TSTP Solution File: RNG062+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG062+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 17.43s 3.13s
% Output : Proof 38.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG062+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32 % Computer : n001.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Aug 27 02:25:03 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.60 ________ _____
% 0.17/0.60 ___ __ \_________(_)________________________________
% 0.17/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.60
% 0.17/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.60 (2023-06-19)
% 0.17/0.60
% 0.17/0.60 (c) Philipp Rümmer, 2009-2023
% 0.17/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.60 Amanda Stjerna.
% 0.17/0.60 Free software under BSD-3-Clause.
% 0.17/0.60
% 0.17/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.60
% 0.17/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.62 Running up to 7 provers in parallel.
% 0.17/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.76/1.24 Prover 4: Preprocessing ...
% 3.76/1.25 Prover 1: Preprocessing ...
% 3.93/1.28 Prover 5: Preprocessing ...
% 3.93/1.28 Prover 2: Preprocessing ...
% 3.93/1.28 Prover 6: Preprocessing ...
% 3.93/1.28 Prover 0: Preprocessing ...
% 3.93/1.28 Prover 3: Preprocessing ...
% 8.64/2.05 Prover 3: Constructing countermodel ...
% 8.64/2.05 Prover 1: Constructing countermodel ...
% 9.16/2.07 Prover 6: Proving ...
% 11.15/2.27 Prover 5: Constructing countermodel ...
% 11.89/2.39 Prover 2: Proving ...
% 12.20/2.41 Prover 4: Constructing countermodel ...
% 12.20/2.43 Prover 0: Proving ...
% 17.43/3.12 Prover 3: proved (2499ms)
% 17.43/3.13
% 17.43/3.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.43/3.13
% 17.43/3.13 Prover 5: stopped
% 17.43/3.14 Prover 6: stopped
% 17.43/3.15 Prover 2: stopped
% 17.43/3.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.43/3.15 Prover 0: stopped
% 17.43/3.15 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.43/3.15 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.43/3.15 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.43/3.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.38/3.26 Prover 7: Preprocessing ...
% 18.38/3.28 Prover 10: Preprocessing ...
% 18.38/3.29 Prover 11: Preprocessing ...
% 18.38/3.31 Prover 13: Preprocessing ...
% 18.38/3.31 Prover 8: Preprocessing ...
% 18.38/3.43 Prover 10: Constructing countermodel ...
% 18.38/3.44 Prover 8: Warning: ignoring some quantifiers
% 18.38/3.46 Prover 8: Constructing countermodel ...
% 18.38/3.50 Prover 7: Constructing countermodel ...
% 19.54/3.51 Prover 13: Constructing countermodel ...
% 21.88/3.71 Prover 11: Constructing countermodel ...
% 38.02/5.81 Prover 10: Found proof (size 269)
% 38.02/5.81 Prover 10: proved (2664ms)
% 38.02/5.81 Prover 13: stopped
% 38.02/5.81 Prover 4: stopped
% 38.02/5.81 Prover 11: stopped
% 38.02/5.81 Prover 7: stopped
% 38.02/5.81 Prover 8: stopped
% 38.02/5.81 Prover 1: stopped
% 38.02/5.82
% 38.02/5.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.02/5.82
% 38.45/5.87 % SZS output start Proof for theBenchmark
% 38.45/5.87 Assumptions after simplification:
% 38.45/5.87 ---------------------------------
% 38.45/5.87
% 38.45/5.87 (mArith)
% 38.45/5.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 38.45/5.90 (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 38.45/5.90 | ~ $i(v0) | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v5:
% 38.45/5.90 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (sdtasdt0(v6, v2) = v7 &
% 38.45/5.90 sdtasdt0(v1, v2) = v8 & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v8) = v7 &
% 38.45/5.90 sdtasdt0(v0, v1) = v6 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v1, v0) = v3 &
% 38.45/5.90 sdtpldt0(v0, v5) = v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 38.45/5.90 $i(v3)))
% 38.45/5.90
% 38.45/5.90 (mDefInit)
% 38.45/5.90 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 38.45/5.90 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 38.45/5.90 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 38.45/5.90 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 38.45/5.90 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 38.45/5.90 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 38.45/5.90 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 38.45/5.90 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 38.45/5.90 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 38.45/5.90 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 38.45/5.90 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 38.45/5.90 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 38.45/5.90 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 38.45/5.90
% 38.45/5.90 (mDistr)
% 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 38.45/5.91 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 38.45/5.91 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 38.45/5.91 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i]
% 38.45/5.91 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 38.45/5.91 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 &
% 38.45/5.91 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 38.45/5.91
% 38.45/5.91 (mDistr2)
% 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 38.45/5.91 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 38.45/5.91 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0,
% 38.45/5.91 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~
% 38.45/5.91 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~
% 38.45/5.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~
% 38.45/5.91 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] :
% 38.45/5.91 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11
% 38.45/5.91 & $i(v12) & $i(v11) & $i(v10)))
% 38.45/5.91
% 38.45/5.91 (mMNeg)
% 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (smndt0(v0) = v2)
% 38.45/5.91 | ~ (sdtasdt0(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~
% 38.45/5.91 aScalar0(v0) | ? [v4: $i] : ? [v5: $i] : (smndt0(v5) = v3 & smndt0(v1) =
% 38.45/5.91 v4 & sdtasdt0(v0, v4) = v3 & sdtasdt0(v0, v1) = v5 & $i(v5) & $i(v4) &
% 38.45/5.91 $i(v3)))
% 38.45/5.91
% 38.45/5.91 (mMulSc)
% 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 38.45/5.91 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 38.45/5.91
% 38.45/5.91 (mNegSc)
% 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 38.45/5.91 aScalar0(v0) | aScalar0(v1))
% 38.45/5.91
% 38.45/5.91 (mSumSc)
% 38.45/5.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~
% 38.45/5.91 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 38.45/5.91
% 38.45/5.91 (m__)
% 38.45/5.91 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 38.45/5.91 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 38.45/5.91 ( ~ (v8 = v2) & smndt0(xN) = v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 &
% 38.45/5.91 sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) = v8 &
% 38.45/5.91 sdtpldt0(v5, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 &
% 38.45/5.91 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 38.45/5.91 $i(v0))
% 38.45/5.91
% 38.45/5.91 (m__1652)
% 38.74/5.92 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 38.74/5.92 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 38.74/5.92 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 38.74/5.92 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 38.74/5.92 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 38.74/5.92 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 38.74/5.92 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 38.74/5.92 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 38.74/5.92
% 38.74/5.92 (m__1678)
% 38.74/5.92 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 38.74/5.92
% 38.74/5.92 (m__1678_01)
% 38.74/5.92 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 38.74/5.92 v0 & $i(v0))
% 38.74/5.92
% 38.74/5.92 (m__1692)
% 38.74/5.92 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 38.74/5.92 $i(v0))
% 38.74/5.92
% 38.74/5.92 (m__1709)
% 38.74/5.92 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp &
% 38.74/5.92 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 &
% 38.74/5.92 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 38.74/5.92 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 38.74/5.92 (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 38.74/5.92
% 38.74/5.92 (m__1726)
% 38.74/5.92 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq &
% 38.74/5.92 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 &
% 38.74/5.92 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 38.74/5.92 (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 38.74/5.92 (sdtlbdtrb0(xq, v2) = v3 & $i(v3))))
% 38.74/5.92
% 38.74/5.92 (m__1746)
% 38.74/5.92 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 38.74/5.92 v0 & $i(v0) & aScalar0(xA))
% 38.74/5.92
% 38.74/5.92 (m__1766)
% 38.74/5.92 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 38.74/5.92 v0 & $i(v0) & aScalar0(xB))
% 38.74/5.92
% 38.74/5.92 (m__1892)
% 38.74/5.92 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR)
% 38.74/5.92
% 38.74/5.92 (m__1930)
% 38.74/5.92 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS)
% 38.74/5.92
% 38.74/5.92 (m__1949)
% 38.74/5.92 sdtasdt0(xR, xS) = xN & $i(xN) & $i(xS) & $i(xR) & aScalar0(xN)
% 38.74/5.92
% 38.74/5.92 (m__2144)
% 38.74/5.92 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 38.74/5.92 (smndt0(xN) = v1 & smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR)
% 38.74/5.92 = v1 & sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) &
% 38.74/5.92 $i(v0))
% 38.74/5.92
% 38.74/5.92 (m__2180)
% 38.74/5.93 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 38.74/5.93 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) =
% 38.74/5.93 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 &
% 38.74/5.93 sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 &
% 38.74/5.93 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) &
% 38.74/5.93 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 38.74/5.93
% 38.74/5.93 (m__2221)
% 38.74/5.93 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 38.74/5.93 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) =
% 38.74/5.93 v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 &
% 38.74/5.93 sdtasdt0(xR, xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 &
% 38.74/5.93 sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) & $i(v5) &
% 38.74/5.93 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 38.74/5.93
% 38.74/5.93 (function-axioms)
% 38.74/5.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.74/5.93 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 38.74/5.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 38.74/5.93 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 38.74/5.93 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 38.74/5.93 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 38.74/5.93 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 38.74/5.93 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 38.74/5.93 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 38.74/5.93 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 38.74/5.93 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 38.74/5.93 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 38.74/5.93 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 38.74/5.93
% 38.74/5.93 Further assumptions not needed in the proof:
% 38.74/5.93 --------------------------------------------
% 38.74/5.93 mDefSPN, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, mLEMon,
% 38.74/5.93 mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mNatExtr, mNatSort, mPosMon,
% 38.74/5.93 mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, mSqrt, mSuccEqu, mSuccNat,
% 38.74/5.93 mVcSort, mZeroNat, m__1783, m__1800, m__1820, m__1837, m__1854, m__1873,
% 38.74/5.93 m__1911, m__1967, m__2004
% 38.74/5.93
% 38.74/5.93 Those formulas are unsatisfiable:
% 38.74/5.93 ---------------------------------
% 38.74/5.93
% 38.74/5.93 Begin of proof
% 38.74/5.93 |
% 38.74/5.93 | ALPHA: (mDefInit) implies:
% 38.74/5.94 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 38.74/5.94 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 38.74/5.94 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 38.74/5.94 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 38.74/5.94 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 38.74/5.94 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 38.74/5.94 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 38.74/5.94 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 38.74/5.94 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 38.74/5.94 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 38.74/5.94 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 38.74/5.94 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 38.74/5.94 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 38.74/5.94 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 38.74/5.94 | aVector0(v1))))))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1678) implies:
% 38.74/5.94 | (2) aVector0(xt)
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1652) implies:
% 38.74/5.94 | (3) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 38.74/5.94 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 38.74/5.94 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 38.74/5.94 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 38.74/5.94 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 38.74/5.94 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 38.74/5.94 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 38.74/5.94 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 38.74/5.94 | $i(v7)))))))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1678_01) implies:
% 38.74/5.94 | (4) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 38.74/5.94 | $i(v0))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1692) implies:
% 38.74/5.94 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1709) implies:
% 38.74/5.94 | (6) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp)
% 38.74/5.94 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 38.74/5.94 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 38.74/5.94 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 38.74/5.94 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1726) implies:
% 38.74/5.94 | (7) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq)
% 38.74/5.94 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 38.74/5.94 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 38.74/5.94 | (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 38.74/5.94 | (sdtlbdtrb0(xq, v2) = v3 & $i(v3))))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1746) implies:
% 38.74/5.94 | (8) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 38.74/5.94 | $i(v0) & aScalar0(xA))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1766) implies:
% 38.74/5.94 | (9) $i(xt)
% 38.74/5.94 | (10) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 &
% 38.74/5.94 | $i(v0) & aScalar0(xB))
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1892) implies:
% 38.74/5.94 | (11) aScalar0(xR)
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1930) implies:
% 38.74/5.94 | (12) aScalar0(xS)
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__1949) implies:
% 38.74/5.94 | (13) aScalar0(xN)
% 38.74/5.94 |
% 38.74/5.94 | ALPHA: (m__2144) implies:
% 38.74/5.95 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xN) = v1 &
% 38.74/5.95 | smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) = v1 &
% 38.74/5.95 | sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) &
% 38.74/5.95 | $i(v0))
% 38.74/5.95 |
% 38.74/5.95 | ALPHA: (m__2180) implies:
% 38.74/5.95 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 38.74/5.95 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS)
% 38.74/5.95 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR,
% 38.74/5.95 | xR) = v3 & sdtpldt0(v5, v7) = v2 & sdtpldt0(v4, v6) = v7 &
% 38.74/5.95 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) &
% 38.74/5.95 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 38.74/5.95 |
% 38.74/5.95 | ALPHA: (m__2221) implies:
% 38.74/5.95 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 38.74/5.95 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (smndt0(xN) = v4 & smndt0(xS)
% 38.74/5.95 | = v0 & sdtasdt0(v1, v1) = v2 & sdtasdt0(xS, xS) = v6 & sdtasdt0(xR,
% 38.74/5.95 | xR) = v3 & sdtpldt0(v6, v4) = v7 & sdtpldt0(v5, v7) = v2 &
% 38.74/5.95 | sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 & $i(v7) & $i(v6) &
% 38.74/5.95 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 38.74/5.95 |
% 38.74/5.95 | ALPHA: (m__) implies:
% 38.74/5.95 | (17) $i(xR)
% 38.74/5.95 | (18) $i(xS)
% 38.74/5.95 | (19) $i(xN)
% 38.74/5.95 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 38.74/5.95 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v2) &
% 38.74/5.95 | smndt0(xN) = v6 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 &
% 38.74/5.95 | sdtasdt0(xS, xS) = v4 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v7, v6) =
% 38.74/5.95 | v8 & sdtpldt0(v5, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR,
% 38.74/5.95 | v0) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 38.74/5.95 | $i(v2) & $i(v1) & $i(v0))
% 38.74/5.95 |
% 38.74/5.95 | ALPHA: (function-axioms) implies:
% 38.74/5.95 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 38.74/5.95 | v1) | ~ (smndt0(v2) = v0))
% 38.74/5.95 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 38.74/5.95 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 38.74/5.95 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.74/5.95 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 38.74/5.95 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.74/5.95 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 38.74/5.95 |
% 38.74/5.95 | DELTA: instantiating (4) with fresh symbol all_33_0 gives:
% 38.74/5.95 | (25) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 38.74/5.95 | $i(all_33_0)
% 38.74/5.95 |
% 38.74/5.95 | ALPHA: (25) implies:
% 38.74/5.95 | (26) aDimensionOf0(xs) = all_33_0
% 38.74/5.95 | (27) aDimensionOf0(xt) = all_33_0
% 38.74/5.95 |
% 38.74/5.95 | DELTA: instantiating (5) with fresh symbol all_37_0 gives:
% 38.74/5.95 | (28) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0)
% 38.74/5.95 |
% 38.74/5.95 | ALPHA: (28) implies:
% 38.74/5.95 | (29) ~ (all_37_0 = sz00)
% 38.74/5.95 | (30) aDimensionOf0(xs) = all_37_0
% 38.74/5.95 |
% 38.74/5.95 | DELTA: instantiating (10) with fresh symbol all_39_0 gives:
% 38.74/5.95 | (31) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 &
% 38.74/5.95 | $i(all_39_0) & aScalar0(xB)
% 38.74/5.95 |
% 38.74/5.95 | ALPHA: (31) implies:
% 38.74/5.95 | (32) aDimensionOf0(xt) = all_39_0
% 38.74/5.95 |
% 38.74/5.95 | DELTA: instantiating (8) with fresh symbol all_41_0 gives:
% 38.74/5.95 | (33) sdtlbdtrb0(xs, all_41_0) = xA & aDimensionOf0(xs) = all_41_0 &
% 38.74/5.96 | $i(all_41_0) & aScalar0(xA)
% 38.74/5.96 |
% 38.74/5.96 | ALPHA: (33) implies:
% 38.74/5.96 | (34) aDimensionOf0(xs) = all_41_0
% 38.74/5.96 |
% 38.74/5.96 | DELTA: instantiating (14) with fresh symbols all_45_0, all_45_1, all_45_2
% 38.74/5.96 | gives:
% 38.74/5.96 | (35) smndt0(xN) = all_45_1 & smndt0(xS) = all_45_2 & sdtasdt0(all_45_2,
% 38.74/5.96 | all_45_2) = all_45_0 & sdtasdt0(all_45_2, xR) = all_45_1 &
% 38.74/5.96 | sdtasdt0(xS, xS) = all_45_0 & sdtasdt0(xR, all_45_2) = all_45_1 &
% 38.74/5.96 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2)
% 38.74/5.96 |
% 38.74/5.96 | ALPHA: (35) implies:
% 38.74/5.96 | (36) sdtasdt0(xR, all_45_2) = all_45_1
% 38.74/5.96 | (37) sdtasdt0(xS, xS) = all_45_0
% 38.74/5.96 | (38) sdtasdt0(all_45_2, xR) = all_45_1
% 38.74/5.96 | (39) sdtasdt0(all_45_2, all_45_2) = all_45_0
% 38.74/5.96 | (40) smndt0(xS) = all_45_2
% 38.74/5.96 | (41) smndt0(xN) = all_45_1
% 38.74/5.96 |
% 38.74/5.96 | DELTA: instantiating (7) with fresh symbols all_47_0, all_47_1 gives:
% 38.74/5.96 | (42) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_47_1 &
% 38.74/5.96 | aDimensionOf0(xt) = all_47_0 & szszuzczcdt0(all_47_1) = all_47_0 &
% 38.74/5.96 | $i(all_47_0) & $i(all_47_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i]
% 38.74/5.96 | : ( ~ (sdtlbdtrb0(xt, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 38.74/5.96 | (sdtlbdtrb0(xq, v0) = v1 & $i(v1)))
% 38.74/5.96 |
% 38.74/5.96 | ALPHA: (42) implies:
% 38.74/5.96 | (43) aDimensionOf0(xt) = all_47_0
% 38.74/5.96 | (44) sziznziztdt0(xt) = xq
% 38.74/5.96 |
% 38.74/5.96 | DELTA: instantiating (6) with fresh symbols all_50_0, all_50_1 gives:
% 38.74/5.96 | (45) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_50_1 &
% 38.74/5.96 | aDimensionOf0(xs) = all_50_0 & szszuzczcdt0(all_50_1) = all_50_0 &
% 38.74/5.96 | $i(all_50_0) & $i(all_50_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i]
% 38.74/5.96 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 38.74/5.96 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1)))
% 38.74/5.96 |
% 38.74/5.96 | ALPHA: (45) implies:
% 38.74/5.96 | (46) aDimensionOf0(xs) = all_50_0
% 38.74/5.96 |
% 38.74/5.96 | DELTA: instantiating (15) with fresh symbols all_53_0, all_53_1, all_53_2,
% 38.74/5.96 | all_53_3, all_53_4, all_53_5, all_53_6, all_53_7 gives:
% 38.74/5.96 | (47) smndt0(xN) = all_53_3 & smndt0(xS) = all_53_7 & sdtasdt0(all_53_6,
% 38.74/5.96 | all_53_6) = all_53_5 & sdtasdt0(xS, xS) = all_53_1 & sdtasdt0(xR,
% 38.74/5.96 | xR) = all_53_4 & sdtpldt0(all_53_2, all_53_0) = all_53_5 &
% 38.74/5.96 | sdtpldt0(all_53_3, all_53_1) = all_53_0 & sdtpldt0(all_53_4, all_53_3)
% 38.74/5.96 | = all_53_2 & sdtpldt0(xR, all_53_7) = all_53_6 & $i(all_53_0) &
% 38.74/5.96 | $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & $i(all_53_4) &
% 38.74/5.96 | $i(all_53_5) & $i(all_53_6) & $i(all_53_7)
% 38.74/5.96 |
% 38.74/5.96 | ALPHA: (47) implies:
% 38.74/5.96 | (48) $i(all_53_7)
% 38.74/5.96 | (49) $i(all_53_1)
% 38.74/5.96 | (50) sdtpldt0(xR, all_53_7) = all_53_6
% 38.74/5.96 | (51) sdtpldt0(all_53_4, all_53_3) = all_53_2
% 38.74/5.96 | (52) sdtpldt0(all_53_3, all_53_1) = all_53_0
% 38.74/5.96 | (53) sdtpldt0(all_53_2, all_53_0) = all_53_5
% 38.97/5.96 | (54) sdtasdt0(xR, xR) = all_53_4
% 38.97/5.96 | (55) sdtasdt0(xS, xS) = all_53_1
% 38.97/5.96 | (56) sdtasdt0(all_53_6, all_53_6) = all_53_5
% 38.97/5.96 | (57) smndt0(xS) = all_53_7
% 38.97/5.96 | (58) smndt0(xN) = all_53_3
% 38.97/5.96 |
% 38.97/5.96 | DELTA: instantiating (16) with fresh symbols all_55_0, all_55_1, all_55_2,
% 38.97/5.96 | all_55_3, all_55_4, all_55_5, all_55_6, all_55_7 gives:
% 38.97/5.96 | (59) smndt0(xN) = all_55_3 & smndt0(xS) = all_55_7 & sdtasdt0(all_55_6,
% 38.97/5.96 | all_55_6) = all_55_5 & sdtasdt0(xS, xS) = all_55_1 & sdtasdt0(xR,
% 38.97/5.96 | xR) = all_55_4 & sdtpldt0(all_55_1, all_55_3) = all_55_0 &
% 38.97/5.96 | sdtpldt0(all_55_2, all_55_0) = all_55_5 & sdtpldt0(all_55_4, all_55_3)
% 38.97/5.96 | = all_55_2 & sdtpldt0(xR, all_55_7) = all_55_6 & $i(all_55_0) &
% 38.97/5.96 | $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & $i(all_55_4) &
% 38.97/5.96 | $i(all_55_5) & $i(all_55_6) & $i(all_55_7)
% 38.97/5.96 |
% 38.97/5.96 | ALPHA: (59) implies:
% 38.97/5.96 | (60) $i(all_55_4)
% 38.97/5.96 | (61) sdtpldt0(xR, all_55_7) = all_55_6
% 38.97/5.96 | (62) sdtpldt0(all_55_4, all_55_3) = all_55_2
% 38.97/5.96 | (63) sdtpldt0(all_55_2, all_55_0) = all_55_5
% 38.97/5.96 | (64) sdtpldt0(all_55_1, all_55_3) = all_55_0
% 38.97/5.96 | (65) sdtasdt0(xR, xR) = all_55_4
% 38.97/5.96 | (66) sdtasdt0(xS, xS) = all_55_1
% 38.97/5.96 | (67) sdtasdt0(all_55_6, all_55_6) = all_55_5
% 38.97/5.96 | (68) smndt0(xS) = all_55_7
% 38.97/5.96 | (69) smndt0(xN) = all_55_3
% 38.97/5.96 |
% 38.97/5.96 | DELTA: instantiating (20) with fresh symbols all_57_0, all_57_1, all_57_2,
% 38.97/5.96 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8 gives:
% 38.97/5.96 | (70) ~ (all_57_0 = all_57_6) & smndt0(xN) = all_57_2 & smndt0(xS) =
% 38.97/5.96 | all_57_8 & sdtasdt0(all_57_7, all_57_7) = all_57_6 & sdtasdt0(xS, xS)
% 38.97/5.96 | = all_57_4 & sdtasdt0(xR, xR) = all_57_5 & sdtpldt0(all_57_1,
% 38.97/5.97 | all_57_2) = all_57_0 & sdtpldt0(all_57_3, all_57_2) = all_57_1 &
% 38.97/5.97 | sdtpldt0(all_57_5, all_57_4) = all_57_3 & sdtpldt0(xR, all_57_8) =
% 38.97/5.97 | all_57_7 & $i(all_57_0) & $i(all_57_1) & $i(all_57_2) & $i(all_57_3) &
% 38.97/5.97 | $i(all_57_4) & $i(all_57_5) & $i(all_57_6) & $i(all_57_7) &
% 38.97/5.97 | $i(all_57_8)
% 38.97/5.97 |
% 38.97/5.97 | ALPHA: (70) implies:
% 38.97/5.97 | (71) ~ (all_57_0 = all_57_6)
% 38.97/5.97 | (72) sdtpldt0(xR, all_57_8) = all_57_7
% 38.97/5.97 | (73) sdtpldt0(all_57_5, all_57_4) = all_57_3
% 38.97/5.97 | (74) sdtpldt0(all_57_3, all_57_2) = all_57_1
% 38.97/5.97 | (75) sdtpldt0(all_57_1, all_57_2) = all_57_0
% 38.97/5.97 | (76) sdtasdt0(xR, xR) = all_57_5
% 38.97/5.97 | (77) sdtasdt0(xS, xS) = all_57_4
% 38.97/5.97 | (78) sdtasdt0(all_57_7, all_57_7) = all_57_6
% 38.97/5.97 | (79) smndt0(xS) = all_57_8
% 38.97/5.97 | (80) smndt0(xN) = all_57_2
% 38.97/5.97 |
% 38.97/5.97 | DELTA: instantiating (3) with fresh symbol all_59_0 gives:
% 38.97/5.97 | (81) aDimensionOf0(xs) = all_59_0 & $i(all_59_0) & ! [v0: $i] : ! [v1:
% 38.97/5.97 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 38.97/5.97 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 38.97/5.97 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 38.97/5.97 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 38.97/5.97 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 38.97/5.97 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 38.97/5.97 | iLess0(v5, all_59_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 38.97/5.97 | & $i(v6))))))
% 38.97/5.97 |
% 38.97/5.97 | ALPHA: (81) implies:
% 38.97/5.97 | (82) aDimensionOf0(xs) = all_59_0
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (24) with all_55_4, all_57_5, xR, xR, simplifying
% 38.97/5.97 | with (65), (76) gives:
% 38.97/5.97 | (83) all_57_5 = all_55_4
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (24) with all_53_4, all_57_5, xR, xR, simplifying
% 38.97/5.97 | with (54), (76) gives:
% 38.97/5.97 | (84) all_57_5 = all_53_4
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (24) with all_55_1, all_57_4, xS, xS, simplifying
% 38.97/5.97 | with (66), (77) gives:
% 38.97/5.97 | (85) all_57_4 = all_55_1
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (24) with all_53_1, all_57_4, xS, xS, simplifying
% 38.97/5.97 | with (55), (77) gives:
% 38.97/5.97 | (86) all_57_4 = all_53_1
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (24) with all_45_0, all_57_4, xS, xS, simplifying
% 38.97/5.97 | with (37), (77) gives:
% 38.97/5.97 | (87) all_57_4 = all_45_0
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (21) with all_55_7, all_57_8, xS, simplifying with
% 38.97/5.97 | (68), (79) gives:
% 38.97/5.97 | (88) all_57_8 = all_55_7
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (21) with all_53_7, all_57_8, xS, simplifying with
% 38.97/5.97 | (57), (79) gives:
% 38.97/5.97 | (89) all_57_8 = all_53_7
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (21) with all_45_2, all_57_8, xS, simplifying with
% 38.97/5.97 | (40), (79) gives:
% 38.97/5.97 | (90) all_57_8 = all_45_2
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (21) with all_45_1, all_55_3, xN, simplifying with
% 38.97/5.97 | (41), (69) gives:
% 38.97/5.97 | (91) all_55_3 = all_45_1
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (21) with all_55_3, all_57_2, xN, simplifying with
% 38.97/5.97 | (69), (80) gives:
% 38.97/5.97 | (92) all_57_2 = all_55_3
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (21) with all_53_3, all_57_2, xN, simplifying with
% 38.97/5.97 | (58), (80) gives:
% 38.97/5.97 | (93) all_57_2 = all_53_3
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (22) with all_41_0, all_50_0, xs, simplifying with
% 38.97/5.97 | (34), (46) gives:
% 38.97/5.97 | (94) all_50_0 = all_41_0
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (22) with all_37_0, all_50_0, xs, simplifying with
% 38.97/5.97 | (30), (46) gives:
% 38.97/5.97 | (95) all_50_0 = all_37_0
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (22) with all_41_0, all_59_0, xs, simplifying with
% 38.97/5.97 | (34), (82) gives:
% 38.97/5.97 | (96) all_59_0 = all_41_0
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (22) with all_33_0, all_59_0, xs, simplifying with
% 38.97/5.97 | (26), (82) gives:
% 38.97/5.97 | (97) all_59_0 = all_33_0
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (22) with all_39_0, all_47_0, xt, simplifying with
% 38.97/5.97 | (32), (43) gives:
% 38.97/5.97 | (98) all_47_0 = all_39_0
% 38.97/5.97 |
% 38.97/5.97 | GROUND_INST: instantiating (22) with all_33_0, all_47_0, xt, simplifying with
% 38.97/5.97 | (27), (43) gives:
% 38.97/5.97 | (99) all_47_0 = all_33_0
% 38.97/5.97 |
% 38.97/5.97 | COMBINE_EQS: (96), (97) imply:
% 38.97/5.97 | (100) all_41_0 = all_33_0
% 38.97/5.97 |
% 38.97/5.97 | SIMP: (100) implies:
% 38.97/5.97 | (101) all_41_0 = all_33_0
% 38.97/5.97 |
% 38.97/5.97 | COMBINE_EQS: (92), (93) imply:
% 38.97/5.97 | (102) all_55_3 = all_53_3
% 38.97/5.97 |
% 38.97/5.97 | SIMP: (102) implies:
% 38.97/5.97 | (103) all_55_3 = all_53_3
% 38.97/5.97 |
% 38.97/5.97 | COMBINE_EQS: (85), (87) imply:
% 38.97/5.97 | (104) all_55_1 = all_45_0
% 38.97/5.97 |
% 38.97/5.97 | COMBINE_EQS: (85), (86) imply:
% 38.97/5.97 | (105) all_55_1 = all_53_1
% 38.97/5.97 |
% 38.97/5.97 | COMBINE_EQS: (83), (84) imply:
% 38.97/5.97 | (106) all_55_4 = all_53_4
% 38.97/5.97 |
% 38.97/5.98 | SIMP: (106) implies:
% 38.97/5.98 | (107) all_55_4 = all_53_4
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (88), (90) imply:
% 38.97/5.98 | (108) all_55_7 = all_45_2
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (88), (89) imply:
% 38.97/5.98 | (109) all_55_7 = all_53_7
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (104), (105) imply:
% 38.97/5.98 | (110) all_53_1 = all_45_0
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (91), (103) imply:
% 38.97/5.98 | (111) all_53_3 = all_45_1
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (108), (109) imply:
% 38.97/5.98 | (112) all_53_7 = all_45_2
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (94), (95) imply:
% 38.97/5.98 | (113) all_41_0 = all_37_0
% 38.97/5.98 |
% 38.97/5.98 | SIMP: (113) implies:
% 38.97/5.98 | (114) all_41_0 = all_37_0
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (98), (99) imply:
% 38.97/5.98 | (115) all_39_0 = all_33_0
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (101), (114) imply:
% 38.97/5.98 | (116) all_37_0 = all_33_0
% 38.97/5.98 |
% 38.97/5.98 | SIMP: (116) implies:
% 38.97/5.98 | (117) all_37_0 = all_33_0
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (93), (111) imply:
% 38.97/5.98 | (118) all_57_2 = all_45_1
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (29), (117) imply:
% 38.97/5.98 | (119) ~ (all_33_0 = sz00)
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (75), (118) imply:
% 38.97/5.98 | (120) sdtpldt0(all_57_1, all_45_1) = all_57_0
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (74), (118) imply:
% 38.97/5.98 | (121) sdtpldt0(all_57_3, all_45_1) = all_57_1
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (73), (84), (87) imply:
% 38.97/5.98 | (122) sdtpldt0(all_53_4, all_45_0) = all_57_3
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (64), (91), (104) imply:
% 38.97/5.98 | (123) sdtpldt0(all_45_0, all_45_1) = all_55_0
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (62), (91), (107) imply:
% 38.97/5.98 | (124) sdtpldt0(all_53_4, all_45_1) = all_55_2
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (52), (110), (111) imply:
% 38.97/5.98 | (125) sdtpldt0(all_45_1, all_45_0) = all_53_0
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (51), (111) imply:
% 38.97/5.98 | (126) sdtpldt0(all_53_4, all_45_1) = all_53_2
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (72), (90) imply:
% 38.97/5.98 | (127) sdtpldt0(xR, all_45_2) = all_57_7
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (61), (108) imply:
% 38.97/5.98 | (128) sdtpldt0(xR, all_45_2) = all_55_6
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (50), (112) imply:
% 38.97/5.98 | (129) sdtpldt0(xR, all_45_2) = all_53_6
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (60), (107) imply:
% 38.97/5.98 | (130) $i(all_53_4)
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (49), (110) imply:
% 38.97/5.98 | (131) $i(all_45_0)
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (48), (112) imply:
% 38.97/5.98 | (132) $i(all_45_2)
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (23) with all_55_6, all_57_7, all_45_2, xR,
% 38.97/5.98 | simplifying with (127), (128) gives:
% 38.97/5.98 | (133) all_57_7 = all_55_6
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (23) with all_53_6, all_57_7, all_45_2, xR,
% 38.97/5.98 | simplifying with (127), (129) gives:
% 38.97/5.98 | (134) all_57_7 = all_53_6
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (23) with all_53_2, all_55_2, all_45_1, all_53_4,
% 38.97/5.98 | simplifying with (124), (126) gives:
% 38.97/5.98 | (135) all_55_2 = all_53_2
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (133), (134) imply:
% 38.97/5.98 | (136) all_55_6 = all_53_6
% 38.97/5.98 |
% 38.97/5.98 | SIMP: (136) implies:
% 38.97/5.98 | (137) all_55_6 = all_53_6
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (78), (134) imply:
% 38.97/5.98 | (138) sdtasdt0(all_53_6, all_53_6) = all_57_6
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (67), (137) imply:
% 38.97/5.98 | (139) sdtasdt0(all_53_6, all_53_6) = all_55_5
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (63), (135) imply:
% 38.97/5.98 | (140) sdtpldt0(all_53_2, all_55_0) = all_55_5
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (24) with all_53_5, all_57_6, all_53_6, all_53_6,
% 38.97/5.98 | simplifying with (56), (138) gives:
% 38.97/5.98 | (141) all_57_6 = all_53_5
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (24) with all_55_5, all_57_6, all_53_6, all_53_6,
% 38.97/5.98 | simplifying with (138), (139) gives:
% 38.97/5.98 | (142) all_57_6 = all_55_5
% 38.97/5.98 |
% 38.97/5.98 | COMBINE_EQS: (141), (142) imply:
% 38.97/5.98 | (143) all_55_5 = all_53_5
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (71), (141) imply:
% 38.97/5.98 | (144) ~ (all_57_0 = all_53_5)
% 38.97/5.98 |
% 38.97/5.98 | REDUCE: (140), (143) imply:
% 38.97/5.98 | (145) sdtpldt0(all_53_2, all_55_0) = all_53_5
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (mMulSc) with xR, xR, all_53_4, simplifying with
% 38.97/5.98 | (11), (17), (54) gives:
% 38.97/5.98 | (146) aScalar0(all_53_4)
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (mMulSc) with xS, xS, all_45_0, simplifying with
% 38.97/5.98 | (12), (18), (37) gives:
% 38.97/5.98 | (147) aScalar0(all_45_0)
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (mMNeg) with xS, xR, all_45_2, all_45_1,
% 38.97/5.98 | simplifying with (11), (12), (17), (18), (38), (40) gives:
% 38.97/5.98 | (148) ? [v0: $i] : ? [v1: $i] : (smndt0(v1) = all_45_1 & smndt0(xR) = v0
% 38.97/5.98 | & sdtasdt0(xS, v0) = all_45_1 & sdtasdt0(xS, xR) = v1 & $i(v1) &
% 38.97/5.98 | $i(v0) & $i(all_45_1))
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (mNegSc) with xS, all_45_2, simplifying with (12),
% 38.97/5.98 | (18), (40) gives:
% 38.97/5.98 | (149) aScalar0(all_45_2)
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (mNegSc) with xN, all_45_1, simplifying with (13),
% 38.97/5.98 | (19), (41) gives:
% 38.97/5.98 | (150) aScalar0(all_45_1)
% 38.97/5.98 |
% 38.97/5.98 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (2), (9), (44)
% 38.97/5.98 | gives:
% 38.97/5.99 | (151) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( !
% 38.97/5.99 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2)
% 38.97/5.99 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq)
% 38.97/5.99 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 &
% 38.97/5.99 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~
% 38.97/5.99 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ?
% 38.97/5.99 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4)
% 38.97/5.99 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt,
% 38.97/5.99 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | (
% 38.97/5.99 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & !
% 38.97/5.99 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) |
% 38.97/5.99 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq)
% 38.97/5.99 | = v1) | ~ $i(xq) | aVector0(xq)))))
% 38.97/5.99 |
% 38.97/5.99 | DELTA: instantiating (148) with fresh symbols all_83_0, all_83_1 gives:
% 38.97/5.99 | (152) smndt0(all_83_0) = all_45_1 & smndt0(xR) = all_83_1 & sdtasdt0(xS,
% 38.97/5.99 | all_83_1) = all_45_1 & sdtasdt0(xS, xR) = all_83_0 & $i(all_83_0) &
% 38.97/5.99 | $i(all_83_1) & $i(all_45_1)
% 38.97/5.99 |
% 38.97/5.99 | ALPHA: (152) implies:
% 38.97/5.99 | (153) $i(all_45_1)
% 38.97/5.99 | (154) $i(all_83_1)
% 38.97/5.99 | (155) sdtasdt0(xS, all_83_1) = all_45_1
% 38.97/5.99 | (156) smndt0(xR) = all_83_1
% 38.97/5.99 |
% 38.97/5.99 | DELTA: instantiating (151) with fresh symbol all_90_0 gives:
% 38.97/5.99 | (157) aDimensionOf0(xt) = all_90_0 & $i(all_90_0) & (all_90_0 = sz00 | ( !
% 38.97/5.99 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 38.97/5.99 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) |
% 38.97/5.99 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) &
% 38.97/5.99 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1)
% 38.97/5.99 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 38.97/5.99 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 38.97/5.99 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 &
% 38.97/5.99 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 38.97/5.99 | all_90_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 38.97/5.99 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) |
% 38.97/5.99 | szszuzczcdt0(v0) = all_90_0) & ! [v0: $i] : ( ~
% 38.97/5.99 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq))))
% 38.97/5.99 |
% 38.97/5.99 | ALPHA: (157) implies:
% 38.97/5.99 | (158) aDimensionOf0(xt) = all_90_0
% 38.97/5.99 | (159) all_90_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 38.97/5.99 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(xq) = v0) | ~
% 38.97/5.99 | $i(v1) | ~ $i(xq) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1)
% 38.97/5.99 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~
% 38.97/5.99 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 38.97/5.99 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 38.97/5.99 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) =
% 38.97/5.99 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 38.97/5.99 | all_90_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 38.97/5.99 | $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0)
% 38.97/5.99 | = all_90_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~
% 38.97/5.99 | $i(xq) | aVector0(xq)))
% 38.97/5.99 |
% 38.97/5.99 | GROUND_INST: instantiating (22) with all_33_0, all_90_0, xt, simplifying with
% 38.97/5.99 | (27), (158) gives:
% 38.97/5.99 | (160) all_90_0 = all_33_0
% 38.97/5.99 |
% 38.97/5.99 | BETA: splitting (159) gives:
% 38.97/5.99 |
% 38.97/5.99 | Case 1:
% 38.97/5.99 | |
% 38.97/5.99 | | (161) all_90_0 = sz00
% 38.97/5.99 | |
% 38.97/5.99 | | COMBINE_EQS: (160), (161) imply:
% 38.97/5.99 | | (162) all_33_0 = sz00
% 38.97/5.99 | |
% 38.97/5.99 | | REDUCE: (119), (162) imply:
% 38.97/5.99 | | (163) $false
% 38.97/5.99 | |
% 38.97/5.99 | | CLOSE: (163) is inconsistent.
% 38.97/5.99 | |
% 38.97/5.99 | Case 2:
% 38.97/5.99 | |
% 38.97/5.99 | |
% 38.97/5.99 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_45_2, all_45_1,
% 38.97/5.99 | | all_45_0, all_53_0, simplifying with (11), (17), (38), (39),
% 38.97/5.99 | | (125), (132), (149) gives:
% 38.97/5.99 | | (164) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/5.99 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_45_2, v0) = all_53_0 &
% 38.97/5.99 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_0, v3) = v2 &
% 38.97/5.99 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_45_2) = v0 &
% 38.97/5.99 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_0))
% 38.97/5.99 | |
% 38.97/5.99 | | GROUND_INST: instantiating (mDistr) with all_45_2, all_45_2, xR, all_45_0,
% 38.97/5.99 | | all_45_1, all_55_0, simplifying with (11), (17), (38), (39),
% 38.97/5.99 | | (123), (132), (149) gives:
% 38.97/6.00 | | (165) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.00 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, v0) = all_55_0 &
% 38.97/6.00 | | sdtasdt0(all_45_2, xR) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 38.97/6.00 | | sdtpldt0(all_45_2, all_45_2) = v1 & sdtpldt0(all_45_2, xR) = v0 &
% 38.97/6.00 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_55_0))
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (mDistr) with xR, xR, all_45_2, all_53_4,
% 38.97/6.00 | | all_45_1, all_53_2, simplifying with (11), (17), (36), (54),
% 38.97/6.00 | | (126), (132), (149) gives:
% 38.97/6.00 | | (166) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.00 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(xR, v0) = all_53_2 &
% 38.97/6.00 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 38.97/6.00 | | sdtpldt0(xR, all_45_2) = v0 & sdtpldt0(xR, xR) = v1 & $i(v3) &
% 38.97/6.00 | | $i(v2) & $i(v1) & $i(v0) & $i(all_53_2))
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (mSumSc) with xR, all_45_2, all_53_6, simplifying
% 38.97/6.00 | | with (11), (17), (129), (132), (149) gives:
% 38.97/6.00 | | (167) aScalar0(all_53_6)
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (mSumSc) with all_45_0, all_45_1, all_55_0,
% 38.97/6.00 | | simplifying with (123), (131), (147), (150), (153) gives:
% 38.97/6.00 | | (168) aScalar0(all_55_0)
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (mSumSc) with all_45_1, all_45_0, all_53_0,
% 38.97/6.00 | | simplifying with (125), (131), (147), (150), (153) gives:
% 38.97/6.00 | | (169) aScalar0(all_53_0)
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (mArith) with all_53_4, all_45_0, all_45_1,
% 38.97/6.00 | | all_57_3, all_57_1, simplifying with (121), (122), (130),
% 38.97/6.00 | | (131), (146), (147), (150), (153) gives:
% 38.97/6.00 | | (170) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.00 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_53_4, v3) = v2 &
% 38.97/6.00 | | sdtasdt0(all_53_4, all_45_0) = v1 & sdtasdt0(all_45_0, all_53_4)
% 38.97/6.00 | | = v1 & sdtasdt0(all_45_0, all_45_1) = v3 & sdtpldt0(all_53_4, v0)
% 38.97/6.00 | | = all_57_1 & sdtpldt0(all_45_0, all_53_4) = all_57_3 &
% 38.97/6.00 | | sdtpldt0(all_45_0, all_45_1) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 38.97/6.00 | | $i(v0) & $i(all_57_1) & $i(all_57_3))
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (mNegSc) with xR, all_83_1, simplifying with
% 38.97/6.00 | | (11), (17), (156) gives:
% 38.97/6.00 | | (171) aScalar0(all_83_1)
% 38.97/6.00 | |
% 38.97/6.00 | | DELTA: instantiating (166) with fresh symbols all_127_0, all_127_1,
% 38.97/6.00 | | all_127_2, all_127_3 gives:
% 38.97/6.00 | | (172) sdtasdt0(all_127_2, all_45_2) = all_127_1 & sdtasdt0(xR, all_127_3)
% 38.97/6.00 | | = all_53_2 & sdtasdt0(xR, all_45_2) = all_127_0 &
% 38.97/6.00 | | sdtpldt0(all_45_1, all_127_0) = all_127_1 & sdtpldt0(xR, all_45_2)
% 38.97/6.00 | | = all_127_3 & sdtpldt0(xR, xR) = all_127_2 & $i(all_127_0) &
% 38.97/6.00 | | $i(all_127_1) & $i(all_127_2) & $i(all_127_3) & $i(all_53_2)
% 38.97/6.00 | |
% 38.97/6.00 | | ALPHA: (172) implies:
% 38.97/6.00 | | (173) $i(all_127_0)
% 38.97/6.00 | | (174) sdtpldt0(xR, all_45_2) = all_127_3
% 38.97/6.00 | | (175) sdtpldt0(all_45_1, all_127_0) = all_127_1
% 38.97/6.00 | | (176) sdtasdt0(xR, all_45_2) = all_127_0
% 38.97/6.00 | | (177) sdtasdt0(xR, all_127_3) = all_53_2
% 38.97/6.00 | |
% 38.97/6.00 | | DELTA: instantiating (164) with fresh symbols all_129_0, all_129_1,
% 38.97/6.00 | | all_129_2, all_129_3 gives:
% 38.97/6.00 | | (178) sdtasdt0(all_129_2, all_45_2) = all_129_1 & sdtasdt0(all_45_2,
% 38.97/6.00 | | all_129_3) = all_53_0 & sdtasdt0(xR, all_45_2) = all_129_0 &
% 38.97/6.00 | | sdtpldt0(all_45_0, all_129_0) = all_129_1 & sdtpldt0(all_45_2, xR)
% 38.97/6.00 | | = all_129_2 & sdtpldt0(xR, all_45_2) = all_129_3 & $i(all_129_0) &
% 38.97/6.00 | | $i(all_129_1) & $i(all_129_2) & $i(all_129_3) & $i(all_53_0)
% 38.97/6.00 | |
% 38.97/6.00 | | ALPHA: (178) implies:
% 38.97/6.00 | | (179) $i(all_53_0)
% 38.97/6.00 | | (180) $i(all_129_1)
% 38.97/6.00 | | (181) sdtpldt0(xR, all_45_2) = all_129_3
% 38.97/6.00 | | (182) sdtpldt0(all_45_2, xR) = all_129_2
% 38.97/6.00 | | (183) sdtpldt0(all_45_0, all_129_0) = all_129_1
% 38.97/6.00 | | (184) sdtasdt0(xR, all_45_2) = all_129_0
% 38.97/6.00 | | (185) sdtasdt0(all_45_2, all_129_3) = all_53_0
% 38.97/6.00 | | (186) sdtasdt0(all_129_2, all_45_2) = all_129_1
% 38.97/6.00 | |
% 38.97/6.00 | | DELTA: instantiating (165) with fresh symbols all_131_0, all_131_1,
% 38.97/6.00 | | all_131_2, all_131_3 gives:
% 38.97/6.00 | | (187) sdtasdt0(all_131_2, xR) = all_131_1 & sdtasdt0(all_45_2, all_131_3)
% 38.97/6.00 | | = all_55_0 & sdtasdt0(all_45_2, xR) = all_131_0 &
% 38.97/6.00 | | sdtpldt0(all_45_1, all_131_0) = all_131_1 & sdtpldt0(all_45_2,
% 38.97/6.00 | | all_45_2) = all_131_2 & sdtpldt0(all_45_2, xR) = all_131_3 &
% 38.97/6.00 | | $i(all_131_0) & $i(all_131_1) & $i(all_131_2) & $i(all_131_3) &
% 38.97/6.00 | | $i(all_55_0)
% 38.97/6.00 | |
% 38.97/6.00 | | ALPHA: (187) implies:
% 38.97/6.00 | | (188) sdtpldt0(all_45_2, xR) = all_131_3
% 38.97/6.00 | | (189) sdtpldt0(all_45_1, all_131_0) = all_131_1
% 38.97/6.00 | | (190) sdtasdt0(all_45_2, xR) = all_131_0
% 38.97/6.00 | | (191) sdtasdt0(all_45_2, all_131_3) = all_55_0
% 38.97/6.00 | |
% 38.97/6.00 | | DELTA: instantiating (170) with fresh symbols all_133_0, all_133_1,
% 38.97/6.00 | | all_133_2, all_133_3 gives:
% 38.97/6.00 | | (192) sdtasdt0(all_133_2, all_45_1) = all_133_1 & sdtasdt0(all_53_4,
% 38.97/6.00 | | all_133_0) = all_133_1 & sdtasdt0(all_53_4, all_45_0) = all_133_2
% 38.97/6.00 | | & sdtasdt0(all_45_0, all_53_4) = all_133_2 & sdtasdt0(all_45_0,
% 38.97/6.00 | | all_45_1) = all_133_0 & sdtpldt0(all_53_4, all_133_3) = all_57_1
% 38.97/6.00 | | & sdtpldt0(all_45_0, all_53_4) = all_57_3 & sdtpldt0(all_45_0,
% 38.97/6.00 | | all_45_1) = all_133_3 & $i(all_133_0) & $i(all_133_1) &
% 38.97/6.00 | | $i(all_133_2) & $i(all_133_3) & $i(all_57_1) & $i(all_57_3)
% 38.97/6.00 | |
% 38.97/6.00 | | ALPHA: (192) implies:
% 38.97/6.00 | | (193) sdtpldt0(all_45_0, all_45_1) = all_133_3
% 38.97/6.00 | | (194) sdtpldt0(all_53_4, all_133_3) = all_57_1
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (23) with all_53_6, all_129_3, all_45_2, xR,
% 38.97/6.00 | | simplifying with (129), (181) gives:
% 38.97/6.00 | | (195) all_129_3 = all_53_6
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (23) with all_127_3, all_129_3, all_45_2, xR,
% 38.97/6.00 | | simplifying with (174), (181) gives:
% 38.97/6.00 | | (196) all_129_3 = all_127_3
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (23) with all_129_2, all_131_3, xR, all_45_2,
% 38.97/6.00 | | simplifying with (182), (188) gives:
% 38.97/6.00 | | (197) all_131_3 = all_129_2
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (23) with all_55_0, all_133_3, all_45_1,
% 38.97/6.00 | | all_45_0, simplifying with (123), (193) gives:
% 38.97/6.00 | | (198) all_133_3 = all_55_0
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (24) with all_45_1, all_129_0, all_45_2, xR,
% 38.97/6.00 | | simplifying with (36), (184) gives:
% 38.97/6.00 | | (199) all_129_0 = all_45_1
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (24) with all_127_0, all_129_0, all_45_2, xR,
% 38.97/6.00 | | simplifying with (176), (184) gives:
% 38.97/6.00 | | (200) all_129_0 = all_127_0
% 38.97/6.00 | |
% 38.97/6.00 | | GROUND_INST: instantiating (24) with all_45_1, all_131_0, xR, all_45_2,
% 38.97/6.00 | | simplifying with (38), (190) gives:
% 38.97/6.00 | | (201) all_131_0 = all_45_1
% 38.97/6.00 | |
% 38.97/6.00 | | COMBINE_EQS: (199), (200) imply:
% 38.97/6.00 | | (202) all_127_0 = all_45_1
% 38.97/6.00 | |
% 38.97/6.00 | | COMBINE_EQS: (195), (196) imply:
% 38.97/6.01 | | (203) all_127_3 = all_53_6
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (191), (197) imply:
% 38.97/6.01 | | (204) sdtasdt0(all_45_2, all_129_2) = all_55_0
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (185), (195) imply:
% 38.97/6.01 | | (205) sdtasdt0(all_45_2, all_53_6) = all_53_0
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (177), (203) imply:
% 38.97/6.01 | | (206) sdtasdt0(xR, all_53_6) = all_53_2
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (194), (198) imply:
% 38.97/6.01 | | (207) sdtpldt0(all_53_4, all_55_0) = all_57_1
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (183), (199) imply:
% 38.97/6.01 | | (208) sdtpldt0(all_45_0, all_45_1) = all_129_1
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (189), (201) imply:
% 38.97/6.01 | | (209) sdtpldt0(all_45_1, all_45_1) = all_131_1
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (175), (202) imply:
% 38.97/6.01 | | (210) sdtpldt0(all_45_1, all_45_1) = all_127_1
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (23) with all_127_1, all_131_1, all_45_1,
% 38.97/6.01 | | all_45_1, simplifying with (209), (210) gives:
% 38.97/6.01 | | (211) all_131_1 = all_127_1
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (23) with all_55_0, all_129_1, all_45_1,
% 38.97/6.01 | | all_45_0, simplifying with (123), (208) gives:
% 38.97/6.01 | | (212) all_129_1 = all_55_0
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (186), (212) imply:
% 38.97/6.01 | | (213) sdtasdt0(all_129_2, all_45_2) = all_55_0
% 38.97/6.01 | |
% 38.97/6.01 | | REDUCE: (180), (212) imply:
% 38.97/6.01 | | (214) $i(all_55_0)
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (mArith) with all_53_4, all_45_1, all_53_0,
% 38.97/6.01 | | all_53_2, all_53_5, simplifying with (53), (126), (130), (146),
% 38.97/6.01 | | (150), (153), (169), (179) gives:
% 38.97/6.01 | | (215) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.01 | | (sdtasdt0(v1, all_53_0) = v2 & sdtasdt0(all_53_4, v3) = v2 &
% 38.97/6.01 | | sdtasdt0(all_53_4, all_45_1) = v1 & sdtasdt0(all_45_1, all_53_0)
% 38.97/6.01 | | = v3 & sdtasdt0(all_45_1, all_53_4) = v1 & sdtpldt0(all_53_4, v0)
% 38.97/6.01 | | = all_53_5 & sdtpldt0(all_45_1, all_53_0) = v0 &
% 38.97/6.01 | | sdtpldt0(all_45_1, all_53_4) = all_53_2 & $i(v3) & $i(v2) &
% 38.97/6.01 | | $i(v1) & $i(v0) & $i(all_53_2) & $i(all_53_5))
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (mArith) with all_53_4, all_45_1, all_55_0,
% 38.97/6.01 | | all_53_2, all_53_5, simplifying with (126), (130), (145),
% 38.97/6.01 | | (146), (150), (153), (168), (214) gives:
% 38.97/6.01 | | (216) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.01 | | (sdtasdt0(v1, all_55_0) = v2 & sdtasdt0(all_53_4, v3) = v2 &
% 38.97/6.01 | | sdtasdt0(all_53_4, all_45_1) = v1 & sdtasdt0(all_45_1, all_55_0)
% 38.97/6.01 | | = v3 & sdtasdt0(all_45_1, all_53_4) = v1 & sdtpldt0(all_53_4, v0)
% 38.97/6.01 | | = all_53_5 & sdtpldt0(all_45_1, all_55_0) = v0 &
% 38.97/6.01 | | sdtpldt0(all_45_1, all_53_4) = all_53_2 & $i(v3) & $i(v2) &
% 38.97/6.01 | | $i(v1) & $i(v0) & $i(all_53_2) & $i(all_53_5))
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (mDistr) with xS, xS, all_83_1, all_45_0,
% 38.97/6.01 | | all_45_1, all_55_0, simplifying with (12), (18), (37), (123),
% 38.97/6.01 | | (154), (155), (171) gives:
% 38.97/6.01 | | (217) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.01 | | (sdtasdt0(v1, all_83_1) = v2 & sdtasdt0(xS, v0) = all_55_0 &
% 38.97/6.01 | | sdtasdt0(xS, all_83_1) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 38.97/6.01 | | sdtpldt0(xS, all_83_1) = v0 & sdtpldt0(xS, xS) = v1 & $i(v3) &
% 38.97/6.01 | | $i(v2) & $i(v1) & $i(v0) & $i(all_55_0))
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (mSumSc) with all_45_2, xR, all_129_2,
% 38.97/6.01 | | simplifying with (11), (17), (132), (149), (182) gives:
% 38.97/6.01 | | (218) aScalar0(all_129_2)
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, xR, all_45_1,
% 38.97/6.01 | | all_45_1, all_127_1, simplifying with (11), (17), (38), (132),
% 38.97/6.01 | | (149), (210) gives:
% 38.97/6.01 | | (219) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.01 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, v0) = all_127_1 &
% 38.97/6.01 | | sdtasdt0(xR, xR) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 38.97/6.01 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, xR) = v0 & $i(v3) &
% 38.97/6.01 | | $i(v2) & $i(v1) & $i(v0) & $i(all_127_1))
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (mDistr) with xR, all_45_2, all_45_2, all_45_1,
% 38.97/6.01 | | all_45_1, all_127_1, simplifying with (11), (17), (36), (132),
% 38.97/6.01 | | (149), (210) gives:
% 38.97/6.01 | | (220) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.01 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_45_2, all_45_2) = v3 &
% 38.97/6.01 | | sdtasdt0(xR, v0) = all_127_1 & sdtpldt0(all_45_1, v3) = v2 &
% 38.97/6.01 | | sdtpldt0(all_45_2, all_45_2) = v0 & sdtpldt0(xR, all_45_2) = v1 &
% 38.97/6.01 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_127_1))
% 38.97/6.01 | |
% 38.97/6.01 | | GROUND_INST: instantiating (mArith) with all_53_4, all_55_0, all_45_1,
% 38.97/6.01 | | all_57_1, all_57_0, simplifying with (120), (130), (146),
% 38.97/6.01 | | (150), (153), (168), (207), (214) gives:
% 38.97/6.01 | | (221) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.01 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_55_0, all_53_4) = v1 &
% 38.97/6.01 | | sdtasdt0(all_55_0, all_45_1) = v3 & sdtasdt0(all_53_4, v3) = v2 &
% 38.97/6.01 | | sdtasdt0(all_53_4, all_55_0) = v1 & sdtpldt0(all_55_0, all_53_4)
% 38.97/6.01 | | = all_57_1 & sdtpldt0(all_55_0, all_45_1) = v0 &
% 38.97/6.01 | | sdtpldt0(all_53_4, v0) = all_57_0 & $i(v3) & $i(v2) & $i(v1) &
% 38.97/6.01 | | $i(v0) & $i(all_57_0) & $i(all_57_1))
% 38.97/6.01 | |
% 38.97/6.01 | | DELTA: instantiating (217) with fresh symbols all_162_0, all_162_1,
% 38.97/6.01 | | all_162_2, all_162_3 gives:
% 38.97/6.01 | | (222) sdtasdt0(all_162_2, all_83_1) = all_162_1 & sdtasdt0(xS, all_162_3)
% 38.97/6.01 | | = all_55_0 & sdtasdt0(xS, all_83_1) = all_162_0 &
% 38.97/6.01 | | sdtpldt0(all_45_1, all_162_0) = all_162_1 & sdtpldt0(xS, all_83_1)
% 38.97/6.01 | | = all_162_3 & sdtpldt0(xS, xS) = all_162_2 & $i(all_162_0) &
% 38.97/6.01 | | $i(all_162_1) & $i(all_162_2) & $i(all_162_3) & $i(all_55_0)
% 38.97/6.01 | |
% 38.97/6.01 | | ALPHA: (222) implies:
% 38.97/6.01 | | (223) $i(all_162_0)
% 38.97/6.01 | | (224) sdtasdt0(xS, all_83_1) = all_162_0
% 38.97/6.01 | |
% 38.97/6.01 | | DELTA: instantiating (220) with fresh symbols all_164_0, all_164_1,
% 38.97/6.01 | | all_164_2, all_164_3 gives:
% 38.97/6.01 | | (225) sdtasdt0(all_164_2, all_45_2) = all_164_1 & sdtasdt0(all_45_2,
% 38.97/6.01 | | all_45_2) = all_164_0 & sdtasdt0(xR, all_164_3) = all_127_1 &
% 38.97/6.01 | | sdtpldt0(all_45_1, all_164_0) = all_164_1 & sdtpldt0(all_45_2,
% 38.97/6.01 | | all_45_2) = all_164_3 & sdtpldt0(xR, all_45_2) = all_164_2 &
% 38.97/6.01 | | $i(all_164_0) & $i(all_164_1) & $i(all_164_2) & $i(all_164_3) &
% 38.97/6.01 | | $i(all_127_1)
% 38.97/6.01 | |
% 38.97/6.01 | | ALPHA: (225) implies:
% 38.97/6.01 | | (226) $i(all_164_2)
% 38.97/6.01 | | (227) $i(all_164_0)
% 38.97/6.01 | | (228) sdtpldt0(xR, all_45_2) = all_164_2
% 38.97/6.01 | | (229) sdtpldt0(all_45_1, all_164_0) = all_164_1
% 38.97/6.01 | | (230) sdtasdt0(all_45_2, all_45_2) = all_164_0
% 38.97/6.01 | |
% 38.97/6.01 | | DELTA: instantiating (219) with fresh symbols all_168_0, all_168_1,
% 38.97/6.01 | | all_168_2, all_168_3 gives:
% 38.97/6.01 | | (231) sdtasdt0(all_168_2, xR) = all_168_1 & sdtasdt0(all_45_2, all_168_3)
% 38.97/6.01 | | = all_127_1 & sdtasdt0(xR, xR) = all_168_0 & sdtpldt0(all_45_1,
% 38.97/6.01 | | all_168_0) = all_168_1 & sdtpldt0(all_45_2, xR) = all_168_2 &
% 38.97/6.01 | | sdtpldt0(xR, xR) = all_168_3 & $i(all_168_0) & $i(all_168_1) &
% 38.97/6.01 | | $i(all_168_2) & $i(all_168_3) & $i(all_127_1)
% 38.97/6.01 | |
% 38.97/6.01 | | ALPHA: (231) implies:
% 38.97/6.01 | | (232) $i(all_168_2)
% 38.97/6.02 | | (233) $i(all_168_0)
% 38.97/6.02 | | (234) sdtpldt0(all_45_2, xR) = all_168_2
% 38.97/6.02 | | (235) sdtpldt0(all_45_1, all_168_0) = all_168_1
% 38.97/6.02 | | (236) sdtasdt0(xR, xR) = all_168_0
% 38.97/6.02 | | (237) sdtasdt0(all_168_2, xR) = all_168_1
% 38.97/6.02 | |
% 38.97/6.02 | | DELTA: instantiating (215) with fresh symbols all_172_0, all_172_1,
% 38.97/6.02 | | all_172_2, all_172_3 gives:
% 38.97/6.02 | | (238) sdtasdt0(all_172_2, all_53_0) = all_172_1 & sdtasdt0(all_53_4,
% 38.97/6.02 | | all_172_0) = all_172_1 & sdtasdt0(all_53_4, all_45_1) = all_172_2
% 38.97/6.02 | | & sdtasdt0(all_45_1, all_53_0) = all_172_0 & sdtasdt0(all_45_1,
% 38.97/6.02 | | all_53_4) = all_172_2 & sdtpldt0(all_53_4, all_172_3) = all_53_5
% 38.97/6.02 | | & sdtpldt0(all_45_1, all_53_0) = all_172_3 & sdtpldt0(all_45_1,
% 38.97/6.02 | | all_53_4) = all_53_2 & $i(all_172_0) & $i(all_172_1) &
% 38.97/6.02 | | $i(all_172_2) & $i(all_172_3) & $i(all_53_2) & $i(all_53_5)
% 38.97/6.02 | |
% 38.97/6.02 | | ALPHA: (238) implies:
% 38.97/6.02 | | (239) sdtpldt0(all_45_1, all_53_0) = all_172_3
% 38.97/6.02 | |
% 38.97/6.02 | | DELTA: instantiating (221) with fresh symbols all_174_0, all_174_1,
% 38.97/6.02 | | all_174_2, all_174_3 gives:
% 38.97/6.02 | | (240) sdtasdt0(all_174_2, all_45_1) = all_174_1 & sdtasdt0(all_55_0,
% 38.97/6.02 | | all_53_4) = all_174_2 & sdtasdt0(all_55_0, all_45_1) = all_174_0
% 38.97/6.02 | | & sdtasdt0(all_53_4, all_174_0) = all_174_1 & sdtasdt0(all_53_4,
% 38.97/6.02 | | all_55_0) = all_174_2 & sdtpldt0(all_55_0, all_53_4) = all_57_1 &
% 38.97/6.02 | | sdtpldt0(all_55_0, all_45_1) = all_174_3 & sdtpldt0(all_53_4,
% 38.97/6.02 | | all_174_3) = all_57_0 & $i(all_174_0) & $i(all_174_1) &
% 38.97/6.02 | | $i(all_174_2) & $i(all_174_3) & $i(all_57_0) & $i(all_57_1)
% 38.97/6.02 | |
% 38.97/6.02 | | ALPHA: (240) implies:
% 38.97/6.02 | | (241) sdtpldt0(all_55_0, all_53_4) = all_57_1
% 38.97/6.02 | |
% 38.97/6.02 | | DELTA: instantiating (216) with fresh symbols all_178_0, all_178_1,
% 38.97/6.02 | | all_178_2, all_178_3 gives:
% 38.97/6.02 | | (242) sdtasdt0(all_178_2, all_55_0) = all_178_1 & sdtasdt0(all_53_4,
% 38.97/6.02 | | all_178_0) = all_178_1 & sdtasdt0(all_53_4, all_45_1) = all_178_2
% 38.97/6.02 | | & sdtasdt0(all_45_1, all_55_0) = all_178_0 & sdtasdt0(all_45_1,
% 38.97/6.02 | | all_53_4) = all_178_2 & sdtpldt0(all_53_4, all_178_3) = all_53_5
% 38.97/6.02 | | & sdtpldt0(all_45_1, all_55_0) = all_178_3 & sdtpldt0(all_45_1,
% 38.97/6.02 | | all_53_4) = all_53_2 & $i(all_178_0) & $i(all_178_1) &
% 38.97/6.02 | | $i(all_178_2) & $i(all_178_3) & $i(all_53_2) & $i(all_53_5)
% 38.97/6.02 | |
% 38.97/6.02 | | ALPHA: (242) implies:
% 38.97/6.02 | | (243) sdtpldt0(all_45_1, all_53_4) = all_53_2
% 38.97/6.02 | | (244) sdtpldt0(all_45_1, all_55_0) = all_178_3
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (23) with all_53_6, all_164_2, all_45_2, xR,
% 38.97/6.02 | | simplifying with (129), (228) gives:
% 38.97/6.02 | | (245) all_164_2 = all_53_6
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (23) with all_129_2, all_168_2, xR, all_45_2,
% 38.97/6.02 | | simplifying with (182), (234) gives:
% 38.97/6.02 | | (246) all_168_2 = all_129_2
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (24) with all_53_4, all_168_0, xR, xR,
% 38.97/6.02 | | simplifying with (54), (236) gives:
% 38.97/6.02 | | (247) all_168_0 = all_53_4
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (24) with all_45_1, all_162_0, all_83_1, xS,
% 38.97/6.02 | | simplifying with (155), (224) gives:
% 38.97/6.02 | | (248) all_162_0 = all_45_1
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (24) with all_45_0, all_164_0, all_45_2,
% 38.97/6.02 | | all_45_2, simplifying with (39), (230) gives:
% 38.97/6.02 | | (249) all_164_0 = all_45_0
% 38.97/6.02 | |
% 38.97/6.02 | | REDUCE: (237), (246) imply:
% 38.97/6.02 | | (250) sdtasdt0(all_129_2, xR) = all_168_1
% 38.97/6.02 | |
% 38.97/6.02 | | REDUCE: (235), (247) imply:
% 38.97/6.02 | | (251) sdtpldt0(all_45_1, all_53_4) = all_168_1
% 38.97/6.02 | |
% 38.97/6.02 | | REDUCE: (229), (249) imply:
% 38.97/6.02 | | (252) sdtpldt0(all_45_1, all_45_0) = all_164_1
% 38.97/6.02 | |
% 38.97/6.02 | | REDUCE: (232), (246) imply:
% 38.97/6.02 | | (253) $i(all_129_2)
% 38.97/6.02 | |
% 38.97/6.02 | | REDUCE: (226), (245) imply:
% 38.97/6.02 | | (254) $i(all_53_6)
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (23) with all_53_0, all_164_1, all_45_0,
% 38.97/6.02 | | all_45_1, simplifying with (125), (252) gives:
% 38.97/6.02 | | (255) all_164_1 = all_53_0
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (23) with all_53_2, all_168_1, all_53_4,
% 38.97/6.02 | | all_45_1, simplifying with (243), (251) gives:
% 38.97/6.02 | | (256) all_168_1 = all_53_2
% 38.97/6.02 | |
% 38.97/6.02 | | REDUCE: (250), (256) imply:
% 38.97/6.02 | | (257) sdtasdt0(all_129_2, xR) = all_53_2
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (mDistr2) with xR, all_45_2, all_45_2, xR,
% 38.97/6.02 | | all_45_1, all_53_4, all_53_2, all_45_0, all_45_1, all_55_0,
% 38.97/6.02 | | all_53_5, simplifying with (11), (17), (36), (38), (39), (54),
% 38.97/6.02 | | (123), (132), (145), (149), (243) gives:
% 38.97/6.02 | | (258) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_53_5 &
% 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_45_2) = v0 &
% 38.97/6.02 | | $i(v1) & $i(v0) & $i(all_53_5))
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (mDistr) with xR, all_45_2, xR, all_45_1,
% 38.97/6.02 | | all_53_4, all_53_2, simplifying with (11), (17), (36), (54),
% 38.97/6.02 | | (132), (149), (243) gives:
% 38.97/6.02 | | (259) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.02 | | (sdtasdt0(v1, xR) = v2 & sdtasdt0(all_45_2, xR) = v3 & sdtasdt0(xR,
% 38.97/6.02 | | v0) = all_53_2 & sdtpldt0(all_53_4, v3) = v2 &
% 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v0 & sdtpldt0(xR, all_45_2) = v1 &
% 38.97/6.02 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_2))
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (mArith) with all_45_1, all_53_4, all_55_0,
% 38.97/6.02 | | all_53_2, all_53_5, simplifying with (130), (145), (146),
% 38.97/6.02 | | (150), (153), (168), (214), (243) gives:
% 38.97/6.02 | | (260) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.02 | | (sdtasdt0(v1, all_55_0) = v2 & sdtasdt0(all_53_4, all_55_0) = v3 &
% 38.97/6.02 | | sdtasdt0(all_53_4, all_45_1) = v1 & sdtasdt0(all_45_1, v3) = v2 &
% 38.97/6.02 | | sdtasdt0(all_45_1, all_53_4) = v1 & sdtpldt0(all_53_4, all_55_0)
% 38.97/6.02 | | = v0 & sdtpldt0(all_53_4, all_45_1) = all_53_2 &
% 38.97/6.02 | | sdtpldt0(all_45_1, v0) = all_53_5 & $i(v3) & $i(v2) & $i(v1) &
% 38.97/6.02 | | $i(v0) & $i(all_53_2) & $i(all_53_5))
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_53_6, all_45_1,
% 38.97/6.02 | | all_53_0, all_172_3, simplifying with (11), (17), (38), (132),
% 38.97/6.02 | | (149), (167), (205), (239), (254) gives:
% 38.97/6.02 | | (261) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.02 | | (sdtasdt0(v1, all_53_6) = v2 & sdtasdt0(all_45_2, v0) = all_172_3 &
% 38.97/6.02 | | sdtasdt0(xR, all_53_6) = v3 & sdtpldt0(all_53_0, v3) = v2 &
% 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_53_6) = v0 &
% 38.97/6.02 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_172_3))
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_129_2, all_45_1,
% 38.97/6.02 | | all_55_0, all_178_3, simplifying with (11), (17), (38), (132),
% 38.97/6.02 | | (149), (204), (218), (244), (253) gives:
% 38.97/6.02 | | (262) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.02 | | (sdtasdt0(v1, all_129_2) = v2 & sdtasdt0(all_45_2, v0) = all_178_3
% 38.97/6.02 | | & sdtasdt0(xR, all_129_2) = v3 & sdtpldt0(all_55_0, v3) = v2 &
% 38.97/6.02 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_129_2) = v0 &
% 38.97/6.02 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_178_3))
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (mArith) with all_55_0, all_53_4, all_45_1,
% 38.97/6.02 | | all_57_1, all_57_0, simplifying with (120), (130), (146),
% 38.97/6.02 | | (150), (153), (168), (214), (241) gives:
% 38.97/6.02 | | (263) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.02 | | (sdtasdt0(v1, all_45_1) = v2 & sdtasdt0(all_55_0, v3) = v2 &
% 38.97/6.02 | | sdtasdt0(all_55_0, all_53_4) = v1 & sdtasdt0(all_53_4, all_55_0)
% 38.97/6.02 | | = v1 & sdtasdt0(all_53_4, all_45_1) = v3 & sdtpldt0(all_55_0, v0)
% 38.97/6.02 | | = all_57_0 & sdtpldt0(all_53_4, all_55_0) = all_57_1 &
% 38.97/6.02 | | sdtpldt0(all_53_4, all_45_1) = v0 & $i(v3) & $i(v2) & $i(v1) &
% 38.97/6.02 | | $i(v0) & $i(all_57_0) & $i(all_57_1))
% 38.97/6.02 | |
% 38.97/6.02 | | GROUND_INST: instantiating (mArith) with all_45_0, all_45_1, all_53_4,
% 38.97/6.02 | | all_55_0, all_57_1, simplifying with (123), (130), (131),
% 38.97/6.02 | | (146), (147), (150), (153), (241) gives:
% 38.97/6.03 | | (264) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.03 | | (sdtasdt0(v1, all_53_4) = v2 & sdtasdt0(all_45_0, v3) = v2 &
% 38.97/6.03 | | sdtasdt0(all_45_0, all_45_1) = v1 & sdtasdt0(all_45_1, all_53_4)
% 38.97/6.03 | | = v3 & sdtasdt0(all_45_1, all_45_0) = v1 & sdtpldt0(all_45_0, v0)
% 38.97/6.03 | | = all_57_1 & sdtpldt0(all_45_1, all_53_4) = v0 &
% 38.97/6.03 | | sdtpldt0(all_45_1, all_45_0) = all_55_0 & $i(v3) & $i(v2) &
% 38.97/6.03 | | $i(v1) & $i(v0) & $i(all_57_1) & $i(all_55_0))
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (mDistr) with all_129_2, xR, all_45_2, all_53_2,
% 38.97/6.03 | | all_55_0, all_53_5, simplifying with (11), (17), (132), (145),
% 38.97/6.03 | | (149), (213), (218), (253), (257) gives:
% 38.97/6.03 | | (265) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 38.97/6.03 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_129_2, v0) = all_53_5 &
% 38.97/6.03 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_129_2, xR) = v1 &
% 38.97/6.03 | | sdtpldt0(all_55_0, v3) = v2 & sdtpldt0(xR, all_45_2) = v0 &
% 38.97/6.03 | | $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_53_5))
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (258) with fresh symbols all_200_0, all_200_1 gives:
% 38.97/6.03 | | (266) sdtasdt0(all_200_1, all_200_0) = all_53_5 & sdtpldt0(all_45_2, xR)
% 38.97/6.03 | | = all_200_0 & sdtpldt0(xR, all_45_2) = all_200_1 & $i(all_200_0) &
% 38.97/6.03 | | $i(all_200_1) & $i(all_53_5)
% 38.97/6.03 | |
% 38.97/6.03 | | ALPHA: (266) implies:
% 38.97/6.03 | | (267) sdtpldt0(all_45_2, xR) = all_200_0
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (265) with fresh symbols all_236_0, all_236_1,
% 38.97/6.03 | | all_236_2, all_236_3 gives:
% 38.97/6.03 | | (268) sdtasdt0(all_236_2, all_45_2) = all_236_1 & sdtasdt0(all_129_2,
% 38.97/6.03 | | all_236_3) = all_53_5 & sdtasdt0(xR, all_45_2) = all_236_0 &
% 38.97/6.03 | | sdtpldt0(all_129_2, xR) = all_236_2 & sdtpldt0(all_55_0, all_236_0)
% 38.97/6.03 | | = all_236_1 & sdtpldt0(xR, all_45_2) = all_236_3 & $i(all_236_0) &
% 38.97/6.03 | | $i(all_236_1) & $i(all_236_2) & $i(all_236_3) & $i(all_53_5)
% 38.97/6.03 | |
% 38.97/6.03 | | ALPHA: (268) implies:
% 38.97/6.03 | | (269) sdtpldt0(xR, all_45_2) = all_236_3
% 38.97/6.03 | | (270) sdtasdt0(all_129_2, all_236_3) = all_53_5
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (262) with fresh symbols all_238_0, all_238_1,
% 38.97/6.03 | | all_238_2, all_238_3 gives:
% 38.97/6.03 | | (271) sdtasdt0(all_238_2, all_129_2) = all_238_1 & sdtasdt0(all_45_2,
% 38.97/6.03 | | all_238_3) = all_178_3 & sdtasdt0(xR, all_129_2) = all_238_0 &
% 38.97/6.03 | | sdtpldt0(all_55_0, all_238_0) = all_238_1 & sdtpldt0(all_45_2, xR)
% 38.97/6.03 | | = all_238_2 & sdtpldt0(xR, all_129_2) = all_238_3 & $i(all_238_0) &
% 38.97/6.03 | | $i(all_238_1) & $i(all_238_2) & $i(all_238_3) & $i(all_178_3)
% 38.97/6.03 | |
% 38.97/6.03 | | ALPHA: (271) implies:
% 38.97/6.03 | | (272) sdtpldt0(all_45_2, xR) = all_238_2
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (261) with fresh symbols all_246_0, all_246_1,
% 38.97/6.03 | | all_246_2, all_246_3 gives:
% 38.97/6.03 | | (273) sdtasdt0(all_246_2, all_53_6) = all_246_1 & sdtasdt0(all_45_2,
% 38.97/6.03 | | all_246_3) = all_172_3 & sdtasdt0(xR, all_53_6) = all_246_0 &
% 38.97/6.03 | | sdtpldt0(all_53_0, all_246_0) = all_246_1 & sdtpldt0(all_45_2, xR)
% 38.97/6.03 | | = all_246_2 & sdtpldt0(xR, all_53_6) = all_246_3 & $i(all_246_0) &
% 38.97/6.03 | | $i(all_246_1) & $i(all_246_2) & $i(all_246_3) & $i(all_172_3)
% 38.97/6.03 | |
% 38.97/6.03 | | ALPHA: (273) implies:
% 38.97/6.03 | | (274) sdtpldt0(all_45_2, xR) = all_246_2
% 38.97/6.03 | | (275) sdtpldt0(all_53_0, all_246_0) = all_246_1
% 38.97/6.03 | | (276) sdtasdt0(xR, all_53_6) = all_246_0
% 38.97/6.03 | | (277) sdtasdt0(all_246_2, all_53_6) = all_246_1
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (259) with fresh symbols all_250_0, all_250_1,
% 38.97/6.03 | | all_250_2, all_250_3 gives:
% 38.97/6.03 | | (278) sdtasdt0(all_250_2, xR) = all_250_1 & sdtasdt0(all_45_2, xR) =
% 38.97/6.03 | | all_250_0 & sdtasdt0(xR, all_250_3) = all_53_2 & sdtpldt0(all_53_4,
% 38.97/6.03 | | all_250_0) = all_250_1 & sdtpldt0(all_45_2, xR) = all_250_3 &
% 38.97/6.03 | | sdtpldt0(xR, all_45_2) = all_250_2 & $i(all_250_0) & $i(all_250_1)
% 38.97/6.03 | | & $i(all_250_2) & $i(all_250_3) & $i(all_53_2)
% 38.97/6.03 | |
% 38.97/6.03 | | ALPHA: (278) implies:
% 38.97/6.03 | | (279) sdtpldt0(xR, all_45_2) = all_250_2
% 38.97/6.03 | | (280) sdtpldt0(all_45_2, xR) = all_250_3
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (264) with fresh symbols all_260_0, all_260_1,
% 38.97/6.03 | | all_260_2, all_260_3 gives:
% 38.97/6.03 | | (281) sdtasdt0(all_260_2, all_53_4) = all_260_1 & sdtasdt0(all_45_0,
% 38.97/6.03 | | all_260_0) = all_260_1 & sdtasdt0(all_45_0, all_45_1) = all_260_2
% 38.97/6.03 | | & sdtasdt0(all_45_1, all_53_4) = all_260_0 & sdtasdt0(all_45_1,
% 38.97/6.03 | | all_45_0) = all_260_2 & sdtpldt0(all_45_0, all_260_3) = all_57_1
% 38.97/6.03 | | & sdtpldt0(all_45_1, all_53_4) = all_260_3 & sdtpldt0(all_45_1,
% 38.97/6.03 | | all_45_0) = all_55_0 & $i(all_260_0) & $i(all_260_1) &
% 38.97/6.03 | | $i(all_260_2) & $i(all_260_3) & $i(all_57_1) & $i(all_55_0)
% 38.97/6.03 | |
% 38.97/6.03 | | ALPHA: (281) implies:
% 38.97/6.03 | | (282) sdtpldt0(all_45_1, all_45_0) = all_55_0
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (260) with fresh symbols all_264_0, all_264_1,
% 38.97/6.03 | | all_264_2, all_264_3 gives:
% 38.97/6.03 | | (283) sdtasdt0(all_264_2, all_55_0) = all_264_1 & sdtasdt0(all_53_4,
% 38.97/6.03 | | all_55_0) = all_264_0 & sdtasdt0(all_53_4, all_45_1) = all_264_2
% 38.97/6.03 | | & sdtasdt0(all_45_1, all_264_0) = all_264_1 & sdtasdt0(all_45_1,
% 38.97/6.03 | | all_53_4) = all_264_2 & sdtpldt0(all_53_4, all_55_0) = all_264_3
% 38.97/6.03 | | & sdtpldt0(all_53_4, all_45_1) = all_53_2 & sdtpldt0(all_45_1,
% 38.97/6.03 | | all_264_3) = all_53_5 & $i(all_264_0) & $i(all_264_1) &
% 38.97/6.03 | | $i(all_264_2) & $i(all_264_3) & $i(all_53_2) & $i(all_53_5)
% 38.97/6.03 | |
% 38.97/6.03 | | DELTA: instantiating (263) with fresh symbols all_266_0, all_266_1,
% 38.97/6.03 | | all_266_2, all_266_3 gives:
% 38.97/6.03 | | (284) sdtasdt0(all_266_2, all_45_1) = all_266_1 & sdtasdt0(all_55_0,
% 38.97/6.03 | | all_266_0) = all_266_1 & sdtasdt0(all_55_0, all_53_4) = all_266_2
% 38.97/6.03 | | & sdtasdt0(all_53_4, all_55_0) = all_266_2 & sdtasdt0(all_53_4,
% 38.97/6.03 | | all_45_1) = all_266_0 & sdtpldt0(all_55_0, all_266_3) = all_57_0
% 38.97/6.03 | | & sdtpldt0(all_53_4, all_55_0) = all_57_1 & sdtpldt0(all_53_4,
% 38.97/6.03 | | all_45_1) = all_266_3 & $i(all_266_0) & $i(all_266_1) &
% 38.97/6.03 | | $i(all_266_2) & $i(all_266_3) & $i(all_57_0) & $i(all_57_1)
% 38.97/6.03 | |
% 38.97/6.03 | | ALPHA: (284) implies:
% 38.97/6.03 | | (285) sdtpldt0(all_53_4, all_45_1) = all_266_3
% 38.97/6.03 | | (286) sdtpldt0(all_55_0, all_266_3) = all_57_0
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_53_6, all_250_2, all_45_2, xR,
% 38.97/6.03 | | simplifying with (129), (279) gives:
% 38.97/6.03 | | (287) all_250_2 = all_53_6
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_236_3, all_250_2, all_45_2, xR,
% 38.97/6.03 | | simplifying with (269), (279) gives:
% 38.97/6.03 | | (288) all_250_2 = all_236_3
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_129_2, all_246_2, xR, all_45_2,
% 38.97/6.03 | | simplifying with (182), (274) gives:
% 38.97/6.03 | | (289) all_246_2 = all_129_2
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_200_0, all_246_2, xR, all_45_2,
% 38.97/6.03 | | simplifying with (267), (274) gives:
% 38.97/6.03 | | (290) all_246_2 = all_200_0
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_246_2, all_250_3, xR, all_45_2,
% 38.97/6.03 | | simplifying with (274), (280) gives:
% 38.97/6.03 | | (291) all_250_3 = all_246_2
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_238_2, all_250_3, xR, all_45_2,
% 38.97/6.03 | | simplifying with (272), (280) gives:
% 38.97/6.03 | | (292) all_250_3 = all_238_2
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_53_0, all_55_0, all_45_0, all_45_1,
% 38.97/6.03 | | simplifying with (125), (282) gives:
% 38.97/6.03 | | (293) all_55_0 = all_53_0
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_53_2, all_266_3, all_45_1,
% 38.97/6.03 | | all_53_4, simplifying with (126), (285) gives:
% 38.97/6.03 | | (294) all_266_3 = all_53_2
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (24) with all_53_2, all_246_0, all_53_6, xR,
% 38.97/6.03 | | simplifying with (206), (276) gives:
% 38.97/6.03 | | (295) all_246_0 = all_53_2
% 38.97/6.03 | |
% 38.97/6.03 | | COMBINE_EQS: (287), (288) imply:
% 38.97/6.03 | | (296) all_236_3 = all_53_6
% 38.97/6.03 | |
% 38.97/6.03 | | COMBINE_EQS: (291), (292) imply:
% 38.97/6.03 | | (297) all_246_2 = all_238_2
% 38.97/6.03 | |
% 38.97/6.03 | | SIMP: (297) implies:
% 38.97/6.03 | | (298) all_246_2 = all_238_2
% 38.97/6.03 | |
% 38.97/6.03 | | COMBINE_EQS: (290), (298) imply:
% 38.97/6.03 | | (299) all_238_2 = all_200_0
% 38.97/6.03 | |
% 38.97/6.03 | | COMBINE_EQS: (289), (298) imply:
% 38.97/6.03 | | (300) all_238_2 = all_129_2
% 38.97/6.03 | |
% 38.97/6.03 | | COMBINE_EQS: (299), (300) imply:
% 38.97/6.03 | | (301) all_200_0 = all_129_2
% 38.97/6.03 | |
% 38.97/6.03 | | REDUCE: (277), (289) imply:
% 38.97/6.03 | | (302) sdtasdt0(all_129_2, all_53_6) = all_246_1
% 38.97/6.03 | |
% 38.97/6.03 | | REDUCE: (270), (296) imply:
% 38.97/6.03 | | (303) sdtasdt0(all_129_2, all_53_6) = all_53_5
% 38.97/6.03 | |
% 38.97/6.03 | | REDUCE: (286), (293), (294) imply:
% 38.97/6.03 | | (304) sdtpldt0(all_53_0, all_53_2) = all_57_0
% 38.97/6.03 | |
% 38.97/6.03 | | REDUCE: (275), (295) imply:
% 38.97/6.03 | | (305) sdtpldt0(all_53_0, all_53_2) = all_246_1
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (23) with all_57_0, all_246_1, all_53_2,
% 38.97/6.03 | | all_53_0, simplifying with (304), (305) gives:
% 38.97/6.03 | | (306) all_246_1 = all_57_0
% 38.97/6.03 | |
% 38.97/6.03 | | GROUND_INST: instantiating (24) with all_53_5, all_246_1, all_53_6,
% 38.97/6.03 | | all_129_2, simplifying with (302), (303) gives:
% 38.97/6.03 | | (307) all_246_1 = all_53_5
% 38.97/6.03 | |
% 38.97/6.03 | | COMBINE_EQS: (306), (307) imply:
% 38.97/6.03 | | (308) all_57_0 = all_53_5
% 38.97/6.03 | |
% 38.97/6.04 | | REDUCE: (144), (308) imply:
% 38.97/6.04 | | (309) $false
% 38.97/6.04 | |
% 38.97/6.04 | | CLOSE: (309) is inconsistent.
% 38.97/6.04 | |
% 38.97/6.04 | End of split
% 38.97/6.04 |
% 38.97/6.04 End of proof
% 38.97/6.04 % SZS output end Proof for theBenchmark
% 38.97/6.04
% 38.97/6.04 5432ms
%------------------------------------------------------------------------------