TSTP Solution File: SWV042+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV042+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n004.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 22:54:41 EDT 2023

% Result   : Theorem 17.51s 3.06s
% Output   : Proof 30.23s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWV042+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue Aug 29 07:18:37 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.72/1.40  Prover 4: Preprocessing ...
% 5.24/1.41  Prover 1: Preprocessing ...
% 5.24/1.44  Prover 5: Preprocessing ...
% 5.24/1.44  Prover 3: Preprocessing ...
% 5.24/1.44  Prover 0: Preprocessing ...
% 5.24/1.44  Prover 6: Preprocessing ...
% 5.24/1.44  Prover 2: Preprocessing ...
% 10.52/2.13  Prover 1: Warning: ignoring some quantifiers
% 11.14/2.23  Prover 1: Constructing countermodel ...
% 11.14/2.25  Prover 3: Warning: ignoring some quantifiers
% 11.14/2.28  Prover 3: Constructing countermodel ...
% 11.82/2.28  Prover 4: Warning: ignoring some quantifiers
% 11.94/2.30  Prover 6: Proving ...
% 12.04/2.40  Prover 4: Constructing countermodel ...
% 12.04/2.46  Prover 0: Proving ...
% 13.09/2.54  Prover 2: Proving ...
% 13.09/2.55  Prover 5: Proving ...
% 17.51/3.06  Prover 3: proved (2404ms)
% 17.51/3.06  
% 17.51/3.06  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.51/3.06  
% 17.51/3.06  Prover 0: stopped
% 17.51/3.07  Prover 2: stopped
% 17.51/3.07  Prover 5: stopped
% 17.51/3.08  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.51/3.08  Prover 6: stopped
% 17.51/3.09  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.51/3.09  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.51/3.09  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.51/3.09  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.94/3.25  Prover 7: Preprocessing ...
% 18.94/3.27  Prover 8: Preprocessing ...
% 18.94/3.31  Prover 13: Preprocessing ...
% 19.49/3.31  Prover 10: Preprocessing ...
% 19.49/3.32  Prover 11: Preprocessing ...
% 20.82/3.52  Prover 10: Warning: ignoring some quantifiers
% 21.29/3.58  Prover 10: Constructing countermodel ...
% 21.29/3.58  Prover 8: Warning: ignoring some quantifiers
% 21.29/3.58  Prover 7: Warning: ignoring some quantifiers
% 21.29/3.60  Prover 7: Constructing countermodel ...
% 21.29/3.61  Prover 8: Constructing countermodel ...
% 21.84/3.65  Prover 13: Warning: ignoring some quantifiers
% 21.84/3.67  Prover 13: Constructing countermodel ...
% 21.84/3.74  Prover 11: Warning: ignoring some quantifiers
% 22.86/3.78  Prover 11: Constructing countermodel ...
% 29.18/4.62  Prover 10: Found proof (size 196)
% 29.18/4.62  Prover 10: proved (1547ms)
% 29.18/4.62  Prover 11: stopped
% 29.18/4.62  Prover 7: stopped
% 29.18/4.62  Prover 8: stopped
% 29.18/4.62  Prover 4: stopped
% 29.18/4.62  Prover 13: stopped
% 29.18/4.63  Prover 1: stopped
% 29.18/4.63  
% 29.18/4.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.18/4.63  
% 29.67/4.64  % SZS output start Proof for theBenchmark
% 29.67/4.65  Assumptions after simplification:
% 29.67/4.65  ---------------------------------
% 29.67/4.65  
% 29.67/4.65    (finite_domain_1)
% 29.67/4.66    $i(n1) & $i(n0) &  ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0,
% 29.67/4.66        n1) |  ~ leq(n0, v0))
% 29.67/4.66  
% 29.67/4.66    (finite_domain_2)
% 29.67/4.66    $i(n2) & $i(n1) & $i(n0) &  ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~
% 29.67/4.66      $i(v0) |  ~ leq(v0, n2) |  ~ leq(n0, v0))
% 29.67/4.66  
% 29.67/4.66    (gauss_init_0081)
% 29.83/4.69    $i(pvar1402_init) & $i(pvar1401_init) & $i(pvar1400_init) & $i(loopcounter) &
% 29.83/4.69    $i(s_center7_init) & $i(s_values7_init) & $i(init) & $i(simplex7_init) &
% 29.83/4.69    $i(n3) & $i(n2) & $i(n1) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 29.83/4.69    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 29.83/4.69      $i] : (minus(v0, n1) = v1 & plus(n1, n2) = v0 & $i(v7) & $i(v6) & $i(v4) &
% 29.83/4.69      $i(v2) & $i(v1) & $i(v0) &  ! [v9: $i] :  ! [v10: $i] :  ! [v11: $i] : (v11
% 29.83/4.69        = init |  ~ (a_select3(simplex7_init, v10, v9) = v11) |  ~ $i(v10) |  ~
% 29.83/4.69        $i(v9) |  ~ leq(v10, n3) |  ~ leq(v9, n2) |  ~ leq(n0, v10) |  ~ leq(n0,
% 29.83/4.69          v9)) &  ! [v9: $i] :  ! [v10: $i] : (v10 = init |  ~
% 29.83/4.69        (a_select2(s_center7_init, v9) = v10) |  ~ $i(v9) |  ~ leq(v9, v1) |  ~
% 29.83/4.69        leq(n0, v9)) &  ! [v9: $i] :  ! [v10: $i] : (v10 = init |  ~
% 29.83/4.69        (a_select2(s_values7_init, v9) = v10) |  ~ $i(v9) |  ~ leq(v9, n3) |  ~
% 29.83/4.69        leq(n0, v9)) & ( ~ gt(loopcounter, n1) | (pvar1402_init = init &
% 29.83/4.69          pvar1401_init = init & pvar1400_init = init)) & (( ~ (v8 = init) &
% 29.83/4.69          a_select3(simplex7_init, v7, v6) = v8 & $i(v8) & leq(v7, n3) & leq(v6,
% 29.83/4.69            n2) & leq(n0, v7) & leq(n0, v6)) | ( ~ (v5 = init) &
% 29.83/4.69          a_select2(s_values7_init, v4) = v5 & $i(v5) & leq(v4, n3) & leq(n0, v4))
% 29.83/4.69        | ( ~ (v3 = init) & a_select2(s_center7_init, v2) = v3 & $i(v3) & leq(v2,
% 29.83/4.69            n2) & leq(n0, v2)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init)
% 29.83/4.69            |  ~ (pvar1401_init = init) |  ~ (pvar1400_init = init)))))
% 29.83/4.69  
% 29.83/4.69    (leq_gt2)
% 29.83/4.69     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v0, v1)
% 29.83/4.69      | gt(v1, v0))
% 29.83/4.69  
% 29.83/4.69    (leq_gt_pred)
% 29.83/4.69     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~ $i(v1) |  ~
% 29.83/4.69      $i(v0) |  ~ leq(v0, v2) | gt(v1, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 29.83/4.69      $i] : ( ~ (pred(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0,
% 29.83/4.69        v2))
% 29.83/4.69  
% 29.83/4.69    (pred_minus_1)
% 29.83/4.69    $i(n1) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (minus(v0, n1) = v1) |  ~ $i(v0) |
% 29.83/4.69      (pred(v0) = v1 & $i(v1)))
% 29.83/4.69  
% 29.83/4.69    (pred_succ)
% 29.83/4.69     ! [v0: $i] :  ! [v1: $i] : ( ~ (succ(v0) = v1) |  ~ $i(v0) | pred(v1) = v0)
% 29.83/4.69  
% 29.83/4.69    (succ_plus_1_l)
% 29.83/4.69    $i(n1) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (plus(n1, v0) = v1) |  ~ $i(v0) |
% 29.83/4.69      (succ(v0) = v1 & $i(v1)))
% 29.83/4.69  
% 29.83/4.69    (successor_1)
% 29.83/4.69    succ(n0) = n1 & $i(n1) & $i(n0)
% 29.83/4.69  
% 29.83/4.69    (successor_2)
% 29.83/4.69    $i(n2) & $i(n0) &  ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 29.83/4.69  
% 29.83/4.69    (successor_3)
% 29.83/4.70    $i(n3) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 29.83/4.70      succ(n0) = v0 & $i(v1) & $i(v0))
% 29.83/4.70  
% 29.83/4.70    (successor_4)
% 29.83/4.70    $i(n4) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (succ(v2) = n4 &
% 29.83/4.70      succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 29.83/4.70  
% 29.83/4.70    (successor_5)
% 29.83/4.70    $i(n5) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :
% 29.83/4.70    (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 29.83/4.70      & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 29.83/4.70  
% 29.83/4.70    (function-axioms)
% 29.83/4.70     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 29.83/4.70      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 29.83/4.70      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 29.83/4.70      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 29.83/4.70        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 29.83/4.70    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 29.83/4.70      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 29.83/4.70    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 29.83/4.70      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 29.83/4.70    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 29.83/4.70        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 29.83/4.70    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 29.83/4.70          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 29.83/4.70      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 29.83/4.70    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 29.83/4.70      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 29.83/4.70    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 29.83/4.70        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 29.83/4.70      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 29.83/4.70    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 29.83/4.70      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 29.83/4.70    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 29.83/4.70          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 29.83/4.70      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 29.83/4.70      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 29.83/4.70      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 29.83/4.70    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~
% 29.83/4.70      (inv(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 29.83/4.70      (trans(v2) = v1) |  ~ (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 29.83/4.70    [v2: $i] : (v1 = v0 |  ~ (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :
% 29.83/4.70     ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) =
% 29.83/4.70        v0))
% 29.83/4.70  
% 29.83/4.70  Further assumptions not needed in the proof:
% 29.83/4.70  --------------------------------------------
% 29.83/4.70  const_array1_select, const_array2_select, defuse, finite_domain_0,
% 29.83/4.70  finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0,
% 29.83/4.70  gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 29.83/4.70  gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 29.83/4.70  gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 29.83/4.70  leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 29.83/4.70  leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 29.83/4.70  matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 29.83/4.70  matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2,
% 29.83/4.70  sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_r,
% 29.83/4.70  succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l,
% 29.83/4.70  succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1,
% 29.83/4.70  sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq,
% 29.83/4.70  ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 29.83/4.70  
% 29.83/4.70  Those formulas are unsatisfiable:
% 29.83/4.70  ---------------------------------
% 29.83/4.70  
% 29.83/4.70  Begin of proof
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (leq_gt_pred) implies:
% 29.83/4.71  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 29.83/4.71  |          $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (succ_plus_1_l) implies:
% 29.83/4.71  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (plus(n1, v0) = v1) |  ~ $i(v0) |
% 29.83/4.71  |          (succ(v0) = v1 & $i(v1)))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (pred_minus_1) implies:
% 29.83/4.71  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (minus(v0, n1) = v1) |  ~ $i(v0) |
% 29.83/4.71  |          (pred(v0) = v1 & $i(v1)))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (finite_domain_1) implies:
% 29.83/4.71  |   (4)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 29.83/4.71  |          leq(n0, v0))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (finite_domain_2) implies:
% 29.83/4.71  |   (5)   ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n2)
% 29.83/4.71  |          |  ~ leq(n0, v0))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (successor_4) implies:
% 29.83/4.71  |   (6)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 29.83/4.71  |          v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (successor_5) implies:
% 29.83/4.71  |   (7)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (succ(v3) = n5
% 29.83/4.71  |          & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 29.83/4.71  |          $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (successor_1) implies:
% 29.83/4.71  |   (8)  succ(n0) = n1
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (successor_2) implies:
% 29.83/4.71  |   (9)   ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (successor_3) implies:
% 29.83/4.71  |   (10)   ? [v0: $i] :  ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 29.83/4.71  |           = v0 & $i(v1) & $i(v0))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (gauss_init_0081) implies:
% 29.83/4.71  |   (11)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 29.83/4.71  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] : (minus(v0, n1)
% 29.83/4.71  |           = v1 & plus(n1, n2) = v0 & $i(v7) & $i(v6) & $i(v4) & $i(v2) &
% 29.83/4.71  |           $i(v1) & $i(v0) &  ! [v9: $i] :  ! [v10: $i] :  ! [v11: $i] : (v11 =
% 29.83/4.71  |             init |  ~ (a_select3(simplex7_init, v10, v9) = v11) |  ~ $i(v10) |
% 29.83/4.71  |              ~ $i(v9) |  ~ leq(v10, n3) |  ~ leq(v9, n2) |  ~ leq(n0, v10) | 
% 29.83/4.71  |             ~ leq(n0, v9)) &  ! [v9: $i] :  ! [v10: $i] : (v10 = init |  ~
% 29.83/4.71  |             (a_select2(s_center7_init, v9) = v10) |  ~ $i(v9) |  ~ leq(v9, v1)
% 29.83/4.71  |             |  ~ leq(n0, v9)) &  ! [v9: $i] :  ! [v10: $i] : (v10 = init |  ~
% 29.83/4.71  |             (a_select2(s_values7_init, v9) = v10) |  ~ $i(v9) |  ~ leq(v9, n3)
% 29.83/4.71  |             |  ~ leq(n0, v9)) & ( ~ gt(loopcounter, n1) | (pvar1402_init =
% 29.83/4.71  |               init & pvar1401_init = init & pvar1400_init = init)) & (( ~ (v8
% 29.83/4.71  |                 = init) & a_select3(simplex7_init, v7, v6) = v8 & $i(v8) &
% 29.83/4.71  |               leq(v7, n3) & leq(v6, n2) & leq(n0, v7) & leq(n0, v6)) | ( ~ (v5
% 29.83/4.71  |                 = init) & a_select2(s_values7_init, v4) = v5 & $i(v5) &
% 29.83/4.71  |               leq(v4, n3) & leq(n0, v4)) | ( ~ (v3 = init) &
% 29.83/4.71  |               a_select2(s_center7_init, v2) = v3 & $i(v3) & leq(v2, n2) &
% 29.83/4.71  |               leq(n0, v2)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init = init)
% 29.83/4.71  |                 |  ~ (pvar1401_init = init) |  ~ (pvar1400_init = init)))))
% 29.83/4.71  | 
% 29.83/4.71  | ALPHA: (function-axioms) implies:
% 29.83/4.72  |   (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (pred(v2) =
% 29.83/4.72  |             v1) |  ~ (pred(v2) = v0))
% 29.83/4.72  |   (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (succ(v2) =
% 29.83/4.72  |             v1) |  ~ (succ(v2) = v0))
% 29.83/4.72  | 
% 29.83/4.72  | DELTA: instantiating (9) with fresh symbol all_54_0 gives:
% 29.83/4.72  |   (14)  succ(all_54_0) = n2 & succ(n0) = all_54_0 & $i(all_54_0)
% 29.83/4.72  | 
% 29.83/4.72  | ALPHA: (14) implies:
% 29.83/4.72  |   (15)  $i(all_54_0)
% 29.83/4.72  |   (16)  succ(n0) = all_54_0
% 29.83/4.72  |   (17)  succ(all_54_0) = n2
% 29.83/4.72  | 
% 29.83/4.72  | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1 gives:
% 29.83/4.72  |   (18)  succ(all_56_0) = n3 & succ(all_56_1) = all_56_0 & succ(n0) = all_56_1
% 29.83/4.72  |         & $i(all_56_0) & $i(all_56_1)
% 29.83/4.72  | 
% 29.83/4.72  | ALPHA: (18) implies:
% 29.83/4.72  |   (19)  $i(all_56_0)
% 29.83/4.72  |   (20)  succ(n0) = all_56_1
% 29.83/4.72  |   (21)  succ(all_56_1) = all_56_0
% 29.83/4.72  |   (22)  succ(all_56_0) = n3
% 29.83/4.72  | 
% 29.83/4.72  | DELTA: instantiating (6) with fresh symbols all_59_0, all_59_1, all_59_2
% 29.83/4.72  |        gives:
% 29.83/4.72  |   (23)  succ(all_59_0) = n4 & succ(all_59_1) = all_59_0 & succ(all_59_2) =
% 29.83/4.72  |         all_59_1 & succ(n0) = all_59_2 & $i(all_59_0) & $i(all_59_1) &
% 29.83/4.72  |         $i(all_59_2)
% 29.83/4.72  | 
% 29.83/4.72  | ALPHA: (23) implies:
% 29.83/4.72  |   (24)  succ(n0) = all_59_2
% 29.83/4.72  |   (25)  succ(all_59_2) = all_59_1
% 29.83/4.72  |   (26)  succ(all_59_1) = all_59_0
% 29.83/4.72  | 
% 29.83/4.72  | DELTA: instantiating (7) with fresh symbols all_61_0, all_61_1, all_61_2,
% 29.83/4.72  |        all_61_3 gives:
% 29.83/4.72  |   (27)  succ(all_61_0) = n5 & succ(all_61_1) = all_61_0 & succ(all_61_2) =
% 29.83/4.72  |         all_61_1 & succ(all_61_3) = all_61_2 & succ(n0) = all_61_3 &
% 29.83/4.72  |         $i(all_61_0) & $i(all_61_1) & $i(all_61_2) & $i(all_61_3)
% 29.83/4.72  | 
% 29.83/4.72  | ALPHA: (27) implies:
% 29.83/4.72  |   (28)  succ(n0) = all_61_3
% 29.83/4.72  |   (29)  succ(all_61_3) = all_61_2
% 29.83/4.72  |   (30)  succ(all_61_2) = all_61_1
% 29.83/4.72  | 
% 29.83/4.72  | DELTA: instantiating (11) with fresh symbols all_69_0, all_69_1, all_69_2,
% 29.83/4.72  |        all_69_3, all_69_4, all_69_5, all_69_6, all_69_7, all_69_8 gives:
% 29.83/4.72  |   (31)  minus(all_69_8, n1) = all_69_7 & plus(n1, n2) = all_69_8 &
% 29.83/4.72  |         $i(all_69_1) & $i(all_69_2) & $i(all_69_4) & $i(all_69_6) &
% 29.83/4.72  |         $i(all_69_7) & $i(all_69_8) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 29.83/4.72  |         : (v2 = init |  ~ (a_select3(simplex7_init, v1, v0) = v2) |  ~ $i(v1)
% 29.83/4.72  |           |  ~ $i(v0) |  ~ leq(v1, n3) |  ~ leq(v0, n2) |  ~ leq(n0, v1) |  ~
% 29.83/4.72  |           leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 29.83/4.72  |           (a_select2(s_center7_init, v0) = v1) |  ~ $i(v0) |  ~ leq(v0,
% 29.83/4.72  |             all_69_7) |  ~ leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 =
% 29.83/4.72  |           init |  ~ (a_select2(s_values7_init, v0) = v1) |  ~ $i(v0) |  ~
% 29.83/4.72  |           leq(v0, n3) |  ~ leq(n0, v0)) & ( ~ gt(loopcounter, n1) |
% 29.83/4.72  |           (pvar1402_init = init & pvar1401_init = init & pvar1400_init =
% 29.83/4.72  |             init)) & (( ~ (all_69_0 = init) & a_select3(simplex7_init,
% 29.83/4.72  |               all_69_1, all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1,
% 29.83/4.72  |               n3) & leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2))
% 29.83/4.72  |           | ( ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) =
% 29.83/4.72  |             all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4)) |
% 29.83/4.72  |           ( ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) =
% 29.83/4.72  |             all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6)) |
% 29.83/4.72  |           (gt(loopcounter, n1) & ( ~ (pvar1402_init = init) |  ~
% 29.83/4.72  |               (pvar1401_init = init) |  ~ (pvar1400_init = init))))
% 29.83/4.72  | 
% 29.83/4.72  | ALPHA: (31) implies:
% 29.83/4.72  |   (32)  $i(all_69_6)
% 29.83/4.72  |   (33)  $i(all_69_4)
% 29.83/4.72  |   (34)  $i(all_69_2)
% 29.83/4.72  |   (35)  $i(all_69_1)
% 29.83/4.72  |   (36)  plus(n1, n2) = all_69_8
% 29.83/4.72  |   (37)  minus(all_69_8, n1) = all_69_7
% 29.83/4.72  |   (38)  ( ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1, all_69_2) =
% 29.83/4.72  |           all_69_0 & $i(all_69_0) & leq(all_69_1, n3) & leq(all_69_2, n2) &
% 29.83/4.72  |           leq(n0, all_69_1) & leq(n0, all_69_2)) | ( ~ (all_69_3 = init) &
% 29.83/4.72  |           a_select2(s_values7_init, all_69_4) = all_69_3 & $i(all_69_3) &
% 29.83/4.72  |           leq(all_69_4, n3) & leq(n0, all_69_4)) | ( ~ (all_69_5 = init) &
% 29.83/4.72  |           a_select2(s_center7_init, all_69_6) = all_69_5 & $i(all_69_5) &
% 29.83/4.72  |           leq(all_69_6, n2) & leq(n0, all_69_6)) | (gt(loopcounter, n1) & ( ~
% 29.83/4.72  |             (pvar1402_init = init) |  ~ (pvar1401_init = init) |  ~
% 29.83/4.72  |             (pvar1400_init = init)))
% 29.83/4.73  |   (39)   ~ gt(loopcounter, n1) | (pvar1402_init = init & pvar1401_init = init
% 29.83/4.73  |           & pvar1400_init = init)
% 29.83/4.73  |   (40)   ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(s_values7_init,
% 29.83/4.73  |               v0) = v1) |  ~ $i(v0) |  ~ leq(v0, n3) |  ~ leq(n0, v0))
% 29.83/4.73  |   (41)   ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(s_center7_init,
% 29.83/4.73  |               v0) = v1) |  ~ $i(v0) |  ~ leq(v0, all_69_7) |  ~ leq(n0, v0))
% 29.83/4.73  |   (42)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 29.83/4.73  |           (a_select3(simplex7_init, v1, v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 29.83/4.73  |           leq(v1, n3) |  ~ leq(v0, n2) |  ~ leq(n0, v1) |  ~ leq(n0, v0))
% 29.83/4.73  | 
% 29.83/4.73  | GROUND_INST: instantiating (13) with all_56_1, all_59_2, n0, simplifying with
% 29.83/4.73  |              (20), (24) gives:
% 29.83/4.73  |   (43)  all_59_2 = all_56_1
% 29.83/4.73  | 
% 29.83/4.73  | GROUND_INST: instantiating (13) with all_54_0, all_59_2, n0, simplifying with
% 29.83/4.73  |              (16), (24) gives:
% 29.83/4.73  |   (44)  all_59_2 = all_54_0
% 29.83/4.73  | 
% 29.83/4.73  | GROUND_INST: instantiating (13) with all_59_2, all_61_3, n0, simplifying with
% 29.83/4.73  |              (24), (28) gives:
% 29.83/4.73  |   (45)  all_61_3 = all_59_2
% 29.83/4.73  | 
% 29.83/4.73  | GROUND_INST: instantiating (13) with n1, all_61_3, n0, simplifying with (8),
% 29.83/4.73  |              (28) gives:
% 29.83/4.73  |   (46)  all_61_3 = n1
% 29.83/4.73  | 
% 29.83/4.73  | COMBINE_EQS: (45), (46) imply:
% 29.83/4.73  |   (47)  all_59_2 = n1
% 29.83/4.73  | 
% 29.83/4.73  | SIMP: (47) implies:
% 29.83/4.73  |   (48)  all_59_2 = n1
% 29.83/4.73  | 
% 29.83/4.73  | COMBINE_EQS: (43), (48) imply:
% 29.83/4.73  |   (49)  all_56_1 = n1
% 29.83/4.73  | 
% 29.83/4.73  | COMBINE_EQS: (43), (44) imply:
% 29.83/4.73  |   (50)  all_56_1 = all_54_0
% 29.83/4.73  | 
% 29.83/4.73  | COMBINE_EQS: (49), (50) imply:
% 29.83/4.73  |   (51)  all_54_0 = n1
% 29.83/4.73  | 
% 29.83/4.73  | REDUCE: (29), (46) imply:
% 30.11/4.73  |   (52)  succ(n1) = all_61_2
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (25), (48) imply:
% 30.11/4.73  |   (53)  succ(n1) = all_59_1
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (21), (49) imply:
% 30.11/4.73  |   (54)  succ(n1) = all_56_0
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (17), (51) imply:
% 30.11/4.73  |   (55)  succ(n1) = n2
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (15), (51) imply:
% 30.11/4.73  |   (56)  $i(n1)
% 30.11/4.73  | 
% 30.11/4.73  | GROUND_INST: instantiating (13) with all_56_0, all_59_1, n1, simplifying with
% 30.11/4.73  |              (53), (54) gives:
% 30.11/4.73  |   (57)  all_59_1 = all_56_0
% 30.11/4.73  | 
% 30.11/4.73  | GROUND_INST: instantiating (13) with all_59_1, all_61_2, n1, simplifying with
% 30.11/4.73  |              (52), (53) gives:
% 30.11/4.73  |   (58)  all_61_2 = all_59_1
% 30.11/4.73  | 
% 30.11/4.73  | GROUND_INST: instantiating (13) with n2, all_61_2, n1, simplifying with (52),
% 30.11/4.73  |              (55) gives:
% 30.11/4.73  |   (59)  all_61_2 = n2
% 30.11/4.73  | 
% 30.11/4.73  | COMBINE_EQS: (58), (59) imply:
% 30.11/4.73  |   (60)  all_59_1 = n2
% 30.11/4.73  | 
% 30.11/4.73  | SIMP: (60) implies:
% 30.11/4.73  |   (61)  all_59_1 = n2
% 30.11/4.73  | 
% 30.11/4.73  | COMBINE_EQS: (57), (61) imply:
% 30.11/4.73  |   (62)  all_56_0 = n2
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (30), (59) imply:
% 30.11/4.73  |   (63)  succ(n2) = all_61_1
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (26), (61) imply:
% 30.11/4.73  |   (64)  succ(n2) = all_59_0
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (22), (62) imply:
% 30.11/4.73  |   (65)  succ(n2) = n3
% 30.11/4.73  | 
% 30.11/4.73  | REDUCE: (19), (62) imply:
% 30.11/4.73  |   (66)  $i(n2)
% 30.11/4.73  | 
% 30.11/4.73  | GROUND_INST: instantiating (13) with all_59_0, all_61_1, n2, simplifying with
% 30.11/4.73  |              (63), (64) gives:
% 30.11/4.73  |   (67)  all_61_1 = all_59_0
% 30.11/4.73  | 
% 30.11/4.73  | GROUND_INST: instantiating (13) with n3, all_61_1, n2, simplifying with (63),
% 30.11/4.73  |              (65) gives:
% 30.11/4.73  |   (68)  all_61_1 = n3
% 30.11/4.73  | 
% 30.11/4.73  | COMBINE_EQS: (67), (68) imply:
% 30.11/4.73  |   (69)  all_59_0 = n3
% 30.11/4.73  | 
% 30.11/4.73  | SIMP: (69) implies:
% 30.11/4.73  |   (70)  all_59_0 = n3
% 30.11/4.73  | 
% 30.11/4.73  | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (55),
% 30.11/4.73  |              (56) gives:
% 30.11/4.73  |   (71)  pred(n2) = n1
% 30.11/4.73  | 
% 30.11/4.73  | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (65),
% 30.11/4.73  |              (66) gives:
% 30.11/4.74  |   (72)  pred(n3) = n2
% 30.11/4.74  | 
% 30.11/4.74  | GROUND_INST: instantiating (2) with n2, all_69_8, simplifying with (36), (66)
% 30.11/4.74  |              gives:
% 30.11/4.74  |   (73)  succ(n2) = all_69_8 & $i(all_69_8)
% 30.11/4.74  | 
% 30.11/4.74  | ALPHA: (73) implies:
% 30.11/4.74  |   (74)  $i(all_69_8)
% 30.11/4.74  |   (75)  succ(n2) = all_69_8
% 30.11/4.74  | 
% 30.11/4.74  | GROUND_INST: instantiating (3) with all_69_8, all_69_7, simplifying with (37),
% 30.11/4.74  |              (74) gives:
% 30.11/4.74  |   (76)  pred(all_69_8) = all_69_7 & $i(all_69_7)
% 30.11/4.74  | 
% 30.11/4.74  | ALPHA: (76) implies:
% 30.11/4.74  |   (77)  $i(all_69_7)
% 30.11/4.74  |   (78)  pred(all_69_8) = all_69_7
% 30.11/4.74  | 
% 30.11/4.74  | GROUND_INST: instantiating (13) with n3, all_69_8, n2, simplifying with (65),
% 30.11/4.74  |              (75) gives:
% 30.11/4.74  |   (79)  all_69_8 = n3
% 30.11/4.74  | 
% 30.11/4.74  | REDUCE: (78), (79) imply:
% 30.11/4.74  |   (80)  pred(n3) = all_69_7
% 30.11/4.74  | 
% 30.11/4.74  | GROUND_INST: instantiating (12) with n2, all_69_7, n3, simplifying with (72),
% 30.11/4.74  |              (80) gives:
% 30.11/4.74  |   (81)  all_69_7 = n2
% 30.11/4.74  | 
% 30.11/4.74  | BETA: splitting (39) gives:
% 30.11/4.74  | 
% 30.11/4.74  | Case 1:
% 30.11/4.74  | | 
% 30.11/4.74  | |   (82)   ~ gt(loopcounter, n1)
% 30.11/4.74  | | 
% 30.11/4.74  | | BETA: splitting (38) gives:
% 30.11/4.74  | | 
% 30.11/4.74  | | Case 1:
% 30.11/4.74  | | | 
% 30.11/4.74  | | |   (83)  ( ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1,
% 30.11/4.74  | | |             all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) &
% 30.11/4.74  | | |           leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2)) | ( ~
% 30.11/4.74  | | |           (all_69_3 = init) & a_select2(s_values7_init, all_69_4) =
% 30.11/4.74  | | |           all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4))
% 30.11/4.74  | | | 
% 30.11/4.74  | | | BETA: splitting (83) gives:
% 30.11/4.74  | | | 
% 30.11/4.74  | | | Case 1:
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | |   (84)   ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1,
% 30.11/4.74  | | | |           all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) &
% 30.11/4.74  | | | |         leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2)
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | ALPHA: (84) implies:
% 30.11/4.74  | | | |   (85)   ~ (all_69_0 = init)
% 30.11/4.74  | | | |   (86)  leq(n0, all_69_2)
% 30.11/4.74  | | | |   (87)  leq(n0, all_69_1)
% 30.11/4.74  | | | |   (88)  leq(all_69_2, n2)
% 30.11/4.74  | | | |   (89)  leq(all_69_1, n3)
% 30.11/4.74  | | | |   (90)  a_select3(simplex7_init, all_69_1, all_69_2) = all_69_0
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | GROUND_INST: instantiating (42) with all_69_2, all_69_1, all_69_0,
% 30.11/4.74  | | | |              simplifying with (34), (35), (86), (87), (88), (89), (90)
% 30.11/4.74  | | | |              gives:
% 30.11/4.74  | | | |   (91)  all_69_0 = init
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | REDUCE: (85), (91) imply:
% 30.11/4.74  | | | |   (92)  $false
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | CLOSE: (92) is inconsistent.
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | Case 2:
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | |   (93)   ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) =
% 30.11/4.74  | | | |         all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4)
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | ALPHA: (93) implies:
% 30.11/4.74  | | | |   (94)   ~ (all_69_3 = init)
% 30.11/4.74  | | | |   (95)  leq(n0, all_69_4)
% 30.11/4.74  | | | |   (96)  leq(all_69_4, n3)
% 30.11/4.74  | | | |   (97)  a_select2(s_values7_init, all_69_4) = all_69_3
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | GROUND_INST: instantiating (40) with all_69_4, all_69_3, simplifying
% 30.11/4.74  | | | |              with (33), (95), (96), (97) gives:
% 30.11/4.74  | | | |   (98)  all_69_3 = init
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | REDUCE: (94), (98) imply:
% 30.11/4.74  | | | |   (99)  $false
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | | CLOSE: (99) is inconsistent.
% 30.11/4.74  | | | | 
% 30.11/4.74  | | | End of split
% 30.11/4.74  | | | 
% 30.11/4.74  | | Case 2:
% 30.11/4.74  | | | 
% 30.11/4.74  | | |   (100)  ( ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) =
% 30.11/4.74  | | |            all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0,
% 30.11/4.74  | | |              all_69_6)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 30.11/4.74  | | |                init) |  ~ (pvar1401_init = init) |  ~ (pvar1400_init =
% 30.11/4.75  | | |                init)))
% 30.11/4.75  | | | 
% 30.11/4.75  | | | BETA: splitting (100) gives:
% 30.11/4.75  | | | 
% 30.11/4.75  | | | Case 1:
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | |   (101)   ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) =
% 30.11/4.75  | | | |          all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6)
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | REF_CLOSE: (1), (4), (5), (32), (41), (66), (71), (81), (101), (leq_gt2)
% 30.11/4.75  | | | |            are inconsistent by sub-proof #1.
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | Case 2:
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | |   (102)  gt(loopcounter, n1) & ( ~ (pvar1402_init = init) |  ~
% 30.11/4.75  | | | |            (pvar1401_init = init) |  ~ (pvar1400_init = init))
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | ALPHA: (102) implies:
% 30.11/4.75  | | | |   (103)  gt(loopcounter, n1)
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | PRED_UNIFY: (82), (103) imply:
% 30.11/4.75  | | | |   (104)  $false
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | CLOSE: (104) is inconsistent.
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | End of split
% 30.11/4.75  | | | 
% 30.11/4.75  | | End of split
% 30.11/4.75  | | 
% 30.11/4.75  | Case 2:
% 30.11/4.75  | | 
% 30.11/4.75  | |   (105)  pvar1402_init = init & pvar1401_init = init & pvar1400_init = init
% 30.11/4.75  | | 
% 30.11/4.75  | | ALPHA: (105) implies:
% 30.11/4.75  | |   (106)  pvar1400_init = init
% 30.11/4.75  | |   (107)  pvar1401_init = init
% 30.11/4.75  | |   (108)  pvar1402_init = init
% 30.11/4.75  | | 
% 30.11/4.75  | | BETA: splitting (38) gives:
% 30.11/4.75  | | 
% 30.11/4.75  | | Case 1:
% 30.11/4.75  | | | 
% 30.11/4.75  | | |   (109)  ( ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1,
% 30.11/4.75  | | |              all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) &
% 30.11/4.75  | | |            leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2)) | (
% 30.11/4.75  | | |            ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) =
% 30.11/4.75  | | |            all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0,
% 30.11/4.75  | | |              all_69_4))
% 30.11/4.75  | | | 
% 30.11/4.75  | | | BETA: splitting (109) gives:
% 30.11/4.75  | | | 
% 30.11/4.75  | | | Case 1:
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | |   (110)   ~ (all_69_0 = init) & a_select3(simplex7_init, all_69_1,
% 30.11/4.75  | | | |            all_69_2) = all_69_0 & $i(all_69_0) & leq(all_69_1, n3) &
% 30.11/4.75  | | | |          leq(all_69_2, n2) & leq(n0, all_69_1) & leq(n0, all_69_2)
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | ALPHA: (110) implies:
% 30.11/4.75  | | | |   (111)   ~ (all_69_0 = init)
% 30.11/4.75  | | | |   (112)  leq(n0, all_69_2)
% 30.11/4.75  | | | |   (113)  leq(n0, all_69_1)
% 30.11/4.75  | | | |   (114)  leq(all_69_2, n2)
% 30.11/4.75  | | | |   (115)  leq(all_69_1, n3)
% 30.11/4.75  | | | |   (116)  a_select3(simplex7_init, all_69_1, all_69_2) = all_69_0
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | GROUND_INST: instantiating (42) with all_69_2, all_69_1, all_69_0,
% 30.11/4.75  | | | |              simplifying with (34), (35), (112), (113), (114), (115),
% 30.11/4.75  | | | |              (116) gives:
% 30.11/4.75  | | | |   (117)  all_69_0 = init
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | REDUCE: (111), (117) imply:
% 30.11/4.75  | | | |   (118)  $false
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | CLOSE: (118) is inconsistent.
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | Case 2:
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | |   (119)   ~ (all_69_3 = init) & a_select2(s_values7_init, all_69_4) =
% 30.11/4.75  | | | |          all_69_3 & $i(all_69_3) & leq(all_69_4, n3) & leq(n0, all_69_4)
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | ALPHA: (119) implies:
% 30.11/4.75  | | | |   (120)   ~ (all_69_3 = init)
% 30.11/4.75  | | | |   (121)  leq(n0, all_69_4)
% 30.11/4.75  | | | |   (122)  leq(all_69_4, n3)
% 30.11/4.75  | | | |   (123)  a_select2(s_values7_init, all_69_4) = all_69_3
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | GROUND_INST: instantiating (40) with all_69_4, all_69_3, simplifying
% 30.11/4.75  | | | |              with (33), (121), (122), (123) gives:
% 30.11/4.75  | | | |   (124)  all_69_3 = init
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | REDUCE: (120), (124) imply:
% 30.11/4.75  | | | |   (125)  $false
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | | CLOSE: (125) is inconsistent.
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | End of split
% 30.11/4.75  | | | 
% 30.11/4.75  | | Case 2:
% 30.11/4.75  | | | 
% 30.11/4.75  | | |   (126)  ( ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) =
% 30.11/4.75  | | |            all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0,
% 30.11/4.75  | | |              all_69_6)) | (gt(loopcounter, n1) & ( ~ (pvar1402_init =
% 30.11/4.75  | | |                init) |  ~ (pvar1401_init = init) |  ~ (pvar1400_init =
% 30.11/4.75  | | |                init)))
% 30.11/4.75  | | | 
% 30.11/4.75  | | | BETA: splitting (126) gives:
% 30.11/4.75  | | | 
% 30.11/4.75  | | | Case 1:
% 30.11/4.75  | | | | 
% 30.11/4.75  | | | |   (127)   ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) =
% 30.11/4.75  | | | |          all_69_5 & $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6)
% 30.11/4.75  | | | | 
% 30.23/4.75  | | | | REF_CLOSE: (1), (4), (5), (32), (41), (66), (71), (81), (127), (leq_gt2)
% 30.23/4.75  | | | |            are inconsistent by sub-proof #1.
% 30.23/4.75  | | | | 
% 30.23/4.75  | | | Case 2:
% 30.23/4.75  | | | | 
% 30.23/4.75  | | | |   (128)  gt(loopcounter, n1) & ( ~ (pvar1402_init = init) |  ~
% 30.23/4.75  | | | |            (pvar1401_init = init) |  ~ (pvar1400_init = init))
% 30.23/4.75  | | | | 
% 30.23/4.75  | | | | ALPHA: (128) implies:
% 30.23/4.75  | | | |   (129)   ~ (pvar1402_init = init) |  ~ (pvar1401_init = init) |  ~
% 30.23/4.76  | | | |          (pvar1400_init = init)
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | BETA: splitting (129) gives:
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | Case 1:
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | |   (130)   ~ (pvar1402_init = init)
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | | REDUCE: (108), (130) imply:
% 30.23/4.76  | | | | |   (131)  $false
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | | CLOSE: (131) is inconsistent.
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | Case 2:
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | |   (132)   ~ (pvar1401_init = init) |  ~ (pvar1400_init = init)
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | | BETA: splitting (132) gives:
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | | Case 1:
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | |   (133)   ~ (pvar1401_init = init)
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | | REDUCE: (107), (133) imply:
% 30.23/4.76  | | | | | |   (134)  $false
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | | CLOSE: (134) is inconsistent.
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | Case 2:
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | |   (135)   ~ (pvar1400_init = init)
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | | REDUCE: (106), (135) imply:
% 30.23/4.76  | | | | | |   (136)  $false
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | | CLOSE: (136) is inconsistent.
% 30.23/4.76  | | | | | | 
% 30.23/4.76  | | | | | End of split
% 30.23/4.76  | | | | | 
% 30.23/4.76  | | | | End of split
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | End of split
% 30.23/4.76  | | | 
% 30.23/4.76  | | End of split
% 30.23/4.76  | | 
% 30.23/4.76  | End of split
% 30.23/4.76  | 
% 30.23/4.76  End of proof
% 30.23/4.76  
% 30.23/4.76  Sub-proof #1 shows that the following formulas are inconsistent:
% 30.23/4.76  ----------------------------------------------------------------
% 30.23/4.76    (1)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v0,
% 30.23/4.76             v1) | gt(v1, v0))
% 30.23/4.76    (2)  all_69_7 = n2
% 30.23/4.76    (3)   ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n2) |
% 30.23/4.76            ~ leq(n0, v0))
% 30.23/4.76    (4)   ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(s_center7_init,
% 30.23/4.76               v0) = v1) |  ~ $i(v0) |  ~ leq(v0, all_69_7) |  ~ leq(n0, v0))
% 30.23/4.76    (5)  pred(n2) = n1
% 30.23/4.76    (6)  $i(all_69_6)
% 30.23/4.76    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~ $i(v1)
% 30.23/4.76           |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 30.23/4.76    (8)  $i(n2)
% 30.23/4.76    (9)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 30.23/4.76           leq(n0, v0))
% 30.23/4.76    (10)   ~ (all_69_5 = init) & a_select2(s_center7_init, all_69_6) = all_69_5 &
% 30.23/4.76          $i(all_69_5) & leq(all_69_6, n2) & leq(n0, all_69_6)
% 30.23/4.76  
% 30.23/4.76  Begin of proof
% 30.23/4.76  | 
% 30.23/4.76  | ALPHA: (10) implies:
% 30.23/4.76  |   (11)   ~ (all_69_5 = init)
% 30.23/4.76  |   (12)  leq(n0, all_69_6)
% 30.23/4.76  |   (13)  leq(all_69_6, n2)
% 30.23/4.76  |   (14)  a_select2(s_center7_init, all_69_6) = all_69_5
% 30.23/4.76  | 
% 30.23/4.76  | GROUND_INST: instantiating (3) with all_69_6, simplifying with (6), (12), (13)
% 30.23/4.76  |              gives:
% 30.23/4.76  |   (15)  all_69_6 = n2 | all_69_6 = n1 | all_69_6 = n0
% 30.23/4.76  | 
% 30.23/4.76  | GROUND_INST: instantiating (1) with all_69_6, n2, simplifying with (6), (8),
% 30.23/4.76  |              (13) gives:
% 30.23/4.76  |   (16)  all_69_6 = n2 | gt(n2, all_69_6)
% 30.23/4.76  | 
% 30.23/4.76  | BETA: splitting (16) gives:
% 30.23/4.76  | 
% 30.23/4.76  | Case 1:
% 30.23/4.76  | | 
% 30.23/4.76  | |   (17)  gt(n2, all_69_6)
% 30.23/4.76  | | 
% 30.23/4.76  | | GROUND_INST: instantiating (7) with all_69_6, n2, n1, simplifying with (5),
% 30.23/4.76  | |              (6), (8), (17) gives:
% 30.23/4.76  | |   (18)  leq(all_69_6, n1)
% 30.23/4.76  | | 
% 30.23/4.76  | | GROUND_INST: instantiating (9) with all_69_6, simplifying with (6), (12),
% 30.23/4.76  | |              (18) gives:
% 30.23/4.76  | |   (19)  all_69_6 = n1 | all_69_6 = n0
% 30.23/4.76  | | 
% 30.23/4.76  | | BETA: splitting (15) gives:
% 30.23/4.76  | | 
% 30.23/4.76  | | Case 1:
% 30.23/4.76  | | | 
% 30.23/4.76  | | |   (20)  all_69_6 = n0
% 30.23/4.76  | | | 
% 30.23/4.76  | | | REDUCE: (14), (20) imply:
% 30.23/4.76  | | |   (21)  a_select2(s_center7_init, n0) = all_69_5
% 30.23/4.76  | | | 
% 30.23/4.76  | | | REDUCE: (6), (20) imply:
% 30.23/4.76  | | |   (22)  $i(n0)
% 30.23/4.76  | | | 
% 30.23/4.76  | | | REDUCE: (13), (20) imply:
% 30.23/4.76  | | |   (23)  leq(n0, n2)
% 30.23/4.76  | | | 
% 30.23/4.76  | | | REDUCE: (12), (20) imply:
% 30.23/4.76  | | |   (24)  leq(n0, n0)
% 30.23/4.76  | | | 
% 30.23/4.76  | | | GROUND_INST: instantiating (4) with n0, all_69_5, simplifying with (21),
% 30.23/4.76  | | |              (22), (24) gives:
% 30.23/4.76  | | |   (25)  all_69_5 = init |  ~ leq(n0, all_69_7)
% 30.23/4.76  | | | 
% 30.23/4.76  | | | BETA: splitting (25) gives:
% 30.23/4.76  | | | 
% 30.23/4.76  | | | Case 1:
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | |   (26)   ~ leq(n0, all_69_7)
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | REDUCE: (2), (26) imply:
% 30.23/4.76  | | | |   (27)   ~ leq(n0, n2)
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | PRED_UNIFY: (23), (27) imply:
% 30.23/4.76  | | | |   (28)  $false
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | CLOSE: (28) is inconsistent.
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | Case 2:
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | |   (29)  all_69_5 = init
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | REDUCE: (11), (29) imply:
% 30.23/4.76  | | | |   (30)  $false
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | CLOSE: (30) is inconsistent.
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | End of split
% 30.23/4.76  | | | 
% 30.23/4.76  | | Case 2:
% 30.23/4.76  | | | 
% 30.23/4.76  | | |   (31)   ~ (all_69_6 = n0)
% 30.23/4.76  | | | 
% 30.23/4.76  | | | BETA: splitting (19) gives:
% 30.23/4.76  | | | 
% 30.23/4.76  | | | Case 1:
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | |   (32)  all_69_6 = n0
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | REDUCE: (31), (32) imply:
% 30.23/4.76  | | | |   (33)  $false
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | CLOSE: (33) is inconsistent.
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | Case 2:
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | |   (34)  all_69_6 = n1
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | REDUCE: (14), (34) imply:
% 30.23/4.76  | | | |   (35)  a_select2(s_center7_init, n1) = all_69_5
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | REDUCE: (6), (34) imply:
% 30.23/4.76  | | | |   (36)  $i(n1)
% 30.23/4.76  | | | | 
% 30.23/4.76  | | | | REDUCE: (13), (34) imply:
% 30.23/4.76  | | | |   (37)  leq(n1, n2)
% 30.23/4.76  | | | | 
% 30.23/4.77  | | | | REDUCE: (12), (34) imply:
% 30.23/4.77  | | | |   (38)  leq(n0, n1)
% 30.23/4.77  | | | | 
% 30.23/4.77  | | | | GROUND_INST: instantiating (4) with n1, all_69_5, simplifying with (35),
% 30.23/4.77  | | | |              (36), (38) gives:
% 30.23/4.77  | | | |   (39)  all_69_5 = init |  ~ leq(n1, all_69_7)
% 30.23/4.77  | | | | 
% 30.23/4.77  | | | | BETA: splitting (39) gives:
% 30.23/4.77  | | | | 
% 30.23/4.77  | | | | Case 1:
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | |   (40)   ~ leq(n1, all_69_7)
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | | REDUCE: (2), (40) imply:
% 30.23/4.77  | | | | |   (41)   ~ leq(n1, n2)
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | | PRED_UNIFY: (37), (41) imply:
% 30.23/4.77  | | | | |   (42)  $false
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | | CLOSE: (42) is inconsistent.
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | Case 2:
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | |   (43)  all_69_5 = init
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | | REDUCE: (11), (43) imply:
% 30.23/4.77  | | | | |   (44)  $false
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | | CLOSE: (44) is inconsistent.
% 30.23/4.77  | | | | | 
% 30.23/4.77  | | | | End of split
% 30.23/4.77  | | | | 
% 30.23/4.77  | | | End of split
% 30.23/4.77  | | | 
% 30.23/4.77  | | End of split
% 30.23/4.77  | | 
% 30.23/4.77  | Case 2:
% 30.23/4.77  | | 
% 30.23/4.77  | |   (45)  all_69_6 = n2
% 30.23/4.77  | | 
% 30.23/4.77  | | REDUCE: (14), (45) imply:
% 30.23/4.77  | |   (46)  a_select2(s_center7_init, n2) = all_69_5
% 30.23/4.77  | | 
% 30.23/4.77  | | REDUCE: (13), (45) imply:
% 30.23/4.77  | |   (47)  leq(n2, n2)
% 30.23/4.77  | | 
% 30.23/4.77  | | REDUCE: (12), (45) imply:
% 30.23/4.77  | |   (48)  leq(n0, n2)
% 30.23/4.77  | | 
% 30.23/4.77  | | GROUND_INST: instantiating (4) with n2, all_69_5, simplifying with (8),
% 30.23/4.77  | |              (46), (48) gives:
% 30.23/4.77  | |   (49)  all_69_5 = init |  ~ leq(n2, all_69_7)
% 30.23/4.77  | | 
% 30.23/4.77  | | BETA: splitting (49) gives:
% 30.23/4.77  | | 
% 30.23/4.77  | | Case 1:
% 30.23/4.77  | | | 
% 30.23/4.77  | | |   (50)   ~ leq(n2, all_69_7)
% 30.23/4.77  | | | 
% 30.23/4.77  | | | REDUCE: (2), (50) imply:
% 30.23/4.77  | | |   (51)   ~ leq(n2, n2)
% 30.23/4.77  | | | 
% 30.23/4.77  | | | PRED_UNIFY: (47), (51) imply:
% 30.23/4.77  | | |   (52)  $false
% 30.23/4.77  | | | 
% 30.23/4.77  | | | CLOSE: (52) is inconsistent.
% 30.23/4.77  | | | 
% 30.23/4.77  | | Case 2:
% 30.23/4.77  | | | 
% 30.23/4.77  | | |   (53)  all_69_5 = init
% 30.23/4.77  | | | 
% 30.23/4.77  | | | REDUCE: (11), (53) imply:
% 30.23/4.77  | | |   (54)  $false
% 30.23/4.77  | | | 
% 30.23/4.77  | | | CLOSE: (54) is inconsistent.
% 30.23/4.77  | | | 
% 30.23/4.77  | | End of split
% 30.23/4.77  | | 
% 30.23/4.77  | End of split
% 30.23/4.77  | 
% 30.23/4.77  End of proof
% 30.23/4.77  % SZS output end Proof for theBenchmark
% 30.23/4.77  
% 30.23/4.77  4149ms
%------------------------------------------------------------------------------