TSTP Solution File: SWV183+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV183+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 : n006.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 22:55:15 EDT 2023

% Result   : Theorem 15.07s 2.78s
% Output   : Proof 18.47s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV183+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Aug 29 08:14:36 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.58/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.58/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.58/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.58/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.58/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.58/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.58/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.14/1.40  Prover 1: Preprocessing ...
% 5.14/1.40  Prover 4: Preprocessing ...
% 5.39/1.43  Prover 2: Preprocessing ...
% 5.39/1.43  Prover 5: Preprocessing ...
% 5.39/1.43  Prover 6: Preprocessing ...
% 5.39/1.43  Prover 0: Preprocessing ...
% 5.39/1.43  Prover 3: Preprocessing ...
% 11.62/2.27  Prover 1: Warning: ignoring some quantifiers
% 11.73/2.28  Prover 3: Warning: ignoring some quantifiers
% 11.95/2.35  Prover 3: Constructing countermodel ...
% 11.95/2.36  Prover 6: Proving ...
% 11.95/2.37  Prover 1: Constructing countermodel ...
% 12.54/2.49  Prover 4: Warning: ignoring some quantifiers
% 12.54/2.50  Prover 5: Proving ...
% 13.83/2.57  Prover 2: Proving ...
% 13.83/2.59  Prover 0: Proving ...
% 13.83/2.62  Prover 4: Constructing countermodel ...
% 15.07/2.77  Prover 3: proved (2142ms)
% 15.07/2.77  
% 15.07/2.78  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.07/2.78  
% 15.07/2.78  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.07/2.78  Prover 2: stopped
% 15.07/2.78  Prover 6: stopped
% 15.07/2.78  Prover 5: stopped
% 15.07/2.80  Prover 0: stopped
% 15.59/2.81  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.59/2.81  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.59/2.81  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.59/2.81  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.08/2.92  Prover 1: Found proof (size 19)
% 16.08/2.92  Prover 1: proved (2305ms)
% 16.08/2.94  Prover 4: stopped
% 16.78/2.97  Prover 8: Preprocessing ...
% 17.01/2.99  Prover 7: Preprocessing ...
% 17.01/3.01  Prover 13: Preprocessing ...
% 17.01/3.02  Prover 10: Preprocessing ...
% 17.01/3.02  Prover 11: Preprocessing ...
% 17.01/3.04  Prover 7: stopped
% 17.50/3.08  Prover 10: stopped
% 17.72/3.10  Prover 11: stopped
% 17.72/3.12  Prover 13: stopped
% 18.15/3.17  Prover 8: Warning: ignoring some quantifiers
% 18.15/3.18  Prover 8: Constructing countermodel ...
% 18.15/3.20  Prover 8: stopped
% 18.15/3.20  
% 18.15/3.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.15/3.20  
% 18.34/3.21  % SZS output start Proof for theBenchmark
% 18.34/3.22  Assumptions after simplification:
% 18.34/3.22  ---------------------------------
% 18.34/3.22  
% 18.34/3.22    (cl5_nebula_init_0091)
% 18.47/3.27    $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(center_init) &
% 18.47/3.27    $i(sigma_init) & $i(mu_init) & $i(rho_init) & $i(init) & $i(q_init) &
% 18.47/3.27    $i(n135299) & $i(loopcounter) & $i(n4) & $i(n1) & $i(n0) &  ? [v0: any] :
% 18.47/3.27    (gt(loopcounter, n1) = v0 & gt(loopcounter, n0) = 0 &  ! [v1: $i] :  ! [v2:
% 18.47/3.27        $i] : (v2 = init |  ~ (a_select3(center_init, v1, n0) = v2) |  ~ $i(v1) | 
% 18.47/3.27        ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~
% 18.47/3.27            (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1: $i] :  ! [v2: $i] : (v2 = init | 
% 18.47/3.27        ~ (a_select2(sigmaold_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 18.47/3.27          any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 18.47/3.27              0)))) &  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 18.47/3.27        (a_select2(rhoold_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 18.47/3.27          any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 18.47/3.27              0)))) &  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 18.47/3.27        (a_select2(muold_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any]
% 18.47/3.27        : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) & 
% 18.47/3.27      ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~ (a_select2(sigma_init, v1) = v2)
% 18.47/3.27        |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0,
% 18.47/3.27            v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1: $i] :  ! [v2: $i] :
% 18.47/3.27      (v2 = init |  ~ (a_select2(mu_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] : 
% 18.47/3.27        ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3
% 18.47/3.27              = 0)))) &  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 18.47/3.27        (a_select2(rho_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :
% 18.47/3.27        (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  !
% 18.47/3.27      [v1: $i] : ( ~ (leq(v1, n135299) = 0) |  ~ $i(v1) |  ? [v2: int] : ( ~ (v2 =
% 18.47/3.27            0) & leq(n0, v1) = v2) |  ! [v2: $i] :  ! [v3: $i] : (v3 = init |  ~
% 18.47/3.27          (a_select3(q_init, v1, v2) = v3) |  ~ $i(v2) |  ? [v4: any] :  ? [v5:
% 18.47/3.27            any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) |  ~ (v4 =
% 18.47/3.27                0))))) &  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = init) &
% 18.47/3.27        a_select2(mu_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 & $i(v2) &
% 18.47/3.27        $i(v1)) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 18.47/3.27          (a_select2(sigmaold_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 18.47/3.27            any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 18.47/3.27                0))))) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init | 
% 18.47/3.27          ~ (a_select2(rhoold_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 18.47/3.27            any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 18.47/3.27                0))))) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init | 
% 18.47/3.27          ~ (a_select2(muold_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 18.47/3.27            any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 18.47/3.27                0))))))
% 18.47/3.27  
% 18.47/3.27    (function-axioms)
% 18.47/3.28     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 18.47/3.28      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 18.47/3.28      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 18.47/3.28      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 18.47/3.28        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 18.47/3.28    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 18.47/3.28      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 18.47/3.28    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 18.47/3.28      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 18.47/3.28    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 18.47/3.28        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 18.47/3.28    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 18.47/3.28          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 18.47/3.28      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.47/3.28    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 18.47/3.28      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 18.47/3.28    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 18.47/3.28        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 18.47/3.28      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.47/3.28    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 18.47/3.28      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 18.47/3.28    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 18.47/3.28          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 18.47/3.28      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 18.47/3.28      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 18.47/3.28      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 18.47/3.28    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 18.47/3.28      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 18.47/3.28      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 18.47/3.28    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 18.47/3.28      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 18.47/3.28    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 18.47/3.28      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 18.47/3.28    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.47/3.28    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 18.47/3.28    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 18.47/3.28      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 18.47/3.28      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 18.47/3.28      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 18.47/3.28  
% 18.47/3.28  Further assumptions not needed in the proof:
% 18.47/3.28  --------------------------------------------
% 18.47/3.28  const_array1_select, const_array2_select, defuse, finite_domain_0,
% 18.47/3.28  finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 18.47/3.28  finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 18.47/3.28  gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 18.47/3.28  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,
% 18.47/3.28  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,
% 18.47/3.28  gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 18.47/3.28  leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 18.47/3.28  leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 18.47/3.28  matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 18.47/3.28  matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 18.47/3.28  reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 18.47/3.28  sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 18.47/3.28  succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 18.47/3.28  succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 18.47/3.28  successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 18.47/3.28  sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 18.47/3.28  uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 18.47/3.28  
% 18.47/3.28  Those formulas are unsatisfiable:
% 18.47/3.28  ---------------------------------
% 18.47/3.28  
% 18.47/3.28  Begin of proof
% 18.47/3.28  | 
% 18.47/3.29  | ALPHA: (cl5_nebula_init_0091) implies:
% 18.47/3.29  |   (1)   ? [v0: any] : (gt(loopcounter, n1) = v0 & gt(loopcounter, n0) = 0 &  !
% 18.47/3.29  |          [v1: $i] :  ! [v2: $i] : (v2 = init |  ~ (a_select3(center_init, v1,
% 18.47/3.29  |                n0) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1,
% 18.47/3.29  |                n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) & 
% 18.47/3.29  |          ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~ (a_select2(sigmaold_init,
% 18.47/3.29  |                v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1,
% 18.47/3.29  |                n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) & 
% 18.47/3.29  |          ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~ (a_select2(rhoold_init,
% 18.47/3.29  |                v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1,
% 18.47/3.29  |                n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) & 
% 18.47/3.29  |          ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~ (a_select2(muold_init, v1)
% 18.47/3.29  |              = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) =
% 18.47/3.29  |              v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1:
% 18.47/3.29  |            $i] :  ! [v2: $i] : (v2 = init |  ~ (a_select2(sigma_init, v1) =
% 18.47/3.29  |              v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4
% 18.47/3.29  |              & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1: $i]
% 18.47/3.29  |          :  ! [v2: $i] : (v2 = init |  ~ (a_select2(mu_init, v1) = v2) |  ~
% 18.47/3.29  |            $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0,
% 18.47/3.29  |                v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1: $i] :  !
% 18.47/3.29  |          [v2: $i] : (v2 = init |  ~ (a_select2(rho_init, v1) = v2) |  ~ $i(v1)
% 18.47/3.29  |            |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) =
% 18.47/3.29  |              v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1: $i] : ( ~ (leq(v1,
% 18.47/3.29  |                n135299) = 0) |  ~ $i(v1) |  ? [v2: int] : ( ~ (v2 = 0) &
% 18.47/3.29  |              leq(n0, v1) = v2) |  ! [v2: $i] :  ! [v3: $i] : (v3 = init |  ~
% 18.47/3.29  |              (a_select3(q_init, v1, v2) = v3) |  ~ $i(v2) |  ? [v4: any] :  ?
% 18.47/3.29  |              [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) |
% 18.47/3.29  |                   ~ (v4 = 0))))) &  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = init)
% 18.47/3.29  |            & a_select2(mu_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 &
% 18.47/3.29  |            $i(v2) & $i(v1)) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2 =
% 18.47/3.29  |              init |  ~ (a_select2(sigmaold_init, v1) = v2) |  ~ $i(v1) |  ?
% 18.47/3.29  |              [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 &
% 18.47/3.29  |                ( ~ (v4 = 0) |  ~ (v3 = 0))))) & ( ~ (v0 = 0) |  ! [v1: $i] : 
% 18.47/3.29  |            ! [v2: $i] : (v2 = init |  ~ (a_select2(rhoold_init, v1) = v2) |  ~
% 18.47/3.29  |              $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 &
% 18.47/3.29  |                leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))) & ( ~ (v0 =
% 18.47/3.29  |              0) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 18.47/3.29  |              (a_select2(muold_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ?
% 18.47/3.29  |              [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |
% 18.47/3.29  |                   ~ (v3 = 0))))))
% 18.47/3.29  | 
% 18.47/3.29  | ALPHA: (function-axioms) implies:
% 18.47/3.29  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 18.47/3.29  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 18.47/3.29  | 
% 18.47/3.30  | DELTA: instantiating (1) with fresh symbol all_76_0 gives:
% 18.47/3.30  |   (3)  gt(loopcounter, n1) = all_76_0 & gt(loopcounter, n0) = 0 &  ! [v0: $i]
% 18.47/3.30  |        :  ! [v1: $i] : (v1 = init |  ~ (a_select3(center_init, v0, n0) = v1) |
% 18.47/3.30  |           ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0,
% 18.47/3.30  |              v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1:
% 18.47/3.30  |          $i] : (v1 = init |  ~ (a_select2(sigmaold_init, v0) = v1) |  ~ $i(v0)
% 18.47/3.30  |          |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2
% 18.47/3.30  |            & ( ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 =
% 18.47/3.30  |          init |  ~ (a_select2(rhoold_init, v0) = v1) |  ~ $i(v0) |  ? [v2:
% 18.47/3.30  |            any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~
% 18.47/3.30  |              (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 =
% 18.47/3.30  |          init |  ~ (a_select2(muold_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any]
% 18.47/3.30  |          :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0)
% 18.47/3.30  |              |  ~ (v2 = 0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 18.47/3.30  |          (a_select2(sigma_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3:
% 18.47/3.30  |            any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2
% 18.47/3.30  |                = 0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 18.47/3.30  |          (a_select2(mu_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3:
% 18.47/3.30  |            any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2
% 18.47/3.30  |                = 0)))) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 18.47/3.30  |          (a_select2(rho_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3:
% 18.47/3.30  |            any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2
% 18.47/3.30  |                = 0)))) &  ! [v0: $i] : ( ~ (leq(v0, n135299) = 0) |  ~ $i(v0)
% 18.47/3.30  |          |  ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) |  ! [v1: $i] :  !
% 18.47/3.30  |          [v2: $i] : (v2 = init |  ~ (a_select3(q_init, v0, v1) = v2) |  ~
% 18.47/3.30  |            $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0,
% 18.47/3.30  |                v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))) &  ? [v0: $i] :  ?
% 18.47/3.30  |        [v1: $i] : ( ~ (v1 = init) & a_select2(mu_init, v0) = v1 & leq(v0, n4)
% 18.47/3.30  |          = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0)) & ( ~ (all_76_0 = 0) |  !
% 18.47/3.30  |          [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(sigmaold_init,
% 18.47/3.30  |                v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0,
% 18.47/3.30  |                n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))) &
% 18.47/3.30  |        ( ~ (all_76_0 = 0) |  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 18.47/3.30  |            (a_select2(rhoold_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ?
% 18.47/3.30  |            [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | 
% 18.47/3.30  |                ~ (v2 = 0))))) & ( ~ (all_76_0 = 0) |  ! [v0: $i] :  ! [v1: $i]
% 18.47/3.30  |          : (v1 = init |  ~ (a_select2(muold_init, v0) = v1) |  ~ $i(v0) |  ?
% 18.47/3.30  |            [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & (
% 18.47/3.30  |                ~ (v3 = 0) |  ~ (v2 = 0)))))
% 18.47/3.30  | 
% 18.47/3.30  | ALPHA: (3) implies:
% 18.47/3.30  |   (4)   ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(mu_init, v0) =
% 18.47/3.30  |            v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 &
% 18.47/3.30  |            leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))
% 18.47/3.31  |   (5)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = init) & a_select2(mu_init, v0) =
% 18.47/3.31  |          v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 18.47/3.31  | 
% 18.47/3.31  | DELTA: instantiating (5) with fresh symbols all_79_0, all_79_1 gives:
% 18.47/3.31  |   (6)   ~ (all_79_0 = init) & a_select2(mu_init, all_79_1) = all_79_0 &
% 18.47/3.31  |        leq(all_79_1, n4) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) &
% 18.47/3.31  |        $i(all_79_1)
% 18.47/3.31  | 
% 18.47/3.31  | ALPHA: (6) implies:
% 18.47/3.31  |   (7)   ~ (all_79_0 = init)
% 18.47/3.31  |   (8)  $i(all_79_1)
% 18.47/3.31  |   (9)  leq(n0, all_79_1) = 0
% 18.47/3.31  |   (10)  leq(all_79_1, n4) = 0
% 18.47/3.31  |   (11)  a_select2(mu_init, all_79_1) = all_79_0
% 18.47/3.31  | 
% 18.47/3.31  | GROUND_INST: instantiating (4) with all_79_1, all_79_0, simplifying with (8),
% 18.47/3.31  |              (11) gives:
% 18.47/3.31  |   (12)  all_79_0 = init |  ? [v0: any] :  ? [v1: any] : (leq(all_79_1, n4) =
% 18.47/3.31  |           v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 18.47/3.31  | 
% 18.47/3.31  | BETA: splitting (12) gives:
% 18.47/3.31  | 
% 18.47/3.31  | Case 1:
% 18.47/3.31  | | 
% 18.47/3.31  | |   (13)  all_79_0 = init
% 18.47/3.31  | | 
% 18.47/3.31  | | REDUCE: (7), (13) imply:
% 18.47/3.31  | |   (14)  $false
% 18.47/3.31  | | 
% 18.47/3.31  | | CLOSE: (14) is inconsistent.
% 18.47/3.31  | | 
% 18.47/3.31  | Case 2:
% 18.47/3.31  | | 
% 18.47/3.31  | |   (15)   ? [v0: any] :  ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0,
% 18.47/3.31  | |             all_79_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 18.47/3.31  | | 
% 18.47/3.31  | | DELTA: instantiating (15) with fresh symbols all_107_0, all_107_1 gives:
% 18.47/3.31  | |   (16)  leq(all_79_1, n4) = all_107_0 & leq(n0, all_79_1) = all_107_1 & ( ~
% 18.47/3.31  | |           (all_107_0 = 0) |  ~ (all_107_1 = 0))
% 18.47/3.31  | | 
% 18.47/3.31  | | ALPHA: (16) implies:
% 18.47/3.31  | |   (17)  leq(n0, all_79_1) = all_107_1
% 18.47/3.31  | |   (18)  leq(all_79_1, n4) = all_107_0
% 18.47/3.31  | |   (19)   ~ (all_107_0 = 0) |  ~ (all_107_1 = 0)
% 18.47/3.31  | | 
% 18.47/3.31  | | GROUND_INST: instantiating (2) with 0, all_107_1, all_79_1, n0, simplifying
% 18.47/3.31  | |              with (9), (17) gives:
% 18.47/3.31  | |   (20)  all_107_1 = 0
% 18.47/3.31  | | 
% 18.47/3.31  | | GROUND_INST: instantiating (2) with 0, all_107_0, n4, all_79_1, simplifying
% 18.47/3.31  | |              with (10), (18) gives:
% 18.47/3.31  | |   (21)  all_107_0 = 0
% 18.47/3.31  | | 
% 18.47/3.31  | | BETA: splitting (19) gives:
% 18.47/3.31  | | 
% 18.47/3.31  | | Case 1:
% 18.47/3.31  | | | 
% 18.47/3.31  | | |   (22)   ~ (all_107_0 = 0)
% 18.47/3.31  | | | 
% 18.47/3.31  | | | REDUCE: (21), (22) imply:
% 18.47/3.31  | | |   (23)  $false
% 18.47/3.31  | | | 
% 18.47/3.31  | | | CLOSE: (23) is inconsistent.
% 18.47/3.31  | | | 
% 18.47/3.31  | | Case 2:
% 18.47/3.31  | | | 
% 18.47/3.31  | | |   (24)   ~ (all_107_1 = 0)
% 18.47/3.31  | | | 
% 18.47/3.31  | | | REDUCE: (20), (24) imply:
% 18.47/3.31  | | |   (25)  $false
% 18.47/3.31  | | | 
% 18.47/3.31  | | | CLOSE: (25) is inconsistent.
% 18.47/3.31  | | | 
% 18.47/3.31  | | End of split
% 18.47/3.31  | | 
% 18.47/3.31  | End of split
% 18.47/3.31  | 
% 18.47/3.31  End of proof
% 18.47/3.31  % SZS output end Proof for theBenchmark
% 18.47/3.31  
% 18.47/3.31  2713ms
%------------------------------------------------------------------------------