TSTP Solution File: RNG067+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : RNG067+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 13:57:39 EDT 2023

% Result   : Theorem 18.21s 3.20s
% Output   : Proof 32.45s
% Verified : 
% SZS Type : -

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