TSTP Solution File: SWV186+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV186+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 : n009.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 22:55:16 EDT 2023

% Result   : Theorem 14.07s 2.64s
% Output   : Proof 17.26s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWV186+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n009.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Tue Aug 29 03:00:20 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.60/0.61  ________       _____
% 0.60/0.61  ___  __ \_________(_)________________________________
% 0.60/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.60/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.60/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.60/0.61  
% 0.60/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.61  (2023-06-19)
% 0.60/0.61  
% 0.60/0.61  (c) Philipp Rümmer, 2009-2023
% 0.60/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.61                Amanda Stjerna.
% 0.60/0.61  Free software under BSD-3-Clause.
% 0.60/0.61  
% 0.60/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.61  
% 0.60/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.62  Running up to 7 provers in parallel.
% 0.76/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.76/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.76/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.76/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.76/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.76/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.76/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.49/1.36  Prover 1: Preprocessing ...
% 4.49/1.36  Prover 4: Preprocessing ...
% 4.93/1.39  Prover 6: Preprocessing ...
% 4.93/1.39  Prover 3: Preprocessing ...
% 4.93/1.39  Prover 5: Preprocessing ...
% 4.93/1.39  Prover 2: Preprocessing ...
% 4.93/1.39  Prover 0: Preprocessing ...
% 11.17/2.25  Prover 1: Warning: ignoring some quantifiers
% 11.86/2.31  Prover 6: Proving ...
% 11.86/2.31  Prover 3: Warning: ignoring some quantifiers
% 11.86/2.32  Prover 1: Constructing countermodel ...
% 11.86/2.35  Prover 3: Constructing countermodel ...
% 11.86/2.35  Prover 4: Warning: ignoring some quantifiers
% 12.59/2.44  Prover 4: Constructing countermodel ...
% 12.59/2.45  Prover 5: Proving ...
% 13.21/2.49  Prover 2: Proving ...
% 13.21/2.51  Prover 0: Proving ...
% 14.07/2.63  Prover 3: proved (1992ms)
% 14.07/2.63  
% 14.07/2.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.07/2.64  
% 14.07/2.64  Prover 5: stopped
% 14.07/2.64  Prover 6: stopped
% 14.07/2.64  Prover 0: stopped
% 14.07/2.64  Prover 2: stopped
% 14.07/2.64  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.07/2.64  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.07/2.64  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.07/2.64  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.07/2.64  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.49/2.81  Prover 10: Preprocessing ...
% 15.49/2.81  Prover 13: Preprocessing ...
% 15.49/2.82  Prover 11: Preprocessing ...
% 15.49/2.82  Prover 8: Preprocessing ...
% 15.49/2.86  Prover 7: Preprocessing ...
% 16.20/2.89  Prover 1: Found proof (size 17)
% 16.20/2.89  Prover 1: proved (2261ms)
% 16.20/2.89  Prover 4: stopped
% 16.31/2.91  Prover 10: stopped
% 16.41/2.92  Prover 7: stopped
% 16.45/2.92  Prover 11: stopped
% 16.45/2.96  Prover 13: stopped
% 16.89/3.03  Prover 8: Warning: ignoring some quantifiers
% 16.89/3.05  Prover 8: Constructing countermodel ...
% 16.89/3.07  Prover 8: stopped
% 16.89/3.07  
% 16.89/3.07  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.89/3.07  
% 16.89/3.07  % SZS output start Proof for theBenchmark
% 16.89/3.08  Assumptions after simplification:
% 16.89/3.08  ---------------------------------
% 16.89/3.08  
% 16.89/3.08    (cl5_nebula_init_0106)
% 17.26/3.11    gt(loopcounter, n1) = 0 & $i(sigma_init) & $i(rho_init) & $i(mu_init) &
% 17.26/3.11    $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(center_init) &
% 17.26/3.11    $i(init) & $i(q_init) & $i(n135299) & $i(loopcounter) & $i(n4) & $i(n1) &
% 17.26/3.11    $i(n0) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select3(center_init,
% 17.26/3.11          v0, n0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) =
% 17.26/3.11        v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] :  !
% 17.26/3.11    [v1: $i] : (v1 = init |  ~ (a_select2(sigma_init, v0) = v1) |  ~ $i(v0) |  ?
% 17.26/3.11      [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 =
% 17.26/3.11            0) |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 17.26/3.11      (a_select2(rho_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] :
% 17.26/3.11      (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  !
% 17.26/3.11    [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(mu_init, v0) = v1) |  ~
% 17.26/3.11      $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2
% 17.26/3.11        & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |
% 17.26/3.11       ~ (a_select2(sigmaold_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3:
% 17.26/3.11        any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 =
% 17.26/3.11            0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 17.26/3.11      (a_select2(rhoold_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any]
% 17.26/3.11      : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  !
% 17.26/3.11    [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(muold_init, v0) = v1) |  ~
% 17.26/3.11      $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2
% 17.26/3.11        & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] : ( ~ (leq(v0, n135299) = 0)
% 17.26/3.11      |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) |  ! [v1: $i]
% 17.26/3.11      :  ! [v2: $i] : (v2 = init |  ~ (a_select3(q_init, v0, v1) = v2) |  ~ $i(v1)
% 17.26/3.11        |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~
% 17.26/3.11            (v4 = 0) |  ~ (v3 = 0))))) &  ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 =
% 17.26/3.11        init) & a_select2(muold_init, v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0
% 17.26/3.11      & $i(v1) & $i(v0))
% 17.26/3.11  
% 17.26/3.11    (function-axioms)
% 17.26/3.12     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 17.26/3.12      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 17.26/3.12      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 17.26/3.12      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 17.26/3.12        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.26/3.12    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 17.26/3.12      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 17.26/3.12    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 17.26/3.12      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.26/3.12    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 17.26/3.12        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.26/3.12    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 17.26/3.12          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 17.26/3.12      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.26/3.12    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 17.26/3.12      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 17.26/3.12    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 17.26/3.12        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 17.26/3.12      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.26/3.12    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 17.26/3.12      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 17.26/3.12    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 17.26/3.12          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 17.26/3.12      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 17.26/3.12      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 17.26/3.12      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 17.26/3.12    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 17.26/3.12      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 17.26/3.12      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.26/3.12    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 17.26/3.12      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.26/3.12    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 17.26/3.12      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.26/3.12    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.26/3.12    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 17.26/3.12    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 17.26/3.12      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 17.26/3.12      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 17.26/3.12      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 17.26/3.12  
% 17.26/3.12  Further assumptions not needed in the proof:
% 17.26/3.12  --------------------------------------------
% 17.26/3.12  const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.26/3.12  finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.26/3.12  finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 17.26/3.12  gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 17.26/3.12  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,
% 17.26/3.12  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,
% 17.26/3.12  gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 17.26/3.12  leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 17.26/3.12  leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 17.26/3.12  matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 17.26/3.12  matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 17.26/3.12  reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 17.26/3.12  sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 17.26/3.12  succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 17.26/3.12  succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 17.26/3.12  successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 17.26/3.12  sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 17.26/3.12  uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 17.26/3.12  
% 17.26/3.12  Those formulas are unsatisfiable:
% 17.26/3.12  ---------------------------------
% 17.26/3.12  
% 17.26/3.12  Begin of proof
% 17.26/3.12  | 
% 17.26/3.12  | ALPHA: (cl5_nebula_init_0106) implies:
% 17.26/3.12  |   (1)   ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(muold_init, v0)
% 17.26/3.12  |            = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3
% 17.26/3.12  |            & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))
% 17.26/3.12  |   (2)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = init) & a_select2(muold_init, v0)
% 17.26/3.12  |          = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 17.26/3.13  | 
% 17.26/3.13  | ALPHA: (function-axioms) implies:
% 17.26/3.13  |   (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 17.26/3.13  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 17.26/3.13  | 
% 17.26/3.13  | DELTA: instantiating (2) with fresh symbols all_54_0, all_54_1 gives:
% 17.26/3.13  |   (4)   ~ (all_54_0 = init) & a_select2(muold_init, all_54_1) = all_54_0 &
% 17.26/3.13  |        leq(all_54_1, n4) = 0 & leq(n0, all_54_1) = 0 & $i(all_54_0) &
% 17.26/3.13  |        $i(all_54_1)
% 17.26/3.13  | 
% 17.26/3.13  | ALPHA: (4) implies:
% 17.26/3.13  |   (5)   ~ (all_54_0 = init)
% 17.26/3.13  |   (6)  $i(all_54_1)
% 17.26/3.13  |   (7)  leq(n0, all_54_1) = 0
% 17.26/3.13  |   (8)  leq(all_54_1, n4) = 0
% 17.26/3.13  |   (9)  a_select2(muold_init, all_54_1) = all_54_0
% 17.26/3.13  | 
% 17.26/3.13  | GROUND_INST: instantiating (1) with all_54_1, all_54_0, simplifying with (6),
% 17.26/3.13  |              (9) gives:
% 17.26/3.13  |   (10)  all_54_0 = init |  ? [v0: any] :  ? [v1: any] : (leq(all_54_1, n4) =
% 17.26/3.13  |           v1 & leq(n0, all_54_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 17.26/3.13  | 
% 17.26/3.13  | BETA: splitting (10) gives:
% 17.26/3.13  | 
% 17.26/3.13  | Case 1:
% 17.26/3.13  | | 
% 17.26/3.13  | |   (11)  all_54_0 = init
% 17.26/3.13  | | 
% 17.26/3.13  | | REDUCE: (5), (11) imply:
% 17.26/3.13  | |   (12)  $false
% 17.26/3.13  | | 
% 17.26/3.13  | | CLOSE: (12) is inconsistent.
% 17.26/3.13  | | 
% 17.26/3.13  | Case 2:
% 17.26/3.13  | | 
% 17.26/3.13  | |   (13)   ? [v0: any] :  ? [v1: any] : (leq(all_54_1, n4) = v1 & leq(n0,
% 17.26/3.13  | |             all_54_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 17.26/3.13  | | 
% 17.26/3.13  | | DELTA: instantiating (13) with fresh symbols all_105_0, all_105_1 gives:
% 17.26/3.13  | |   (14)  leq(all_54_1, n4) = all_105_0 & leq(n0, all_54_1) = all_105_1 & ( ~
% 17.26/3.13  | |           (all_105_0 = 0) |  ~ (all_105_1 = 0))
% 17.26/3.13  | | 
% 17.26/3.13  | | ALPHA: (14) implies:
% 17.26/3.13  | |   (15)  leq(n0, all_54_1) = all_105_1
% 17.26/3.13  | |   (16)  leq(all_54_1, n4) = all_105_0
% 17.26/3.13  | |   (17)   ~ (all_105_0 = 0) |  ~ (all_105_1 = 0)
% 17.26/3.13  | | 
% 17.26/3.13  | | GROUND_INST: instantiating (3) with 0, all_105_1, all_54_1, n0, simplifying
% 17.26/3.13  | |              with (7), (15) gives:
% 17.26/3.13  | |   (18)  all_105_1 = 0
% 17.26/3.13  | | 
% 17.26/3.13  | | GROUND_INST: instantiating (3) with 0, all_105_0, n4, all_54_1, simplifying
% 17.26/3.13  | |              with (8), (16) gives:
% 17.26/3.13  | |   (19)  all_105_0 = 0
% 17.26/3.13  | | 
% 17.26/3.13  | | BETA: splitting (17) gives:
% 17.26/3.13  | | 
% 17.26/3.13  | | Case 1:
% 17.26/3.13  | | | 
% 17.26/3.13  | | |   (20)   ~ (all_105_0 = 0)
% 17.26/3.13  | | | 
% 17.26/3.13  | | | REDUCE: (19), (20) imply:
% 17.26/3.13  | | |   (21)  $false
% 17.26/3.13  | | | 
% 17.26/3.13  | | | CLOSE: (21) is inconsistent.
% 17.26/3.13  | | | 
% 17.26/3.13  | | Case 2:
% 17.26/3.13  | | | 
% 17.26/3.14  | | |   (22)   ~ (all_105_1 = 0)
% 17.26/3.14  | | | 
% 17.26/3.14  | | | REDUCE: (18), (22) imply:
% 17.26/3.14  | | |   (23)  $false
% 17.26/3.14  | | | 
% 17.26/3.14  | | | CLOSE: (23) is inconsistent.
% 17.26/3.14  | | | 
% 17.26/3.14  | | End of split
% 17.26/3.14  | | 
% 17.26/3.14  | End of split
% 17.26/3.14  | 
% 17.26/3.14  End of proof
% 17.26/3.14  % SZS output end Proof for theBenchmark
% 17.26/3.14  
% 17.26/3.14  2526ms
%------------------------------------------------------------------------------