119) sdtasdt0(all_125_2, all_35_0) = all_125_1 & sdtasdt0(all_35_0,
% 31.89/5.19 | | all_125_0) = all_125_1 & sdtasdt0(all_35_0, all_35_0) = all_125_0
% 31.89/5.19 | | & sdtasdt0(all_35_0, all_35_0) = all_125_2 & sdtpldt0(all_35_0,
% 31.89/5.19 | | all_125_3) = all_47_6 & sdtpldt0(all_35_0, all_35_0) = all_125_3
% 31.89/5.19 | | & $i(all_125_0) & $i(all_125_1) & $i(all_125_2) & $i(all_125_3) &
% 31.89/5.19 | | $i(all_47_6) & $i(all_45_3)
% 31.89/5.19 | |
% 31.89/5.19 | | ALPHA: (119) implies:
% 31.89/5.19 | | (120) $i(all_125_3)
% 31.89/5.19 | | (121) sdtpldt0(all_35_0, all_35_0) = all_125_3
% 31.89/5.19 | | (122) sdtpldt0(all_35_0, all_125_3) = all_47_6
% 31.89/5.19 | |
% 31.89/5.19 | | DELTA: instantiating (113) with fresh symbols all_127_0, all_127_1,
% 31.89/5.19 | | all_127_2, all_127_3 gives:
% 31.89/5.19 | | (123) sdtasdt0(all_127_2, xN) = all_127_1 & sdtasdt0(all_45_1, all_45_2)
% 31.89/5.19 | | = all_127_2 & sdtasdt0(all_45_1, xN) = all_127_0 &
% 31.89/5.19 | | sdtasdt0(all_45_2, all_127_0) = all_127_1 & sdtasdt0(all_45_2,
% 31.89/5.19 | | all_45_1) = all_127_2 & sdtpldt0(all_45_1, all_45_2) = all_45_0 &
% 31.89/5.19 | | sdtpldt0(all_45_1, xN) = all_127_3 & sdtpldt0(all_45_2, all_127_3)
% 31.89/5.19 | | = all_47_1 & $i(all_127_0) & $i(all_127_1) & $i(all_127_2) &
% 31.89/5.19 | | $i(all_127_3) & $i(all_47_1) & $i(all_45_0)
% 31.89/5.19 | |
% 31.89/5.19 | | ALPHA: (123) implies:
% 31.89/5.19 | | (124) $i(all_45_0)
% 31.89/5.19 | | (125) sdtpldt0(all_45_1, all_45_2) = all_45_0
% 31.89/5.19 | |
% 31.89/5.19 | | GROUND_INST: instantiating (26) with all_45_3, all_125_3, all_35_0,
% 31.89/5.19 | | all_35_0, simplifying with (77), (121) gives:
% 31.89/5.19 | | (126) all_125_3 = all_45_3
% 31.89/5.19 | |
% 31.89/5.19 | | REDUCE: (122), (126) imply:
% 31.89/5.19 | | (127) sdtpldt0(all_35_0, all_45_3) = all_47_6
% 31.89/5.19 | |
% 31.89/5.19 | | REDUCE: (120), (126) imply:
% 31.89/5.19 | | (128) $i(all_45_3)
% 31.89/5.19 | |
% 31.89/5.19 | | GROUND_INST: instantiating (mArith) with all_45_3, all_35_0, all_35_0,
% 31.89/5.19 | | all_47_6, all_47_5, simplifying with (74), (83), (86), (105),
% 31.89/5.19 | | (112), (128) gives:
% 31.89/5.19 | | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 31.89/5.19 | | (sdtasdt0(v1, all_35_0) = v2 & sdtasdt0(all_45_3, v3) = v2 &
% 31.89/5.19 | | sdtasdt0(all_45_3, all_35_0) = v1 & sdtasdt0(all_35_0, all_45_3)
% 31.89/5.19 | | = v1 & sdtasdt0(all_35_0, all_35_0) = v3 & sdtpldt0(all_45_3, v0)
% 31.89/5.19 | | = all_47_5 & sdtpldt0(all_35_0, all_45_3) = all_47_6 &
% 31.89/5.19 | | sdtpldt0(all_35_0, all_35_0) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 31.89/5.19 | | $i(v0) & $i(all_47_5) & $i(all_47_6))
% 31.89/5.19 | |
% 31.89/5.20 | | GROUND_INST: instantiating (mLEMon) with all_45_3, all_45_0, all_35_0, xN,
% 31.89/5.20 | | all_47_6, all_47_1, simplifying with (16), (23), (31), (39),
% 31.89/5.20 | | (82), (83), (86), (105), (112), (114), (124), (128) gives:
% 31.89/5.20 | | (130) sdtlseqdt0(all_47_6, all_47_1)
% 31.89/5.20 | |
% 32.45/5.20 | | GROUND_INST: instantiating (mSumSc) with all_45_0, xN, all_47_1, simplifying
% 32.45/5.20 | | with (16), (23), (82), (114), (124) gives:
% 32.45/5.20 | | (131) aScalar0(all_47_1)
% 32.45/5.20 | |
% 32.45/5.20 | | GROUND_INST: instantiating (mDistr) with xP, all_73_3, xP, all_45_3,
% 32.45/5.20 | | all_35_0, all_47_6, simplifying with (12), (21), (32), (83),
% 32.45/5.20 | | (95), (116), (118) gives:
% 32.45/5.20 | | (132) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 32.45/5.20 | | (sdtasdt0(v1, xP) = v2 & sdtasdt0(all_73_3, xP) = v3 & sdtasdt0(xP,
% 32.45/5.20 | | v0) = all_47_6 & sdtpldt0(all_73_3, xP) = v0 &
% 32.45/5.20 | | sdtpldt0(all_35_0, v3) = v2 & sdtpldt0(xP, all_73_3) = v1 &
% 32.45/5.20 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_6))
% 32.45/5.20 | |
% 32.45/5.20 | | GROUND_INST: instantiating (mSumSc) with all_35_0, all_45_3, all_47_6,
% 32.45/5.20 | | simplifying with (86), (105), (112), (127), (128) gives:
% 32.45/5.20 | | (133) aScalar0(all_47_6)
% 32.45/5.20 | |
% 32.45/5.20 | | GROUND_INST: instantiating (mArith) with all_45_1, all_45_2, xN, all_45_0,
% 32.45/5.20 | | all_47_1, simplifying with (16), (23), (78), (79), (82), (84),
% 32.45/5.20 | | (87), (125) gives:
% 32.45/5.20 | | (134) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 32.45/5.20 | | (sdtasdt0(v1, xN) = v2 & sdtasdt0(all_45_1, v3) = v2 &
% 32.45/5.20 | | sdtasdt0(all_45_1, all_45_2) = v1 & sdtasdt0(all_45_2, all_45_1)
% 32.45/5.20 | | = v1 & sdtasdt0(all_45_2, xN) = v3 & sdtpldt0(all_45_1, v0) =
% 32.45/5.20 | | all_47_1 & sdtpldt0(all_45_2, all_45_1) = all_45_0 &
% 32.45/5.20 | | sdtpldt0(all_45_2, xN) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 32.45/5.20 | | $i(all_47_1) & $i(all_45_0))
% 32.45/5.20 | |
% 32.45/5.20 | | DELTA: instantiating (132) with fresh symbols all_153_0, all_153_1,
% 32.45/5.20 | | all_153_2, all_153_3 gives:
% 32.45/5.20 | | (135) sdtasdt0(all_153_2, xP) = all_153_1 & sdtasdt0(all_73_3, xP) =
% 32.45/5.20 | | all_153_0 & sdtasdt0(xP, all_153_3) = all_47_6 & sdtpldt0(all_73_3,
% 32.45/5.20 | | xP) = all_153_3 & sdtpldt0(all_35_0, all_153_0) = all_153_1 &
% 32.45/5.20 | | sdtpldt0(xP, all_73_3) = all_153_2 & $i(all_153_0) & $i(all_153_1)
% 32.45/5.20 | | & $i(all_153_2) & $i(all_153_3) & $i(all_47_6)
% 32.45/5.20 | |
% 32.45/5.20 | | ALPHA: (135) implies:
% 32.45/5.20 | | (136) $i(all_153_1)
% 32.45/5.20 | | (137) sdtpldt0(all_35_0, all_153_0) = all_153_1
% 32.45/5.20 | | (138) sdtasdt0(all_73_3, xP) = all_153_0
% 32.45/5.20 | |
% 32.45/5.20 | | DELTA: instantiating (129) with fresh symbols all_159_0, all_159_1,
% 32.45/5.20 | | all_159_2, all_159_3 gives:
% 32.45/5.20 | | (139) sdtasdt0(all_159_2, all_35_0) = all_159_1 & sdtasdt0(all_45_3,
% 32.45/5.20 | | all_159_0) = all_159_1 & sdtasdt0(all_45_3, all_35_0) = all_159_2
% 32.45/5.20 | | & sdtasdt0(all_35_0, all_45_3) = all_159_2 & sdtasdt0(all_35_0,
% 32.45/5.20 | | all_35_0) = all_159_0 & sdtpldt0(all_45_3, all_159_3) = all_47_5
% 32.45/5.20 | | & sdtpldt0(all_35_0, all_45_3) = all_47_6 & sdtpldt0(all_35_0,
% 32.45/5.20 | | all_35_0) = all_159_3 & $i(all_159_0) & $i(all_159_1) &
% 32.45/5.20 | | $i(all_159_2) & $i(all_159_3) & $i(all_47_5) & $i(all_47_6)
% 32.45/5.20 | |
% 32.45/5.20 | | DELTA: instantiating (134) with fresh symbols all_165_0, all_165_1,
% 32.45/5.20 | | all_165_2, all_165_3 gives:
% 32.45/5.20 | | (140) sdtasdt0(all_165_2, xN) = all_165_1 & sdtasdt0(all_45_1, all_165_0)
% 32.45/5.20 | | = all_165_1 & sdtasdt0(all_45_1, all_45_2) = all_165_2 &
% 32.45/5.20 | | sdtasdt0(all_45_2, all_45_1) = all_165_2 & sdtasdt0(all_45_2, xN) =
% 32.45/5.20 | | all_165_0 & sdtpldt0(all_45_1, all_165_3) = all_47_1 &
% 32.45/5.20 | | sdtpldt0(all_45_2, all_45_1) = all_45_0 & sdtpldt0(all_45_2, xN) =
% 32.45/5.20 | | all_165_3 & $i(all_165_0) & $i(all_165_1) & $i(all_165_2) &
% 32.45/5.20 | | $i(all_165_3) & $i(all_47_1) & $i(all_45_0)
% 32.45/5.20 | |
% 32.45/5.20 | | ALPHA: (140) implies:
% 32.45/5.20 | | (141) $i(all_47_1)
% 32.45/5.20 | |
% 32.45/5.20 | | GROUND_INST: instantiating (27) with all_45_3, all_153_0, xP, all_73_3,
% 32.45/5.20 | | simplifying with (110), (138) gives:
% 32.45/5.20 | | (142) all_153_0 = all_45_3
% 32.45/5.20 | |
% 32.45/5.20 | | REDUCE: (137), (142) imply:
% 32.45/5.20 | | (143) sdtpldt0(all_35_0, all_45_3) = all_153_1
% 32.45/5.20 | |
% 32.45/5.20 | | GROUND_INST: instantiating (26) with all_47_6, all_153_1, all_45_3,
% 32.45/5.20 | | all_35_0, simplifying with (127), (143) gives:
% 32.45/5.20 | | (144) all_153_1 = all_47_6
% 32.45/5.20 | |
% 32.45/5.20 | | REDUCE: (136), (144) imply:
% 32.45/5.20 | | (145) $i(all_47_6)
% 32.45/5.20 | |
% 32.45/5.20 | | GROUND_INST: instantiating (mLEMon) with all_47_6, all_47_1, all_35_0, xN,
% 32.45/5.20 | | all_47_5, all_47_0, simplifying with (16), (23), (31), (46),
% 32.45/5.20 | | (54), (74), (86), (105), (130), (131), (133), (141), (145)
% 32.45/5.20 | | gives:
% 32.45/5.20 | | (146) $false
% 32.45/5.20 | |
% 32.45/5.20 | | CLOSE: (146) is inconsistent.
% 32.45/5.20 | |
% 32.45/5.20 | End of split
% 32.45/5.20 |
% 32.45/5.20 End of proof
% 32.45/5.21 % SZS output end Proof for theBenchmark
% 32.45/5.21
% 32.45/5.21 4599ms
%------------------------------------------------------------------------------