TSTP Solution File: RNG060+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG060+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n017.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 13:57:36 EDT 2023
% Result : Theorem 12.12s 2.56s
% Output : Proof 21.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG060+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:12:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.20/1.22 Prover 4: Preprocessing ...
% 3.20/1.23 Prover 1: Preprocessing ...
% 3.80/1.27 Prover 5: Preprocessing ...
% 3.80/1.27 Prover 6: Preprocessing ...
% 3.80/1.27 Prover 3: Preprocessing ...
% 3.80/1.27 Prover 2: Preprocessing ...
% 3.80/1.27 Prover 0: Preprocessing ...
% 9.21/2.09 Prover 3: Constructing countermodel ...
% 9.21/2.09 Prover 1: Constructing countermodel ...
% 9.60/2.14 Prover 6: Proving ...
% 10.93/2.31 Prover 5: Constructing countermodel ...
% 12.12/2.48 Prover 4: Constructing countermodel ...
% 12.12/2.55 Prover 3: proved (1919ms)
% 12.12/2.55
% 12.12/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.12/2.56
% 12.12/2.56 Prover 5: stopped
% 12.12/2.57 Prover 6: stopped
% 12.12/2.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.12/2.57 Prover 2: Proving ...
% 12.12/2.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.12/2.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.12/2.58 Prover 2: stopped
% 12.12/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.16/2.64 Prover 0: Proving ...
% 13.16/2.65 Prover 0: stopped
% 13.16/2.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.70/2.67 Prover 10: Preprocessing ...
% 14.05/2.71 Prover 7: Preprocessing ...
% 14.05/2.72 Prover 8: Preprocessing ...
% 14.05/2.73 Prover 11: Preprocessing ...
% 14.32/2.78 Prover 13: Preprocessing ...
% 15.10/2.87 Prover 10: Constructing countermodel ...
% 15.48/2.92 Prover 8: Warning: ignoring some quantifiers
% 15.48/2.93 Prover 7: Constructing countermodel ...
% 15.48/2.94 Prover 8: Constructing countermodel ...
% 16.30/3.01 Prover 13: Constructing countermodel ...
% 17.41/3.18 Prover 11: Constructing countermodel ...
% 21.18/3.70 Prover 10: Found proof (size 79)
% 21.18/3.70 Prover 10: proved (1124ms)
% 21.18/3.70 Prover 13: stopped
% 21.18/3.70 Prover 11: stopped
% 21.64/3.70 Prover 4: stopped
% 21.64/3.70 Prover 8: stopped
% 21.64/3.70 Prover 7: stopped
% 21.64/3.70 Prover 1: Found proof (size 197)
% 21.64/3.70 Prover 1: proved (3079ms)
% 21.64/3.70
% 21.64/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.64/3.70
% 21.64/3.71 % SZS output start Proof for theBenchmark
% 21.64/3.72 Assumptions after simplification:
% 21.64/3.72 ---------------------------------
% 21.64/3.72
% 21.64/3.72 (mDefInit)
% 21.64/3.74 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0)
% 21.64/3.74 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2 =
% 21.64/3.74 sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlbdtrb0(v0,
% 21.64/3.74 v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~ $i(v4) | ~ $i(v1)
% 21.64/3.74 | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1, v4) = v5 & $i(v5))) & !
% 21.64/3.75 [v3: $i] : ! [v4: $i] : (v3 = v1 | ~ (aDimensionOf0(v3) = v4) | ~
% 21.64/3.75 $i(v3) | ~ aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 21.64/3.75 ? [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7 &
% 21.64/3.75 sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 21.64/3.75 aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4) = v5 &
% 21.64/3.75 $i(v5))))) & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~
% 21.64/3.75 $i(v1) | szszuzczcdt0(v3) = v2) & ! [v3: $i] : ( ~
% 21.64/3.75 (aDimensionOf0(v1) = v3) | ~ $i(v1) | aVector0(v1))))))
% 21.64/3.75
% 21.64/3.75 (mDistr)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 21.64/3.75 $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~
% 21.64/3.75 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 21.64/3.75 aScalar0(v2) | ~ aScalar0(v1) | ~ aScalar0(v0) | ? [v6: $i] : ? [v7: $i]
% 21.64/3.75 : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v7, v2) = v8 & sdtasdt0(v1, v2) = v9
% 21.64/3.75 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v4, v9) = v8 & sdtpldt0(v1, v2) = v6 &
% 21.64/3.75 sdtpldt0(v0, v1) = v7 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 21.64/3.75
% 21.64/3.75 (mDistr2)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 21.64/3.75 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : ! [v9: $i] : ! [v10: $i] :
% 21.64/3.75 ( ~ (sdtasdt0(v1, v3) = v8) | ~ (sdtasdt0(v1, v2) = v7) | ~ (sdtasdt0(v0,
% 21.64/3.75 v3) = v5) | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtpldt0(v7, v8) = v9) | ~
% 21.64/3.75 (sdtpldt0(v6, v9) = v10) | ~ (sdtpldt0(v4, v5) = v6) | ~ $i(v3) | ~
% 21.64/3.75 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aScalar0(v3) | ~ aScalar0(v2) | ~
% 21.64/3.75 aScalar0(v1) | ~ aScalar0(v0) | ? [v11: $i] : ? [v12: $i] :
% 21.64/3.75 (sdtasdt0(v11, v12) = v10 & sdtpldt0(v2, v3) = v12 & sdtpldt0(v0, v1) = v11
% 21.64/3.75 & $i(v12) & $i(v11) & $i(v10)))
% 21.64/3.75
% 21.64/3.75 (mNegSc)
% 21.64/3.75 ! [v0: $i] : ! [v1: $i] : ( ~ (smndt0(v0) = v1) | ~ $i(v0) | ~
% 21.64/3.75 aScalar0(v0) | aScalar0(v1))
% 21.64/3.75
% 21.64/3.75 (m__)
% 21.64/3.75 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 21.64/3.75 $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 21.64/3.75 ( ~ (v8 = v2) & smndt0(xN) = v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 &
% 21.64/3.75 sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) = v8 &
% 21.64/3.75 sdtpldt0(v4, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR, v0) = v1 &
% 21.64/3.75 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 21.64/3.75 $i(v0))
% 21.64/3.75
% 21.64/3.75 (m__1652)
% 21.91/3.76 $i(xs) & ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : !
% 21.91/3.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2, v2)
% 21.91/3.76 = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4) = v5) | ~
% 21.91/3.76 $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1) | ? [v6: $i] : ?
% 21.91/3.76 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((sdtasasdt0(v1, v2) = v8 &
% 21.91/3.76 sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8) & sdtlseqdt0(v9, v5)) |
% 21.91/3.76 (aDimensionOf0(v1) = v6 & $i(v6) & ( ~ iLess0(v6, v0) | ( ~ (v7 = v6) &
% 21.91/3.76 aDimensionOf0(v2) = v7 & $i(v7)))))))
% 21.91/3.76
% 21.91/3.76 (m__1678)
% 21.91/3.76 $i(xt) & $i(xs) & aVector0(xt) & aVector0(xs)
% 21.91/3.76
% 21.91/3.76 (m__1678_01)
% 21.91/3.76 $i(xt) & $i(xs) & ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) =
% 21.91/3.76 v0 & $i(v0))
% 21.91/3.76
% 21.91/3.76 (m__1692)
% 21.91/3.76 $i(xs) & $i(sz00) & ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 &
% 21.91/3.76 $i(v0))
% 21.91/3.76
% 21.91/3.76 (m__1726)
% 21.91/3.76 sziznziztdt0(xt) = xq & $i(xq) & $i(xt) & aVector0(xq)
% 21.91/3.76
% 21.91/3.76 (m__1746)
% 21.91/3.76 $i(xA) & $i(xs) & ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) =
% 21.91/3.76 v0 & $i(v0) & aScalar0(xA))
% 21.91/3.76
% 21.91/3.76 (m__1766)
% 21.91/3.76 $i(xB) & $i(xt) & ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) =
% 21.91/3.76 v0 & $i(v0) & aScalar0(xB))
% 21.91/3.76
% 21.91/3.76 (m__1892)
% 21.91/3.76 sdtasdt0(xC, xG) = xR & $i(xR) & $i(xG) & $i(xC) & aScalar0(xR)
% 21.91/3.76
% 21.91/3.76 (m__1930)
% 21.91/3.76 sdtasdt0(xF, xD) = xS & $i(xS) & $i(xF) & $i(xD) & aScalar0(xS)
% 21.91/3.76
% 21.91/3.76 (m__2144)
% 21.91/3.76 $i(xN) & $i(xS) & $i(xR) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 21.91/3.76 (smndt0(xN) = v1 & smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR)
% 21.91/3.76 = v1 & sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) &
% 21.91/3.76 $i(v0))
% 21.91/3.76
% 21.91/3.76 (function-axioms)
% 21.91/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.91/3.76 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 21.91/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 21.91/3.76 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 21.91/3.76 ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) =
% 21.91/3.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 21.91/3.76 ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 21.91/3.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sziznziztdt0(v2) = v1) | ~
% 21.91/3.76 (sziznziztdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 21.91/3.76 v0 | ~ (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0)) & ! [v0:
% 21.91/3.76 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~
% 21.91/3.76 (smndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.91/3.76 (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 21.91/3.76
% 21.91/3.76 Further assumptions not needed in the proof:
% 21.91/3.76 --------------------------------------------
% 21.91/3.77 mArith, mDefSPN, mDefSPZ, mDimNat, mElmSc, mEqInit, mIH, mIHOrd, mLEASm, mLEMon,
% 21.91/3.77 mLEMonM, mLERef, mLETot, mLETrn, mLess, mMDNeg, mMNeg, mMulSc, mNatExtr,
% 21.91/3.77 mNatSort, mPosMon, mSZeroSc, mScPr, mScSort, mScSqPos, mScZero, mSqPos, mSqrt,
% 21.91/3.77 mSuccEqu, mSuccNat, mSumSc, mVcSort, mZeroNat, m__1709, m__1783, m__1800,
% 21.91/3.77 m__1820, m__1837, m__1854, m__1873, m__1911, m__1949, m__1967, m__2004
% 21.91/3.77
% 21.91/3.77 Those formulas are unsatisfiable:
% 21.91/3.77 ---------------------------------
% 21.91/3.77
% 21.91/3.77 Begin of proof
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (mDefInit) implies:
% 21.91/3.77 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sziznziztdt0(v0) = v1) | ~ $i(v0) |
% 21.91/3.77 | ~ aVector0(v0) | ? [v2: $i] : (aDimensionOf0(v0) = v2 & $i(v2) & (v2
% 21.91/3.77 | = sz00 | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 21.91/3.77 | (sdtlbdtrb0(v0, v4) = v5) | ~ (aDimensionOf0(v1) = v3) | ~
% 21.91/3.77 | $i(v4) | ~ $i(v1) | ~ aNaturalNumber0(v4) | (sdtlbdtrb0(v1,
% 21.91/3.77 | v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] : (v3 =
% 21.91/3.77 | v1 | ~ (aDimensionOf0(v3) = v4) | ~ $i(v3) | ~
% 21.91/3.77 | aVector0(v3) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 21.91/3.77 | [v8: $i] : ($i(v6) & (( ~ (v8 = v7) & sdtlbdtrb0(v3, v6) = v7
% 21.91/3.77 | & sdtlbdtrb0(v0, v6) = v8 & $i(v8) & $i(v7) &
% 21.91/3.77 | aNaturalNumber0(v6)) | ( ~ (v5 = v2) & szszuzczcdt0(v4)
% 21.91/3.77 | = v5 & $i(v5))))) & ! [v3: $i] : ( ~
% 21.91/3.77 | (aDimensionOf0(v1) = v3) | ~ $i(v1) | szszuzczcdt0(v3) = v2)
% 21.91/3.77 | & ! [v3: $i] : ( ~ (aDimensionOf0(v1) = v3) | ~ $i(v1) |
% 21.91/3.77 | aVector0(v1))))))
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (m__1678) implies:
% 21.91/3.77 | (2) aVector0(xt)
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (m__1652) implies:
% 21.91/3.77 | (3) ? [v0: $i] : (aDimensionOf0(xs) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 21.91/3.77 | $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasasdt0(v2,
% 21.91/3.77 | v2) = v4) | ~ (sdtasasdt0(v1, v1) = v3) | ~ (sdtasdt0(v3, v4)
% 21.91/3.77 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ aVector0(v2) | ~ aVector0(v1)
% 21.91/3.77 | | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 21.91/3.77 | ((sdtasasdt0(v1, v2) = v8 & sdtasdt0(v8, v8) = v9 & $i(v9) & $i(v8)
% 21.91/3.77 | & sdtlseqdt0(v9, v5)) | (aDimensionOf0(v1) = v6 & $i(v6) & ( ~
% 21.91/3.77 | iLess0(v6, v0) | ( ~ (v7 = v6) & aDimensionOf0(v2) = v7 &
% 21.91/3.77 | $i(v7)))))))
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (m__1678_01) implies:
% 21.91/3.77 | (4) ? [v0: $i] : (aDimensionOf0(xt) = v0 & aDimensionOf0(xs) = v0 &
% 21.91/3.77 | $i(v0))
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (m__1692) implies:
% 21.91/3.77 | (5) ? [v0: $i] : ( ~ (v0 = sz00) & aDimensionOf0(xs) = v0 & $i(v0))
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (m__1726) implies:
% 21.91/3.77 | (6) sziznziztdt0(xt) = xq
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (m__1746) implies:
% 21.91/3.77 | (7) ? [v0: $i] : (sdtlbdtrb0(xs, v0) = xA & aDimensionOf0(xs) = v0 &
% 21.91/3.77 | $i(v0) & aScalar0(xA))
% 21.91/3.77 |
% 21.91/3.77 | ALPHA: (m__1766) implies:
% 21.91/3.78 | (8) $i(xt)
% 21.91/3.78 | (9) ? [v0: $i] : (sdtlbdtrb0(xt, v0) = xB & aDimensionOf0(xt) = v0 &
% 21.91/3.78 | $i(v0) & aScalar0(xB))
% 21.91/3.78 |
% 21.91/3.78 | ALPHA: (m__1892) implies:
% 21.91/3.78 | (10) aScalar0(xR)
% 21.91/3.78 |
% 21.91/3.78 | ALPHA: (m__1930) implies:
% 21.91/3.78 | (11) aScalar0(xS)
% 21.91/3.78 |
% 21.91/3.78 | ALPHA: (m__2144) implies:
% 21.91/3.78 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (smndt0(xN) = v1 &
% 21.91/3.78 | smndt0(xS) = v0 & sdtasdt0(v0, v0) = v2 & sdtasdt0(v0, xR) = v1 &
% 21.91/3.78 | sdtasdt0(xS, xS) = v2 & sdtasdt0(xR, v0) = v1 & $i(v2) & $i(v1) &
% 21.91/3.78 | $i(v0))
% 21.91/3.78 |
% 21.91/3.78 | ALPHA: (m__) implies:
% 21.91/3.78 | (13) $i(xR)
% 21.91/3.78 | (14) $i(xS)
% 21.91/3.78 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 21.91/3.78 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v2) &
% 21.91/3.78 | smndt0(xN) = v4 & smndt0(xS) = v0 & sdtasdt0(v1, v1) = v2 &
% 21.91/3.78 | sdtasdt0(xS, xS) = v6 & sdtasdt0(xR, xR) = v3 & sdtpldt0(v5, v7) =
% 21.91/3.78 | v8 & sdtpldt0(v4, v6) = v7 & sdtpldt0(v3, v4) = v5 & sdtpldt0(xR,
% 21.91/3.78 | v0) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 21.91/3.78 | $i(v2) & $i(v1) & $i(v0))
% 21.91/3.78 |
% 21.91/3.78 | ALPHA: (function-axioms) implies:
% 21.91/3.78 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) =
% 21.91/3.78 | v1) | ~ (smndt0(v2) = v0))
% 21.91/3.78 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.91/3.78 | (aDimensionOf0(v2) = v1) | ~ (aDimensionOf0(v2) = v0))
% 21.91/3.78 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.91/3.78 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 21.91/3.78 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.91/3.78 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 21.91/3.78 |
% 21.91/3.78 | DELTA: instantiating (4) with fresh symbol all_33_0 gives:
% 21.91/3.78 | (20) aDimensionOf0(xt) = all_33_0 & aDimensionOf0(xs) = all_33_0 &
% 21.91/3.78 | $i(all_33_0)
% 21.91/3.78 |
% 21.91/3.78 | ALPHA: (20) implies:
% 21.91/3.78 | (21) aDimensionOf0(xs) = all_33_0
% 21.91/3.78 | (22) aDimensionOf0(xt) = all_33_0
% 21.91/3.78 |
% 21.91/3.78 | DELTA: instantiating (5) with fresh symbol all_37_0 gives:
% 21.91/3.78 | (23) ~ (all_37_0 = sz00) & aDimensionOf0(xs) = all_37_0 & $i(all_37_0)
% 21.91/3.78 |
% 21.91/3.78 | ALPHA: (23) implies:
% 21.91/3.78 | (24) ~ (all_37_0 = sz00)
% 21.91/3.78 | (25) aDimensionOf0(xs) = all_37_0
% 21.91/3.78 |
% 21.91/3.78 | DELTA: instantiating (9) with fresh symbol all_39_0 gives:
% 21.91/3.78 | (26) sdtlbdtrb0(xt, all_39_0) = xB & aDimensionOf0(xt) = all_39_0 &
% 21.91/3.78 | $i(all_39_0) & aScalar0(xB)
% 21.91/3.79 |
% 21.91/3.79 | ALPHA: (26) implies:
% 21.91/3.79 | (27) aDimensionOf0(xt) = all_39_0
% 21.91/3.79 |
% 21.91/3.79 | DELTA: instantiating (7) with fresh symbol all_41_0 gives:
% 21.91/3.79 | (28) sdtlbdtrb0(xs, all_41_0) = xA & aDimensionOf0(xs) = all_41_0 &
% 21.91/3.79 | $i(all_41_0) & aScalar0(xA)
% 21.91/3.79 |
% 21.91/3.79 | ALPHA: (28) implies:
% 21.91/3.79 | (29) aDimensionOf0(xs) = all_41_0
% 21.91/3.79 |
% 21.91/3.79 | DELTA: instantiating (12) with fresh symbols all_45_0, all_45_1, all_45_2
% 21.91/3.79 | gives:
% 21.91/3.79 | (30) smndt0(xN) = all_45_1 & smndt0(xS) = all_45_2 & sdtasdt0(all_45_2,
% 21.91/3.79 | all_45_2) = all_45_0 & sdtasdt0(all_45_2, xR) = all_45_1 &
% 21.91/3.79 | sdtasdt0(xS, xS) = all_45_0 & sdtasdt0(xR, all_45_2) = all_45_1 &
% 21.91/3.79 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2)
% 21.91/3.79 |
% 21.91/3.79 | ALPHA: (30) implies:
% 21.91/3.79 | (31) sdtasdt0(xR, all_45_2) = all_45_1
% 21.91/3.79 | (32) sdtasdt0(xS, xS) = all_45_0
% 21.91/3.79 | (33) sdtasdt0(all_45_2, xR) = all_45_1
% 21.91/3.79 | (34) sdtasdt0(all_45_2, all_45_2) = all_45_0
% 21.91/3.79 | (35) smndt0(xS) = all_45_2
% 21.91/3.79 | (36) smndt0(xN) = all_45_1
% 21.91/3.79 |
% 21.91/3.79 | DELTA: instantiating (15) with fresh symbols all_47_0, all_47_1, all_47_2,
% 21.91/3.79 | all_47_3, all_47_4, all_47_5, all_47_6, all_47_7, all_47_8 gives:
% 21.91/3.79 | (37) ~ (all_47_0 = all_47_6) & smndt0(xN) = all_47_4 & smndt0(xS) =
% 21.91/3.79 | all_47_8 & sdtasdt0(all_47_7, all_47_7) = all_47_6 & sdtasdt0(xS, xS)
% 21.91/3.79 | = all_47_2 & sdtasdt0(xR, xR) = all_47_5 & sdtpldt0(all_47_3,
% 21.91/3.79 | all_47_1) = all_47_0 & sdtpldt0(all_47_4, all_47_2) = all_47_1 &
% 21.91/3.79 | sdtpldt0(all_47_5, all_47_4) = all_47_3 & sdtpldt0(xR, all_47_8) =
% 21.91/3.79 | all_47_7 & $i(all_47_0) & $i(all_47_1) & $i(all_47_2) & $i(all_47_3) &
% 21.91/3.79 | $i(all_47_4) & $i(all_47_5) & $i(all_47_6) & $i(all_47_7) &
% 21.91/3.79 | $i(all_47_8)
% 21.91/3.79 |
% 21.91/3.79 | ALPHA: (37) implies:
% 21.91/3.79 | (38) ~ (all_47_0 = all_47_6)
% 21.91/3.79 | (39) $i(all_47_8)
% 21.91/3.79 | (40) sdtpldt0(xR, all_47_8) = all_47_7
% 21.91/3.79 | (41) sdtpldt0(all_47_5, all_47_4) = all_47_3
% 21.91/3.79 | (42) sdtpldt0(all_47_4, all_47_2) = all_47_1
% 21.91/3.79 | (43) sdtpldt0(all_47_3, all_47_1) = all_47_0
% 21.91/3.79 | (44) sdtasdt0(xR, xR) = all_47_5
% 21.91/3.79 | (45) sdtasdt0(xS, xS) = all_47_2
% 21.91/3.79 | (46) sdtasdt0(all_47_7, all_47_7) = all_47_6
% 21.91/3.79 | (47) smndt0(xS) = all_47_8
% 21.91/3.79 | (48) smndt0(xN) = all_47_4
% 21.91/3.79 |
% 21.91/3.79 | DELTA: instantiating (3) with fresh symbol all_49_0 gives:
% 21.91/3.79 | (49) aDimensionOf0(xs) = all_49_0 & $i(all_49_0) & ! [v0: $i] : ! [v1:
% 21.91/3.79 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasasdt0(v1,
% 21.91/3.79 | v1) = v3) | ~ (sdtasasdt0(v0, v0) = v2) | ~ (sdtasdt0(v2, v3)
% 21.91/3.79 | = v4) | ~ $i(v1) | ~ $i(v0) | ~ aVector0(v1) | ~ aVector0(v0)
% 21.91/3.79 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 21.91/3.79 | ((sdtasasdt0(v0, v1) = v7 & sdtasdt0(v7, v7) = v8 & $i(v8) & $i(v7)
% 21.91/3.79 | & sdtlseqdt0(v8, v4)) | (aDimensionOf0(v0) = v5 & $i(v5) & ( ~
% 21.91/3.79 | iLess0(v5, all_49_0) | ( ~ (v6 = v5) & aDimensionOf0(v1) = v6
% 21.91/3.79 | & $i(v6))))))
% 21.91/3.79 |
% 21.91/3.79 | ALPHA: (49) implies:
% 21.91/3.79 | (50) aDimensionOf0(xs) = all_49_0
% 21.91/3.79 |
% 21.91/3.80 | GROUND_INST: instantiating (19) with all_45_0, all_47_2, xS, xS, simplifying
% 21.91/3.80 | with (32), (45) gives:
% 21.91/3.80 | (51) all_47_2 = all_45_0
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (16) with all_45_2, all_47_8, xS, simplifying with
% 21.91/3.80 | (35), (47) gives:
% 21.91/3.80 | (52) all_47_8 = all_45_2
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (16) with all_45_1, all_47_4, xN, simplifying with
% 21.91/3.80 | (36), (48) gives:
% 21.91/3.80 | (53) all_47_4 = all_45_1
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (17) with all_41_0, all_49_0, xs, simplifying with
% 21.91/3.80 | (29), (50) gives:
% 21.91/3.80 | (54) all_49_0 = all_41_0
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (17) with all_37_0, all_49_0, xs, simplifying with
% 21.91/3.80 | (25), (50) gives:
% 21.91/3.80 | (55) all_49_0 = all_37_0
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (17) with all_33_0, all_49_0, xs, simplifying with
% 21.91/3.80 | (21), (50) gives:
% 21.91/3.80 | (56) all_49_0 = all_33_0
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (17) with all_33_0, all_39_0, xt, simplifying with
% 21.91/3.80 | (22), (27) gives:
% 21.91/3.80 | (57) all_39_0 = all_33_0
% 21.91/3.80 |
% 21.91/3.80 | COMBINE_EQS: (54), (56) imply:
% 21.91/3.80 | (58) all_41_0 = all_33_0
% 21.91/3.80 |
% 21.91/3.80 | COMBINE_EQS: (54), (55) imply:
% 21.91/3.80 | (59) all_41_0 = all_37_0
% 21.91/3.80 |
% 21.91/3.80 | COMBINE_EQS: (58), (59) imply:
% 21.91/3.80 | (60) all_37_0 = all_33_0
% 21.91/3.80 |
% 21.91/3.80 | REDUCE: (24), (60) imply:
% 21.91/3.80 | (61) ~ (all_33_0 = sz00)
% 21.91/3.80 |
% 21.91/3.80 | REDUCE: (42), (51), (53) imply:
% 21.91/3.80 | (62) sdtpldt0(all_45_1, all_45_0) = all_47_1
% 21.91/3.80 |
% 21.91/3.80 | REDUCE: (41), (53) imply:
% 21.91/3.80 | (63) sdtpldt0(all_47_5, all_45_1) = all_47_3
% 21.91/3.80 |
% 21.91/3.80 | REDUCE: (40), (52) imply:
% 21.91/3.80 | (64) sdtpldt0(xR, all_45_2) = all_47_7
% 21.91/3.80 |
% 21.91/3.80 | REDUCE: (39), (52) imply:
% 21.91/3.80 | (65) $i(all_45_2)
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (mNegSc) with xS, all_45_2, simplifying with (11),
% 21.91/3.80 | (14), (35) gives:
% 21.91/3.80 | (66) aScalar0(all_45_2)
% 21.91/3.80 |
% 21.91/3.80 | GROUND_INST: instantiating (1) with xt, xq, simplifying with (2), (6), (8)
% 21.91/3.80 | gives:
% 21.91/3.80 | (67) ? [v0: $i] : (aDimensionOf0(xt) = v0 & $i(v0) & (v0 = sz00 | ( ! [v1:
% 21.91/3.80 | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlbdtrb0(xt, v2) =
% 21.91/3.80 | v3) | ~ (aDimensionOf0(xq) = v1) | ~ $i(v2) | ~ $i(xq) |
% 21.91/3.80 | ~ aNaturalNumber0(v2) | (sdtlbdtrb0(xq, v2) = v3 & $i(v3))) &
% 21.91/3.80 | ! [v1: $i] : ! [v2: $i] : (v1 = xq | ~ (aDimensionOf0(v1) =
% 21.91/3.80 | v2) | ~ $i(v1) | ~ aVector0(v1) | ? [v3: $i] : ? [v4:
% 21.91/3.80 | $i] : ? [v5: $i] : ? [v6: $i] : ($i(v4) & (( ~ (v6 = v5) &
% 21.91/3.80 | sdtlbdtrb0(v1, v4) = v5 & sdtlbdtrb0(xt, v4) = v6 &
% 21.91/3.80 | $i(v6) & $i(v5) & aNaturalNumber0(v4)) | ( ~ (v3 = v0) &
% 21.91/3.80 | szszuzczcdt0(v2) = v3 & $i(v3))))) & ! [v1: $i] : ( ~
% 21.91/3.80 | (aDimensionOf0(xq) = v1) | ~ $i(xq) | szszuzczcdt0(v1) = v0)
% 21.91/3.80 | & ! [v1: $i] : ( ~ (aDimensionOf0(xq) = v1) | ~ $i(xq) |
% 21.91/3.80 | aVector0(xq)))))
% 21.91/3.80 |
% 21.91/3.80 | DELTA: instantiating (67) with fresh symbol all_74_0 gives:
% 21.91/3.81 | (68) aDimensionOf0(xt) = all_74_0 & $i(all_74_0) & (all_74_0 = sz00 | ( !
% 21.91/3.81 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(xt, v1) =
% 21.91/3.81 | v2) | ~ (aDimensionOf0(xq) = v0) | ~ $i(v1) | ~ $i(xq) | ~
% 21.91/3.81 | aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1) = v2 & $i(v2))) & !
% 21.91/3.81 | [v0: $i] : ! [v1: $i] : (v0 = xq | ~ (aDimensionOf0(v0) = v1) |
% 21.91/3.81 | ~ $i(v0) | ~ aVector0(v0) | ? [v2: any] : ? [v3: $i] : ?
% 21.91/3.81 | [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~ (v5 = v4) &
% 21.91/3.81 | sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) = v5 & $i(v5)
% 21.91/3.81 | & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 = all_74_0) &
% 21.91/3.81 | szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0: $i] : ( ~
% 21.91/3.81 | (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0) =
% 21.91/3.81 | all_74_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~
% 21.91/3.81 | $i(xq) | aVector0(xq))))
% 21.91/3.81 |
% 21.91/3.81 | ALPHA: (68) implies:
% 21.91/3.81 | (69) aDimensionOf0(xt) = all_74_0
% 21.91/3.81 | (70) all_74_0 = sz00 | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 21.91/3.81 | (sdtlbdtrb0(xt, v1) = v2) | ~ (aDimensionOf0(xq) = v0) | ~
% 21.91/3.81 | $i(v1) | ~ $i(xq) | ~ aNaturalNumber0(v1) | (sdtlbdtrb0(xq, v1)
% 21.91/3.81 | = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v0 = xq | ~
% 21.91/3.81 | (aDimensionOf0(v0) = v1) | ~ $i(v0) | ~ aVector0(v0) | ? [v2:
% 21.91/3.81 | any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ($i(v3) & (( ~
% 21.91/3.81 | (v5 = v4) & sdtlbdtrb0(v0, v3) = v4 & sdtlbdtrb0(xt, v3) =
% 21.91/3.81 | v5 & $i(v5) & $i(v4) & aNaturalNumber0(v3)) | ( ~ (v2 =
% 21.91/3.81 | all_74_0) & szszuzczcdt0(v1) = v2 & $i(v2))))) & ! [v0:
% 21.91/3.81 | $i] : ( ~ (aDimensionOf0(xq) = v0) | ~ $i(xq) | szszuzczcdt0(v0)
% 21.91/3.81 | = all_74_0) & ! [v0: $i] : ( ~ (aDimensionOf0(xq) = v0) | ~
% 21.91/3.81 | $i(xq) | aVector0(xq)))
% 21.91/3.81 |
% 21.91/3.81 | GROUND_INST: instantiating (17) with all_33_0, all_74_0, xt, simplifying with
% 21.91/3.81 | (22), (69) gives:
% 21.91/3.81 | (71) all_74_0 = all_33_0
% 21.91/3.81 |
% 21.91/3.81 | BETA: splitting (70) gives:
% 21.91/3.81 |
% 21.91/3.81 | Case 1:
% 21.91/3.81 | |
% 21.91/3.81 | | (72) all_74_0 = sz00
% 21.91/3.81 | |
% 21.91/3.81 | | COMBINE_EQS: (71), (72) imply:
% 21.91/3.81 | | (73) all_33_0 = sz00
% 21.91/3.81 | |
% 21.91/3.81 | | REDUCE: (61), (73) imply:
% 21.91/3.81 | | (74) $false
% 21.91/3.81 | |
% 21.91/3.81 | | CLOSE: (74) is inconsistent.
% 21.91/3.81 | |
% 21.91/3.81 | Case 2:
% 21.91/3.81 | |
% 21.91/3.81 | |
% 21.91/3.81 | | GROUND_INST: instantiating (mDistr2) with xR, all_45_2, xR, all_45_2,
% 21.91/3.81 | | all_47_5, all_45_1, all_47_3, all_45_1, all_45_0, all_47_1,
% 21.91/3.81 | | all_47_0, simplifying with (10), (13), (31), (33), (34), (43),
% 21.91/3.81 | | (44), (62), (63), (65), (66) gives:
% 21.91/3.81 | | (75) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(v0, v1) = all_47_0 &
% 21.91/3.81 | | sdtpldt0(xR, all_45_2) = v1 & sdtpldt0(xR, all_45_2) = v0 & $i(v1)
% 21.91/3.81 | | & $i(v0) & $i(all_47_0))
% 21.91/3.81 | |
% 21.91/3.81 | | GROUND_INST: instantiating (mDistr) with all_45_2, xR, all_45_2, all_45_1,
% 21.91/3.81 | | all_45_0, all_47_1, simplifying with (10), (13), (33), (34),
% 21.91/3.81 | | (62), (65), (66) gives:
% 21.91/3.82 | | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 21.91/3.82 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(all_45_2, v0) = all_47_1 &
% 21.91/3.82 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_0, v3) = v2 &
% 21.91/3.82 | | sdtpldt0(all_45_2, xR) = v1 & sdtpldt0(xR, all_45_2) = v0 & $i(v3)
% 21.91/3.82 | | & $i(v2) & $i(v1) & $i(v0) & $i(all_47_1))
% 21.91/3.82 | |
% 21.91/3.82 | | GROUND_INST: instantiating (mDistr) with xR, xR, all_45_2, all_47_5,
% 21.91/3.82 | | all_45_1, all_47_3, simplifying with (10), (13), (31), (44),
% 21.91/3.82 | | (63), (65), (66) gives:
% 21.91/3.82 | | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 21.91/3.82 | | (sdtasdt0(v1, all_45_2) = v2 & sdtasdt0(xR, v0) = all_47_3 &
% 21.91/3.82 | | sdtasdt0(xR, all_45_2) = v3 & sdtpldt0(all_45_1, v3) = v2 &
% 21.91/3.82 | | sdtpldt0(xR, all_45_2) = v0 & sdtpldt0(xR, xR) = v1 & $i(v3) &
% 21.91/3.82 | | $i(v2) & $i(v1) & $i(v0) & $i(all_47_3))
% 21.91/3.82 | |
% 21.91/3.82 | | DELTA: instantiating (75) with fresh symbols all_116_0, all_116_1 gives:
% 21.91/3.82 | | (78) sdtasdt0(all_116_1, all_116_0) = all_47_0 & sdtpldt0(xR, all_45_2) =
% 21.91/3.82 | | all_116_0 & sdtpldt0(xR, all_45_2) = all_116_1 & $i(all_116_0) &
% 21.91/3.82 | | $i(all_116_1) & $i(all_47_0)
% 21.91/3.82 | |
% 21.91/3.82 | | ALPHA: (78) implies:
% 21.91/3.82 | | (79) sdtpldt0(xR, all_45_2) = all_116_1
% 21.91/3.82 | | (80) sdtpldt0(xR, all_45_2) = all_116_0
% 21.91/3.82 | | (81) sdtasdt0(all_116_1, all_116_0) = all_47_0
% 21.91/3.82 | |
% 21.91/3.82 | | DELTA: instantiating (77) with fresh symbols all_120_0, all_120_1,
% 21.91/3.82 | | all_120_2, all_120_3 gives:
% 21.91/3.82 | | (82) sdtasdt0(all_120_2, all_45_2) = all_120_1 & sdtasdt0(xR, all_120_3)
% 21.91/3.82 | | = all_47_3 & sdtasdt0(xR, all_45_2) = all_120_0 & sdtpldt0(all_45_1,
% 21.91/3.82 | | all_120_0) = all_120_1 & sdtpldt0(xR, all_45_2) = all_120_3 &
% 21.91/3.82 | | sdtpldt0(xR, xR) = all_120_2 & $i(all_120_0) & $i(all_120_1) &
% 21.91/3.82 | | $i(all_120_2) & $i(all_120_3) & $i(all_47_3)
% 21.91/3.82 | |
% 21.91/3.82 | | ALPHA: (82) implies:
% 21.91/3.82 | | (83) sdtpldt0(xR, all_45_2) = all_120_3
% 21.91/3.82 | |
% 21.91/3.82 | | DELTA: instantiating (76) with fresh symbols all_122_0, all_122_1,
% 21.91/3.82 | | all_122_2, all_122_3 gives:
% 21.91/3.82 | | (84) sdtasdt0(all_122_2, all_45_2) = all_122_1 & sdtasdt0(all_45_2,
% 21.91/3.82 | | all_122_3) = all_47_1 & sdtasdt0(xR, all_45_2) = all_122_0 &
% 21.91/3.82 | | sdtpldt0(all_45_0, all_122_0) = all_122_1 & sdtpldt0(all_45_2, xR) =
% 21.91/3.82 | | all_122_2 & sdtpldt0(xR, all_45_2) = all_122_3 & $i(all_122_0) &
% 21.91/3.82 | | $i(all_122_1) & $i(all_122_2) & $i(all_122_3) & $i(all_47_1)
% 21.91/3.82 | |
% 21.91/3.82 | | ALPHA: (84) implies:
% 21.91/3.82 | | (85) sdtpldt0(xR, all_45_2) = all_122_3
% 21.91/3.82 | |
% 21.91/3.82 | | GROUND_INST: instantiating (18) with all_116_1, all_120_3, all_45_2, xR,
% 21.91/3.82 | | simplifying with (79), (83) gives:
% 21.91/3.82 | | (86) all_120_3 = all_116_1
% 21.91/3.82 | |
% 21.91/3.82 | | GROUND_INST: instantiating (18) with all_47_7, all_122_3, all_45_2, xR,
% 21.91/3.82 | | simplifying with (64), (85) gives:
% 21.91/3.82 | | (87) all_122_3 = all_47_7
% 21.91/3.82 | |
% 21.91/3.82 | | GROUND_INST: instantiating (18) with all_120_3, all_122_3, all_45_2, xR,
% 21.91/3.82 | | simplifying with (83), (85) gives:
% 21.91/3.82 | | (88) all_122_3 = all_120_3
% 21.91/3.82 | |
% 21.91/3.82 | | GROUND_INST: instantiating (18) with all_116_0, all_122_3, all_45_2, xR,
% 21.91/3.82 | | simplifying with (80), (85) gives:
% 21.91/3.82 | | (89) all_122_3 = all_116_0
% 21.91/3.82 | |
% 21.91/3.82 | | COMBINE_EQS: (87), (89) imply:
% 21.91/3.82 | | (90) all_116_0 = all_47_7
% 21.91/3.82 | |
% 21.91/3.82 | | COMBINE_EQS: (88), (89) imply:
% 21.91/3.82 | | (91) all_120_3 = all_116_0
% 21.91/3.82 | |
% 21.91/3.82 | | SIMP: (91) implies:
% 21.91/3.82 | | (92) all_120_3 = all_116_0
% 21.91/3.82 | |
% 21.91/3.82 | | COMBINE_EQS: (86), (92) imply:
% 21.91/3.82 | | (93) all_116_0 = all_116_1
% 21.91/3.82 | |
% 21.91/3.82 | | SIMP: (93) implies:
% 21.91/3.82 | | (94) all_116_0 = all_116_1
% 21.91/3.82 | |
% 21.91/3.82 | | COMBINE_EQS: (90), (94) imply:
% 21.91/3.82 | | (95) all_116_1 = all_47_7
% 21.91/3.82 | |
% 21.91/3.82 | | SIMP: (95) implies:
% 21.91/3.82 | | (96) all_116_1 = all_47_7
% 21.91/3.82 | |
% 21.91/3.82 | | REDUCE: (81), (90), (96) imply:
% 21.91/3.82 | | (97) sdtasdt0(all_47_7, all_47_7) = all_47_0
% 21.91/3.82 | |
% 21.91/3.82 | | GROUND_INST: instantiating (19) with all_47_6, all_47_0, all_47_7, all_47_7,
% 21.91/3.82 | | simplifying with (46), (97) gives:
% 21.91/3.82 | | (98) all_47_0 = all_47_6
% 21.91/3.82 | |
% 21.91/3.82 | | REDUCE: (38), (98) imply:
% 21.91/3.82 | | (99) $false
% 21.91/3.82 | |
% 21.91/3.82 | | CLOSE: (99) is inconsistent.
% 21.91/3.82 | |
% 21.91/3.82 | End of split
% 21.91/3.82 |
% 21.91/3.82 End of proof
% 21.91/3.82 % SZS output end Proof for theBenchmark
% 21.91/3.82
% 21.91/3.82 3218ms
%------------------------------------------------------------------------------