TSTP Solution File: SWV165+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV165+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 22:55:10 EDT 2023

% Result   : Theorem 19.38s 3.58s
% Output   : Proof 22.83s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SWV165+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.09/0.11  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.32  % Computer : n007.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue Aug 29 06:47:13 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.61/0.62  ________       _____
% 0.61/0.62  ___  __ \_________(_)________________________________
% 0.61/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.61/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.61/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.61/0.62  
% 0.61/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.61/0.62  (2023-06-19)
% 0.61/0.62  
% 0.61/0.62  (c) Philipp Rümmer, 2009-2023
% 0.61/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.61/0.62                Amanda Stjerna.
% 0.61/0.62  Free software under BSD-3-Clause.
% 0.61/0.62  
% 0.61/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.61/0.62  
% 0.61/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.64  Running up to 7 provers in parallel.
% 0.65/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.65/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.17/1.55  Prover 4: Preprocessing ...
% 5.66/1.66  Prover 1: Preprocessing ...
% 5.66/1.67  Prover 0: Preprocessing ...
% 5.66/1.67  Prover 5: Preprocessing ...
% 5.66/1.67  Prover 2: Preprocessing ...
% 5.66/1.68  Prover 3: Preprocessing ...
% 5.66/1.68  Prover 6: Preprocessing ...
% 13.72/2.73  Prover 1: Warning: ignoring some quantifiers
% 14.45/2.86  Prover 1: Constructing countermodel ...
% 14.45/2.88  Prover 6: Proving ...
% 15.21/2.98  Prover 3: Warning: ignoring some quantifiers
% 15.91/3.03  Prover 3: Constructing countermodel ...
% 15.91/3.09  Prover 4: Warning: ignoring some quantifiers
% 17.19/3.21  Prover 5: Proving ...
% 17.19/3.25  Prover 4: Constructing countermodel ...
% 17.19/3.26  Prover 0: Proving ...
% 18.04/3.39  Prover 2: Proving ...
% 19.38/3.58  Prover 3: proved (2926ms)
% 19.38/3.58  
% 19.38/3.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.38/3.58  
% 19.38/3.58  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.38/3.58  Prover 5: stopped
% 19.38/3.58  Prover 0: stopped
% 19.38/3.58  Prover 6: stopped
% 19.38/3.59  Prover 2: stopped
% 20.17/3.60  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.17/3.60  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.17/3.60  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.17/3.61  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.95/3.76  Prover 7: Preprocessing ...
% 20.95/3.76  Prover 1: Found proof (size 21)
% 20.95/3.76  Prover 1: proved (3115ms)
% 20.95/3.76  Prover 4: stopped
% 20.95/3.77  Prover 11: Preprocessing ...
% 20.95/3.79  Prover 13: Preprocessing ...
% 20.95/3.79  Prover 10: Preprocessing ...
% 20.95/3.79  Prover 8: Preprocessing ...
% 21.55/3.84  Prover 7: stopped
% 21.55/3.86  Prover 10: stopped
% 21.55/3.87  Prover 11: stopped
% 22.25/3.90  Prover 13: stopped
% 22.39/3.98  Prover 8: Warning: ignoring some quantifiers
% 22.39/3.99  Prover 8: Constructing countermodel ...
% 22.83/4.01  Prover 8: stopped
% 22.83/4.01  
% 22.83/4.01  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.83/4.01  
% 22.83/4.02  % SZS output start Proof for theBenchmark
% 22.83/4.02  Assumptions after simplification:
% 22.83/4.02  ---------------------------------
% 22.83/4.02  
% 22.83/4.02    (cl5_nebula_init_0001)
% 22.83/4.05    $i(uninit) & $i(init) & $i(tptp_minus_1) & $i(n0) &  ? [v0: $i] : ( ~ (uninit
% 22.83/4.05        = init) & leq(v0, tptp_minus_1) = 0 & leq(n0, v0) = 0 & $i(v0))
% 22.83/4.05  
% 22.83/4.05    (finite_domain_0)
% 22.83/4.05    $i(n0) &  ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 22.83/4.05        int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 22.83/4.05  
% 22.83/4.05    (irreflexivity_gt)
% 22.83/4.05     ! [v0: $i] : ( ~ (gt(v0, v0) = 0) |  ~ $i(v0))
% 22.83/4.05  
% 22.83/4.05    (leq_gt1)
% 22.83/4.05     ! [v0: $i] :  ! [v1: $i] : ( ~ (gt(v1, v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 22.83/4.05      leq(v0, v1) = 0)
% 22.83/4.05  
% 22.83/4.05    (leq_gt_pred)
% 22.83/4.05     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 22.83/4.05      (pred(v1) = v2) |  ~ (leq(v0, v2) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4:
% 22.83/4.05        int] : ( ~ (v4 = 0) & gt(v1, v0) = v4)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 22.83/4.05    [v2: $i] : ( ~ (pred(v1) = v2) |  ~ (leq(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0)
% 22.83/4.05      | gt(v1, v0) = 0)
% 22.83/4.05  
% 22.83/4.05    (pred_succ)
% 22.83/4.05     ! [v0: $i] :  ! [v1: $i] : ( ~ (succ(v0) = v1) |  ~ $i(v0) | pred(v1) = v0)
% 22.83/4.05  
% 22.83/4.05    (succ_tptp_minus_1)
% 22.83/4.05    succ(tptp_minus_1) = n0 & $i(tptp_minus_1) & $i(n0)
% 22.83/4.05  
% 22.83/4.05    (function-axioms)
% 22.83/4.06     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 22.83/4.06      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 22.83/4.06      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 22.83/4.06      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 22.83/4.06        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 22.83/4.06    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 22.83/4.06      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 22.83/4.06    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 22.83/4.06      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 22.83/4.06    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 22.83/4.06        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 22.83/4.06    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 22.83/4.06          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 22.83/4.06      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 22.83/4.06    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 22.83/4.06      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 22.83/4.06    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 22.83/4.06        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 22.83/4.06      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 22.83/4.06    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 22.83/4.06      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 22.83/4.06    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 22.83/4.06          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 22.83/4.06      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 22.83/4.06      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 22.83/4.06      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 22.83/4.06    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 22.83/4.06      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 22.83/4.06      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 22.83/4.06    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 22.83/4.06      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 22.83/4.06    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 22.83/4.06      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 22.83/4.06    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 22.83/4.06    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 22.83/4.06    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 22.83/4.06      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 22.83/4.06      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 22.83/4.06      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 22.83/4.06  
% 22.83/4.06  Further assumptions not needed in the proof:
% 22.83/4.06  --------------------------------------------
% 22.83/4.07  const_array1_select, const_array2_select, defuse, finite_domain_1,
% 22.83/4.07  finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5,
% 22.83/4.07  gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1,
% 22.83/4.07  gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 22.83/4.07  gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1,
% 22.83/4.07  gt_succ, leq_geq, leq_gt2, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 22.83/4.07  leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 22.83/4.07  matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 22.83/4.07  matrix_symm_update_diagonal, pred_minus_1, reflexivity_leq, sel2_update_1,
% 22.83/4.07  sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3,
% 22.83/4.07  succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l,
% 22.83/4.07  succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r,
% 22.83/4.07  succ_pred, successor_1, successor_2, successor_3, successor_4, successor_5,
% 22.83/4.07  sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq,
% 22.83/4.07  ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 22.83/4.07  
% 22.83/4.07  Those formulas are unsatisfiable:
% 22.83/4.07  ---------------------------------
% 22.83/4.07  
% 22.83/4.07  Begin of proof
% 22.83/4.07  | 
% 22.83/4.07  | ALPHA: (leq_gt_pred) implies:
% 22.83/4.07  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 22.83/4.07  |          (leq(v0, v2) = 0) |  ~ $i(v1) |  ~ $i(v0) | gt(v1, v0) = 0)
% 22.83/4.07  | 
% 22.83/4.07  | ALPHA: (succ_tptp_minus_1) implies:
% 22.83/4.07  |   (2)  succ(tptp_minus_1) = n0
% 22.83/4.07  | 
% 22.83/4.07  | ALPHA: (finite_domain_0) implies:
% 22.83/4.07  |   (3)   ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 22.83/4.07  |            int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 22.83/4.07  | 
% 22.83/4.07  | ALPHA: (cl5_nebula_init_0001) implies:
% 22.83/4.07  |   (4)  $i(n0)
% 22.83/4.07  |   (5)  $i(tptp_minus_1)
% 22.83/4.07  |   (6)   ? [v0: $i] : ( ~ (uninit = init) & leq(v0, tptp_minus_1) = 0 & leq(n0,
% 22.83/4.07  |            v0) = 0 & $i(v0))
% 22.83/4.07  | 
% 22.83/4.07  | ALPHA: (function-axioms) implies:
% 22.83/4.07  |   (7)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 22.83/4.07  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 22.83/4.07  | 
% 22.83/4.07  | DELTA: instantiating (6) with fresh symbol all_51_0 gives:
% 22.83/4.07  |   (8)   ~ (uninit = init) & leq(all_51_0, tptp_minus_1) = 0 & leq(n0,
% 22.83/4.07  |          all_51_0) = 0 & $i(all_51_0)
% 22.83/4.07  | 
% 22.83/4.07  | ALPHA: (8) implies:
% 22.83/4.07  |   (9)  $i(all_51_0)
% 22.83/4.07  |   (10)  leq(n0, all_51_0) = 0
% 22.83/4.07  |   (11)  leq(all_51_0, tptp_minus_1) = 0
% 22.83/4.07  | 
% 22.83/4.07  | GROUND_INST: instantiating (3) with all_51_0, simplifying with (9), (10)
% 22.83/4.07  |              gives:
% 22.83/4.08  |   (12)  all_51_0 = n0 |  ? [v0: int] : ( ~ (v0 = 0) & leq(all_51_0, n0) = v0)
% 22.83/4.08  | 
% 22.83/4.08  | GROUND_INST: instantiating (pred_succ) with tptp_minus_1, n0, simplifying with
% 22.83/4.08  |              (2), (5) gives:
% 22.83/4.08  |   (13)  pred(n0) = tptp_minus_1
% 22.83/4.08  | 
% 22.83/4.08  | GROUND_INST: instantiating (1) with all_51_0, n0, tptp_minus_1, simplifying
% 22.83/4.08  |              with (4), (9), (11), (13) gives:
% 22.83/4.08  |   (14)  gt(n0, all_51_0) = 0
% 22.83/4.08  | 
% 22.83/4.08  | GROUND_INST: instantiating (leq_gt1) with all_51_0, n0, simplifying with (4),
% 22.83/4.08  |              (9), (14) gives:
% 22.83/4.08  |   (15)  leq(all_51_0, n0) = 0
% 22.83/4.08  | 
% 22.83/4.08  | BETA: splitting (12) gives:
% 22.83/4.08  | 
% 22.83/4.08  | Case 1:
% 22.83/4.08  | | 
% 22.83/4.08  | |   (16)  all_51_0 = n0
% 22.83/4.08  | | 
% 22.83/4.08  | | REDUCE: (14), (16) imply:
% 22.83/4.08  | |   (17)  gt(n0, n0) = 0
% 22.83/4.08  | | 
% 22.83/4.08  | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with (4),
% 22.83/4.08  | |              (17) gives:
% 22.83/4.08  | |   (18)  $false
% 22.83/4.08  | | 
% 22.83/4.08  | | CLOSE: (18) is inconsistent.
% 22.83/4.08  | | 
% 22.83/4.08  | Case 2:
% 22.83/4.08  | | 
% 22.83/4.08  | |   (19)   ? [v0: int] : ( ~ (v0 = 0) & leq(all_51_0, n0) = v0)
% 22.83/4.08  | | 
% 22.83/4.08  | | DELTA: instantiating (19) with fresh symbol all_116_0 gives:
% 22.83/4.08  | |   (20)   ~ (all_116_0 = 0) & leq(all_51_0, n0) = all_116_0
% 22.83/4.08  | | 
% 22.83/4.08  | | ALPHA: (20) implies:
% 22.83/4.08  | |   (21)   ~ (all_116_0 = 0)
% 22.83/4.08  | |   (22)  leq(all_51_0, n0) = all_116_0
% 22.83/4.08  | | 
% 22.83/4.08  | | GROUND_INST: instantiating (7) with 0, all_116_0, n0, all_51_0, simplifying
% 22.83/4.08  | |              with (15), (22) gives:
% 22.83/4.08  | |   (23)  all_116_0 = 0
% 22.83/4.08  | | 
% 22.83/4.08  | | REDUCE: (21), (23) imply:
% 22.83/4.08  | |   (24)  $false
% 22.83/4.08  | | 
% 22.83/4.08  | | CLOSE: (24) is inconsistent.
% 22.83/4.08  | | 
% 22.83/4.08  | End of split
% 22.83/4.08  | 
% 22.83/4.08  End of proof
% 22.83/4.08  % SZS output end Proof for theBenchmark
% 22.83/4.08  
% 22.83/4.08  3460ms
%------------------------------------------------------------------------------