TSTP Solution File: SWV099+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV099+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 : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 22:54:54 EDT 2023

% Result   : Theorem 15.31s 2.73s
% Output   : Proof 17.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV099+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n005.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 10:07:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.62  ________       _____
% 0.21/0.62  ___  __ \_________(_)________________________________
% 0.21/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62  
% 0.21/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62  (2023-06-19)
% 0.21/0.62  
% 0.21/0.62  (c) Philipp Rümmer, 2009-2023
% 0.21/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62                Amanda Stjerna.
% 0.21/0.62  Free software under BSD-3-Clause.
% 0.21/0.62  
% 0.21/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62  
% 0.21/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64  Running up to 7 provers in parallel.
% 0.21/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.02/1.50  Prover 4: Preprocessing ...
% 6.02/1.50  Prover 1: Preprocessing ...
% 6.02/1.54  Prover 5: Preprocessing ...
% 6.02/1.54  Prover 6: Preprocessing ...
% 6.02/1.54  Prover 2: Preprocessing ...
% 6.02/1.54  Prover 3: Preprocessing ...
% 6.02/1.54  Prover 0: Preprocessing ...
% 11.07/2.25  Prover 1: Warning: ignoring some quantifiers
% 12.06/2.33  Prover 3: Warning: ignoring some quantifiers
% 12.35/2.33  Prover 6: Proving ...
% 12.39/2.34  Prover 1: Constructing countermodel ...
% 12.39/2.36  Prover 3: Constructing countermodel ...
% 12.39/2.37  Prover 4: Warning: ignoring some quantifiers
% 13.31/2.48  Prover 4: Constructing countermodel ...
% 13.31/2.56  Prover 5: Proving ...
% 13.31/2.56  Prover 0: Proving ...
% 13.31/2.62  Prover 2: Proving ...
% 15.31/2.73  Prover 3: proved (2081ms)
% 15.31/2.73  
% 15.31/2.73  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.31/2.73  
% 15.31/2.73  Prover 2: stopped
% 15.31/2.73  Prover 0: stopped
% 15.31/2.74  Prover 5: stopped
% 15.36/2.74  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.36/2.74  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.36/2.74  Prover 6: stopped
% 15.36/2.74  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.36/2.74  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.36/2.74  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.37/2.91  Prover 8: Preprocessing ...
% 16.37/2.92  Prover 10: Preprocessing ...
% 16.37/2.93  Prover 7: Preprocessing ...
% 16.37/2.93  Prover 13: Preprocessing ...
% 17.08/2.96  Prover 1: Found proof (size 27)
% 17.08/2.96  Prover 1: proved (2313ms)
% 17.08/2.96  Prover 4: stopped
% 17.08/2.96  Prover 11: Preprocessing ...
% 17.08/2.98  Prover 10: stopped
% 17.30/2.99  Prover 7: stopped
% 17.30/3.02  Prover 13: stopped
% 17.30/3.03  Prover 11: stopped
% 17.61/3.10  Prover 8: Warning: ignoring some quantifiers
% 17.93/3.12  Prover 8: Constructing countermodel ...
% 17.93/3.13  Prover 8: stopped
% 17.93/3.13  
% 17.93/3.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.93/3.13  
% 17.93/3.14  % SZS output start Proof for theBenchmark
% 17.93/3.15  Assumptions after simplification:
% 17.93/3.15  ---------------------------------
% 17.93/3.15  
% 17.93/3.15    (quaternion_ds1_inuse_0011)
% 17.93/3.18    $i(z_defuse) & $i(n999) & $i(pv5) & $i(xinit_noise_defuse) &
% 17.93/3.18    $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 17.93/3.18    $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 17.93/3.18    &  ? [v0: $i] :  ? [v1: $i] : (minus(n999, n1) = v0 & minus(pv5, n1) = v1 &
% 17.93/3.18      a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 17.93/3.18      a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use
% 17.93/3.18      & a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse,
% 17.93/3.18        n3) = use & a_select2(xinit_noise_defuse, n2) = use &
% 17.93/3.18      a_select2(xinit_noise_defuse, n1) = use & a_select2(xinit_noise_defuse, n0)
% 17.93/3.18      = use & a_select2(xinit_mean_defuse, n5) = use &
% 17.93/3.18      a_select2(xinit_mean_defuse, n4) = use & a_select2(xinit_mean_defuse, n3) =
% 17.93/3.18      use & a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 17.93/3.18        n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 17.93/3.18      a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use &
% 17.93/3.18      a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use &
% 17.93/3.18      a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use &
% 17.93/3.18      a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use &
% 17.93/3.18      a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use &
% 17.93/3.18      a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & leq(pv5,
% 17.93/3.18        v0) = 0 & leq(n0, pv5) = 0 & $i(v1) & $i(v0) &  ! [v2: $i] :  ! [v3: $i] :
% 17.93/3.18      ( ~ (leq(v3, v1) = 0) |  ~ (leq(v2, n2) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ?
% 17.93/3.18        [v4: any] :  ? [v5: any] :  ? [v6: $i] :  ? [v7: $i] :
% 17.93/3.18        (a_select3(z_defuse, v2, v3) = v7 & a_select3(u_defuse, v2, v3) = v6 &
% 17.93/3.18          leq(n0, v3) = v5 & leq(n0, v2) = v4 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | 
% 17.93/3.18            ~ (v4 = 0) | (v7 = use & v6 = use)))) &  ? [v2: $i] :  ? [v3: $i] :  ?
% 17.93/3.18      [v4: $i] :  ? [v5: $i] : (a_select3(z_defuse, v2, v3) = v5 &
% 17.93/3.18        a_select3(u_defuse, v2, v3) = v4 & leq(v3, v1) = 0 & leq(v2, n2) = 0 &
% 17.93/3.18        leq(n0, v3) = 0 & leq(n0, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & (
% 17.93/3.18          ~ (v5 = use) |  ~ (v4 = use))))
% 17.93/3.18  
% 17.93/3.18    (function-axioms)
% 17.93/3.19     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 17.93/3.19      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 17.93/3.19      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 17.93/3.19      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 17.93/3.19        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.93/3.19    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 17.93/3.19      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 17.93/3.19    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 17.93/3.19      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.93/3.19    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 17.93/3.19        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 17.93/3.19    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 17.93/3.19          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 17.93/3.19      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.93/3.19    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 17.93/3.19      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 17.93/3.19    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 17.93/3.19        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 17.93/3.19      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.93/3.19    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 17.93/3.19      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 17.93/3.19    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 17.93/3.19          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 17.93/3.19      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 17.93/3.19      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 17.93/3.19      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 17.93/3.19    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 17.93/3.19      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 17.93/3.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.93/3.19    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 17.93/3.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.93/3.19    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 17.93/3.19      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 17.93/3.19    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 17.93/3.19    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 17.93/3.19    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 17.93/3.19      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 17.93/3.19      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 17.93/3.19      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 17.93/3.19  
% 17.93/3.19  Further assumptions not needed in the proof:
% 17.93/3.19  --------------------------------------------
% 17.93/3.19  const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.93/3.19  finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.93/3.19  finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1,
% 17.93/3.19  gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1,
% 17.93/3.19  gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4,
% 17.93/3.19  gt_5_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, gt_999_3, gt_999_4, gt_999_5,
% 17.93/3.19  gt_999_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2,
% 17.93/3.19  leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ,
% 17.93/3.19  lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 17.93/3.19  matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 17.93/3.19  matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 17.93/3.19  sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 17.93/3.19  sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 17.93/3.19  succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 17.93/3.19  succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2,
% 17.93/3.19  successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float,
% 17.93/3.19  totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 17.93/3.19  uniform_int_rand_ranges_lo
% 17.93/3.19  
% 17.93/3.19  Those formulas are unsatisfiable:
% 17.93/3.19  ---------------------------------
% 17.93/3.19  
% 17.93/3.19  Begin of proof
% 17.93/3.19  | 
% 17.93/3.19  | ALPHA: (quaternion_ds1_inuse_0011) implies:
% 17.93/3.20  |   (1)   ? [v0: $i] :  ? [v1: $i] : (minus(n999, n1) = v0 & minus(pv5, n1) = v1
% 17.93/3.20  |          & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) =
% 17.93/3.20  |          use & a_select3(u_defuse, n0, n0) = use &
% 17.93/3.20  |          a_select2(xinit_noise_defuse, n5) = use &
% 17.93/3.20  |          a_select2(xinit_noise_defuse, n4) = use &
% 17.93/3.20  |          a_select2(xinit_noise_defuse, n3) = use &
% 17.93/3.20  |          a_select2(xinit_noise_defuse, n2) = use &
% 17.93/3.20  |          a_select2(xinit_noise_defuse, n1) = use &
% 17.93/3.20  |          a_select2(xinit_noise_defuse, n0) = use &
% 17.93/3.20  |          a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 17.93/3.20  |            n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 17.93/3.20  |          a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 17.93/3.20  |            n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 17.93/3.20  |          a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 17.93/3.20  |          & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 17.93/3.20  |          use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 17.93/3.20  |          = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 17.93/3.20  |            n1) = use & a_select2(sigma_defuse, n0) = use &
% 17.93/3.20  |          a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 17.93/3.20  |          a_select2(rho_defuse, n0) = use & leq(pv5, v0) = 0 & leq(n0, pv5) = 0
% 17.93/3.20  |          & $i(v1) & $i(v0) &  ! [v2: $i] :  ! [v3: $i] : ( ~ (leq(v3, v1) = 0)
% 17.93/3.20  |            |  ~ (leq(v2, n2) = 0) |  ~ $i(v3) |  ~ $i(v2) |  ? [v4: any] :  ?
% 17.93/3.20  |            [v5: any] :  ? [v6: $i] :  ? [v7: $i] : (a_select3(z_defuse, v2,
% 17.93/3.20  |                v3) = v7 & a_select3(u_defuse, v2, v3) = v6 & leq(n0, v3) = v5
% 17.93/3.20  |              & leq(n0, v2) = v4 & $i(v7) & $i(v6) & ( ~ (v5 = 0) |  ~ (v4 = 0)
% 17.93/3.20  |                | (v7 = use & v6 = use)))) &  ? [v2: $i] :  ? [v3: $i] :  ?
% 17.93/3.20  |          [v4: $i] :  ? [v5: $i] : (a_select3(z_defuse, v2, v3) = v5 &
% 17.93/3.20  |            a_select3(u_defuse, v2, v3) = v4 & leq(v3, v1) = 0 & leq(v2, n2) =
% 17.93/3.20  |            0 & leq(n0, v3) = 0 & leq(n0, v2) = 0 & $i(v5) & $i(v4) & $i(v3) &
% 17.93/3.20  |            $i(v2) & ( ~ (v5 = use) |  ~ (v4 = use))))
% 17.93/3.20  | 
% 17.93/3.20  | ALPHA: (function-axioms) implies:
% 17.93/3.20  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 17.93/3.20  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 17.93/3.20  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 17.93/3.20  |        (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2)
% 17.93/3.20  |            = v0))
% 17.93/3.20  | 
% 17.93/3.20  | DELTA: instantiating (1) with fresh symbols all_74_0, all_74_1 gives:
% 17.93/3.21  |   (4)  minus(n999, n1) = all_74_1 & minus(pv5, n1) = all_74_0 &
% 17.93/3.21  |        a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 17.93/3.21  |        a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 17.93/3.21  |        use & a_select2(xinit_noise_defuse, n4) = use &
% 17.93/3.21  |        a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 17.93/3.21  |          n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 17.93/3.21  |        a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 17.93/3.21  |          n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 17.93/3.21  |        a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 17.93/3.21  |          n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 17.93/3.21  |        a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 17.93/3.21  |        use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 17.93/3.21  |        use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 17.93/3.21  |        use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 17.93/3.21  |        use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 17.93/3.21  |        use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 17.93/3.21  |        & a_select2(rho_defuse, n0) = use & leq(pv5, all_74_1) = 0 & leq(n0,
% 17.93/3.21  |          pv5) = 0 & $i(all_74_0) & $i(all_74_1) &  ! [v0: $i] :  ! [v1: $i] :
% 17.93/3.21  |        ( ~ (leq(v1, all_74_0) = 0) |  ~ (leq(v0, n2) = 0) |  ~ $i(v1) |  ~
% 17.93/3.21  |          $i(v0) |  ? [v2: any] :  ? [v3: any] :  ? [v4: $i] :  ? [v5: $i] :
% 17.93/3.21  |          (a_select3(z_defuse, v0, v1) = v5 & a_select3(u_defuse, v0, v1) = v4
% 17.93/3.21  |            & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v5) & $i(v4) & ( ~ (v3 =
% 17.93/3.21  |                0) |  ~ (v2 = 0) | (v5 = use & v4 = use)))) &  ? [v0: $i] :  ?
% 17.93/3.21  |        [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (a_select3(z_defuse, v0, v1) =
% 17.93/3.21  |          v3 & a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_74_0) = 0 &
% 17.93/3.21  |          leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2)
% 17.93/3.21  |          & $i(v1) & $i(v0) & ( ~ (v3 = use) |  ~ (v2 = use)))
% 17.93/3.21  | 
% 17.93/3.21  | ALPHA: (4) implies:
% 17.93/3.21  |   (5)   ! [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_74_0) = 0) |  ~ (leq(v0,
% 17.93/3.21  |              n2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : 
% 17.93/3.21  |          ? [v4: $i] :  ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 &
% 17.93/3.21  |            a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) =
% 17.93/3.21  |            v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0) | (v5 = use & v4
% 17.93/3.21  |                = use))))
% 17.93/3.21  |   (6)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :
% 17.93/3.21  |        (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 &
% 17.93/3.21  |          leq(v1, all_74_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0,
% 17.93/3.21  |            v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) |  ~
% 17.93/3.21  |            (v2 = use)))
% 17.93/3.21  | 
% 17.93/3.21  | DELTA: instantiating (6) with fresh symbols all_79_0, all_79_1, all_79_2,
% 17.93/3.21  |        all_79_3 gives:
% 17.93/3.21  |   (7)  a_select3(z_defuse, all_79_3, all_79_2) = all_79_0 &
% 17.93/3.21  |        a_select3(u_defuse, all_79_3, all_79_2) = all_79_1 & leq(all_79_2,
% 17.93/3.21  |          all_74_0) = 0 & leq(all_79_3, n2) = 0 & leq(n0, all_79_2) = 0 &
% 17.93/3.21  |        leq(n0, all_79_3) = 0 & $i(all_79_0) & $i(all_79_1) & $i(all_79_2) &
% 17.93/3.21  |        $i(all_79_3) & ( ~ (all_79_0 = use) |  ~ (all_79_1 = use))
% 17.93/3.21  | 
% 17.93/3.21  | ALPHA: (7) implies:
% 17.93/3.21  |   (8)  $i(all_79_3)
% 17.93/3.21  |   (9)  $i(all_79_2)
% 17.93/3.21  |   (10)  leq(n0, all_79_3) = 0
% 17.93/3.21  |   (11)  leq(n0, all_79_2) = 0
% 17.93/3.21  |   (12)  leq(all_79_3, n2) = 0
% 17.93/3.21  |   (13)  leq(all_79_2, all_74_0) = 0
% 17.93/3.21  |   (14)  a_select3(u_defuse, all_79_3, all_79_2) = all_79_1
% 17.93/3.21  |   (15)  a_select3(z_defuse, all_79_3, all_79_2) = all_79_0
% 17.93/3.21  |   (16)   ~ (all_79_0 = use) |  ~ (all_79_1 = use)
% 17.93/3.22  | 
% 17.93/3.22  | GROUND_INST: instantiating (5) with all_79_3, all_79_2, simplifying with (8),
% 17.93/3.22  |              (9), (12), (13) gives:
% 17.93/3.22  |   (17)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :  ? [v3: $i] :
% 17.93/3.22  |         (a_select3(z_defuse, all_79_3, all_79_2) = v3 & a_select3(u_defuse,
% 17.93/3.22  |             all_79_3, all_79_2) = v2 & leq(n0, all_79_2) = v1 & leq(n0,
% 17.93/3.22  |             all_79_3) = v0 & $i(v3) & $i(v2) & ( ~ (v1 = 0) |  ~ (v0 = 0) |
% 17.93/3.22  |             (v3 = use & v2 = use)))
% 17.93/3.22  | 
% 17.93/3.22  | DELTA: instantiating (17) with fresh symbols all_103_0, all_103_1, all_103_2,
% 17.93/3.22  |        all_103_3 gives:
% 17.93/3.22  |   (18)  a_select3(z_defuse, all_79_3, all_79_2) = all_103_0 &
% 17.93/3.22  |         a_select3(u_defuse, all_79_3, all_79_2) = all_103_1 & leq(n0,
% 17.93/3.22  |           all_79_2) = all_103_2 & leq(n0, all_79_3) = all_103_3 &
% 17.93/3.22  |         $i(all_103_0) & $i(all_103_1) & ( ~ (all_103_2 = 0) |  ~ (all_103_3 =
% 17.93/3.22  |             0) | (all_103_0 = use & all_103_1 = use))
% 17.93/3.22  | 
% 17.93/3.22  | ALPHA: (18) implies:
% 17.93/3.22  |   (19)  leq(n0, all_79_3) = all_103_3
% 17.93/3.22  |   (20)  leq(n0, all_79_2) = all_103_2
% 17.93/3.22  |   (21)  a_select3(u_defuse, all_79_3, all_79_2) = all_103_1
% 17.93/3.22  |   (22)  a_select3(z_defuse, all_79_3, all_79_2) = all_103_0
% 17.93/3.22  |   (23)   ~ (all_103_2 = 0) |  ~ (all_103_3 = 0) | (all_103_0 = use & all_103_1
% 17.93/3.22  |           = use)
% 17.93/3.22  | 
% 17.93/3.22  | GROUND_INST: instantiating (2) with 0, all_103_3, all_79_3, n0, simplifying
% 17.93/3.22  |              with (10), (19) gives:
% 17.93/3.22  |   (24)  all_103_3 = 0
% 17.93/3.22  | 
% 17.93/3.22  | GROUND_INST: instantiating (2) with 0, all_103_2, all_79_2, n0, simplifying
% 17.93/3.22  |              with (11), (20) gives:
% 17.93/3.22  |   (25)  all_103_2 = 0
% 17.93/3.22  | 
% 17.93/3.22  | GROUND_INST: instantiating (3) with all_79_1, all_103_1, all_79_2, all_79_3,
% 17.93/3.22  |              u_defuse, simplifying with (14), (21) gives:
% 17.93/3.22  |   (26)  all_103_1 = all_79_1
% 17.93/3.22  | 
% 17.93/3.22  | GROUND_INST: instantiating (3) with all_79_0, all_103_0, all_79_2, all_79_3,
% 17.93/3.22  |              z_defuse, simplifying with (15), (22) gives:
% 17.93/3.22  |   (27)  all_103_0 = all_79_0
% 17.93/3.22  | 
% 17.93/3.22  | BETA: splitting (23) gives:
% 17.93/3.22  | 
% 17.93/3.22  | Case 1:
% 17.93/3.22  | | 
% 17.93/3.22  | |   (28)   ~ (all_103_2 = 0)
% 17.93/3.22  | | 
% 17.93/3.22  | | REDUCE: (25), (28) imply:
% 17.93/3.22  | |   (29)  $false
% 17.93/3.22  | | 
% 17.93/3.22  | | CLOSE: (29) is inconsistent.
% 17.93/3.22  | | 
% 17.93/3.22  | Case 2:
% 17.93/3.22  | | 
% 17.93/3.22  | |   (30)   ~ (all_103_3 = 0) | (all_103_0 = use & all_103_1 = use)
% 17.93/3.22  | | 
% 17.93/3.22  | | BETA: splitting (30) gives:
% 17.93/3.22  | | 
% 17.93/3.22  | | Case 1:
% 17.93/3.22  | | | 
% 17.93/3.23  | | |   (31)   ~ (all_103_3 = 0)
% 17.93/3.23  | | | 
% 17.93/3.23  | | | REDUCE: (24), (31) imply:
% 17.93/3.23  | | |   (32)  $false
% 17.93/3.23  | | | 
% 17.93/3.23  | | | CLOSE: (32) is inconsistent.
% 17.93/3.23  | | | 
% 17.93/3.23  | | Case 2:
% 17.93/3.23  | | | 
% 17.93/3.23  | | |   (33)  all_103_0 = use & all_103_1 = use
% 17.93/3.23  | | | 
% 17.93/3.23  | | | ALPHA: (33) implies:
% 17.93/3.23  | | |   (34)  all_103_1 = use
% 17.93/3.23  | | |   (35)  all_103_0 = use
% 17.93/3.23  | | | 
% 17.93/3.23  | | | COMBINE_EQS: (27), (35) imply:
% 17.93/3.23  | | |   (36)  all_79_0 = use
% 17.93/3.23  | | | 
% 17.93/3.23  | | | COMBINE_EQS: (26), (34) imply:
% 17.93/3.23  | | |   (37)  all_79_1 = use
% 17.93/3.23  | | | 
% 17.93/3.23  | | | BETA: splitting (16) gives:
% 17.93/3.23  | | | 
% 17.93/3.23  | | | Case 1:
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | |   (38)   ~ (all_79_0 = use)
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | | REDUCE: (36), (38) imply:
% 17.93/3.23  | | | |   (39)  $false
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | | CLOSE: (39) is inconsistent.
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | Case 2:
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | |   (40)   ~ (all_79_1 = use)
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | | REDUCE: (37), (40) imply:
% 17.93/3.23  | | | |   (41)  $false
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | | CLOSE: (41) is inconsistent.
% 17.93/3.23  | | | | 
% 17.93/3.23  | | | End of split
% 17.93/3.23  | | | 
% 17.93/3.23  | | End of split
% 17.93/3.23  | | 
% 17.93/3.23  | End of split
% 17.93/3.23  | 
% 17.93/3.23  End of proof
% 17.93/3.23  % SZS output end Proof for theBenchmark
% 17.93/3.23  
% 17.93/3.23  2602ms
%------------------------------------------------------------------------------