TSTP Solution File: RNG062+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG062+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 : n019.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 13:57:37 EDT 2023
% Result : Theorem 18.94s 3.40s
% Output : Proof 42.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG062+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 : n019.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 01:33:28 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 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 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 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 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
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.45/1.20 Prover 4: Preprocessing ...
% 3.45/1.20 Prover 1: Preprocessing ...
% 3.96/1.24 Prover 5: Preprocessing ...
% 3.96/1.24 Prover 2: Preprocessing ...
% 3.96/1.26 Prover 6: Preprocessing ...
% 3.96/1.26 Prover 0: Preprocessing ...
% 3.96/1.26 Prover 3: Preprocessing ...
% 9.21/2.02 Prover 1: Constructing countermodel ...
% 9.21/2.03 Prover 3: Constructing countermodel ...
% 9.21/2.04 Prover 6: Proving ...
% 11.94/2.37 Prover 5: Constructing countermodel ...
% 12.54/2.43 Prover 4: Constructing countermodel ...
% 12.54/2.47 Prover 2: Proving ...
% 12.97/2.48 Prover 0: Proving ...
% 18.94/3.39 Prover 3: proved (2753ms)
% 18.94/3.39
% 18.94/3.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.94/3.40
% 18.94/3.40 Prover 0: stopped
% 18.94/3.40 Prover 5: stopped
% 18.94/3.40 Prover 6: stopped
% 18.94/3.40 Prover 2: stopped
% 18.94/3.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 18.94/3.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.94/3.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.94/3.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 18.94/3.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.94/3.48 Prover 10: Preprocessing ...
% 20.21/3.50 Prover 8: Preprocessing ...
% 20.21/3.51 Prover 11: Preprocessing ...
% 20.21/3.51 Prover 7: Preprocessing ...
% 20.75/3.56 Prover 13: Preprocessing ...
% 21.45/3.60 Prover 10: Constructing countermodel ...
% 21.45/3.66 Prover 8: Warning: ignoring some quantifiers
% 22.09/3.69 Prover 8: Constructing countermodel ...
% 22.09/3.71 Prover 7: Constructing countermodel ...
% 23.01/3.82 Prover 13: Constructing countermodel ...
% 23.70/3.94 Prover 11: Constructing countermodel ...
% 41.14/6.25 Prover 10: Found proof (size 261)
% 41.14/6.25 Prover 10: proved (2853ms)
% 41.14/6.25 Prover 4: stopped
% 41.14/6.25 Prover 7: stopped
% 41.14/6.25 Prover 11: stopped
% 41.14/6.25 Prover 13: stopped
% 41.14/6.25 Prover 1: stopped
% 41.14/6.26 Prover 8: stopped
% 41.14/6.26
% 41.14/6.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.14/6.26
% 41.14/6.31 % SZS output start Proof for theBenchmark
% 41.14/6.31 Assumptions after simplification:
% 41.14/6.31 ---------------------------------
% 41.14/6.31
% 41.14/6.31 (mArith)
% 42.00/6.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 42.00/6.34 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 42.00/6.34 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5:
% 42.00/6.34 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 &
% 42.00/6.34 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 &
% 42.00/6.34 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 &
% 42.00/6.34 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 42.00/6.34 $i(v3)))
% 42.00/6.34
% 42.00/6.34 (mDefInit)
% 42.00/6.35 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 42.00/6.35 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 42.00/6.35 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 42.00/6.35 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 42.00/6.35 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 42.00/6.35 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 42.00/6.35 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 42.00/6.35 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 42.00/6.35 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 42.00/6.35 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 42.00/6.35 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 42.00/6.35 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 42.00/6.35 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 42.05/6.35
% 42.05/6.35 (mDistr)
% 42.05/6.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 42.05/6.35 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 42.05/6.35 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 42.05/6.35 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i]
% 42.05/6.35 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 42.05/6.35 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 &
% 42.05/6.35 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 42.05/6.35
% 42.05/6.35 (mDistr2)
% 42.05/6.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 42.05/6.35 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 42.05/6.35 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0,
% 42.05/6.35 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~
% 42.05/6.35 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~
% 42.05/6.35 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~
% 42.05/6.35 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] :
% 42.05/6.35 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11
% 42.05/6.35 & $i(v12) & $i(v11) & $i(v10)))
% 42.05/6.35
% 42.05/6.35 (mMNeg)
% 42.05/6.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0) = v2)
% 42.05/6.35 | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~
% 42.05/6.35 aScalar0(v0) | ? [v4: $i] : ? [v5: $i] : (smndt0(v5) = v3 & smndt0(v1) =
% 42.05/6.35 v4 & sdtasdt0(v0, v4) = v3 & sdtasdt0(v0, v1) = v5 & $i(v5) & $i(v4) &
% 42.05/6.35 $i(v3)))
% 42.05/6.35
% 42.05/6.35 (mMulSc)
% 42.05/6.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 42.05/6.35 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 42.05/6.35
% 42.05/6.35 (mNegSc)
% 42.05/6.35 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 42.05/6.35 aScalar0(v0) | aScalar0(v1))
% 42.05/6.35
% 42.05/6.35 (mSumSc)
% 42.05/6.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 42.05/6.35 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 42.05/6.35
% 42.05/6.35 (m__)
% 42.05/6.35 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 42.05/6.35 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 42.05/6.35 ( ~ (v8 = v2) & smndt0(xN) = v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 &
% 42.05/6.35 sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) = v8 &
% 42.05/6.35 sdtpldt0(v5, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 &
% 42.05/6.35 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 42.05/6.35 $i(v0))
% 42.05/6.35
% 42.05/6.35 (m__1652)
% 42.05/6.36 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 42.05/6.36 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 42.05/6.36 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 42.05/6.36 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 42.05/6.36 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 42.05/6.36 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 42.05/6.36 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 42.05/6.36 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 42.05/6.36
% 42.05/6.36 (m__1678)
% 42.05/6.36 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 42.05/6.36
% 42.05/6.36 (m__1678_01)
% 42.05/6.36 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 42.05/6.36 v0 & $i(v0))
% 42.05/6.36
% 42.05/6.36 (m__1692)
% 42.05/6.36 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 42.05/6.36 $i(v0))
% 42.05/6.36
% 42.05/6.36 (m__1726)
% 42.05/6.36 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq)
% 42.05/6.36
% 42.05/6.36 (m__1746)
% 42.05/6.36 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 42.05/6.36 v0 & $i(v0) & aScalar0(xA))
% 42.05/6.36
% 42.05/6.36 (m__1766)
% 42.05/6.36 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 42.05/6.36 v0 & $i(v0) & aScalar0(xB))
% 42.05/6.36
% 42.05/6.36 (m__1892)
% 42.05/6.36 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR)
% 42.05/6.36
% 42.05/6.36 (m__1930)
% 42.05/6.36 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS)
% 42.05/6.36
% 42.05/6.36 (m__1949)
% 42.05/6.36 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN)
% 42.05/6.36
% 42.05/6.36 (m__2144)
% 42.05/6.36 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 42.05/6.36 (smndt0(xN) = v1 & smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR)
% 42.05/6.36 = v1 & sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) &
% 42.05/6.36 $i(v0))
% 42.05/6.36
% 42.05/6.36 (m__2180)
% 42.05/6.36 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 42.05/6.36 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) =
% 42.05/6.36 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 &
% 42.05/6.36 sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 &
% 42.05/6.36 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) &
% 42.05/6.36 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 42.05/6.36
% 42.05/6.36 (m__2221)
% 42.05/6.36 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 42.05/6.36 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) =
% 42.05/6.36 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 &
% 42.05/6.36 sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 &
% 42.05/6.36 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) &
% 42.05/6.36 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 42.05/6.36
% 42.05/6.36 (function-axioms)
% 42.05/6.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 42.05/6.36 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 42.05/6.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 42.05/6.36 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 42.05/6.36 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 42.05/6.36 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 42.05/6.36 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 42.05/6.36 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 42.05/6.36 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 42.05/6.36 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 42.05/6.36 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 42.05/6.36 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 42.05/6.36 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 42.05/6.36
% 42.05/6.36 Further assumptions not needed in the proof:
% 42.05/6.36 --------------------------------------------
% 42.05/6.37 mDefSPN, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, mLEMon,
% 42.05/6.37 mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mNatExtr, mNatSort, mPosMon,
% 42.05/6.37 mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat,
% 42.05/6.37 mVcSort, mZeroNat, m__1709, m__1783, m__1800, m__1820, m__1837, m__1854,
% 42.05/6.37 m__1873, m__1911, m__1967, m__2004
% 42.05/6.37
% 42.05/6.37 Those formulas are unsatisfiable:
% 42.05/6.37 ---------------------------------
% 42.05/6.37
% 42.05/6.37 Begin of proof
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (mDefInit) implies:
% 42.05/6.37 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 42.05/6.37 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 42.05/6.37 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 42.05/6.37 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 42.05/6.37 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 42.05/6.37 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 42.05/6.37 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 42.05/6.37 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 42.05/6.37 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 42.05/6.37 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 42.05/6.37 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 42.05/6.37 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 42.05/6.37 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 42.05/6.37 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 42.05/6.37 | aVector0(v1))))))
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1678) implies:
% 42.05/6.37 | (2) aVector0(xt)
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1652) implies:
% 42.05/6.37 | (3) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 42.05/6.37 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 42.05/6.37 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 42.05/6.37 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 42.05/6.37 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 42.05/6.37 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 42.05/6.37 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 42.05/6.37 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 42.05/6.37 | $i(v7)))))))
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1678_01) implies:
% 42.05/6.37 | (4) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 42.05/6.37 | $i(v0))
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1692) implies:
% 42.05/6.37 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1726) implies:
% 42.05/6.37 | (6) sziznziztdt0(xt) = xq
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1746) implies:
% 42.05/6.37 | (7) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 42.05/6.37 | $i(v0) & aScalar0(xA))
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1766) implies:
% 42.05/6.37 | (8) $i(xt)
% 42.05/6.37 | (9) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 &
% 42.05/6.37 | $i(v0) & aScalar0(xB))
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1892) implies:
% 42.05/6.37 | (10) aScalar0(xR)
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1930) implies:
% 42.05/6.37 | (11) aScalar0(xS)
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__1949) implies:
% 42.05/6.37 | (12) aScalar0(xN)
% 42.05/6.37 |
% 42.05/6.37 | ALPHA: (m__2144) implies:
% 42.05/6.38 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xN) = v1 &
% 42.05/6.38 | smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) = v1 &
% 42.05/6.38 | sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) &
% 42.05/6.38 | $i(v0))
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (m__2180) implies:
% 42.05/6.38 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 42.05/6.38 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS)
% 42.05/6.38 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR,
% 42.05/6.38 | xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 &
% 42.05/6.38 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) &
% 42.05/6.38 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (m__2221) implies:
% 42.05/6.38 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 42.05/6.38 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS)
% 42.05/6.38 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR,
% 42.05/6.38 | xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 &
% 42.05/6.38 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) &
% 42.05/6.38 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (m__) implies:
% 42.05/6.38 | (16) $i(xR)
% 42.05/6.38 | (17) $i(xS)
% 42.05/6.38 | (18) $i(xN)
% 42.05/6.38 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 42.05/6.38 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v2) &
% 42.05/6.38 | smndt0(xN) = v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 &
% 42.05/6.38 | sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) =
% 42.05/6.38 | v8 & sdtpldt0(v5, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR,
% 42.05/6.38 | v0) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 42.05/6.38 | $i(v2) & $i(v1) & $i(v0))
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (function-axioms) implies:
% 42.05/6.38 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 42.05/6.38 | v1) | ~ (smndt0(v2) = v0))
% 42.05/6.38 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 42.05/6.38 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 42.05/6.38 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 42.05/6.38 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 42.05/6.38 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 42.05/6.38 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 42.05/6.38 |
% 42.05/6.38 | DELTA: instantiating (4) with fresh symbol all_33_0 gives:
% 42.05/6.38 | (24) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 42.05/6.38 | $i(all_33_0)
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (24) implies:
% 42.05/6.38 | (25) aDimensionOf0(xs) = all_33_0
% 42.05/6.38 | (26) aDimensionOf0(xt) = all_33_0
% 42.05/6.38 |
% 42.05/6.38 | DELTA: instantiating (5) with fresh symbol all_37_0 gives:
% 42.05/6.38 | (27) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0)
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (27) implies:
% 42.05/6.38 | (28) ~ (all_37_0 = sz00)
% 42.05/6.38 | (29) aDimensionOf0(xs) = all_37_0
% 42.05/6.38 |
% 42.05/6.38 | DELTA: instantiating (9) with fresh symbol all_39_0 gives:
% 42.05/6.38 | (30) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 &
% 42.05/6.38 | $i(all_39_0) & aScalar0(xB)
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (30) implies:
% 42.05/6.38 | (31) aDimensionOf0(xt) = all_39_0
% 42.05/6.38 |
% 42.05/6.38 | DELTA: instantiating (7) with fresh symbol all_41_0 gives:
% 42.05/6.38 | (32) sdtlbdtrb0(xs, all_41_0) = xA & aDimensionOf0(xs) = all_41_0 &
% 42.05/6.38 | $i(all_41_0) & aScalar0(xA)
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (32) implies:
% 42.05/6.38 | (33) aDimensionOf0(xs) = all_41_0
% 42.05/6.38 |
% 42.05/6.38 | DELTA: instantiating (13) with fresh symbols all_45_0, all_45_1, all_45_2
% 42.05/6.38 | gives:
% 42.05/6.38 | (34) smndt0(xN) = all_45_1 & smndt0(xS) = all_45_2 & sdtasdt0(all_45_2,
% 42.05/6.38 | all_45_2) = all_45_0 & sdtasdt0(all_45_2, xR) = all_45_1 &
% 42.05/6.38 | sdtasdt0(xS, xS) = all_45_0 & sdtasdt0(xR, all_45_2) = all_45_1 &
% 42.05/6.38 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2)
% 42.05/6.38 |
% 42.05/6.38 | ALPHA: (34) implies:
% 42.05/6.39 | (35) sdtasdt0(xR, all_45_2) = all_45_1
% 42.05/6.39 | (36) sdtasdt0(xS, xS) = all_45_0
% 42.05/6.39 | (37) sdtasdt0(all_45_2, xR) = all_45_1
% 42.05/6.39 | (38) sdtasdt0(all_45_2, all_45_2) = all_45_0
% 42.05/6.39 | (39) smndt0(xS) = all_45_2
% 42.05/6.39 | (40) smndt0(xN) = all_45_1
% 42.05/6.39 |
% 42.05/6.39 | DELTA: instantiating (14) with fresh symbols all_47_0, all_47_1, all_47_2,
% 42.05/6.39 | all_47_3, all_47_4, all_47_5, all_47_6, all_47_7 gives:
% 42.05/6.39 | (41) smndt0(xN) = all_47_3 & smndt0(xS) = all_47_7 & sdtasdt0(all_47_6,
% 42.05/6.39 | all_47_6) = all_47_5 & sdtasdt0(xS, xS) = all_47_1 & sdtasdt0(xR,
% 42.05/6.39 | xR) = all_47_4 & sdtpldt0(all_47_2, all_47_0) = all_47_5 &
% 42.05/6.39 | sdtpldt0(all_47_3, all_47_1) = all_47_0 & sdtpldt0(all_47_4, all_47_3)
% 42.05/6.39 | = all_47_2 & sdtpldt0(xR, all_47_7) = all_47_6 & $i(all_47_0) &
% 42.05/6.39 | $i(all_47_1) & $i(all_47_2) & $i(all_47_3) & $i(all_47_4) &
% 42.05/6.39 | $i(all_47_5) & $i(all_47_6) & $i(all_47_7)
% 42.05/6.39 |
% 42.05/6.39 | ALPHA: (41) implies:
% 42.05/6.39 | (42) $i(all_47_7)
% 42.05/6.39 | (43) $i(all_47_1)
% 42.05/6.39 | (44) sdtpldt0(xR, all_47_7) = all_47_6
% 42.05/6.39 | (45) sdtpldt0(all_47_4, all_47_3) = all_47_2
% 42.05/6.39 | (46) sdtpldt0(all_47_3, all_47_1) = all_47_0
% 42.05/6.39 | (47) sdtpldt0(all_47_2, all_47_0) = all_47_5
% 42.05/6.39 | (48) sdtasdt0(xR, xR) = all_47_4
% 42.05/6.39 | (49) sdtasdt0(xS, xS) = all_47_1
% 42.05/6.39 | (50) sdtasdt0(all_47_6, all_47_6) = all_47_5
% 42.05/6.39 | (51) smndt0(xS) = all_47_7
% 42.05/6.39 | (52) smndt0(xN) = all_47_3
% 42.05/6.39 |
% 42.05/6.39 | DELTA: instantiating (15) with fresh symbols all_49_0, all_49_1, all_49_2,
% 42.05/6.39 | all_49_3, all_49_4, all_49_5, all_49_6, all_49_7 gives:
% 42.05/6.39 | (53) smndt0(xN) = all_49_3 & smndt0(xS) = all_49_7 & sdtasdt0(all_49_6,
% 42.05/6.39 | all_49_6) = all_49_5 & sdtasdt0(xS, xS) = all_49_1 & sdtasdt0(xR,
% 42.05/6.39 | xR) = all_49_4 & sdtpldt0(all_49_1, all_49_3) = all_49_0 &
% 42.05/6.39 | sdtpldt0(all_49_2, all_49_0) = all_49_5 & sdtpldt0(all_49_4, all_49_3)
% 42.05/6.39 | = all_49_2 & sdtpldt0(xR, all_49_7) = all_49_6 & $i(all_49_0) &
% 42.05/6.39 | $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & $i(all_49_4) &
% 42.05/6.39 | $i(all_49_5) & $i(all_49_6) & $i(all_49_7)
% 42.05/6.39 |
% 42.05/6.39 | ALPHA: (53) implies:
% 42.05/6.39 | (54) $i(all_49_4)
% 42.05/6.39 | (55) sdtpldt0(xR, all_49_7) = all_49_6
% 42.05/6.39 | (56) sdtpldt0(all_49_4, all_49_3) = all_49_2
% 42.05/6.39 | (57) sdtpldt0(all_49_2, all_49_0) = all_49_5
% 42.05/6.39 | (58) sdtpldt0(all_49_1, all_49_3) = all_49_0
% 42.05/6.39 | (59) sdtasdt0(xR, xR) = all_49_4
% 42.05/6.39 | (60) sdtasdt0(xS, xS) = all_49_1
% 42.05/6.39 | (61) sdtasdt0(all_49_6, all_49_6) = all_49_5
% 42.05/6.39 | (62) smndt0(xS) = all_49_7
% 42.05/6.39 | (63) smndt0(xN) = all_49_3
% 42.05/6.39 |
% 42.05/6.39 | DELTA: instantiating (19) with fresh symbols all_51_0, all_51_1, all_51_2,
% 42.05/6.39 | all_51_3, all_51_4, all_51_5, all_51_6, all_51_7, all_51_8 gives:
% 42.05/6.39 | (64) ~ (all_51_0 = all_51_6) & smndt0(xN) = all_51_2 & smndt0(xS) =
% 42.05/6.39 | all_51_8 & sdtasdt0(all_51_7, all_51_7) = all_51_6 & sdtasdt0(xS, xS)
% 42.05/6.39 | = all_51_4 & sdtasdt0(xR, xR) = all_51_5 & sdtpldt0(all_51_1,
% 42.05/6.39 | all_51_2) = all_51_0 & sdtpldt0(all_51_3, all_51_2) = all_51_1 &
% 42.05/6.39 | sdtpldt0(all_51_5, all_51_4) = all_51_3 & sdtpldt0(xR, all_51_8) =
% 42.05/6.39 | all_51_7 & $i(all_51_0) & $i(all_51_1) & $i(all_51_2) & $i(all_51_3) &
% 42.05/6.39 | $i(all_51_4) & $i(all_51_5) & $i(all_51_6) & $i(all_51_7) &
% 42.05/6.39 | $i(all_51_8)
% 42.05/6.39 |
% 42.05/6.39 | ALPHA: (64) implies:
% 42.05/6.39 | (65) ~ (all_51_0 = all_51_6)
% 42.05/6.39 | (66) sdtpldt0(xR, all_51_8) = all_51_7
% 42.05/6.39 | (67) sdtpldt0(all_51_5, all_51_4) = all_51_3
% 42.05/6.39 | (68) sdtpldt0(all_51_3, all_51_2) = all_51_1
% 42.05/6.39 | (69) sdtpldt0(all_51_1, all_51_2) = all_51_0
% 42.05/6.39 | (70) sdtasdt0(xR, xR) = all_51_5
% 42.05/6.39 | (71) sdtasdt0(xS, xS) = all_51_4
% 42.05/6.39 | (72) sdtasdt0(all_51_7, all_51_7) = all_51_6
% 42.05/6.39 | (73) smndt0(xS) = all_51_8
% 42.05/6.39 | (74) smndt0(xN) = all_51_2
% 42.05/6.39 |
% 42.05/6.39 | DELTA: instantiating (3) with fresh symbol all_53_0 gives:
% 42.05/6.40 | (75) aDimensionOf0(xs) = all_53_0 & $i(all_53_0) & ! [v0: $i] : ! [v1:
% 42.05/6.40 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 42.05/6.40 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 42.05/6.40 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 42.05/6.40 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 42.05/6.40 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 42.05/6.40 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 42.05/6.40 | iLess0(v5, all_53_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 42.05/6.40 | & $i(v6))))))
% 42.05/6.40 |
% 42.05/6.40 | ALPHA: (75) implies:
% 42.05/6.40 | (76) aDimensionOf0(xs) = all_53_0
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (23) with all_49_4, all_51_5, xR, xR, simplifying
% 42.05/6.40 | with (59), (70) gives:
% 42.05/6.40 | (77) all_51_5 = all_49_4
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (23) with all_47_4, all_51_5, xR, xR, simplifying
% 42.05/6.40 | with (48), (70) gives:
% 42.05/6.40 | (78) all_51_5 = all_47_4
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (23) with all_47_1, all_49_1, xS, xS, simplifying
% 42.05/6.40 | with (49), (60) gives:
% 42.05/6.40 | (79) all_49_1 = all_47_1
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (23) with all_49_1, all_51_4, xS, xS, simplifying
% 42.05/6.40 | with (60), (71) gives:
% 42.05/6.40 | (80) all_51_4 = all_49_1
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (23) with all_45_0, all_51_4, xS, xS, simplifying
% 42.05/6.40 | with (36), (71) gives:
% 42.05/6.40 | (81) all_51_4 = all_45_0
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (20) with all_47_7, all_49_7, xS, simplifying with
% 42.05/6.40 | (51), (62) gives:
% 42.05/6.40 | (82) all_49_7 = all_47_7
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (20) with all_49_7, all_51_8, xS, simplifying with
% 42.05/6.40 | (62), (73) gives:
% 42.05/6.40 | (83) all_51_8 = all_49_7
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (20) with all_45_2, all_51_8, xS, simplifying with
% 42.05/6.40 | (39), (73) gives:
% 42.05/6.40 | (84) all_51_8 = all_45_2
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (20) with all_47_3, all_49_3, xN, simplifying with
% 42.05/6.40 | (52), (63) gives:
% 42.05/6.40 | (85) all_49_3 = all_47_3
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (20) with all_49_3, all_51_2, xN, simplifying with
% 42.05/6.40 | (63), (74) gives:
% 42.05/6.40 | (86) all_51_2 = all_49_3
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (20) with all_45_1, all_51_2, xN, simplifying with
% 42.05/6.40 | (40), (74) gives:
% 42.05/6.40 | (87) all_51_2 = all_45_1
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (21) with all_37_0, all_41_0, xs, simplifying with
% 42.05/6.40 | (29), (33) gives:
% 42.05/6.40 | (88) all_41_0 = all_37_0
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (21) with all_41_0, all_53_0, xs, simplifying with
% 42.05/6.40 | (33), (76) gives:
% 42.05/6.40 | (89) all_53_0 = all_41_0
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (21) with all_33_0, all_53_0, xs, simplifying with
% 42.05/6.40 | (25), (76) gives:
% 42.05/6.40 | (90) all_53_0 = all_33_0
% 42.05/6.40 |
% 42.05/6.40 | GROUND_INST: instantiating (21) with all_33_0, all_39_0, xt, simplifying with
% 42.05/6.40 | (26), (31) gives:
% 42.05/6.40 | (91) all_39_0 = all_33_0
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (89), (90) imply:
% 42.05/6.40 | (92) all_41_0 = all_33_0
% 42.05/6.40 |
% 42.05/6.40 | SIMP: (92) implies:
% 42.05/6.40 | (93) all_41_0 = all_33_0
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (86), (87) imply:
% 42.05/6.40 | (94) all_49_3 = all_45_1
% 42.05/6.40 |
% 42.05/6.40 | SIMP: (94) implies:
% 42.05/6.40 | (95) all_49_3 = all_45_1
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (80), (81) imply:
% 42.05/6.40 | (96) all_49_1 = all_45_0
% 42.05/6.40 |
% 42.05/6.40 | SIMP: (96) implies:
% 42.05/6.40 | (97) all_49_1 = all_45_0
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (77), (78) imply:
% 42.05/6.40 | (98) all_49_4 = all_47_4
% 42.05/6.40 |
% 42.05/6.40 | SIMP: (98) implies:
% 42.05/6.40 | (99) all_49_4 = all_47_4
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (83), (84) imply:
% 42.05/6.40 | (100) all_49_7 = all_45_2
% 42.05/6.40 |
% 42.05/6.40 | SIMP: (100) implies:
% 42.05/6.40 | (101) all_49_7 = all_45_2
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (79), (97) imply:
% 42.05/6.40 | (102) all_47_1 = all_45_0
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (85), (95) imply:
% 42.05/6.40 | (103) all_47_3 = all_45_1
% 42.05/6.40 |
% 42.05/6.40 | SIMP: (103) implies:
% 42.05/6.40 | (104) all_47_3 = all_45_1
% 42.05/6.40 |
% 42.05/6.40 | COMBINE_EQS: (82), (101) imply:
% 42.05/6.40 | (105) all_47_7 = all_45_2
% 42.05/6.40 |
% 42.05/6.40 | SIMP: (105) implies:
% 42.05/6.41 | (106) all_47_7 = all_45_2
% 42.34/6.41 |
% 42.34/6.41 | COMBINE_EQS: (88), (93) imply:
% 42.34/6.41 | (107) all_37_0 = all_33_0
% 42.34/6.41 |
% 42.34/6.41 | SIMP: (107) implies:
% 42.34/6.41 | (108) all_37_0 = all_33_0
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (28), (108) imply:
% 42.34/6.41 | (109) ~ (all_33_0 = sz00)
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (69), (87) imply:
% 42.34/6.41 | (110) sdtpldt0(all_51_1, all_45_1) = all_51_0
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (68), (87) imply:
% 42.34/6.41 | (111) sdtpldt0(all_51_3, all_45_1) = all_51_1
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (67), (78), (81) imply:
% 42.34/6.41 | (112) sdtpldt0(all_47_4, all_45_0) = all_51_3
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (58), (95), (97) imply:
% 42.34/6.41 | (113) sdtpldt0(all_45_0, all_45_1) = all_49_0
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (56), (95), (99) imply:
% 42.34/6.41 | (114) sdtpldt0(all_47_4, all_45_1) = all_49_2
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (46), (102), (104) imply:
% 42.34/6.41 | (115) sdtpldt0(all_45_1, all_45_0) = all_47_0
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (45), (104) imply:
% 42.34/6.41 | (116) sdtpldt0(all_47_4, all_45_1) = all_47_2
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (66), (84) imply:
% 42.34/6.41 | (117) sdtpldt0(xR, all_45_2) = all_51_7
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (55), (101) imply:
% 42.34/6.41 | (118) sdtpldt0(xR, all_45_2) = all_49_6
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (44), (106) imply:
% 42.34/6.41 | (119) sdtpldt0(xR, all_45_2) = all_47_6
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (54), (99) imply:
% 42.34/6.41 | (120) $i(all_47_4)
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (43), (102) imply:
% 42.34/6.41 | (121) $i(all_45_0)
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (42), (106) imply:
% 42.34/6.41 | (122) $i(all_45_2)
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (22) with all_49_6, all_51_7, all_45_2, xR,
% 42.34/6.41 | simplifying with (117), (118) gives:
% 42.34/6.41 | (123) all_51_7 = all_49_6
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (22) with all_47_6, all_51_7, all_45_2, xR,
% 42.34/6.41 | simplifying with (117), (119) gives:
% 42.34/6.41 | (124) all_51_7 = all_47_6
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (22) with all_47_2, all_49_2, all_45_1, all_47_4,
% 42.34/6.41 | simplifying with (114), (116) gives:
% 42.34/6.41 | (125) all_49_2 = all_47_2
% 42.34/6.41 |
% 42.34/6.41 | COMBINE_EQS: (123), (124) imply:
% 42.34/6.41 | (126) all_49_6 = all_47_6
% 42.34/6.41 |
% 42.34/6.41 | SIMP: (126) implies:
% 42.34/6.41 | (127) all_49_6 = all_47_6
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (72), (124) imply:
% 42.34/6.41 | (128) sdtasdt0(all_47_6, all_47_6) = all_51_6
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (61), (127) imply:
% 42.34/6.41 | (129) sdtasdt0(all_47_6, all_47_6) = all_49_5
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (57), (125) imply:
% 42.34/6.41 | (130) sdtpldt0(all_47_2, all_49_0) = all_49_5
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (23) with all_47_5, all_51_6, all_47_6, all_47_6,
% 42.34/6.41 | simplifying with (50), (128) gives:
% 42.34/6.41 | (131) all_51_6 = all_47_5
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (23) with all_49_5, all_51_6, all_47_6, all_47_6,
% 42.34/6.41 | simplifying with (128), (129) gives:
% 42.34/6.41 | (132) all_51_6 = all_49_5
% 42.34/6.41 |
% 42.34/6.41 | COMBINE_EQS: (131), (132) imply:
% 42.34/6.41 | (133) all_49_5 = all_47_5
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (65), (131) imply:
% 42.34/6.41 | (134) ~ (all_51_0 = all_47_5)
% 42.34/6.41 |
% 42.34/6.41 | REDUCE: (130), (133) imply:
% 42.34/6.41 | (135) sdtpldt0(all_47_2, all_49_0) = all_47_5
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (mMulSc) with xR, xR, all_47_4, simplifying with
% 42.34/6.41 | (10), (16), (48) gives:
% 42.34/6.41 | (136) aScalar0(all_47_4)
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_45_0, simplifying with
% 42.34/6.41 | (11), (17), (36) gives:
% 42.34/6.41 | (137) aScalar0(all_45_0)
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (mMNeg) with xS, xR, all_45_2, all_45_1,
% 42.34/6.41 | simplifying with (10), (11), (16), (17), (37), (39) gives:
% 42.34/6.41 | (138) ? [v0: $i] : ? [v1: $i] : (smndt0(v1) = all_45_1 & smndt0(xR) = v0
% 42.34/6.41 | & sdtasdt0(xS, v0) = all_45_1 & sdtasdt0(xS, xR) = v1 & $i(v1) &
% 42.34/6.41 | $i(v0) & $i(all_45_1))
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (mNegSc) with xS, all_45_2, simplifying with (11),
% 42.34/6.41 | (17), (39) gives:
% 42.34/6.41 | (139) aScalar0(all_45_2)
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (mNegSc) with xN, all_45_1, simplifying with (12),
% 42.34/6.41 | (18), (40) gives:
% 42.34/6.41 | (140) aScalar0(all_45_1)
% 42.34/6.41 |
% 42.34/6.41 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (2), (6), (8)
% 42.34/6.41 | gives:
% 42.34/6.42 | (141) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( !
% 42.34/6.42 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2)
% 42.34/6.42 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq)
% 42.34/6.42 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 &
% 42.34/6.42 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~
% 42.34/6.42 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ?
% 42.34/6.42 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4)
% 42.34/6.42 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt,
% 42.34/6.42 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | (
% 42.34/6.42 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & !
% 42.34/6.42 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) |
% 42.34/6.42 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq)
% 42.34/6.42 | = v1) | ~ $i(xq) | aVector0(xq)))))
% 42.34/6.42 |
% 42.34/6.42 | DELTA: instantiating (138) with fresh symbols all_77_0, all_77_1 gives:
% 42.34/6.42 | (142) smndt0(all_77_0) = all_45_1 & smndt0(xR) = all_77_1 & sdtasdt0(xS,
% 42.34/6.42 | all_77_1) = all_45_1 & sdtasdt0(xS, xR) = all_77_0 & $i(all_77_0) &
% 42.34/6.42 | $i(all_77_1) & $i(all_45_1)
% 42.34/6.42 |
% 42.34/6.42 | ALPHA: (142) implies:
% 42.34/6.42 | (143) $i(all_45_1)
% 42.34/6.42 | (144) $i(all_77_1)
% 42.34/6.42 | (145) sdtasdt0(xS, all_77_1) = all_45_1
% 42.34/6.42 | (146) smndt0(xR) = all_77_1
% 42.34/6.42 |
% 42.34/6.42 | DELTA: instantiating (141) with fresh symbol all_86_0 gives:
% 42.34/6.42 | (147) aDimensionOf0(xt) = all_86_0 & $i(all_86_0) & (all_86_0 = sz00 | ( !
% 42.34/6.42 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 42.34/6.42 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) |
% 42.34/6.42 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) &
% 42.34/6.42 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1)
% 42.34/6.42 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 42.34/6.42 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 42.34/6.42 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 &
% 42.34/6.42 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 42.34/6.42 | all_86_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 42.34/6.42 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) |
% 42.34/6.42 | szszuzczcdt0(v0) = all_86_0) & ! [v0: $i] : ( ~
% 42.34/6.42 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq))))
% 42.34/6.42 |
% 42.34/6.42 | ALPHA: (147) implies:
% 42.34/6.42 | (148) aDimensionOf0(xt) = all_86_0
% 42.34/6.42 | (149) all_86_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 42.34/6.42 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(xq) = v0) | ~
% 42.34/6.42 | $i(v1) | ~ $i(xq) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1)
% 42.34/6.42 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~
% 42.34/6.42 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 42.34/6.42 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 42.34/6.42 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) =
% 42.34/6.42 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 42.34/6.42 | all_86_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 42.34/6.42 | $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0)
% 42.34/6.42 | = all_86_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~
% 42.34/6.42 | $i(xq) | aVector0(xq)))
% 42.34/6.42 |
% 42.34/6.42 | GROUND_INST: instantiating (21) with all_33_0, all_86_0, xt, simplifying with
% 42.34/6.42 | (26), (148) gives:
% 42.34/6.42 | (150) all_86_0 = all_33_0
% 42.34/6.42 |
% 42.34/6.42 | BETA: splitting (149) gives:
% 42.34/6.42 |
% 42.34/6.42 | Case 1:
% 42.34/6.42 | |
% 42.34/6.42 | | (151) all_86_0 = sz00
% 42.34/6.42 | |
% 42.34/6.42 | | COMBINE_EQS: (150), (151) imply:
% 42.34/6.42 | | (152) all_33_0 = sz00
% 42.34/6.42 | |
% 42.34/6.42 | | REDUCE: (109), (152) imply:
% 42.34/6.42 | | (153) $false
% 42.34/6.42 | |
% 42.34/6.42 | | CLOSE: (153) is inconsistent.
% 42.34/6.42 | |
% 42.34/6.42 | Case 2:
% 42.34/6.42 | |
% 42.34/6.42 | |
% 42.34/6.42 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_45_2, all_45_1,
% 42.34/6.42 | | all_45_0, all_47_0, simplifying with (10), (16), (37), (38),
% 42.34/6.42 | | (115), (122), (139) gives:
% 42.34/6.42 | | (154) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.42 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_45_2, v0) = all_47_0 &
% 42.34/6.42 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_0, v3) = v2 &
% 42.34/6.42 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_45_2) = v0 &
% 42.34/6.42 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_0))
% 42.34/6.42 | |
% 42.34/6.42 | | GROUND_INST: instantiating (mDistr) with all_45_2, all_45_2, xR, all_45_0,
% 42.34/6.42 | | all_45_1, all_49_0, simplifying with (10), (16), (37), (38),
% 42.34/6.42 | | (113), (122), (139) gives:
% 42.34/6.42 | | (155) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.42 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, v0) = all_49_0 &
% 42.34/6.42 | | sdtasdt0(all_45_2, xR) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 42.34/6.42 | | sdtpldt0(all_45_2, all_45_2) = v1 & sdtpldt0(all_45_2, xR) = v0 &
% 42.34/6.42 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_49_0))
% 42.34/6.42 | |
% 42.34/6.42 | | GROUND_INST: instantiating (mDistr) with xR, xR, all_45_2, all_47_4,
% 42.34/6.42 | | all_45_1, all_47_2, simplifying with (10), (16), (35), (48),
% 42.34/6.42 | | (116), (122), (139) gives:
% 42.34/6.43 | | (156) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.43 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(xR, v0) = all_47_2 &
% 42.34/6.43 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 42.34/6.43 | | sdtpldt0(xR, all_45_2) = v0 & sdtpldt0(xR, xR) = v1 & $i(v3) &
% 42.34/6.43 | | $i(v2) & $i(v1) & $i(v0) & $i(all_47_2))
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (mSumSc) with xR, all_45_2, all_47_6, simplifying
% 42.34/6.43 | | with (10), (16), (119), (122), (139) gives:
% 42.34/6.43 | | (157) aScalar0(all_47_6)
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (mSumSc) with all_45_0, all_45_1, all_49_0,
% 42.34/6.43 | | simplifying with (113), (121), (137), (140), (143) gives:
% 42.34/6.43 | | (158) aScalar0(all_49_0)
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (mSumSc) with all_45_1, all_45_0, all_47_0,
% 42.34/6.43 | | simplifying with (115), (121), (137), (140), (143) gives:
% 42.34/6.43 | | (159) aScalar0(all_47_0)
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (mArith) with all_47_4, all_45_0, all_45_1,
% 42.34/6.43 | | all_51_3, all_51_1, simplifying with (111), (112), (120),
% 42.34/6.43 | | (121), (136), (137), (140), (143) gives:
% 42.34/6.43 | | (160) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.43 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_47_4, v3) = v2 &
% 42.34/6.43 | | sdtasdt0(all_47_4, all_45_0) = v1 & sdtasdt0(all_45_0, all_47_4)
% 42.34/6.43 | | = v1 & sdtasdt0(all_45_0, all_45_1) = v3 & sdtpldt0(all_47_4, v0)
% 42.34/6.43 | | = all_51_1 & sdtpldt0(all_45_0, all_47_4) = all_51_3 &
% 42.34/6.43 | | sdtpldt0(all_45_0, all_45_1) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 42.34/6.43 | | $i(v0) & $i(all_51_1) & $i(all_51_3))
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (mNegSc) with xR, all_77_1, simplifying with
% 42.34/6.43 | | (10), (16), (146) gives:
% 42.34/6.43 | | (161) aScalar0(all_77_1)
% 42.34/6.43 | |
% 42.34/6.43 | | DELTA: instantiating (156) with fresh symbols all_132_0, all_132_1,
% 42.34/6.43 | | all_132_2, all_132_3 gives:
% 42.34/6.43 | | (162) sdtasdt0(all_132_2, all_45_2) = all_132_1 & sdtasdt0(xR, all_132_3)
% 42.34/6.43 | | = all_47_2 & sdtasdt0(xR, all_45_2) = all_132_0 &
% 42.34/6.43 | | sdtpldt0(all_45_1, all_132_0) = all_132_1 & sdtpldt0(xR, all_45_2)
% 42.34/6.43 | | = all_132_3 & sdtpldt0(xR, xR) = all_132_2 & $i(all_132_0) &
% 42.34/6.43 | | $i(all_132_1) & $i(all_132_2) & $i(all_132_3) & $i(all_47_2)
% 42.34/6.43 | |
% 42.34/6.43 | | ALPHA: (162) implies:
% 42.34/6.43 | | (163) $i(all_132_0)
% 42.34/6.43 | | (164) sdtpldt0(xR, all_45_2) = all_132_3
% 42.34/6.43 | | (165) sdtpldt0(all_45_1, all_132_0) = all_132_1
% 42.34/6.43 | | (166) sdtasdt0(xR, all_45_2) = all_132_0
% 42.34/6.43 | | (167) sdtasdt0(xR, all_132_3) = all_47_2
% 42.34/6.43 | |
% 42.34/6.43 | | DELTA: instantiating (155) with fresh symbols all_134_0, all_134_1,
% 42.34/6.43 | | all_134_2, all_134_3 gives:
% 42.34/6.43 | | (168) sdtasdt0(all_134_2, xR) = all_134_1 & sdtasdt0(all_45_2, all_134_3)
% 42.34/6.43 | | = all_49_0 & sdtasdt0(all_45_2, xR) = all_134_0 &
% 42.34/6.43 | | sdtpldt0(all_45_1, all_134_0) = all_134_1 & sdtpldt0(all_45_2,
% 42.34/6.43 | | all_45_2) = all_134_2 & sdtpldt0(all_45_2, xR) = all_134_3 &
% 42.34/6.43 | | $i(all_134_0) & $i(all_134_1) & $i(all_134_2) & $i(all_134_3) &
% 42.34/6.43 | | $i(all_49_0)
% 42.34/6.43 | |
% 42.34/6.43 | | ALPHA: (168) implies:
% 42.34/6.43 | | (169) sdtpldt0(all_45_2, xR) = all_134_3
% 42.34/6.43 | | (170) sdtpldt0(all_45_1, all_134_0) = all_134_1
% 42.34/6.43 | | (171) sdtasdt0(all_45_2, xR) = all_134_0
% 42.34/6.43 | | (172) sdtasdt0(all_45_2, all_134_3) = all_49_0
% 42.34/6.43 | |
% 42.34/6.43 | | DELTA: instantiating (154) with fresh symbols all_136_0, all_136_1,
% 42.34/6.43 | | all_136_2, all_136_3 gives:
% 42.34/6.43 | | (173) sdtasdt0(all_136_2, all_45_2) = all_136_1 & sdtasdt0(all_45_2,
% 42.34/6.43 | | all_136_3) = all_47_0 & sdtasdt0(xR, all_45_2) = all_136_0 &
% 42.34/6.43 | | sdtpldt0(all_45_0, all_136_0) = all_136_1 & sdtpldt0(all_45_2, xR)
% 42.34/6.43 | | = all_136_2 & sdtpldt0(xR, all_45_2) = all_136_3 & $i(all_136_0) &
% 42.34/6.43 | | $i(all_136_1) & $i(all_136_2) & $i(all_136_3) & $i(all_47_0)
% 42.34/6.43 | |
% 42.34/6.43 | | ALPHA: (173) implies:
% 42.34/6.43 | | (174) $i(all_47_0)
% 42.34/6.43 | | (175) $i(all_136_1)
% 42.34/6.43 | | (176) sdtpldt0(xR, all_45_2) = all_136_3
% 42.34/6.43 | | (177) sdtpldt0(all_45_2, xR) = all_136_2
% 42.34/6.43 | | (178) sdtpldt0(all_45_0, all_136_0) = all_136_1
% 42.34/6.43 | | (179) sdtasdt0(xR, all_45_2) = all_136_0
% 42.34/6.43 | | (180) sdtasdt0(all_45_2, all_136_3) = all_47_0
% 42.34/6.43 | | (181) sdtasdt0(all_136_2, all_45_2) = all_136_1
% 42.34/6.43 | |
% 42.34/6.43 | | DELTA: instantiating (160) with fresh symbols all_138_0, all_138_1,
% 42.34/6.43 | | all_138_2, all_138_3 gives:
% 42.34/6.43 | | (182) sdtasdt0(all_138_2, all_45_1) = all_138_1 & sdtasdt0(all_47_4,
% 42.34/6.43 | | all_138_0) = all_138_1 & sdtasdt0(all_47_4, all_45_0) = all_138_2
% 42.34/6.43 | | & sdtasdt0(all_45_0, all_47_4) = all_138_2 & sdtasdt0(all_45_0,
% 42.34/6.43 | | all_45_1) = all_138_0 & sdtpldt0(all_47_4, all_138_3) = all_51_1
% 42.34/6.43 | | & sdtpldt0(all_45_0, all_47_4) = all_51_3 & sdtpldt0(all_45_0,
% 42.34/6.43 | | all_45_1) = all_138_3 & $i(all_138_0) & $i(all_138_1) &
% 42.34/6.43 | | $i(all_138_2) & $i(all_138_3) & $i(all_51_1) & $i(all_51_3)
% 42.34/6.43 | |
% 42.34/6.43 | | ALPHA: (182) implies:
% 42.34/6.43 | | (183) sdtpldt0(all_45_0, all_45_1) = all_138_3
% 42.34/6.43 | | (184) sdtpldt0(all_47_4, all_138_3) = all_51_1
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (22) with all_47_6, all_136_3, all_45_2, xR,
% 42.34/6.43 | | simplifying with (119), (176) gives:
% 42.34/6.43 | | (185) all_136_3 = all_47_6
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (22) with all_132_3, all_136_3, all_45_2, xR,
% 42.34/6.43 | | simplifying with (164), (176) gives:
% 42.34/6.43 | | (186) all_136_3 = all_132_3
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (22) with all_134_3, all_136_2, xR, all_45_2,
% 42.34/6.43 | | simplifying with (169), (177) gives:
% 42.34/6.43 | | (187) all_136_2 = all_134_3
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (22) with all_49_0, all_138_3, all_45_1,
% 42.34/6.43 | | all_45_0, simplifying with (113), (183) gives:
% 42.34/6.43 | | (188) all_138_3 = all_49_0
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (23) with all_45_1, all_136_0, all_45_2, xR,
% 42.34/6.43 | | simplifying with (35), (179) gives:
% 42.34/6.43 | | (189) all_136_0 = all_45_1
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (23) with all_132_0, all_136_0, all_45_2, xR,
% 42.34/6.43 | | simplifying with (166), (179) gives:
% 42.34/6.43 | | (190) all_136_0 = all_132_0
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (23) with all_45_1, all_134_0, xR, all_45_2,
% 42.34/6.43 | | simplifying with (37), (171) gives:
% 42.34/6.43 | | (191) all_134_0 = all_45_1
% 42.34/6.43 | |
% 42.34/6.43 | | COMBINE_EQS: (189), (190) imply:
% 42.34/6.43 | | (192) all_132_0 = all_45_1
% 42.34/6.43 | |
% 42.34/6.43 | | COMBINE_EQS: (185), (186) imply:
% 42.34/6.43 | | (193) all_132_3 = all_47_6
% 42.34/6.43 | |
% 42.34/6.43 | | REDUCE: (181), (187) imply:
% 42.34/6.43 | | (194) sdtasdt0(all_134_3, all_45_2) = all_136_1
% 42.34/6.43 | |
% 42.34/6.43 | | REDUCE: (180), (185) imply:
% 42.34/6.43 | | (195) sdtasdt0(all_45_2, all_47_6) = all_47_0
% 42.34/6.43 | |
% 42.34/6.43 | | REDUCE: (167), (193) imply:
% 42.34/6.43 | | (196) sdtasdt0(xR, all_47_6) = all_47_2
% 42.34/6.43 | |
% 42.34/6.43 | | REDUCE: (184), (188) imply:
% 42.34/6.43 | | (197) sdtpldt0(all_47_4, all_49_0) = all_51_1
% 42.34/6.43 | |
% 42.34/6.43 | | REDUCE: (178), (189) imply:
% 42.34/6.43 | | (198) sdtpldt0(all_45_0, all_45_1) = all_136_1
% 42.34/6.43 | |
% 42.34/6.43 | | REDUCE: (170), (191) imply:
% 42.34/6.43 | | (199) sdtpldt0(all_45_1, all_45_1) = all_134_1
% 42.34/6.43 | |
% 42.34/6.43 | | REDUCE: (165), (192) imply:
% 42.34/6.43 | | (200) sdtpldt0(all_45_1, all_45_1) = all_132_1
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (22) with all_132_1, all_134_1, all_45_1,
% 42.34/6.43 | | all_45_1, simplifying with (199), (200) gives:
% 42.34/6.43 | | (201) all_134_1 = all_132_1
% 42.34/6.43 | |
% 42.34/6.43 | | GROUND_INST: instantiating (22) with all_49_0, all_136_1, all_45_1,
% 42.34/6.43 | | all_45_0, simplifying with (113), (198) gives:
% 42.34/6.44 | | (202) all_136_1 = all_49_0
% 42.34/6.44 | |
% 42.34/6.44 | | REDUCE: (194), (202) imply:
% 42.34/6.44 | | (203) sdtasdt0(all_134_3, all_45_2) = all_49_0
% 42.34/6.44 | |
% 42.34/6.44 | | REDUCE: (175), (202) imply:
% 42.34/6.44 | | (204) $i(all_49_0)
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (mArith) with all_47_4, all_45_1, all_47_0,
% 42.34/6.44 | | all_47_2, all_47_5, simplifying with (47), (116), (120), (136),
% 42.34/6.44 | | (140), (143), (159), (174) gives:
% 42.34/6.44 | | (205) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.44 | | (sdtasdt0(v1, all_47_0) = v2 & sdtasdt0(all_47_4, v3) = v2 &
% 42.34/6.44 | | sdtasdt0(all_47_4, all_45_1) = v1 & sdtasdt0(all_45_1, all_47_0)
% 42.34/6.44 | | = v3 & sdtasdt0(all_45_1, all_47_4) = v1 & sdtpldt0(all_47_4, v0)
% 42.34/6.44 | | = all_47_5 & sdtpldt0(all_45_1, all_47_0) = v0 &
% 42.34/6.44 | | sdtpldt0(all_45_1, all_47_4) = all_47_2 & $i(v3) & $i(v2) &
% 42.34/6.44 | | $i(v1) & $i(v0) & $i(all_47_2) & $i(all_47_5))
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (mArith) with all_47_4, all_45_1, all_49_0,
% 42.34/6.44 | | all_47_2, all_47_5, simplifying with (116), (120), (135),
% 42.34/6.44 | | (136), (140), (143), (158), (204) gives:
% 42.34/6.44 | | (206) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.44 | | (sdtasdt0(v1, all_49_0) = v2 & sdtasdt0(all_47_4, v3) = v2 &
% 42.34/6.44 | | sdtasdt0(all_47_4, all_45_1) = v1 & sdtasdt0(all_45_1, all_49_0)
% 42.34/6.44 | | = v3 & sdtasdt0(all_45_1, all_47_4) = v1 & sdtpldt0(all_47_4, v0)
% 42.34/6.44 | | = all_47_5 & sdtpldt0(all_45_1, all_49_0) = v0 &
% 42.34/6.44 | | sdtpldt0(all_45_1, all_47_4) = all_47_2 & $i(v3) & $i(v2) &
% 42.34/6.44 | | $i(v1) & $i(v0) & $i(all_47_2) & $i(all_47_5))
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (mDistr) with xS, xS, all_77_1, all_45_0,
% 42.34/6.44 | | all_45_1, all_49_0, simplifying with (11), (17), (36), (113),
% 42.34/6.44 | | (144), (145), (161) gives:
% 42.34/6.44 | | (207) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.44 | | (sdtasdt0(v1, all_77_1) = v2 & sdtasdt0(xS, v0) = all_49_0 &
% 42.34/6.44 | | sdtasdt0(xS, all_77_1) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 42.34/6.44 | | sdtpldt0(xS, all_77_1) = v0 & sdtpldt0(xS, xS) = v1 & $i(v3) &
% 42.34/6.44 | | $i(v2) & $i(v1) & $i(v0) & $i(all_49_0))
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (mSumSc) with all_45_2, xR, all_134_3,
% 42.34/6.44 | | simplifying with (10), (16), (122), (139), (169) gives:
% 42.34/6.44 | | (208) aScalar0(all_134_3)
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, xR, all_45_1,
% 42.34/6.44 | | all_45_1, all_132_1, simplifying with (10), (16), (37), (122),
% 42.34/6.44 | | (139), (200) gives:
% 42.34/6.44 | | (209) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.44 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, v0) = all_132_1 &
% 42.34/6.44 | | sdtasdt0(xR, xR) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 42.34/6.44 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, xR) = v0 & $i(v3) &
% 42.34/6.44 | | $i(v2) & $i(v1) & $i(v0) & $i(all_132_1))
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (mDistr) with xR, all_45_2, all_45_2, all_45_1,
% 42.34/6.44 | | all_45_1, all_132_1, simplifying with (10), (16), (35), (122),
% 42.34/6.44 | | (139), (200) gives:
% 42.34/6.44 | | (210) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.44 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_45_2, all_45_2) = v3 &
% 42.34/6.44 | | sdtasdt0(xR, v0) = all_132_1 & sdtpldt0(all_45_1, v3) = v2 &
% 42.34/6.44 | | sdtpldt0(all_45_2, all_45_2) = v0 & sdtpldt0(xR, all_45_2) = v1 &
% 42.34/6.44 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_132_1))
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (mArith) with all_47_4, all_49_0, all_45_1,
% 42.34/6.44 | | all_51_1, all_51_0, simplifying with (110), (120), (136),
% 42.34/6.44 | | (140), (143), (158), (197), (204) gives:
% 42.34/6.44 | | (211) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.44 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_49_0, all_47_4) = v1 &
% 42.34/6.44 | | sdtasdt0(all_49_0, all_45_1) = v3 & sdtasdt0(all_47_4, v3) = v2 &
% 42.34/6.44 | | sdtasdt0(all_47_4, all_49_0) = v1 & sdtpldt0(all_49_0, all_47_4)
% 42.34/6.44 | | = all_51_1 & sdtpldt0(all_49_0, all_45_1) = v0 &
% 42.34/6.44 | | sdtpldt0(all_47_4, v0) = all_51_0 & $i(v3) & $i(v2) & $i(v1) &
% 42.34/6.44 | | $i(v0) & $i(all_51_0) & $i(all_51_1))
% 42.34/6.44 | |
% 42.34/6.44 | | DELTA: instantiating (210) with fresh symbols all_168_0, all_168_1,
% 42.34/6.44 | | all_168_2, all_168_3 gives:
% 42.34/6.44 | | (212) sdtasdt0(all_168_2, all_45_2) = all_168_1 & sdtasdt0(all_45_2,
% 42.34/6.44 | | all_45_2) = all_168_0 & sdtasdt0(xR, all_168_3) = all_132_1 &
% 42.34/6.44 | | sdtpldt0(all_45_1, all_168_0) = all_168_1 & sdtpldt0(all_45_2,
% 42.34/6.44 | | all_45_2) = all_168_3 & sdtpldt0(xR, all_45_2) = all_168_2 &
% 42.34/6.44 | | $i(all_168_0) & $i(all_168_1) & $i(all_168_2) & $i(all_168_3) &
% 42.34/6.44 | | $i(all_132_1)
% 42.34/6.44 | |
% 42.34/6.44 | | ALPHA: (212) implies:
% 42.34/6.44 | | (213) $i(all_168_2)
% 42.34/6.44 | | (214) $i(all_168_1)
% 42.34/6.44 | | (215) $i(all_168_0)
% 42.34/6.44 | | (216) sdtpldt0(xR, all_45_2) = all_168_2
% 42.34/6.44 | | (217) sdtpldt0(all_45_1, all_168_0) = all_168_1
% 42.34/6.44 | | (218) sdtasdt0(all_45_2, all_45_2) = all_168_0
% 42.34/6.44 | |
% 42.34/6.44 | | DELTA: instantiating (209) with fresh symbols all_170_0, all_170_1,
% 42.34/6.44 | | all_170_2, all_170_3 gives:
% 42.34/6.44 | | (219) sdtasdt0(all_170_2, xR) = all_170_1 & sdtasdt0(all_45_2, all_170_3)
% 42.34/6.44 | | = all_132_1 & sdtasdt0(xR, xR) = all_170_0 & sdtpldt0(all_45_1,
% 42.34/6.44 | | all_170_0) = all_170_1 & sdtpldt0(all_45_2, xR) = all_170_2 &
% 42.34/6.44 | | sdtpldt0(xR, xR) = all_170_3 & $i(all_170_0) & $i(all_170_1) &
% 42.34/6.44 | | $i(all_170_2) & $i(all_170_3) & $i(all_132_1)
% 42.34/6.44 | |
% 42.34/6.44 | | ALPHA: (219) implies:
% 42.34/6.44 | | (220) $i(all_170_2)
% 42.34/6.44 | | (221) $i(all_170_0)
% 42.34/6.44 | | (222) sdtpldt0(all_45_2, xR) = all_170_2
% 42.34/6.44 | | (223) sdtpldt0(all_45_1, all_170_0) = all_170_1
% 42.34/6.44 | | (224) sdtasdt0(xR, xR) = all_170_0
% 42.34/6.44 | | (225) sdtasdt0(all_170_2, xR) = all_170_1
% 42.34/6.44 | |
% 42.34/6.44 | | DELTA: instantiating (207) with fresh symbols all_172_0, all_172_1,
% 42.34/6.44 | | all_172_2, all_172_3 gives:
% 42.34/6.44 | | (226) sdtasdt0(all_172_2, all_77_1) = all_172_1 & sdtasdt0(xS, all_172_3)
% 42.34/6.44 | | = all_49_0 & sdtasdt0(xS, all_77_1) = all_172_0 &
% 42.34/6.44 | | sdtpldt0(all_45_1, all_172_0) = all_172_1 & sdtpldt0(xS, all_77_1)
% 42.34/6.44 | | = all_172_3 & sdtpldt0(xS, xS) = all_172_2 & $i(all_172_0) &
% 42.34/6.44 | | $i(all_172_1) & $i(all_172_2) & $i(all_172_3) & $i(all_49_0)
% 42.34/6.44 | |
% 42.34/6.44 | | ALPHA: (226) implies:
% 42.34/6.44 | | (227) $i(all_172_0)
% 42.34/6.44 | | (228) sdtasdt0(xS, all_77_1) = all_172_0
% 42.34/6.44 | |
% 42.34/6.44 | | DELTA: instantiating (206) with fresh symbols all_174_0, all_174_1,
% 42.34/6.44 | | all_174_2, all_174_3 gives:
% 42.34/6.44 | | (229) sdtasdt0(all_174_2, all_49_0) = all_174_1 & sdtasdt0(all_47_4,
% 42.34/6.44 | | all_174_0) = all_174_1 & sdtasdt0(all_47_4, all_45_1) = all_174_2
% 42.34/6.44 | | & sdtasdt0(all_45_1, all_49_0) = all_174_0 & sdtasdt0(all_45_1,
% 42.34/6.44 | | all_47_4) = all_174_2 & sdtpldt0(all_47_4, all_174_3) = all_47_5
% 42.34/6.44 | | & sdtpldt0(all_45_1, all_49_0) = all_174_3 & sdtpldt0(all_45_1,
% 42.34/6.44 | | all_47_4) = all_47_2 & $i(all_174_0) & $i(all_174_1) &
% 42.34/6.44 | | $i(all_174_2) & $i(all_174_3) & $i(all_47_2) & $i(all_47_5)
% 42.34/6.44 | |
% 42.34/6.44 | | ALPHA: (229) implies:
% 42.34/6.44 | | (230) sdtpldt0(all_45_1, all_49_0) = all_174_3
% 42.34/6.44 | |
% 42.34/6.44 | | DELTA: instantiating (211) with fresh symbols all_176_0, all_176_1,
% 42.34/6.44 | | all_176_2, all_176_3 gives:
% 42.34/6.44 | | (231) sdtasdt0(all_176_2, all_45_1) = all_176_1 & sdtasdt0(all_49_0,
% 42.34/6.44 | | all_47_4) = all_176_2 & sdtasdt0(all_49_0, all_45_1) = all_176_0
% 42.34/6.44 | | & sdtasdt0(all_47_4, all_176_0) = all_176_1 & sdtasdt0(all_47_4,
% 42.34/6.44 | | all_49_0) = all_176_2 & sdtpldt0(all_49_0, all_47_4) = all_51_1 &
% 42.34/6.44 | | sdtpldt0(all_49_0, all_45_1) = all_176_3 & sdtpldt0(all_47_4,
% 42.34/6.44 | | all_176_3) = all_51_0 & $i(all_176_0) & $i(all_176_1) &
% 42.34/6.44 | | $i(all_176_2) & $i(all_176_3) & $i(all_51_0) & $i(all_51_1)
% 42.34/6.44 | |
% 42.34/6.44 | | ALPHA: (231) implies:
% 42.34/6.44 | | (232) sdtpldt0(all_49_0, all_45_1) = all_176_3
% 42.34/6.44 | | (233) sdtpldt0(all_49_0, all_47_4) = all_51_1
% 42.34/6.44 | |
% 42.34/6.44 | | DELTA: instantiating (205) with fresh symbols all_180_0, all_180_1,
% 42.34/6.44 | | all_180_2, all_180_3 gives:
% 42.34/6.44 | | (234) sdtasdt0(all_180_2, all_47_0) = all_180_1 & sdtasdt0(all_47_4,
% 42.34/6.44 | | all_180_0) = all_180_1 & sdtasdt0(all_47_4, all_45_1) = all_180_2
% 42.34/6.44 | | & sdtasdt0(all_45_1, all_47_0) = all_180_0 & sdtasdt0(all_45_1,
% 42.34/6.44 | | all_47_4) = all_180_2 & sdtpldt0(all_47_4, all_180_3) = all_47_5
% 42.34/6.44 | | & sdtpldt0(all_45_1, all_47_0) = all_180_3 & sdtpldt0(all_45_1,
% 42.34/6.44 | | all_47_4) = all_47_2 & $i(all_180_0) & $i(all_180_1) &
% 42.34/6.44 | | $i(all_180_2) & $i(all_180_3) & $i(all_47_2) & $i(all_47_5)
% 42.34/6.44 | |
% 42.34/6.44 | | ALPHA: (234) implies:
% 42.34/6.44 | | (235) sdtpldt0(all_45_1, all_47_4) = all_47_2
% 42.34/6.44 | | (236) sdtpldt0(all_45_1, all_47_0) = all_180_3
% 42.34/6.44 | |
% 42.34/6.44 | | GROUND_INST: instantiating (22) with all_47_6, all_168_2, all_45_2, xR,
% 42.34/6.44 | | simplifying with (119), (216) gives:
% 42.34/6.44 | | (237) all_168_2 = all_47_6
% 42.34/6.44 | |
% 42.34/6.45 | | GROUND_INST: instantiating (22) with all_134_3, all_170_2, xR, all_45_2,
% 42.34/6.45 | | simplifying with (169), (222) gives:
% 42.34/6.45 | | (238) all_170_2 = all_134_3
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (23) with all_47_4, all_170_0, xR, xR,
% 42.34/6.45 | | simplifying with (48), (224) gives:
% 42.34/6.45 | | (239) all_170_0 = all_47_4
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (23) with all_45_1, all_172_0, all_77_1, xS,
% 42.34/6.45 | | simplifying with (145), (228) gives:
% 42.34/6.45 | | (240) all_172_0 = all_45_1
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (23) with all_45_0, all_168_0, all_45_2,
% 42.34/6.45 | | all_45_2, simplifying with (38), (218) gives:
% 42.34/6.45 | | (241) all_168_0 = all_45_0
% 42.34/6.45 | |
% 42.34/6.45 | | REDUCE: (225), (238) imply:
% 42.34/6.45 | | (242) sdtasdt0(all_134_3, xR) = all_170_1
% 42.34/6.45 | |
% 42.34/6.45 | | REDUCE: (223), (239) imply:
% 42.34/6.45 | | (243) sdtpldt0(all_45_1, all_47_4) = all_170_1
% 42.34/6.45 | |
% 42.34/6.45 | | REDUCE: (217), (241) imply:
% 42.34/6.45 | | (244) sdtpldt0(all_45_1, all_45_0) = all_168_1
% 42.34/6.45 | |
% 42.34/6.45 | | REDUCE: (220), (238) imply:
% 42.34/6.45 | | (245) $i(all_134_3)
% 42.34/6.45 | |
% 42.34/6.45 | | REDUCE: (213), (237) imply:
% 42.34/6.45 | | (246) $i(all_47_6)
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (22) with all_47_0, all_168_1, all_45_0,
% 42.34/6.45 | | all_45_1, simplifying with (115), (244) gives:
% 42.34/6.45 | | (247) all_168_1 = all_47_0
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (22) with all_47_2, all_170_1, all_47_4,
% 42.34/6.45 | | all_45_1, simplifying with (235), (243) gives:
% 42.34/6.45 | | (248) all_170_1 = all_47_2
% 42.34/6.45 | |
% 42.34/6.45 | | REDUCE: (242), (248) imply:
% 42.34/6.45 | | (249) sdtasdt0(all_134_3, xR) = all_47_2
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mDistr2) with xR, all_45_2, all_45_2, xR,
% 42.34/6.45 | | all_45_1, all_47_4, all_47_2, all_45_0, all_45_1, all_49_0,
% 42.34/6.45 | | all_47_5, simplifying with (10), (16), (35), (37), (38), (48),
% 42.34/6.45 | | (113), (122), (135), (139), (235) gives:
% 42.34/6.45 | | (250) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_47_5 &
% 42.34/6.45 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_45_2) = v0 &
% 42.34/6.45 | | $i(v1) & $i(v0) & $i(all_47_5))
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mDistr) with xR, all_45_2, xR, all_45_1,
% 42.34/6.45 | | all_47_4, all_47_2, simplifying with (10), (16), (35), (48),
% 42.34/6.45 | | (122), (139), (235) gives:
% 42.34/6.45 | | (251) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.45 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, xR) = v3 & sdtasdt0(xR,
% 42.34/6.45 | | v0) = all_47_2 & sdtpldt0(all_47_4, v3) = v2 &
% 42.34/6.45 | | sdtpldt0(all_45_2, xR) = v0 & sdtpldt0(xR, all_45_2) = v1 &
% 42.34/6.45 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_2))
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mArith) with all_45_1, all_47_4, all_47_0,
% 42.34/6.45 | | all_47_2, all_47_5, simplifying with (47), (120), (136), (140),
% 42.34/6.45 | | (143), (159), (174), (235) gives:
% 42.34/6.45 | | (252) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.45 | | (sdtasdt0(v1, all_47_0) = v2 & sdtasdt0(all_47_4, all_47_0) = v3 &
% 42.34/6.45 | | sdtasdt0(all_47_4, all_45_1) = v1 & sdtasdt0(all_45_1, v3) = v2 &
% 42.34/6.45 | | sdtasdt0(all_45_1, all_47_4) = v1 & sdtpldt0(all_47_4, all_47_0)
% 42.34/6.45 | | = v0 & sdtpldt0(all_47_4, all_45_1) = all_47_2 &
% 42.34/6.45 | | sdtpldt0(all_45_1, v0) = all_47_5 & $i(v3) & $i(v2) & $i(v1) &
% 42.34/6.45 | | $i(v0) & $i(all_47_2) & $i(all_47_5))
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_47_6, all_45_1,
% 42.34/6.45 | | all_47_0, all_180_3, simplifying with (10), (16), (37), (122),
% 42.34/6.45 | | (139), (157), (195), (236), (246) gives:
% 42.34/6.45 | | (253) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.45 | | (sdtasdt0(v1, all_47_6) = v2 & sdtasdt0(all_45_2, v0) = all_180_3 &
% 42.34/6.45 | | sdtasdt0(xR, all_47_6) = v3 & sdtpldt0(all_47_0, v3) = v2 &
% 42.34/6.45 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_47_6) = v0 &
% 42.34/6.45 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_180_3))
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_134_3, all_45_1,
% 42.34/6.45 | | all_49_0, all_174_3, simplifying with (10), (16), (37), (122),
% 42.34/6.45 | | (139), (172), (208), (230), (245) gives:
% 42.34/6.45 | | (254) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.45 | | (sdtasdt0(v1, all_134_3) = v2 & sdtasdt0(all_45_2, v0) = all_174_3
% 42.34/6.45 | | & sdtasdt0(xR, all_134_3) = v3 & sdtpldt0(all_49_0, v3) = v2 &
% 42.34/6.45 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_134_3) = v0 &
% 42.34/6.45 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_174_3))
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mArith) with all_45_0, all_45_1, all_45_1,
% 42.34/6.45 | | all_49_0, all_176_3, simplifying with (113), (121), (137),
% 42.34/6.45 | | (140), (143), (232) gives:
% 42.34/6.45 | | (255) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.45 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_45_0, v3) = v2 &
% 42.34/6.45 | | sdtasdt0(all_45_0, all_45_1) = v1 & sdtasdt0(all_45_1, all_45_0)
% 42.34/6.45 | | = v1 & sdtasdt0(all_45_1, all_45_1) = v3 & sdtpldt0(all_45_0, v0)
% 42.34/6.45 | | = all_176_3 & sdtpldt0(all_45_1, all_45_0) = all_49_0 &
% 42.34/6.45 | | sdtpldt0(all_45_1, all_45_1) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 42.34/6.45 | | $i(v0) & $i(all_176_3) & $i(all_49_0))
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mArith) with all_49_0, all_47_4, all_45_1,
% 42.34/6.45 | | all_51_1, all_51_0, simplifying with (110), (120), (136),
% 42.34/6.45 | | (140), (143), (158), (204), (233) gives:
% 42.34/6.45 | | (256) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.45 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_49_0, v3) = v2 &
% 42.34/6.45 | | sdtasdt0(all_49_0, all_47_4) = v1 & sdtasdt0(all_47_4, all_49_0)
% 42.34/6.45 | | = v1 & sdtasdt0(all_47_4, all_45_1) = v3 & sdtpldt0(all_49_0, v0)
% 42.34/6.45 | | = all_51_0 & sdtpldt0(all_47_4, all_49_0) = all_51_1 &
% 42.34/6.45 | | sdtpldt0(all_47_4, all_45_1) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 42.34/6.45 | | $i(v0) & $i(all_51_0) & $i(all_51_1))
% 42.34/6.45 | |
% 42.34/6.45 | | GROUND_INST: instantiating (mDistr) with all_134_3, xR, all_45_2, all_47_2,
% 42.34/6.45 | | all_49_0, all_47_5, simplifying with (10), (16), (122), (135),
% 42.34/6.45 | | (139), (203), (208), (245), (249) gives:
% 42.34/6.45 | | (257) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 42.34/6.45 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_134_3, v0) = all_47_5 &
% 42.34/6.45 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_134_3, xR) = v1 &
% 42.34/6.45 | | sdtpldt0(all_49_0, v3) = v2 & sdtpldt0(xR, all_45_2) = v0 &
% 42.34/6.45 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_47_5))
% 42.34/6.45 | |
% 42.34/6.45 | | DELTA: instantiating (250) with fresh symbols all_206_0, all_206_1 gives:
% 42.34/6.45 | | (258) sdtasdt0(all_206_1, all_206_0) = all_47_5 & sdtpldt0(all_45_2, xR)
% 42.34/6.45 | | = all_206_0 & sdtpldt0(xR, all_45_2) = all_206_1 & $i(all_206_0) &
% 42.34/6.45 | | $i(all_206_1) & $i(all_47_5)
% 42.34/6.45 | |
% 42.34/6.45 | | ALPHA: (258) implies:
% 42.34/6.45 | | (259) sdtpldt0(xR, all_45_2) = all_206_1
% 42.34/6.45 | | (260) sdtpldt0(all_45_2, xR) = all_206_0
% 42.34/6.45 | |
% 42.34/6.45 | | DELTA: instantiating (257) with fresh symbols all_246_0, all_246_1,
% 42.34/6.45 | | all_246_2, all_246_3 gives:
% 42.34/6.45 | | (261) sdtasdt0(all_246_2, all_45_2) = all_246_1 & sdtasdt0(all_134_3,
% 42.34/6.45 | | all_246_3) = all_47_5 & sdtasdt0(xR, all_45_2) = all_246_0 &
% 42.34/6.45 | | sdtpldt0(all_134_3, xR) = all_246_2 & sdtpldt0(all_49_0, all_246_0)
% 42.34/6.45 | | = all_246_1 & sdtpldt0(xR, all_45_2) = all_246_3 & $i(all_246_0) &
% 42.34/6.45 | | $i(all_246_1) & $i(all_246_2) & $i(all_246_3) & $i(all_47_5)
% 42.34/6.45 | |
% 42.34/6.45 | | ALPHA: (261) implies:
% 42.34/6.45 | | (262) sdtpldt0(xR, all_45_2) = all_246_3
% 42.34/6.45 | | (263) sdtasdt0(all_134_3, all_246_3) = all_47_5
% 42.34/6.45 | |
% 42.34/6.45 | | DELTA: instantiating (254) with fresh symbols all_250_0, all_250_1,
% 42.34/6.45 | | all_250_2, all_250_3 gives:
% 42.34/6.45 | | (264) sdtasdt0(all_250_2, all_134_3) = all_250_1 & sdtasdt0(all_45_2,
% 42.34/6.45 | | all_250_3) = all_174_3 & sdtasdt0(xR, all_134_3) = all_250_0 &
% 42.34/6.45 | | sdtpldt0(all_49_0, all_250_0) = all_250_1 & sdtpldt0(all_45_2, xR)
% 42.34/6.45 | | = all_250_2 & sdtpldt0(xR, all_134_3) = all_250_3 & $i(all_250_0) &
% 42.34/6.45 | | $i(all_250_1) & $i(all_250_2) & $i(all_250_3) & $i(all_174_3)
% 42.34/6.45 | |
% 42.34/6.45 | | ALPHA: (264) implies:
% 42.34/6.45 | | (265) sdtpldt0(all_45_2, xR) = all_250_2
% 42.34/6.45 | |
% 42.34/6.45 | | DELTA: instantiating (253) with fresh symbols all_254_0, all_254_1,
% 42.34/6.45 | | all_254_2, all_254_3 gives:
% 42.34/6.45 | | (266) sdtasdt0(all_254_2, all_47_6) = all_254_1 & sdtasdt0(all_45_2,
% 42.34/6.45 | | all_254_3) = all_180_3 & sdtasdt0(xR, all_47_6) = all_254_0 &
% 42.34/6.45 | | sdtpldt0(all_47_0, all_254_0) = all_254_1 & sdtpldt0(all_45_2, xR)
% 42.34/6.45 | | = all_254_2 & sdtpldt0(xR, all_47_6) = all_254_3 & $i(all_254_0) &
% 42.34/6.45 | | $i(all_254_1) & $i(all_254_2) & $i(all_254_3) & $i(all_180_3)
% 42.34/6.45 | |
% 42.34/6.45 | | ALPHA: (266) implies:
% 42.34/6.45 | | (267) sdtpldt0(all_45_2, xR) = all_254_2
% 42.34/6.45 | | (268) sdtpldt0(all_47_0, all_254_0) = all_254_1
% 42.34/6.45 | | (269) sdtasdt0(xR, all_47_6) = all_254_0
% 42.34/6.45 | | (270) sdtasdt0(all_254_2, all_47_6) = all_254_1
% 42.34/6.45 | |
% 42.34/6.45 | | DELTA: instantiating (251) with fresh symbols all_256_0, all_256_1,
% 42.34/6.45 | | all_256_2, all_256_3 gives:
% 42.34/6.45 | | (271) sdtasdt0(all_256_2, xR) = all_256_1 & sdtasdt0(all_45_2, xR) =
% 42.34/6.45 | | all_256_0 & sdtasdt0(xR, all_256_3) = all_47_2 & sdtpldt0(all_47_4,
% 42.34/6.45 | | all_256_0) = all_256_1 & sdtpldt0(all_45_2, xR) = all_256_3 &
% 42.34/6.45 | | sdtpldt0(xR, all_45_2) = all_256_2 & $i(all_256_0) & $i(all_256_1)
% 42.34/6.45 | | & $i(all_256_2) & $i(all_256_3) & $i(all_47_2)
% 42.34/6.45 | |
% 42.34/6.45 | | ALPHA: (271) implies:
% 42.34/6.45 | | (272) sdtpldt0(xR, all_45_2) = all_256_2
% 42.34/6.45 | | (273) sdtpldt0(all_45_2, xR) = all_256_3
% 42.34/6.45 | |
% 42.34/6.45 | | DELTA: instantiating (256) with fresh symbols all_260_0, all_260_1,
% 42.34/6.45 | | all_260_2, all_260_3 gives:
% 42.34/6.46 | | (274) sdtasdt0(all_260_2, all_45_1) = all_260_1 & sdtasdt0(all_49_0,
% 42.34/6.46 | | all_260_0) = all_260_1 & sdtasdt0(all_49_0, all_47_4) = all_260_2
% 42.34/6.46 | | & sdtasdt0(all_47_4, all_49_0) = all_260_2 & sdtasdt0(all_47_4,
% 42.34/6.46 | | all_45_1) = all_260_0 & sdtpldt0(all_49_0, all_260_3) = all_51_0
% 42.34/6.46 | | & sdtpldt0(all_47_4, all_49_0) = all_51_1 & sdtpldt0(all_47_4,
% 42.34/6.46 | | all_45_1) = all_260_3 & $i(all_260_0) & $i(all_260_1) &
% 42.34/6.46 | | $i(all_260_2) & $i(all_260_3) & $i(all_51_0) & $i(all_51_1)
% 42.34/6.46 | |
% 42.34/6.46 | | ALPHA: (274) implies:
% 42.59/6.46 | | (275) sdtpldt0(all_47_4, all_45_1) = all_260_3
% 42.59/6.46 | | (276) sdtpldt0(all_49_0, all_260_3) = all_51_0
% 42.59/6.46 | |
% 42.59/6.46 | | DELTA: instantiating (255) with fresh symbols all_272_0, all_272_1,
% 42.59/6.46 | | all_272_2, all_272_3 gives:
% 42.59/6.46 | | (277) sdtasdt0(all_272_2, all_45_1) = all_272_1 & sdtasdt0(all_45_0,
% 42.59/6.46 | | all_272_0) = all_272_1 & sdtasdt0(all_45_0, all_45_1) = all_272_2
% 42.59/6.46 | | & sdtasdt0(all_45_1, all_45_0) = all_272_2 & sdtasdt0(all_45_1,
% 42.59/6.46 | | all_45_1) = all_272_0 & sdtpldt0(all_45_0, all_272_3) = all_176_3
% 42.59/6.46 | | & sdtpldt0(all_45_1, all_45_0) = all_49_0 & sdtpldt0(all_45_1,
% 42.59/6.46 | | all_45_1) = all_272_3 & $i(all_272_0) & $i(all_272_1) &
% 42.59/6.46 | | $i(all_272_2) & $i(all_272_3) & $i(all_176_3) & $i(all_49_0)
% 42.59/6.46 | |
% 42.59/6.46 | | ALPHA: (277) implies:
% 42.59/6.46 | | (278) sdtpldt0(all_45_1, all_45_0) = all_49_0
% 42.59/6.46 | |
% 42.59/6.46 | | DELTA: instantiating (252) with fresh symbols all_274_0, all_274_1,
% 42.59/6.46 | | all_274_2, all_274_3 gives:
% 42.59/6.46 | | (279) sdtasdt0(all_274_2, all_47_0) = all_274_1 & sdtasdt0(all_47_4,
% 42.59/6.46 | | all_47_0) = all_274_0 & sdtasdt0(all_47_4, all_45_1) = all_274_2
% 42.59/6.46 | | & sdtasdt0(all_45_1, all_274_0) = all_274_1 & sdtasdt0(all_45_1,
% 42.59/6.46 | | all_47_4) = all_274_2 & sdtpldt0(all_47_4, all_47_0) = all_274_3
% 42.59/6.46 | | & sdtpldt0(all_47_4, all_45_1) = all_47_2 & sdtpldt0(all_45_1,
% 42.59/6.46 | | all_274_3) = all_47_5 & $i(all_274_0) & $i(all_274_1) &
% 42.59/6.46 | | $i(all_274_2) & $i(all_274_3) & $i(all_47_2) & $i(all_47_5)
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_47_6, all_256_2, all_45_2, xR,
% 42.59/6.46 | | simplifying with (119), (272) gives:
% 42.59/6.46 | | (280) all_256_2 = all_47_6
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_246_3, all_256_2, all_45_2, xR,
% 42.59/6.46 | | simplifying with (262), (272) gives:
% 42.59/6.46 | | (281) all_256_2 = all_246_3
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_206_1, all_256_2, all_45_2, xR,
% 42.59/6.46 | | simplifying with (259), (272) gives:
% 42.59/6.46 | | (282) all_256_2 = all_206_1
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_134_3, all_254_2, xR, all_45_2,
% 42.59/6.46 | | simplifying with (169), (267) gives:
% 42.59/6.46 | | (283) all_254_2 = all_134_3
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_250_2, all_254_2, xR, all_45_2,
% 42.59/6.46 | | simplifying with (265), (267) gives:
% 42.59/6.46 | | (284) all_254_2 = all_250_2
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_254_2, all_256_3, xR, all_45_2,
% 42.59/6.46 | | simplifying with (267), (273) gives:
% 42.59/6.46 | | (285) all_256_3 = all_254_2
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_206_0, all_256_3, xR, all_45_2,
% 42.59/6.46 | | simplifying with (260), (273) gives:
% 42.59/6.46 | | (286) all_256_3 = all_206_0
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_47_0, all_49_0, all_45_0, all_45_1,
% 42.59/6.46 | | simplifying with (115), (278) gives:
% 42.59/6.46 | | (287) all_49_0 = all_47_0
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_47_2, all_260_3, all_45_1,
% 42.59/6.46 | | all_47_4, simplifying with (116), (275) gives:
% 42.59/6.46 | | (288) all_260_3 = all_47_2
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (23) with all_47_2, all_254_0, all_47_6, xR,
% 42.59/6.46 | | simplifying with (196), (269) gives:
% 42.59/6.46 | | (289) all_254_0 = all_47_2
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (280), (281) imply:
% 42.59/6.46 | | (290) all_246_3 = all_47_6
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (281), (282) imply:
% 42.59/6.46 | | (291) all_246_3 = all_206_1
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (285), (286) imply:
% 42.59/6.46 | | (292) all_254_2 = all_206_0
% 42.59/6.46 | |
% 42.59/6.46 | | SIMP: (292) implies:
% 42.59/6.46 | | (293) all_254_2 = all_206_0
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (283), (284) imply:
% 42.59/6.46 | | (294) all_250_2 = all_134_3
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (284), (293) imply:
% 42.59/6.46 | | (295) all_250_2 = all_206_0
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (294), (295) imply:
% 42.59/6.46 | | (296) all_206_0 = all_134_3
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (290), (291) imply:
% 42.59/6.46 | | (297) all_206_1 = all_47_6
% 42.59/6.46 | |
% 42.59/6.46 | | REDUCE: (270), (283) imply:
% 42.59/6.46 | | (298) sdtasdt0(all_134_3, all_47_6) = all_254_1
% 42.59/6.46 | |
% 42.59/6.46 | | REDUCE: (263), (290) imply:
% 42.59/6.46 | | (299) sdtasdt0(all_134_3, all_47_6) = all_47_5
% 42.59/6.46 | |
% 42.59/6.46 | | REDUCE: (276), (287), (288) imply:
% 42.59/6.46 | | (300) sdtpldt0(all_47_0, all_47_2) = all_51_0
% 42.59/6.46 | |
% 42.59/6.46 | | REDUCE: (268), (289) imply:
% 42.59/6.46 | | (301) sdtpldt0(all_47_0, all_47_2) = all_254_1
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (22) with all_51_0, all_254_1, all_47_2,
% 42.59/6.46 | | all_47_0, simplifying with (300), (301) gives:
% 42.59/6.46 | | (302) all_254_1 = all_51_0
% 42.59/6.46 | |
% 42.59/6.46 | | GROUND_INST: instantiating (23) with all_47_5, all_254_1, all_47_6,
% 42.59/6.46 | | all_134_3, simplifying with (298), (299) gives:
% 42.59/6.46 | | (303) all_254_1 = all_47_5
% 42.59/6.46 | |
% 42.59/6.46 | | COMBINE_EQS: (302), (303) imply:
% 42.59/6.46 | | (304) all_51_0 = all_47_5
% 42.59/6.46 | |
% 42.59/6.46 | | REDUCE: (134), (304) imply:
% 42.59/6.46 | | (305) $false
% 42.59/6.46 | |
% 42.59/6.46 | | CLOSE: (305) is inconsistent.
% 42.59/6.46 | |
% 42.59/6.46 | End of split
% 42.59/6.46 |
% 42.59/6.46 End of proof
% 42.59/6.46 % SZS output end Proof for theBenchmark
% 42.59/6.46
% 42.59/6.46 5849ms
%------------------------------------------------------------------------------