TSTP Solution File: SWV182+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV182+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 : n007.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 13.39s 2.48s
% Output   : Proof 17.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV182+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue Aug 29 02:54:58 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.59/0.60  ________       _____
% 0.59/0.60  ___  __ \_________(_)________________________________
% 0.59/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.59/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.59/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.59/0.60  
% 0.59/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.59/0.60  (2023-06-19)
% 0.59/0.60  
% 0.59/0.60  (c) Philipp Rümmer, 2009-2023
% 0.59/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.59/0.60                Amanda Stjerna.
% 0.59/0.60  Free software under BSD-3-Clause.
% 0.59/0.60  
% 0.59/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.59/0.60  
% 0.59/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.59/0.62  Running up to 7 provers in parallel.
% 0.59/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.59/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.59/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.59/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.59/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.59/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.59/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.31/1.29  Prover 4: Preprocessing ...
% 4.31/1.30  Prover 1: Preprocessing ...
% 4.75/1.33  Prover 6: Preprocessing ...
% 4.75/1.33  Prover 3: Preprocessing ...
% 4.75/1.33  Prover 2: Preprocessing ...
% 4.75/1.33  Prover 0: Preprocessing ...
% 4.75/1.34  Prover 5: Preprocessing ...
% 9.95/2.05  Prover 1: Warning: ignoring some quantifiers
% 10.72/2.09  Prover 3: Warning: ignoring some quantifiers
% 11.10/2.13  Prover 3: Constructing countermodel ...
% 11.16/2.15  Prover 1: Constructing countermodel ...
% 11.16/2.15  Prover 6: Proving ...
% 11.16/2.19  Prover 4: Warning: ignoring some quantifiers
% 12.30/2.29  Prover 4: Constructing countermodel ...
% 12.30/2.30  Prover 5: Proving ...
% 12.30/2.33  Prover 2: Proving ...
% 12.30/2.34  Prover 0: Proving ...
% 13.39/2.48  Prover 3: proved (1853ms)
% 13.39/2.48  
% 13.39/2.48  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.39/2.48  
% 13.39/2.48  Prover 5: stopped
% 13.39/2.48  Prover 2: stopped
% 13.39/2.49  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.39/2.49  Prover 6: stopped
% 13.39/2.50  Prover 0: stopped
% 14.05/2.51  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.05/2.51  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.05/2.51  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.05/2.51  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.64/2.67  Prover 1: Found proof (size 48)
% 14.64/2.67  Prover 1: proved (2044ms)
% 15.33/2.67  Prover 4: stopped
% 15.45/2.70  Prover 7: Preprocessing ...
% 15.71/2.73  Prover 13: Preprocessing ...
% 15.71/2.73  Prover 10: Preprocessing ...
% 15.79/2.74  Prover 8: Preprocessing ...
% 15.79/2.74  Prover 11: Preprocessing ...
% 15.79/2.78  Prover 7: stopped
% 15.79/2.80  Prover 10: stopped
% 16.46/2.84  Prover 11: stopped
% 16.46/2.84  Prover 13: stopped
% 16.82/2.93  Prover 8: Warning: ignoring some quantifiers
% 16.82/2.94  Prover 8: Constructing countermodel ...
% 16.82/2.96  Prover 8: stopped
% 17.19/2.96  
% 17.19/2.96  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.19/2.96  
% 17.19/2.97  % SZS output start Proof for theBenchmark
% 17.26/2.98  Assumptions after simplification:
% 17.26/2.98  ---------------------------------
% 17.26/2.98  
% 17.26/2.98    (cl5_nebula_init_0086)
% 17.43/3.01    $i(sigma_init) & $i(rho_init) & $i(mu_init) & $i(center_init) & $i(init) &
% 17.43/3.01    $i(q_init) & $i(n135299) & $i(loopcounter) & $i(pv76) & $i(tptp_float_0_001) &
% 17.43/3.01    $i(n4) & $i(n1) & $i(n0) &  ? [v0: any] : (leq(tptp_float_0_001, pv76) = 0 &
% 17.43/3.01      leq(n1, loopcounter) = 0 & gt(loopcounter, n0) = v0 &  ! [v1: $i] :  ! [v2:
% 17.43/3.01        $i] : (v2 = init |  ~ (a_select3(center_init, v1, n0) = v2) |  ~ $i(v1) | 
% 17.43/3.01        ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~
% 17.43/3.01            (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) |
% 17.43/3.01         ~ $i(v1) |  ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) |  ! [v2: $i]
% 17.43/3.01        :  ! [v3: $i] : (v3 = init |  ~ (a_select3(q_init, v1, v2) = v3) |  ~
% 17.43/3.01          $i(v2) |  ? [v4: any] :  ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) =
% 17.43/3.01            v4 & ( ~ (v5 = 0) |  ~ (v4 = 0))))) &  ? [v1: $i] :  ? [v2: $i] : ( ~
% 17.43/3.01        (v2 = init) & a_select2(rho_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1)
% 17.43/3.01        = 0 & $i(v2) & $i(v1)) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2 =
% 17.43/3.01          init |  ~ (a_select2(sigma_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] : 
% 17.43/3.01          ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~
% 17.43/3.01              (v3 = 0))))) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init
% 17.43/3.01          |  ~ (a_select2(rho_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 17.43/3.01            any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 17.43/3.01                0))))) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init | 
% 17.43/3.01          ~ (a_select2(mu_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 17.43/3.01            any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 =
% 17.43/3.01                0))))))
% 17.43/3.01  
% 17.43/3.01    (leq_succ_gt)
% 17.43/3.02     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (succ(v0) = v2) |  ~ (leq(v2,
% 17.43/3.02          v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | gt(v1, v0) = 0)
% 17.43/3.02  
% 17.43/3.02    (successor_1)
% 17.43/3.02    succ(n0) = n1 & $i(n1) & $i(n0)
% 17.43/3.02  
% 17.43/3.02    (successor_2)
% 17.43/3.02    $i(n2) & $i(n0) &  ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 17.43/3.02  
% 17.43/3.02    (successor_3)
% 17.43/3.02    $i(n3) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 17.43/3.02      succ(n0) = v0 & $i(v1) & $i(v0))
% 17.43/3.02  
% 17.43/3.02    (successor_4)
% 17.43/3.02    $i(n4) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (succ(v2) = n4 &
% 17.43/3.02      succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 17.43/3.02  
% 17.43/3.02    (successor_5)
% 17.43/3.02    $i(n5) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :
% 17.43/3.02    (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 17.43/3.02      & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.43/3.02  
% 17.43/3.02    (function-axioms)
% 17.43/3.02     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 17.43/3.02      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 17.43/3.02      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 17.43/3.02      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 17.43/3.02        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.43/3.02    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 17.43/3.02      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 17.43/3.02    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 17.43/3.02      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.43/3.02    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 17.43/3.02        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.43/3.02    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 17.43/3.02          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 17.43/3.02      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.43/3.02    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 17.43/3.02      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 17.43/3.02    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 17.43/3.02        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 17.43/3.02      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.43/3.02    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 17.43/3.02      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 17.43/3.02    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 17.43/3.02          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 17.43/3.02      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 17.43/3.02      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 17.43/3.03      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 17.43/3.03    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 17.43/3.03      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 17.43/3.03      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.43/3.03    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 17.43/3.03      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.43/3.03    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 17.43/3.03      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.43/3.03    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.43/3.03    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 17.43/3.03    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 17.43/3.03      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 17.43/3.03      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 17.43/3.03      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 17.43/3.03  
% 17.43/3.03  Further assumptions not needed in the proof:
% 17.43/3.03  --------------------------------------------
% 17.43/3.03  const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.43/3.03  finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.43/3.03  finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 17.43/3.03  gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 17.43/3.03  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,
% 17.43/3.03  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,
% 17.43/3.03  gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 17.43/3.03  leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt_equiv,
% 17.43/3.03  leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 17.43/3.03  matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 17.43/3.03  matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 17.43/3.03  sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 17.43/3.03  sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 17.43/3.03  succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 17.43/3.03  succ_plus_5_r, succ_pred, succ_tptp_minus_1, sum_plus_base, sum_plus_base_float,
% 17.43/3.03  totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 17.43/3.03  uniform_int_rand_ranges_lo
% 17.43/3.03  
% 17.43/3.03  Those formulas are unsatisfiable:
% 17.43/3.03  ---------------------------------
% 17.43/3.03  
% 17.43/3.03  Begin of proof
% 17.43/3.03  | 
% 17.43/3.03  | ALPHA: (successor_4) implies:
% 17.43/3.03  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 17.43/3.03  |          v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 17.43/3.03  | 
% 17.43/3.03  | ALPHA: (successor_5) implies:
% 17.43/3.03  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (succ(v3) = n5
% 17.43/3.03  |          & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 17.43/3.03  |          $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.43/3.03  | 
% 17.43/3.03  | ALPHA: (successor_1) implies:
% 17.43/3.03  |   (3)  succ(n0) = n1
% 17.43/3.03  | 
% 17.43/3.03  | ALPHA: (successor_2) implies:
% 17.43/3.03  |   (4)   ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 17.43/3.03  | 
% 17.43/3.03  | ALPHA: (successor_3) implies:
% 17.43/3.03  |   (5)   ? [v0: $i] :  ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) =
% 17.43/3.03  |          v0 & $i(v1) & $i(v0))
% 17.43/3.03  | 
% 17.43/3.03  | ALPHA: (cl5_nebula_init_0086) implies:
% 17.43/3.03  |   (6)  $i(n0)
% 17.43/3.03  |   (7)  $i(loopcounter)
% 17.53/3.03  |   (8)   ? [v0: any] : (leq(tptp_float_0_001, pv76) = 0 & leq(n1, loopcounter)
% 17.53/3.03  |          = 0 & gt(loopcounter, n0) = v0 &  ! [v1: $i] :  ! [v2: $i] : (v2 =
% 17.53/3.03  |            init |  ~ (a_select3(center_init, v1, n0) = v2) |  ~ $i(v1) |  ?
% 17.53/3.03  |            [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & (
% 17.53/3.03  |                ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v1: $i] : ( ~ (leq(v1,
% 17.53/3.04  |                n135299) = 0) |  ~ $i(v1) |  ? [v2: int] : ( ~ (v2 = 0) &
% 17.53/3.04  |              leq(n0, v1) = v2) |  ! [v2: $i] :  ! [v3: $i] : (v3 = init |  ~
% 17.53/3.04  |              (a_select3(q_init, v1, v2) = v3) |  ~ $i(v2) |  ? [v4: any] :  ?
% 17.53/3.04  |              [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) |
% 17.53/3.04  |                   ~ (v4 = 0))))) &  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = init)
% 17.53/3.04  |            & a_select2(rho_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0
% 17.53/3.04  |            & $i(v2) & $i(v1)) & ( ~ (v0 = 0) |  ! [v1: $i] :  ! [v2: $i] : (v2
% 17.53/3.04  |              = init |  ~ (a_select2(sigma_init, v1) = v2) |  ~ $i(v1) |  ?
% 17.53/3.04  |              [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 &
% 17.53/3.04  |                ( ~ (v4 = 0) |  ~ (v3 = 0))))) & ( ~ (v0 = 0) |  ! [v1: $i] : 
% 17.53/3.04  |            ! [v2: $i] : (v2 = init |  ~ (a_select2(rho_init, v1) = v2) |  ~
% 17.53/3.04  |              $i(v1) |  ? [v3: any] :  ? [v4: any] : (leq(v1, n4) = v4 &
% 17.53/3.04  |                leq(n0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))) & ( ~ (v0 =
% 17.53/3.04  |              0) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 17.53/3.04  |              (a_select2(mu_init, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ?
% 17.53/3.04  |              [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |
% 17.53/3.04  |                   ~ (v3 = 0))))))
% 17.53/3.04  | 
% 17.53/3.04  | ALPHA: (function-axioms) implies:
% 17.53/3.04  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (succ(v2) = v1)
% 17.53/3.04  |          |  ~ (succ(v2) = v0))
% 17.53/3.04  |   (10)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 17.53/3.04  |         :  ! [v3: $i] : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) =
% 17.53/3.04  |             v0))
% 17.53/3.04  |   (11)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 17.53/3.04  |         :  ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) =
% 17.53/3.04  |             v0))
% 17.53/3.04  | 
% 17.53/3.04  | DELTA: instantiating (4) with fresh symbol all_49_0 gives:
% 17.53/3.04  |   (12)  succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0)
% 17.53/3.04  | 
% 17.53/3.04  | ALPHA: (12) implies:
% 17.53/3.04  |   (13)  succ(n0) = all_49_0
% 17.53/3.04  | 
% 17.53/3.04  | DELTA: instantiating (5) with fresh symbols all_51_0, all_51_1 gives:
% 17.53/3.04  |   (14)  succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1
% 17.53/3.04  |         & $i(all_51_0) & $i(all_51_1)
% 17.53/3.04  | 
% 17.53/3.04  | ALPHA: (14) implies:
% 17.53/3.04  |   (15)  succ(n0) = all_51_1
% 17.53/3.04  | 
% 17.53/3.04  | DELTA: instantiating (1) with fresh symbols all_53_0, all_53_1, all_53_2
% 17.53/3.04  |        gives:
% 17.53/3.04  |   (16)  succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) =
% 17.53/3.04  |         all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) &
% 17.53/3.04  |         $i(all_53_2)
% 17.53/3.04  | 
% 17.53/3.04  | ALPHA: (16) implies:
% 17.53/3.04  |   (17)  succ(n0) = all_53_2
% 17.53/3.04  | 
% 17.53/3.04  | DELTA: instantiating (2) with fresh symbols all_55_0, all_55_1, all_55_2,
% 17.53/3.04  |        all_55_3 gives:
% 17.53/3.04  |   (18)  succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) =
% 17.53/3.04  |         all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 &
% 17.53/3.04  |         $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3)
% 17.53/3.04  | 
% 17.53/3.04  | ALPHA: (18) implies:
% 17.53/3.04  |   (19)  succ(n0) = all_55_3
% 17.53/3.04  | 
% 17.53/3.04  | DELTA: instantiating (8) with fresh symbol all_74_0 gives:
% 17.53/3.04  |   (20)  leq(tptp_float_0_001, pv76) = 0 & leq(n1, loopcounter) = 0 &
% 17.53/3.04  |         gt(loopcounter, n0) = all_74_0 &  ! [v0: $i] :  ! [v1: $i] : (v1 =
% 17.53/3.04  |           init |  ~ (a_select3(center_init, v0, n0) = v1) |  ~ $i(v0) |  ?
% 17.53/3.04  |           [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & (
% 17.53/3.04  |               ~ (v3 = 0) |  ~ (v2 = 0)))) &  ! [v0: $i] : ( ~ (leq(v0,
% 17.53/3.04  |               n135299) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) &
% 17.53/3.04  |             leq(n0, v0) = v1) |  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 17.53/3.04  |             (a_select3(q_init, v0, v1) = v2) |  ~ $i(v1) |  ? [v3: any] :  ?
% 17.53/3.04  |             [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | 
% 17.53/3.04  |                 ~ (v3 = 0))))) &  ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = init) &
% 17.53/3.04  |           a_select2(rho_init, v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 &
% 17.53/3.04  |           $i(v1) & $i(v0)) & ( ~ (all_74_0 = 0) |  ! [v0: $i] :  ! [v1: $i] :
% 17.53/3.04  |           (v1 = init |  ~ (a_select2(sigma_init, v0) = v1) |  ~ $i(v0) |  ?
% 17.53/3.04  |             [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 &
% 17.53/3.04  |               ( ~ (v3 = 0) |  ~ (v2 = 0))))) & ( ~ (all_74_0 = 0) |  ! [v0:
% 17.53/3.04  |             $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(rho_init, v0) = v1)
% 17.53/3.04  |             |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) = v3 &
% 17.53/3.04  |               leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))) & ( ~
% 17.53/3.04  |           (all_74_0 = 0) |  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 17.53/3.04  |             (a_select2(mu_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3:
% 17.53/3.04  |               any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~
% 17.53/3.04  |                 (v2 = 0)))))
% 17.53/3.04  | 
% 17.53/3.04  | ALPHA: (20) implies:
% 17.53/3.05  |   (21)  gt(loopcounter, n0) = all_74_0
% 17.53/3.05  |   (22)  leq(n1, loopcounter) = 0
% 17.53/3.05  |   (23)   ~ (all_74_0 = 0) |  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 17.53/3.05  |           (a_select2(rho_init, v0) = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3:
% 17.53/3.05  |             any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~
% 17.53/3.05  |               (v2 = 0))))
% 17.53/3.05  |   (24)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = init) & a_select2(rho_init, v0)
% 17.53/3.05  |           = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 17.53/3.05  | 
% 17.53/3.05  | DELTA: instantiating (24) with fresh symbols all_79_0, all_79_1 gives:
% 17.53/3.05  |   (25)   ~ (all_79_0 = init) & a_select2(rho_init, all_79_1) = all_79_0 &
% 17.53/3.05  |         leq(all_79_1, n4) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) &
% 17.53/3.05  |         $i(all_79_1)
% 17.53/3.05  | 
% 17.53/3.05  | ALPHA: (25) implies:
% 17.53/3.05  |   (26)   ~ (all_79_0 = init)
% 17.53/3.05  |   (27)  $i(all_79_1)
% 17.53/3.05  |   (28)  leq(n0, all_79_1) = 0
% 17.53/3.05  |   (29)  leq(all_79_1, n4) = 0
% 17.53/3.05  |   (30)  a_select2(rho_init, all_79_1) = all_79_0
% 17.53/3.05  | 
% 17.53/3.05  | GROUND_INST: instantiating (9) with all_51_1, all_53_2, n0, simplifying with
% 17.53/3.05  |              (15), (17) gives:
% 17.53/3.05  |   (31)  all_53_2 = all_51_1
% 17.53/3.05  | 
% 17.53/3.05  | GROUND_INST: instantiating (9) with all_49_0, all_53_2, n0, simplifying with
% 17.53/3.05  |              (13), (17) gives:
% 17.53/3.05  |   (32)  all_53_2 = all_49_0
% 17.53/3.05  | 
% 17.53/3.05  | GROUND_INST: instantiating (9) with all_53_2, all_55_3, n0, simplifying with
% 17.53/3.05  |              (17), (19) gives:
% 17.53/3.05  |   (33)  all_55_3 = all_53_2
% 17.53/3.05  | 
% 17.53/3.05  | GROUND_INST: instantiating (9) with n1, all_55_3, n0, simplifying with (3),
% 17.53/3.05  |              (19) gives:
% 17.53/3.05  |   (34)  all_55_3 = n1
% 17.53/3.05  | 
% 17.53/3.05  | COMBINE_EQS: (33), (34) imply:
% 17.53/3.05  |   (35)  all_53_2 = n1
% 17.53/3.05  | 
% 17.53/3.05  | SIMP: (35) implies:
% 17.53/3.05  |   (36)  all_53_2 = n1
% 17.53/3.05  | 
% 17.53/3.05  | COMBINE_EQS: (31), (36) imply:
% 17.53/3.05  |   (37)  all_51_1 = n1
% 17.53/3.05  | 
% 17.53/3.05  | COMBINE_EQS: (31), (32) imply:
% 17.53/3.05  |   (38)  all_51_1 = all_49_0
% 17.53/3.05  | 
% 17.53/3.05  | COMBINE_EQS: (37), (38) imply:
% 17.53/3.05  |   (39)  all_49_0 = n1
% 17.53/3.05  | 
% 17.53/3.05  | GROUND_INST: instantiating (leq_succ_gt) with n0, loopcounter, n1, simplifying
% 17.53/3.05  |              with (3), (6), (7), (22) gives:
% 17.53/3.05  |   (40)  gt(loopcounter, n0) = 0
% 17.53/3.05  | 
% 17.53/3.05  | GROUND_INST: instantiating (10) with all_74_0, 0, n0, loopcounter, simplifying
% 17.53/3.05  |              with (21), (40) gives:
% 17.53/3.05  |   (41)  all_74_0 = 0
% 17.53/3.05  | 
% 17.53/3.05  | BETA: splitting (23) gives:
% 17.53/3.05  | 
% 17.53/3.05  | Case 1:
% 17.53/3.05  | | 
% 17.53/3.05  | |   (42)   ~ (all_74_0 = 0)
% 17.53/3.05  | | 
% 17.53/3.05  | | REDUCE: (41), (42) imply:
% 17.53/3.05  | |   (43)  $false
% 17.53/3.05  | | 
% 17.53/3.05  | | CLOSE: (43) is inconsistent.
% 17.53/3.05  | | 
% 17.53/3.05  | Case 2:
% 17.53/3.05  | | 
% 17.53/3.05  | |   (44)   ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~ (a_select2(rho_init, v0)
% 17.53/3.05  | |             = v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : (leq(v0, n4) =
% 17.53/3.05  | |             v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |  ~ (v2 = 0))))
% 17.53/3.06  | | 
% 17.53/3.06  | | GROUND_INST: instantiating (44) with all_79_1, all_79_0, simplifying with
% 17.53/3.06  | |              (27), (30) gives:
% 17.53/3.06  | |   (45)  all_79_0 = init |  ? [v0: any] :  ? [v1: any] : (leq(all_79_1, n4) =
% 17.53/3.06  | |           v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 17.53/3.06  | | 
% 17.53/3.06  | | BETA: splitting (45) gives:
% 17.53/3.06  | | 
% 17.53/3.06  | | Case 1:
% 17.53/3.06  | | | 
% 17.53/3.06  | | |   (46)  all_79_0 = init
% 17.53/3.06  | | | 
% 17.53/3.06  | | | REDUCE: (26), (46) imply:
% 17.53/3.06  | | |   (47)  $false
% 17.53/3.06  | | | 
% 17.53/3.06  | | | CLOSE: (47) is inconsistent.
% 17.53/3.06  | | | 
% 17.53/3.06  | | Case 2:
% 17.53/3.06  | | | 
% 17.53/3.06  | | |   (48)   ? [v0: any] :  ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0,
% 17.53/3.06  | | |             all_79_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 17.53/3.06  | | | 
% 17.53/3.06  | | | DELTA: instantiating (48) with fresh symbols all_124_0, all_124_1 gives:
% 17.53/3.06  | | |   (49)  leq(all_79_1, n4) = all_124_0 & leq(n0, all_79_1) = all_124_1 & (
% 17.53/3.06  | | |           ~ (all_124_0 = 0) |  ~ (all_124_1 = 0))
% 17.53/3.06  | | | 
% 17.53/3.06  | | | ALPHA: (49) implies:
% 17.53/3.06  | | |   (50)  leq(n0, all_79_1) = all_124_1
% 17.53/3.06  | | |   (51)  leq(all_79_1, n4) = all_124_0
% 17.53/3.06  | | |   (52)   ~ (all_124_0 = 0) |  ~ (all_124_1 = 0)
% 17.53/3.06  | | | 
% 17.53/3.06  | | | GROUND_INST: instantiating (11) with 0, all_124_1, all_79_1, n0,
% 17.53/3.06  | | |              simplifying with (28), (50) gives:
% 17.53/3.06  | | |   (53)  all_124_1 = 0
% 17.53/3.06  | | | 
% 17.53/3.06  | | | GROUND_INST: instantiating (11) with 0, all_124_0, n4, all_79_1,
% 17.53/3.06  | | |              simplifying with (29), (51) gives:
% 17.53/3.06  | | |   (54)  all_124_0 = 0
% 17.53/3.06  | | | 
% 17.53/3.06  | | | BETA: splitting (52) gives:
% 17.53/3.06  | | | 
% 17.53/3.06  | | | Case 1:
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | |   (55)   ~ (all_124_0 = 0)
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | | REDUCE: (54), (55) imply:
% 17.53/3.06  | | | |   (56)  $false
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | | CLOSE: (56) is inconsistent.
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | Case 2:
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | |   (57)   ~ (all_124_1 = 0)
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | | REDUCE: (53), (57) imply:
% 17.53/3.06  | | | |   (58)  $false
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | | CLOSE: (58) is inconsistent.
% 17.53/3.06  | | | | 
% 17.53/3.06  | | | End of split
% 17.53/3.06  | | | 
% 17.53/3.06  | | End of split
% 17.53/3.06  | | 
% 17.53/3.06  | End of split
% 17.53/3.06  | 
% 17.53/3.06  End of proof
% 17.53/3.06  % SZS output end Proof for theBenchmark
% 17.53/3.06  
% 17.53/3.06  2456ms
%------------------------------------------------------------------------------