TSTP Solution File: RNG057+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG057+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 : n012.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 13:57:35 EDT 2023
% Result : Theorem 16.51s 2.97s
% Output : Proof 26.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG057+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 01:50:40 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 ________ _____
% 0.19/0.57 ___ __ \_________(_)________________________________
% 0.19/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.78/1.23 Prover 4: Preprocessing ...
% 3.78/1.23 Prover 1: Preprocessing ...
% 3.78/1.27 Prover 2: Preprocessing ...
% 3.78/1.27 Prover 3: Preprocessing ...
% 3.78/1.27 Prover 0: Preprocessing ...
% 3.78/1.27 Prover 5: Preprocessing ...
% 3.78/1.27 Prover 6: Preprocessing ...
% 9.31/2.08 Prover 3: Constructing countermodel ...
% 9.31/2.09 Prover 1: Constructing countermodel ...
% 9.52/2.09 Prover 6: Proving ...
% 11.41/2.28 Prover 5: Constructing countermodel ...
% 12.53/2.43 Prover 4: Constructing countermodel ...
% 12.74/2.47 Prover 2: Proving ...
% 13.31/2.56 Prover 0: Proving ...
% 16.51/2.97 Prover 3: proved (2370ms)
% 16.51/2.97
% 16.51/2.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.51/2.97
% 16.51/2.97 Prover 5: stopped
% 16.51/2.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.51/2.98 Prover 2: stopped
% 16.51/2.99 Prover 0: stopped
% 16.51/3.00 Prover 6: stopped
% 16.51/3.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.51/3.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.51/3.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.51/3.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.18/3.07 Prover 8: Preprocessing ...
% 17.18/3.07 Prover 7: Preprocessing ...
% 17.45/3.14 Prover 11: Preprocessing ...
% 17.88/3.15 Prover 13: Preprocessing ...
% 17.98/3.16 Prover 10: Preprocessing ...
% 18.46/3.33 Prover 8: Warning: ignoring some quantifiers
% 18.46/3.34 Prover 10: Constructing countermodel ...
% 18.46/3.34 Prover 8: Constructing countermodel ...
% 19.04/3.48 Prover 7: Constructing countermodel ...
% 20.35/3.50 Prover 13: Constructing countermodel ...
% 21.37/3.65 Prover 11: Constructing countermodel ...
% 25.93/4.23 Prover 10: Found proof (size 161)
% 25.93/4.23 Prover 10: proved (1217ms)
% 25.93/4.23 Prover 13: stopped
% 25.93/4.23 Prover 7: stopped
% 25.93/4.23 Prover 11: stopped
% 25.93/4.23 Prover 8: stopped
% 25.93/4.23 Prover 4: stopped
% 25.93/4.23 Prover 1: stopped
% 25.93/4.23
% 25.93/4.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.93/4.23
% 25.93/4.26 % SZS output start Proof for theBenchmark
% 25.93/4.26 Assumptions after simplification:
% 25.93/4.26 ---------------------------------
% 25.93/4.26
% 25.93/4.26 (mDefInit)
% 25.93/4.29 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 25.93/4.29 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 25.93/4.29 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 25.93/4.29 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 25.93/4.29 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 25.93/4.29 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 25.93/4.29 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 25.93/4.29 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 25.93/4.29 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 25.93/4.29 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 25.93/4.29 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 25.93/4.29 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 25.93/4.29 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 25.93/4.29
% 25.93/4.29 (mDimNat)
% 25.93/4.29 ! [v0: $i] : ! [v1: $i] : ( ~ (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~
% 25.93/4.29 aVector0(v0) | aNaturalNumber0(v1))
% 25.93/4.29
% 25.93/4.29 (mEqInit)
% 25.93/4.29 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 25.93/4.29 (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 25.93/4.29 | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 25.93/4.29 $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) = v6 & aDimensionOf0(v2)
% 25.93/4.29 = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 & $i(v5) & (v5 = sz00 | ( ~ (v5
% 25.93/4.29 = v4) & aDimensionOf0(v0) = v4 & $i(v4))))))
% 25.93/4.29
% 25.93/4.29 (mIH)
% 25.93/4.29 ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~
% 25.93/4.29 aNaturalNumber0(v0) | iLess0(v0, v1))
% 25.93/4.29
% 25.93/4.29 (mLEMonM)
% 25.93/4.29 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 25.93/4.29 $i] : ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4)
% 25.93/4.29 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3) | ~
% 25.93/4.29 sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3) | ~
% 25.93/4.29 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | sdtlseqdt0(v4, v5))
% 25.93/4.29
% 25.93/4.29 (mLETot)
% 25.93/4.29 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~
% 25.93/4.29 aScalar0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 25.93/4.29
% 25.93/4.29 (mMulSc)
% 25.93/4.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 25.93/4.30 $i(v1) | ~ $i(v0) | ~ aScalar0(v1) | ~ aScalar0(v0) | aScalar0(v2))
% 25.93/4.30
% 25.93/4.30 (mSqPos)
% 25.93/4.30 $i(sz0z00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~
% 25.93/4.30 $i(v0) | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1))
% 25.93/4.30
% 25.93/4.30 (m__)
% 25.93/4.30 $i(xN) & $i(xP) & ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & ~
% 25.93/4.30 sdtlseqdt0(v0, xN))
% 25.93/4.30
% 25.93/4.30 (m__1652)
% 25.93/4.30 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 25.93/4.30 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 25.93/4.30 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 25.93/4.30 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 25.93/4.30 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 25.93/4.30 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 25.93/4.30 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 25.93/4.30 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 25.93/4.30
% 25.93/4.30 (m__1678)
% 25.93/4.30 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 25.93/4.30
% 25.93/4.30 (m__1678_01)
% 25.93/4.30 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 25.93/4.30 v0 & $i(v0))
% 25.93/4.30
% 25.93/4.30 (m__1692)
% 25.93/4.30 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 25.93/4.30 $i(v0))
% 25.93/4.30
% 25.93/4.30 (m__1709)
% 25.93/4.30 $i(xp) & $i(xs) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp &
% 25.93/4.30 aDimensionOf0(xp) = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 &
% 25.93/4.30 $i(v1) & $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 25.93/4.30 (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 25.93/4.30 (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 25.93/4.30
% 25.93/4.30 (m__1726)
% 25.93/4.30 $i(xq) & $i(xt) & ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq &
% 25.93/4.30 aDimensionOf0(xq) = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 &
% 25.93/4.30 $i(v1) & $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 25.93/4.30 (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 25.93/4.30 (sdtlbdtrb0(xq, v2) = v3 & $i(v3))))
% 25.93/4.30
% 25.93/4.30 (m__1746)
% 25.93/4.30 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 25.93/4.30 v0 & $i(v0) & aScalar0(xA))
% 25.93/4.30
% 25.93/4.30 (m__1766)
% 25.93/4.30 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 25.93/4.30 v0 & $i(v0) & aScalar0(xB))
% 25.93/4.30
% 25.93/4.30 (m__1783)
% 25.93/4.30 sdtasasdt0(xp, xp) = xC & $i(xC) & $i(xp) & aScalar0(xC)
% 25.93/4.30
% 25.93/4.30 (m__1800)
% 25.93/4.30 sdtasasdt0(xq, xq) = xD & $i(xD) & $i(xq) & aScalar0(xD)
% 25.93/4.30
% 25.93/4.30 (m__1820)
% 25.93/4.30 sdtasasdt0(xp, xq) = xE & $i(xE) & $i(xq) & $i(xp) & aScalar0(xE)
% 25.93/4.30
% 25.93/4.30 (m__1873)
% 25.93/4.30 sdtasdt0(xA, xB) = xH & $i(xH) & $i(xB) & $i(xA) & aScalar0(xH)
% 25.93/4.30
% 25.93/4.30 (m__1967)
% 25.93/4.30 $i(xE) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0
% 25.93/4.30 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 25.93/4.30
% 25.93/4.30 (m__2027)
% 25.93/4.30 $i(xP) & $i(xH) & $i(xE) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 25.93/4.30 (sdtasdt0(v1, v2) = v0 & sdtasdt0(xP, xP) = v0 & sdtasdt0(xH, xH) = v1 &
% 25.93/4.30 sdtasdt0(xE, xE) = v2 & $i(v2) & $i(v1) & $i(v0))
% 25.93/4.30
% 25.93/4.30 (m__2052)
% 25.93/4.30 $i(xN) & $i(xH) & $i(xD) & $i(xC) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0,
% 25.93/4.30 v1) = xN & sdtasdt0(xH, xH) = v0 & sdtasdt0(xC, xD) = v1 & $i(v1) &
% 25.93/4.30 $i(v0))
% 25.93/4.30
% 25.93/4.31 (function-axioms)
% 25.93/4.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.93/4.31 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 25.93/4.31 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 25.93/4.31 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 25.93/4.31 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 25.93/4.31 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 25.93/4.31 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 25.93/4.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 25.93/4.31 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 25.93/4.31 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 25.93/4.31 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 25.93/4.31 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 25.93/4.31 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 25.93/4.31
% 25.93/4.31 Further assumptions not needed in the proof:
% 25.93/4.31 --------------------------------------------
% 25.93/4.31 mArith, mDefSPN, mDefSPZ, mDistr, mDistr2, mElmSc, mIHOrd, mLEASm, mLEMon,
% 25.93/4.31 mLERef, mLETrn, mLess, mMDNeg, mMNeg, mNatExtr, mNatSort, mNegSc, mPosMon,
% 25.93/4.31 mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqrt, mSuccEqu, mSuccNat, mSumSc,
% 25.93/4.31 mVcSort, mZeroNat, m__1837, m__1854, m__1892, m__1911, m__1930, m__1949
% 25.93/4.31
% 25.93/4.31 Those formulas are unsatisfiable:
% 25.93/4.31 ---------------------------------
% 25.93/4.31
% 25.93/4.31 Begin of proof
% 25.93/4.31 |
% 25.93/4.31 | ALPHA: (mLEMonM) implies:
% 25.93/4.31 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 25.93/4.31 | ! [v5: $i] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) |
% 25.93/4.31 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v2, v3)
% 25.93/4.31 | | ~ sdtlseqdt0(v0, v1) | ~ sdtlseqdt0(sz0z00, v2) | ~ aScalar0(v3)
% 25.93/4.31 | | ~ aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) |
% 25.93/4.31 | sdtlseqdt0(v4, v5))
% 25.93/4.31 |
% 25.93/4.31 | ALPHA: (mSqPos) implies:
% 25.93/4.31 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v0) = v1) | ~ $i(v0) |
% 25.93/4.31 | ~ aScalar0(v0) | sdtlseqdt0(sz0z00, v1))
% 25.93/4.31 |
% 25.93/4.31 | ALPHA: (mDefInit) implies:
% 25.93/4.31 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 25.93/4.31 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 25.93/4.31 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 25.93/4.31 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 25.93/4.31 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 25.93/4.31 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 25.93/4.31 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 25.93/4.31 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 25.93/4.31 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 25.93/4.31 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 25.93/4.31 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 25.93/4.31 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 25.93/4.31 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 25.93/4.31 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 25.93/4.31 | aVector0(v1))))))
% 25.93/4.31 |
% 25.93/4.31 | ALPHA: (mEqInit) implies:
% 25.93/4.31 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 25.93/4.31 | (sziznziztdt0(v1) = v3) | ~ (sziznziztdt0(v0) = v2) | ~ $i(v1) | ~
% 25.93/4.31 | $i(v0) | ~ aVector0(v1) | ~ aVector0(v0) | ? [v4: $i] : ? [v5:
% 25.93/4.31 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & aDimensionOf0(v3) =
% 25.93/4.31 | v6 & aDimensionOf0(v2) = v6 & $i(v6)) | (aDimensionOf0(v1) = v5 &
% 25.93/4.31 | $i(v5) & (v5 = sz00 | ( ~ (v5 = v4) & aDimensionOf0(v0) = v4 &
% 25.93/4.31 | $i(v4))))))
% 26.38/4.31 |
% 26.38/4.31 | ALPHA: (m__1678) implies:
% 26.38/4.32 | (5) aVector0(xs)
% 26.38/4.32 | (6) aVector0(xt)
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1652) implies:
% 26.38/4.32 | (7) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 26.38/4.32 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 26.38/4.32 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 26.38/4.32 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 26.38/4.32 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 26.38/4.32 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 26.38/4.32 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 26.38/4.32 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 26.38/4.32 | $i(v7)))))))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1678_01) implies:
% 26.38/4.32 | (8) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 26.38/4.32 | $i(v0))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1692) implies:
% 26.38/4.32 | (9) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1709) implies:
% 26.38/4.32 | (10) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xs) = xp & aDimensionOf0(xp)
% 26.38/4.32 | = v0 & aDimensionOf0(xs) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 26.38/4.32 | $i(v0) & aVector0(xp) & ! [v2: $i] : ! [v3: $i] : ( ~
% 26.38/4.32 | (sdtlbdtrb0(xp, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 26.38/4.32 | (sdtlbdtrb0(xs, v2) = v3 & $i(v3))))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1726) implies:
% 26.38/4.32 | (11) ? [v0: $i] : ? [v1: $i] : (sziznziztdt0(xt) = xq & aDimensionOf0(xq)
% 26.38/4.32 | = v0 & aDimensionOf0(xt) = v1 & szszuzczcdt0(v0) = v1 & $i(v1) &
% 26.38/4.32 | $i(v0) & aVector0(xq) & ! [v2: $i] : ! [v3: $i] : ( ~
% 26.38/4.32 | (sdtlbdtrb0(xt, v2) = v3) | ~ $i(v2) | ~ aNaturalNumber0(v2) |
% 26.38/4.32 | (sdtlbdtrb0(xq, v2) = v3 & $i(v3))))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1746) implies:
% 26.38/4.32 | (12) $i(xs)
% 26.38/4.32 | (13) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 26.38/4.32 | $i(v0) & aScalar0(xA))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1766) implies:
% 26.38/4.32 | (14) $i(xt)
% 26.38/4.32 | (15) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 &
% 26.38/4.32 | $i(v0) & aScalar0(xB))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1783) implies:
% 26.38/4.32 | (16) aScalar0(xC)
% 26.38/4.32 | (17) sdtasasdt0(xp, xp) = xC
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1800) implies:
% 26.38/4.32 | (18) aScalar0(xD)
% 26.38/4.32 | (19) sdtasasdt0(xq, xq) = xD
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1820) implies:
% 26.38/4.32 | (20) aScalar0(xE)
% 26.38/4.32 | (21) $i(xp)
% 26.38/4.32 | (22) $i(xq)
% 26.38/4.32 | (23) sdtasasdt0(xp, xq) = xE
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1873) implies:
% 26.38/4.32 | (24) aScalar0(xH)
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__1967) implies:
% 26.38/4.32 | (25) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xE, xE) = v0 & sdtasdt0(xC, xD)
% 26.38/4.32 | = v1 & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__2027) implies:
% 26.38/4.32 | (26) $i(xE)
% 26.38/4.32 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(v1, v2) = v0 &
% 26.38/4.32 | sdtasdt0(xP, xP) = v0 & sdtasdt0(xH, xH) = v1 & sdtasdt0(xE, xE) =
% 26.38/4.32 | v2 & $i(v2) & $i(v1) & $i(v0))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__2052) implies:
% 26.38/4.32 | (28) $i(xC)
% 26.38/4.32 | (29) $i(xD)
% 26.38/4.32 | (30) $i(xH)
% 26.38/4.32 | (31) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = xN & sdtasdt0(xH, xH)
% 26.38/4.32 | = v0 & sdtasdt0(xC, xD) = v1 & $i(v1) & $i(v0))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (m__) implies:
% 26.38/4.32 | (32) ? [v0: $i] : (sdtasdt0(xP, xP) = v0 & $i(v0) & ~ sdtlseqdt0(v0, xN))
% 26.38/4.32 |
% 26.38/4.32 | ALPHA: (function-axioms) implies:
% 26.38/4.33 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.38/4.33 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 26.38/4.33 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 26.38/4.33 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 26.38/4.33 | (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 26.38/4.33 | (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0))
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (8) with fresh symbol all_33_0 gives:
% 26.38/4.33 | (36) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 26.38/4.33 | $i(all_33_0)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (36) implies:
% 26.38/4.33 | (37) aDimensionOf0(xs) = all_33_0
% 26.38/4.33 | (38) aDimensionOf0(xt) = all_33_0
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (9) with fresh symbol all_35_0 gives:
% 26.38/4.33 | (39) ~ (all_35_0 = sz00) & aDimensionOf0(xs) = all_35_0 & $i(all_35_0)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (39) implies:
% 26.38/4.33 | (40) ~ (all_35_0 = sz00)
% 26.38/4.33 | (41) aDimensionOf0(xs) = all_35_0
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (32) with fresh symbol all_37_0 gives:
% 26.38/4.33 | (42) sdtasdt0(xP, xP) = all_37_0 & $i(all_37_0) & ~ sdtlseqdt0(all_37_0,
% 26.38/4.33 | xN)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (42) implies:
% 26.38/4.33 | (43) ~ sdtlseqdt0(all_37_0, xN)
% 26.38/4.33 | (44) sdtasdt0(xP, xP) = all_37_0
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (13) with fresh symbol all_39_0 gives:
% 26.38/4.33 | (45) sdtlbdtrb0(xs, all_39_0) = xA & aDimensionOf0(xs) = all_39_0 &
% 26.38/4.33 | $i(all_39_0) & aScalar0(xA)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (45) implies:
% 26.38/4.33 | (46) aDimensionOf0(xs) = all_39_0
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (15) with fresh symbol all_41_0 gives:
% 26.38/4.33 | (47) sdtlbdtrb0(xt, all_41_0) = xB & aDimensionOf0(xt) = all_41_0 &
% 26.38/4.33 | $i(all_41_0) & aScalar0(xB)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (47) implies:
% 26.38/4.33 | (48) aDimensionOf0(xt) = all_41_0
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (25) with fresh symbols all_43_0, all_43_1 gives:
% 26.38/4.33 | (49) sdtasdt0(xE, xE) = all_43_1 & sdtasdt0(xC, xD) = all_43_0 &
% 26.38/4.33 | $i(all_43_0) & $i(all_43_1) & sdtlseqdt0(all_43_1, all_43_0)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (49) implies:
% 26.38/4.33 | (50) sdtasdt0(xC, xD) = all_43_0
% 26.38/4.33 | (51) sdtasdt0(xE, xE) = all_43_1
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (31) with fresh symbols all_45_0, all_45_1 gives:
% 26.38/4.33 | (52) sdtasdt0(all_45_1, all_45_0) = xN & sdtasdt0(xH, xH) = all_45_1 &
% 26.38/4.33 | sdtasdt0(xC, xD) = all_45_0 & $i(all_45_0) & $i(all_45_1)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (52) implies:
% 26.38/4.33 | (53) $i(all_45_0)
% 26.38/4.33 | (54) sdtasdt0(xC, xD) = all_45_0
% 26.38/4.33 | (55) sdtasdt0(xH, xH) = all_45_1
% 26.38/4.33 | (56) sdtasdt0(all_45_1, all_45_0) = xN
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (27) with fresh symbols all_47_0, all_47_1, all_47_2
% 26.38/4.33 | gives:
% 26.38/4.33 | (57) sdtasdt0(all_47_1, all_47_0) = all_47_2 & sdtasdt0(xP, xP) = all_47_2
% 26.38/4.33 | & sdtasdt0(xH, xH) = all_47_1 & sdtasdt0(xE, xE) = all_47_0 &
% 26.38/4.33 | $i(all_47_0) & $i(all_47_1) & $i(all_47_2)
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (57) implies:
% 26.38/4.33 | (58) $i(all_47_1)
% 26.38/4.33 | (59) sdtasdt0(xE, xE) = all_47_0
% 26.38/4.33 | (60) sdtasdt0(xH, xH) = all_47_1
% 26.38/4.33 | (61) sdtasdt0(xP, xP) = all_47_2
% 26.38/4.33 | (62) sdtasdt0(all_47_1, all_47_0) = all_47_2
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (10) with fresh symbols all_49_0, all_49_1 gives:
% 26.38/4.33 | (63) sziznziztdt0(xs) = xp & aDimensionOf0(xp) = all_49_1 &
% 26.38/4.33 | aDimensionOf0(xs) = all_49_0 & szszuzczcdt0(all_49_1) = all_49_0 &
% 26.38/4.33 | $i(all_49_0) & $i(all_49_1) & aVector0(xp) & ! [v0: $i] : ! [v1: $i]
% 26.38/4.33 | : ( ~ (sdtlbdtrb0(xp, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 26.38/4.33 | (sdtlbdtrb0(xs, v0) = v1 & $i(v1)))
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (63) implies:
% 26.38/4.33 | (64) aVector0(xp)
% 26.38/4.33 | (65) aDimensionOf0(xs) = all_49_0
% 26.38/4.33 | (66) aDimensionOf0(xp) = all_49_1
% 26.38/4.33 | (67) sziznziztdt0(xs) = xp
% 26.38/4.33 |
% 26.38/4.33 | DELTA: instantiating (11) with fresh symbols all_52_0, all_52_1 gives:
% 26.38/4.33 | (68) sziznziztdt0(xt) = xq & aDimensionOf0(xq) = all_52_1 &
% 26.38/4.33 | aDimensionOf0(xt) = all_52_0 & szszuzczcdt0(all_52_1) = all_52_0 &
% 26.38/4.33 | $i(all_52_0) & $i(all_52_1) & aVector0(xq) & ! [v0: $i] : ! [v1: $i]
% 26.38/4.33 | : ( ~ (sdtlbdtrb0(xt, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) |
% 26.38/4.33 | (sdtlbdtrb0(xq, v0) = v1 & $i(v1)))
% 26.38/4.33 |
% 26.38/4.33 | ALPHA: (68) implies:
% 26.38/4.33 | (69) aVector0(xq)
% 26.38/4.34 | (70) $i(all_52_1)
% 26.38/4.34 | (71) szszuzczcdt0(all_52_1) = all_52_0
% 26.38/4.34 | (72) aDimensionOf0(xt) = all_52_0
% 26.38/4.34 | (73) aDimensionOf0(xq) = all_52_1
% 26.38/4.34 | (74) sziznziztdt0(xt) = xq
% 26.38/4.34 |
% 26.38/4.34 | DELTA: instantiating (7) with fresh symbol all_55_0 gives:
% 26.38/4.34 | (75) aDimensionOf0(xs) = all_55_0 & $i(all_55_0) & ! [v0: $i] : ! [v1:
% 26.38/4.34 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 26.38/4.34 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 26.38/4.34 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 26.38/4.34 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 26.38/4.34 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 26.38/4.34 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 26.38/4.34 | iLess0(v5, all_55_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 26.38/4.34 | & $i(v6))))))
% 26.38/4.34 |
% 26.38/4.34 | ALPHA: (75) implies:
% 26.38/4.34 | (76) aDimensionOf0(xs) = all_55_0
% 26.38/4.34 | (77) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 26.38/4.34 | ( ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~
% 26.38/4.34 | (sdtasdt0(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) |
% 26.38/4.34 | ~ aVector0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 26.38/4.34 | $i] : ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) &
% 26.38/4.34 | $i(v7) & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5)
% 26.38/4.34 | & ( ~ iLess0(v5, all_55_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) =
% 26.38/4.34 | v6 & $i(v6))))))
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (34) with all_43_0, all_45_0, xD, xC, simplifying
% 26.38/4.34 | with (50), (54) gives:
% 26.38/4.34 | (78) all_45_0 = all_43_0
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (34) with all_43_1, all_47_0, xE, xE, simplifying
% 26.38/4.34 | with (51), (59) gives:
% 26.38/4.34 | (79) all_47_0 = all_43_1
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (34) with all_45_1, all_47_1, xH, xH, simplifying
% 26.38/4.34 | with (55), (60) gives:
% 26.38/4.34 | (80) all_47_1 = all_45_1
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (34) with all_37_0, all_47_2, xP, xP, simplifying
% 26.38/4.34 | with (44), (61) gives:
% 26.38/4.34 | (81) all_47_2 = all_37_0
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (33) with all_39_0, all_49_0, xs, simplifying with
% 26.38/4.34 | (46), (65) gives:
% 26.38/4.34 | (82) all_49_0 = all_39_0
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (33) with all_35_0, all_49_0, xs, simplifying with
% 26.38/4.34 | (41), (65) gives:
% 26.38/4.34 | (83) all_49_0 = all_35_0
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (33) with all_49_0, all_55_0, xs, simplifying with
% 26.38/4.34 | (65), (76) gives:
% 26.38/4.34 | (84) all_55_0 = all_49_0
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (33) with all_33_0, all_55_0, xs, simplifying with
% 26.38/4.34 | (37), (76) gives:
% 26.38/4.34 | (85) all_55_0 = all_33_0
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (33) with all_41_0, all_52_0, xt, simplifying with
% 26.38/4.34 | (48), (72) gives:
% 26.38/4.34 | (86) all_52_0 = all_41_0
% 26.38/4.34 |
% 26.38/4.34 | GROUND_INST: instantiating (33) with all_33_0, all_52_0, xt, simplifying with
% 26.38/4.34 | (38), (72) gives:
% 26.38/4.34 | (87) all_52_0 = all_33_0
% 26.38/4.34 |
% 26.38/4.34 | COMBINE_EQS: (84), (85) imply:
% 26.38/4.34 | (88) all_49_0 = all_33_0
% 26.38/4.34 |
% 26.38/4.34 | SIMP: (88) implies:
% 26.38/4.34 | (89) all_49_0 = all_33_0
% 26.38/4.34 |
% 26.38/4.34 | COMBINE_EQS: (86), (87) imply:
% 26.38/4.34 | (90) all_41_0 = all_33_0
% 26.38/4.34 |
% 26.38/4.34 | SIMP: (90) implies:
% 26.38/4.34 | (91) all_41_0 = all_33_0
% 26.38/4.34 |
% 26.38/4.34 | COMBINE_EQS: (82), (83) imply:
% 26.38/4.34 | (92) all_39_0 = all_35_0
% 26.38/4.34 |
% 26.38/4.34 | COMBINE_EQS: (82), (89) imply:
% 26.38/4.34 | (93) all_39_0 = all_33_0
% 26.38/4.34 |
% 26.38/4.34 | COMBINE_EQS: (92), (93) imply:
% 26.38/4.35 | (94) all_35_0 = all_33_0
% 26.38/4.35 |
% 26.38/4.35 | SIMP: (94) implies:
% 26.38/4.35 | (95) all_35_0 = all_33_0
% 26.38/4.35 |
% 26.38/4.35 | REDUCE: (40), (95) imply:
% 26.38/4.35 | (96) ~ (all_33_0 = sz00)
% 26.38/4.35 |
% 26.38/4.35 | REDUCE: (62), (79), (80), (81) imply:
% 26.38/4.35 | (97) sdtasdt0(all_45_1, all_43_1) = all_37_0
% 26.38/4.35 |
% 26.38/4.35 | REDUCE: (56), (78) imply:
% 26.38/4.35 | (98) sdtasdt0(all_45_1, all_43_0) = xN
% 26.38/4.35 |
% 26.38/4.35 | REDUCE: (71), (87) imply:
% 26.38/4.35 | (99) szszuzczcdt0(all_52_1) = all_33_0
% 26.38/4.35 |
% 26.38/4.35 | REDUCE: (58), (80) imply:
% 26.38/4.35 | (100) $i(all_45_1)
% 26.38/4.35 |
% 26.38/4.35 | REDUCE: (53), (78) imply:
% 26.38/4.35 | (101) $i(all_43_0)
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (mMulSc) with xC, xD, all_43_0, simplifying with
% 26.38/4.35 | (16), (18), (28), (29), (50) gives:
% 26.38/4.35 | (102) aScalar0(all_43_0)
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (mMulSc) with xE, xE, all_43_1, simplifying with
% 26.38/4.35 | (20), (26), (51) gives:
% 26.38/4.35 | (103) aScalar0(all_43_1)
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (2) with xE, all_43_1, simplifying with (20), (26),
% 26.38/4.35 | (51) gives:
% 26.38/4.35 | (104) sdtlseqdt0(sz0z00, all_43_1)
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (mMulSc) with xH, xH, all_45_1, simplifying with
% 26.38/4.35 | (24), (30), (55) gives:
% 26.38/4.35 | (105) aScalar0(all_45_1)
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (mDimNat) with xq, all_52_1, simplifying with (22),
% 26.38/4.35 | (69), (73) gives:
% 26.38/4.35 | (106) aNaturalNumber0(all_52_1)
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (3) with xs, xp, simplifying with (5), (12), (67)
% 26.38/4.35 | gives:
% 26.38/4.35 | (107) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & (v0 = sz00 | ( !
% 26.38/4.35 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xs, v2)
% 26.38/4.35 | = v3) | ~ (aDimensionOf0(xp) = v1) | ~ $i(v2) | ~ $i(xp)
% 26.38/4.35 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xp, v2) = v3 &
% 26.38/4.35 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xp | ~
% 26.38/4.35 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ?
% 26.38/4.35 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4)
% 26.38/4.35 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xs,
% 26.38/4.35 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | (
% 26.38/4.35 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & !
% 26.38/4.35 | [v1: $i] : ( ~ (aDimensionOf0(xp) = v1) | ~ $i(xp) |
% 26.38/4.35 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xp)
% 26.38/4.35 | = v1) | ~ $i(xp) | aVector0(xp)))))
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (4) with xs, xt, xp, xq, simplifying with (5), (6),
% 26.38/4.35 | (12), (14), (67), (74) gives:
% 26.38/4.35 | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 26.38/4.35 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) |
% 26.38/4.35 | (aDimensionOf0(xt) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) &
% 26.38/4.35 | aDimensionOf0(xs) = v0 & $i(v0)))))
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (4) with xt, xs, xq, xp, simplifying with (5), (6),
% 26.38/4.35 | (12), (14), (67), (74) gives:
% 26.38/4.35 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 &
% 26.38/4.35 | aDimensionOf0(xq) = v2 & aDimensionOf0(xp) = v2 & $i(v2)) |
% 26.38/4.35 | (aDimensionOf0(xs) = v1 & $i(v1) & (v1 = sz00 | ( ~ (v1 = v0) &
% 26.38/4.35 | aDimensionOf0(xt) = v0 & $i(v0)))))
% 26.38/4.35 |
% 26.38/4.35 | GROUND_INST: instantiating (3) with xt, xq, simplifying with (6), (14), (74)
% 26.38/4.35 | gives:
% 26.38/4.35 | (110) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( !
% 26.38/4.35 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2)
% 26.38/4.35 | = v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq)
% 26.38/4.35 | | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 &
% 26.38/4.35 | $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~
% 26.38/4.35 | (aDimensionOf0(v1) = v2) | ~ $i(v1) | ~ aVector0(v1) | ?
% 26.38/4.35 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4)
% 26.38/4.36 | & (( ~ (v6 = v5) & sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt,
% 26.38/4.36 | v4) = v6 & $i(v6) & $i(v5) & aNaturalNumber0(v4)) | (
% 26.38/4.36 | ~ (v3 = v0) & szszuzczcdt0(v2) = v3 & $i(v3))))) & !
% 26.38/4.36 | [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) |
% 26.38/4.36 | szszuzczcdt0(v1) = v0) & ! [v1: $i] : ( ~ (aDimensionOf0(xq)
% 26.38/4.36 | = v1) | ~ $i(xq) | aVector0(xq)))))
% 26.38/4.36 |
% 26.38/4.36 | GROUND_INST: instantiating (77) with xp, xq, xC, xD, all_43_0, simplifying
% 26.38/4.36 | with (17), (19), (21), (22), (50), (64), (69) gives:
% 26.38/4.36 | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 26.38/4.36 | ((sdtasasdt0(xp, xq) = v2 & sdtasdt0(v2, v2) = v3 & $i(v3) & $i(v2) &
% 26.38/4.36 | sdtlseqdt0(v3, all_43_0)) | (aDimensionOf0(xp) = v0 & $i(v0) & (
% 26.38/4.36 | ~ iLess0(v0, all_55_0) | ( ~ (v1 = v0) & aDimensionOf0(xq) = v1
% 26.38/4.36 | & $i(v1)))))
% 26.38/4.36 |
% 26.38/4.36 | DELTA: instantiating (109) with fresh symbols all_71_0, all_71_1, all_71_2,
% 26.38/4.36 | all_71_3 gives:
% 26.38/4.36 | (112) (all_71_0 = all_71_1 & aDimensionOf0(xq) = all_71_1 &
% 26.38/4.36 | aDimensionOf0(xp) = all_71_1 & $i(all_71_1)) | (aDimensionOf0(xs) =
% 26.38/4.36 | all_71_2 & $i(all_71_2) & (all_71_2 = sz00 | ( ~ (all_71_2 =
% 26.38/4.36 | all_71_3) & aDimensionOf0(xt) = all_71_3 & $i(all_71_3))))
% 26.38/4.36 |
% 26.38/4.36 | DELTA: instantiating (108) with fresh symbols all_72_0, all_72_1, all_72_2,
% 26.38/4.36 | all_72_3 gives:
% 26.38/4.36 | (113) (all_72_0 = all_72_1 & aDimensionOf0(xq) = all_72_1 &
% 26.38/4.36 | aDimensionOf0(xp) = all_72_1 & $i(all_72_1)) | (aDimensionOf0(xt) =
% 26.38/4.36 | all_72_2 & $i(all_72_2) & (all_72_2 = sz00 | ( ~ (all_72_2 =
% 26.38/4.36 | all_72_3) & aDimensionOf0(xs) = all_72_3 & $i(all_72_3))))
% 26.38/4.36 |
% 26.38/4.36 | DELTA: instantiating (111) with fresh symbols all_73_0, all_73_1, all_73_2,
% 26.38/4.36 | all_73_3 gives:
% 26.38/4.36 | (114) (sdtasasdt0(xp, xq) = all_73_1 & sdtasdt0(all_73_1, all_73_1) =
% 26.38/4.36 | all_73_0 & $i(all_73_0) & $i(all_73_1) & sdtlseqdt0(all_73_0,
% 26.38/4.36 | all_43_0)) | (aDimensionOf0(xp) = all_73_3 & $i(all_73_3) & ( ~
% 26.38/4.36 | iLess0(all_73_3, all_55_0) | ( ~ (all_73_2 = all_73_3) &
% 26.38/4.36 | aDimensionOf0(xq) = all_73_2 & $i(all_73_2))))
% 26.38/4.36 |
% 26.38/4.36 | DELTA: instantiating (110) with fresh symbol all_74_0 gives:
% 26.38/4.36 | (115) aDimensionOf0(xt) = all_74_0 & $i(all_74_0) & (all_74_0 = sz00 | ( !
% 26.38/4.36 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 26.38/4.36 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) |
% 26.38/4.36 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) &
% 26.38/4.36 | ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1)
% 26.38/4.36 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 26.38/4.36 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 26.38/4.36 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 &
% 26.38/4.36 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 26.38/4.36 | all_74_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 26.38/4.36 | [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) |
% 26.38/4.36 | szszuzczcdt0(v0) = all_74_0) & ! [v0: $i] : ( ~
% 26.38/4.36 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | aVector0(xq))))
% 26.38/4.36 |
% 26.38/4.36 | ALPHA: (115) implies:
% 26.38/4.36 | (116) aDimensionOf0(xt) = all_74_0
% 26.38/4.36 |
% 26.38/4.36 | DELTA: instantiating (107) with fresh symbol all_76_0 gives:
% 26.38/4.36 | (117) aDimensionOf0(xs) = all_76_0 & $i(all_76_0) & (all_76_0 = sz00 | ( !
% 26.38/4.36 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xs, v1) =
% 26.38/4.36 | v2) | ~ (aDimensionOf0(xp) = v0) | ~ $i(v1) | ~ $i(xp) |
% 26.38/4.36 | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xp, v1) = v2 & $i(v2))) &
% 26.38/4.36 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | ~ (aDimensionOf0(v0) = v1)
% 26.38/4.36 | | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 26.38/4.36 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 26.38/4.36 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xs, v3) = v5 &
% 26.38/4.36 | $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 26.38/4.36 | all_76_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & !
% 26.38/4.36 | [v0: $i] : ( ~ (aDimensionOf0(xp) = v0) | ~ $i(xp) |
% 26.38/4.36 | szszuzczcdt0(v0) = all_76_0) & ! [v0: $i] : ( ~
% 26.38/4.36 | (aDimensionOf0(xp) = v0) | ~ $i(xp) | aVector0(xp))))
% 26.38/4.36 |
% 26.38/4.36 | ALPHA: (117) implies:
% 26.38/4.36 | (118) aDimensionOf0(xs) = all_76_0
% 26.38/4.36 |
% 26.38/4.36 | GROUND_INST: instantiating (33) with all_33_0, all_76_0, xs, simplifying with
% 26.38/4.36 | (37), (118) gives:
% 26.38/4.36 | (119) all_76_0 = all_33_0
% 26.38/4.36 |
% 26.38/4.36 | GROUND_INST: instantiating (33) with all_33_0, all_74_0, xt, simplifying with
% 26.38/4.36 | (38), (116) gives:
% 26.38/4.36 | (120) all_74_0 = all_33_0
% 26.38/4.36 |
% 26.38/4.36 | BETA: splitting (112) gives:
% 26.38/4.36 |
% 26.38/4.36 | Case 1:
% 26.38/4.36 | |
% 26.38/4.36 | | (121) all_71_0 = all_71_1 & aDimensionOf0(xq) = all_71_1 &
% 26.38/4.36 | | aDimensionOf0(xp) = all_71_1 & $i(all_71_1)
% 26.38/4.36 | |
% 26.38/4.36 | | ALPHA: (121) implies:
% 26.38/4.36 | | (122) aDimensionOf0(xp) = all_71_1
% 26.38/4.36 | | (123) aDimensionOf0(xq) = all_71_1
% 26.38/4.36 | |
% 26.38/4.36 | | BETA: splitting (113) gives:
% 26.38/4.36 | |
% 26.38/4.36 | | Case 1:
% 26.38/4.36 | | |
% 26.38/4.36 | | | (124) all_72_0 = all_72_1 & aDimensionOf0(xq) = all_72_1 &
% 26.38/4.36 | | | aDimensionOf0(xp) = all_72_1 & $i(all_72_1)
% 26.38/4.36 | | |
% 26.38/4.36 | | | ALPHA: (124) implies:
% 26.38/4.36 | | | (125) aDimensionOf0(xp) = all_72_1
% 26.38/4.36 | | | (126) aDimensionOf0(xq) = all_72_1
% 26.38/4.36 | | |
% 26.38/4.36 | | | GROUND_INST: instantiating (33) with all_49_1, all_72_1, xp, simplifying
% 26.38/4.36 | | | with (66), (125) gives:
% 26.38/4.36 | | | (127) all_72_1 = all_49_1
% 26.38/4.36 | | |
% 26.38/4.36 | | | GROUND_INST: instantiating (33) with all_52_1, all_72_1, xq, simplifying
% 26.38/4.36 | | | with (73), (126) gives:
% 26.38/4.37 | | | (128) all_72_1 = all_52_1
% 26.38/4.37 | | |
% 26.38/4.37 | | | GROUND_INST: instantiating (33) with all_71_1, all_72_1, xq, simplifying
% 26.38/4.37 | | | with (123), (126) gives:
% 26.38/4.37 | | | (129) all_72_1 = all_71_1
% 26.38/4.37 | | |
% 26.38/4.37 | | | COMBINE_EQS: (127), (129) imply:
% 26.38/4.37 | | | (130) all_71_1 = all_49_1
% 26.38/4.37 | | |
% 26.38/4.37 | | | COMBINE_EQS: (128), (129) imply:
% 26.38/4.37 | | | (131) all_71_1 = all_52_1
% 26.38/4.37 | | |
% 26.38/4.37 | | | COMBINE_EQS: (130), (131) imply:
% 26.38/4.37 | | | (132) all_52_1 = all_49_1
% 26.38/4.37 | | |
% 26.38/4.37 | | | SIMP: (132) implies:
% 26.38/4.37 | | | (133) all_52_1 = all_49_1
% 26.38/4.37 | | |
% 26.38/4.37 | | | REDUCE: (73), (133) imply:
% 26.38/4.37 | | | (134) aDimensionOf0(xq) = all_49_1
% 26.38/4.37 | | |
% 26.38/4.37 | | | REDUCE: (99), (133) imply:
% 26.38/4.37 | | | (135) szszuzczcdt0(all_49_1) = all_33_0
% 26.38/4.37 | | |
% 26.38/4.37 | | | REDUCE: (70), (133) imply:
% 26.38/4.37 | | | (136) $i(all_49_1)
% 26.38/4.37 | | |
% 26.38/4.37 | | | REDUCE: (106), (133) imply:
% 26.38/4.37 | | | (137) aNaturalNumber0(all_49_1)
% 26.38/4.37 | | |
% 26.38/4.37 | | | GROUND_INST: instantiating (mIH) with all_49_1, all_33_0, simplifying with
% 26.38/4.37 | | | (135), (136), (137) gives:
% 26.38/4.37 | | | (138) iLess0(all_49_1, all_33_0)
% 26.38/4.37 | | |
% 26.38/4.37 | | | GROUND_INST: instantiating (mLETot) with all_45_1, all_45_1, simplifying
% 26.38/4.37 | | | with (100), (105) gives:
% 26.38/4.37 | | | (139) sdtlseqdt0(all_45_1, all_45_1)
% 26.38/4.37 | | |
% 26.38/4.37 | | | BETA: splitting (114) gives:
% 26.38/4.37 | | |
% 26.38/4.37 | | | Case 1:
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | (140) sdtasasdt0(xp, xq) = all_73_1 & sdtasdt0(all_73_1, all_73_1) =
% 26.38/4.37 | | | | all_73_0 & $i(all_73_0) & $i(all_73_1) & sdtlseqdt0(all_73_0,
% 26.38/4.37 | | | | all_43_0)
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | ALPHA: (140) implies:
% 26.38/4.37 | | | | (141) sdtlseqdt0(all_73_0, all_43_0)
% 26.38/4.37 | | | | (142) $i(all_73_0)
% 26.38/4.37 | | | | (143) sdtasdt0(all_73_1, all_73_1) = all_73_0
% 26.38/4.37 | | | | (144) sdtasasdt0(xp, xq) = all_73_1
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | GROUND_INST: instantiating (35) with xE, all_73_1, xq, xp, simplifying
% 26.38/4.37 | | | | with (23), (144) gives:
% 26.38/4.37 | | | | (145) all_73_1 = xE
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | REDUCE: (143), (145) imply:
% 26.38/4.37 | | | | (146) sdtasdt0(xE, xE) = all_73_0
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | GROUND_INST: instantiating (34) with all_43_1, all_73_0, xE, xE,
% 26.38/4.37 | | | | simplifying with (51), (146) gives:
% 26.38/4.37 | | | | (147) all_73_0 = all_43_1
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | REDUCE: (142), (147) imply:
% 26.38/4.37 | | | | (148) $i(all_43_1)
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | REDUCE: (141), (147) imply:
% 26.38/4.37 | | | | (149) sdtlseqdt0(all_43_1, all_43_0)
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | GROUND_INST: instantiating (1) with all_45_1, all_45_1, all_43_1,
% 26.38/4.37 | | | | all_43_0, all_37_0, xN, simplifying with (43), (97), (98),
% 26.38/4.37 | | | | (100), (101), (102), (103), (104), (105), (139), (148),
% 26.38/4.37 | | | | (149) gives:
% 26.38/4.37 | | | | (150) $false
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | CLOSE: (150) is inconsistent.
% 26.38/4.37 | | | |
% 26.38/4.37 | | | Case 2:
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | (151) aDimensionOf0(xp) = all_73_3 & $i(all_73_3) & ( ~
% 26.38/4.37 | | | | iLess0(all_73_3, all_55_0) | ( ~ (all_73_2 = all_73_3) &
% 26.38/4.37 | | | | aDimensionOf0(xq) = all_73_2 & $i(all_73_2)))
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | ALPHA: (151) implies:
% 26.38/4.37 | | | | (152) aDimensionOf0(xp) = all_73_3
% 26.38/4.37 | | | | (153) ~ iLess0(all_73_3, all_55_0) | ( ~ (all_73_2 = all_73_3) &
% 26.38/4.37 | | | | aDimensionOf0(xq) = all_73_2 & $i(all_73_2))
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | GROUND_INST: instantiating (33) with all_49_1, all_73_3, xp, simplifying
% 26.38/4.37 | | | | with (66), (152) gives:
% 26.38/4.37 | | | | (154) all_73_3 = all_49_1
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | BETA: splitting (153) gives:
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | Case 1:
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | (155) ~ iLess0(all_73_3, all_55_0)
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | REDUCE: (85), (154), (155) imply:
% 26.38/4.37 | | | | | (156) ~ iLess0(all_49_1, all_33_0)
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | PRED_UNIFY: (138), (156) imply:
% 26.38/4.37 | | | | | (157) $false
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | CLOSE: (157) is inconsistent.
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | Case 2:
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | (158) ~ (all_73_2 = all_73_3) & aDimensionOf0(xq) = all_73_2 &
% 26.38/4.37 | | | | | $i(all_73_2)
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | ALPHA: (158) implies:
% 26.38/4.37 | | | | | (159) ~ (all_73_2 = all_73_3)
% 26.38/4.37 | | | | | (160) aDimensionOf0(xq) = all_73_2
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | REDUCE: (154), (159) imply:
% 26.38/4.37 | | | | | (161) ~ (all_73_2 = all_49_1)
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | GROUND_INST: instantiating (33) with all_49_1, all_73_2, xq,
% 26.38/4.37 | | | | | simplifying with (134), (160) gives:
% 26.38/4.37 | | | | | (162) all_73_2 = all_49_1
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | REDUCE: (161), (162) imply:
% 26.38/4.37 | | | | | (163) $false
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | | CLOSE: (163) is inconsistent.
% 26.38/4.37 | | | | |
% 26.38/4.37 | | | | End of split
% 26.38/4.37 | | | |
% 26.38/4.37 | | | End of split
% 26.38/4.37 | | |
% 26.38/4.37 | | Case 2:
% 26.38/4.37 | | |
% 26.38/4.37 | | | (164) aDimensionOf0(xt) = all_72_2 & $i(all_72_2) & (all_72_2 = sz00 |
% 26.38/4.37 | | | ( ~ (all_72_2 = all_72_3) & aDimensionOf0(xs) = all_72_3 &
% 26.38/4.37 | | | $i(all_72_3)))
% 26.38/4.37 | | |
% 26.38/4.37 | | | ALPHA: (164) implies:
% 26.38/4.37 | | | (165) aDimensionOf0(xt) = all_72_2
% 26.38/4.37 | | | (166) all_72_2 = sz00 | ( ~ (all_72_2 = all_72_3) & aDimensionOf0(xs) =
% 26.38/4.37 | | | all_72_3 & $i(all_72_3))
% 26.38/4.37 | | |
% 26.38/4.37 | | | GROUND_INST: instantiating (33) with all_33_0, all_72_2, xt, simplifying
% 26.38/4.37 | | | with (38), (165) gives:
% 26.38/4.37 | | | (167) all_72_2 = all_33_0
% 26.38/4.37 | | |
% 26.38/4.37 | | | BETA: splitting (166) gives:
% 26.38/4.37 | | |
% 26.38/4.37 | | | Case 1:
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | (168) all_72_2 = sz00
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | COMBINE_EQS: (167), (168) imply:
% 26.38/4.37 | | | | (169) all_33_0 = sz00
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | SIMP: (169) implies:
% 26.38/4.37 | | | | (170) all_33_0 = sz00
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | REDUCE: (96), (170) imply:
% 26.38/4.37 | | | | (171) $false
% 26.38/4.37 | | | |
% 26.38/4.37 | | | | CLOSE: (171) is inconsistent.
% 26.38/4.37 | | | |
% 26.38/4.37 | | | Case 2:
% 26.38/4.37 | | | |
% 26.38/4.38 | | | | (172) ~ (all_72_2 = all_72_3) & aDimensionOf0(xs) = all_72_3 &
% 26.38/4.38 | | | | $i(all_72_3)
% 26.38/4.38 | | | |
% 26.38/4.38 | | | | ALPHA: (172) implies:
% 26.38/4.38 | | | | (173) ~ (all_72_2 = all_72_3)
% 26.38/4.38 | | | | (174) aDimensionOf0(xs) = all_72_3
% 26.38/4.38 | | | |
% 26.38/4.38 | | | | REDUCE: (167), (173) imply:
% 26.38/4.38 | | | | (175) ~ (all_72_3 = all_33_0)
% 26.38/4.38 | | | |
% 26.38/4.38 | | | | SIMP: (175) implies:
% 26.38/4.38 | | | | (176) ~ (all_72_3 = all_33_0)
% 26.38/4.38 | | | |
% 26.38/4.38 | | | | GROUND_INST: instantiating (33) with all_33_0, all_72_3, xs, simplifying
% 26.38/4.38 | | | | with (37), (174) gives:
% 26.38/4.38 | | | | (177) all_72_3 = all_33_0
% 26.38/4.38 | | | |
% 26.38/4.38 | | | | REDUCE: (176), (177) imply:
% 26.38/4.38 | | | | (178) $false
% 26.38/4.38 | | | |
% 26.38/4.38 | | | | CLOSE: (178) is inconsistent.
% 26.38/4.38 | | | |
% 26.38/4.38 | | | End of split
% 26.38/4.38 | | |
% 26.38/4.38 | | End of split
% 26.38/4.38 | |
% 26.38/4.38 | Case 2:
% 26.38/4.38 | |
% 26.38/4.38 | | (179) aDimensionOf0(xs) = all_71_2 & $i(all_71_2) & (all_71_2 = sz00 | (
% 26.38/4.38 | | ~ (all_71_2 = all_71_3) & aDimensionOf0(xt) = all_71_3 &
% 26.38/4.38 | | $i(all_71_3)))
% 26.38/4.38 | |
% 26.38/4.38 | | ALPHA: (179) implies:
% 26.38/4.38 | | (180) aDimensionOf0(xs) = all_71_2
% 26.38/4.38 | | (181) all_71_2 = sz00 | ( ~ (all_71_2 = all_71_3) & aDimensionOf0(xt) =
% 26.38/4.38 | | all_71_3 & $i(all_71_3))
% 26.38/4.38 | |
% 26.38/4.38 | | GROUND_INST: instantiating (33) with all_33_0, all_71_2, xs, simplifying
% 26.38/4.38 | | with (37), (180) gives:
% 26.38/4.38 | | (182) all_71_2 = all_33_0
% 26.38/4.38 | |
% 26.38/4.38 | | BETA: splitting (181) gives:
% 26.38/4.38 | |
% 26.38/4.38 | | Case 1:
% 26.38/4.38 | | |
% 26.38/4.38 | | | (183) all_71_2 = sz00
% 26.38/4.38 | | |
% 26.38/4.38 | | | COMBINE_EQS: (182), (183) imply:
% 26.38/4.38 | | | (184) all_33_0 = sz00
% 26.38/4.38 | | |
% 26.38/4.38 | | | REDUCE: (96), (184) imply:
% 26.38/4.38 | | | (185) $false
% 26.38/4.38 | | |
% 26.38/4.38 | | | CLOSE: (185) is inconsistent.
% 26.38/4.38 | | |
% 26.38/4.38 | | Case 2:
% 26.38/4.38 | | |
% 26.38/4.38 | | | (186) ~ (all_71_2 = all_71_3) & aDimensionOf0(xt) = all_71_3 &
% 26.38/4.38 | | | $i(all_71_3)
% 26.38/4.38 | | |
% 26.38/4.38 | | | ALPHA: (186) implies:
% 26.38/4.38 | | | (187) ~ (all_71_2 = all_71_3)
% 26.38/4.38 | | | (188) aDimensionOf0(xt) = all_71_3
% 26.38/4.38 | | |
% 26.38/4.38 | | | REDUCE: (182), (187) imply:
% 26.38/4.38 | | | (189) ~ (all_71_3 = all_33_0)
% 26.38/4.38 | | |
% 26.38/4.38 | | | SIMP: (189) implies:
% 26.38/4.38 | | | (190) ~ (all_71_3 = all_33_0)
% 26.38/4.38 | | |
% 26.38/4.38 | | | GROUND_INST: instantiating (33) with all_33_0, all_71_3, xt, simplifying
% 26.38/4.38 | | | with (38), (188) gives:
% 26.38/4.38 | | | (191) all_71_3 = all_33_0
% 26.38/4.38 | | |
% 26.38/4.38 | | | REDUCE: (190), (191) imply:
% 26.38/4.38 | | | (192) $false
% 26.38/4.38 | | |
% 26.38/4.38 | | | CLOSE: (192) is inconsistent.
% 26.38/4.38 | | |
% 26.38/4.38 | | End of split
% 26.38/4.38 | |
% 26.38/4.38 | End of split
% 26.38/4.38 |
% 26.38/4.38 End of proof
% 26.38/4.38 % SZS output end Proof for theBenchmark
% 26.38/4.38
% 26.38/4.38 3803ms
%------------------------------------------------------------------------------