TSTP Solution File: SWV197+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV197+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 : n011.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 22:55:18 EDT 2023

% Result   : Theorem 15.11s 2.76s
% Output   : Proof 18.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV197+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 09:50:41 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59  ________       _____
% 0.19/0.59  ___  __ \_________(_)________________________________
% 0.19/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59  
% 0.19/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59  (2023-06-19)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2023
% 0.19/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59                Amanda Stjerna.
% 0.19/0.59  Free software under BSD-3-Clause.
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59  
% 0.19/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.30/1.37  Prover 4: Preprocessing ...
% 4.30/1.37  Prover 1: Preprocessing ...
% 4.30/1.41  Prover 2: Preprocessing ...
% 4.30/1.41  Prover 5: Preprocessing ...
% 4.30/1.41  Prover 6: Preprocessing ...
% 4.30/1.41  Prover 0: Preprocessing ...
% 4.30/1.41  Prover 3: Preprocessing ...
% 11.14/2.26  Prover 1: Warning: ignoring some quantifiers
% 11.14/2.30  Prover 3: Warning: ignoring some quantifiers
% 11.14/2.31  Prover 6: Proving ...
% 11.79/2.33  Prover 1: Constructing countermodel ...
% 11.79/2.33  Prover 3: Constructing countermodel ...
% 11.79/2.36  Prover 4: Warning: ignoring some quantifiers
% 13.03/2.49  Prover 4: Constructing countermodel ...
% 13.27/2.51  Prover 0: Proving ...
% 13.38/2.57  Prover 2: Proving ...
% 13.38/2.59  Prover 5: Proving ...
% 14.29/2.76  Prover 3: proved (2137ms)
% 15.11/2.76  
% 15.11/2.76  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.11/2.76  
% 15.11/2.77  Prover 6: stopped
% 15.11/2.77  Prover 5: stopped
% 15.11/2.77  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.11/2.77  Prover 2: stopped
% 15.11/2.77  Prover 0: stopped
% 15.11/2.77  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.11/2.77  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.11/2.77  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.11/2.77  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.04/2.93  Prover 13: Preprocessing ...
% 16.04/2.93  Prover 8: Preprocessing ...
% 16.51/2.96  Prover 11: Preprocessing ...
% 16.51/2.96  Prover 10: Preprocessing ...
% 16.51/2.96  Prover 7: Preprocessing ...
% 16.98/3.04  Prover 1: Found proof (size 30)
% 16.98/3.04  Prover 1: proved (2426ms)
% 16.98/3.05  Prover 4: stopped
% 16.98/3.05  Prover 10: stopped
% 17.35/3.07  Prover 7: stopped
% 17.35/3.09  Prover 11: stopped
% 17.35/3.10  Prover 13: stopped
% 17.98/3.20  Prover 8: Warning: ignoring some quantifiers
% 17.98/3.22  Prover 8: Constructing countermodel ...
% 18.22/3.24  Prover 8: stopped
% 18.22/3.24  
% 18.22/3.24  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.22/3.24  
% 18.22/3.25  % SZS output start Proof for theBenchmark
% 18.22/3.26  Assumptions after simplification:
% 18.22/3.26  ---------------------------------
% 18.22/3.26  
% 18.22/3.26    (finite_domain_0)
% 18.22/3.30    $i(n0) &  ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 18.22/3.30        int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 18.22/3.30  
% 18.22/3.30    (quaternion_ds1_inuse_0008)
% 18.38/3.31    $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 18.38/3.31    $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 18.38/3.31    $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 18.38/3.31    &  ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 18.38/3.31        n0) = use & a_select3(u_defuse, n0, n0) = use &
% 18.38/3.31      a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 18.38/3.31      = use & a_select2(xinit_noise_defuse, n3) = use &
% 18.38/3.31      a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 18.38/3.31      = use & a_select2(xinit_noise_defuse, n0) = use &
% 18.38/3.31      a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 18.38/3.31      use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 18.38/3.31        n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 18.38/3.31      a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 18.38/3.31      a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 18.38/3.31      a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 18.38/3.31      a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 18.38/3.31      a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 18.38/3.31      a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 18.38/3.31      a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 &
% 18.38/3.31      leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) &  ! [v1: $i] :  ! [v2: $i] : (
% 18.38/3.31        ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ?
% 18.38/3.31        [v3: any] :  ? [v4: any] :  ? [v5: $i] : (a_select3(z_defuse, v1, v2) = v5
% 18.38/3.31          & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 =
% 18.38/3.31              0) | v5 = use))) &  ! [v1: $i] :  ! [v2: $i] : ( ~ (leq(v2, v0) = 0)
% 18.38/3.31        |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 18.38/3.31          any] :  ? [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) =
% 18.38/3.31          v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 =
% 18.38/3.31            use))) &  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = use) &
% 18.38/3.31        a_select3(z_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) = 0 &
% 18.38/3.31        leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v2 =
% 18.38/3.31            pv5) |  ~ (v1 = n2)) & ( ~ (v2 = pv5) |  ~ (v1 = n1)) & ( ~ (v2 = pv5)
% 18.38/3.31          |  ~ (v1 = n0))))
% 18.38/3.31  
% 18.38/3.31    (function-axioms)
% 18.38/3.32     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 18.38/3.32      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 18.38/3.32      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 18.38/3.32      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 18.38/3.32        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 18.38/3.32    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 18.38/3.32      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 18.38/3.32    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 18.38/3.32      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 18.38/3.32    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 18.38/3.32        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 18.38/3.32    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 18.38/3.32          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 18.38/3.32      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.38/3.32    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 18.38/3.32      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 18.38/3.32    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 18.38/3.32        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 18.38/3.32      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.38/3.32    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 18.38/3.32      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 18.38/3.32    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 18.38/3.32          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 18.38/3.32      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 18.38/3.32      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 18.38/3.32      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 18.38/3.32    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 18.38/3.32      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 18.38/3.32      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 18.38/3.32    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 18.38/3.32      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 18.38/3.32    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 18.38/3.32      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 18.38/3.32    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.38/3.32    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 18.38/3.32    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 18.38/3.32      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 18.38/3.32      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 18.38/3.32      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 18.38/3.32  
% 18.38/3.32  Further assumptions not needed in the proof:
% 18.38/3.32  --------------------------------------------
% 18.38/3.32  const_array1_select, const_array2_select, defuse, finite_domain_1,
% 18.38/3.32  finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5,
% 18.38/3.32  gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1,
% 18.38/3.32  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,
% 18.38/3.32  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,
% 18.38/3.32  gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1,
% 18.38/3.32  gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus,
% 18.38/3.32  leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt,
% 18.38/3.32  matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 18.38/3.32  matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 18.38/3.32  matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 18.38/3.32  sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 18.38/3.32  sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 18.38/3.32  succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 18.38/3.32  succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2,
% 18.38/3.32  successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float,
% 18.38/3.32  totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 18.38/3.32  uniform_int_rand_ranges_lo
% 18.38/3.32  
% 18.38/3.32  Those formulas are unsatisfiable:
% 18.38/3.32  ---------------------------------
% 18.38/3.32  
% 18.38/3.32  Begin of proof
% 18.38/3.32  | 
% 18.38/3.32  | ALPHA: (finite_domain_0) implies:
% 18.38/3.33  |   (1)   ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 18.38/3.33  |            int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 18.38/3.33  | 
% 18.38/3.33  | ALPHA: (quaternion_ds1_inuse_0008) implies:
% 18.38/3.33  |   (2)  $i(pv5)
% 18.38/3.33  |   (3)   ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 18.38/3.33  |            n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 18.38/3.33  |          a_select2(xinit_noise_defuse, n5) = use &
% 18.38/3.33  |          a_select2(xinit_noise_defuse, n4) = use &
% 18.38/3.33  |          a_select2(xinit_noise_defuse, n3) = use &
% 18.38/3.33  |          a_select2(xinit_noise_defuse, n2) = use &
% 18.38/3.33  |          a_select2(xinit_noise_defuse, n1) = use &
% 18.38/3.33  |          a_select2(xinit_noise_defuse, n0) = use &
% 18.38/3.33  |          a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 18.38/3.33  |            n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 18.38/3.33  |          a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 18.38/3.33  |            n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 18.38/3.33  |          a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 18.38/3.33  |          & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 18.38/3.33  |          use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 18.38/3.33  |          = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 18.38/3.33  |            n1) = use & a_select2(sigma_defuse, n0) = use &
% 18.38/3.33  |          a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 18.38/3.33  |          a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0
% 18.38/3.33  |          & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) &  ! [v1: $i] :  !
% 18.38/3.33  |          [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) |
% 18.38/3.33  |             ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] :
% 18.38/3.33  |            (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1)
% 18.38/3.33  |              = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = use))) &  !
% 18.38/3.33  |          [v1: $i] :  ! [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0)
% 18.38/3.33  |            |  ~ $i(v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i]
% 18.38/3.33  |            : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0,
% 18.38/3.33  |                v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = use))) & 
% 18.38/3.33  |          ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = use) &
% 18.38/3.33  |            a_select3(z_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) =
% 18.38/3.33  |            0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 18.38/3.33  |            ( ~ (v2 = pv5) |  ~ (v1 = n2)) & ( ~ (v2 = pv5) |  ~ (v1 = n1)) & (
% 18.38/3.33  |              ~ (v2 = pv5) |  ~ (v1 = n0))))
% 18.38/3.33  | 
% 18.38/3.33  | ALPHA: (function-axioms) implies:
% 18.38/3.33  |   (4)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 18.38/3.33  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 18.38/3.33  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 18.38/3.33  |        (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2)
% 18.38/3.33  |            = v0))
% 18.38/3.33  | 
% 18.38/3.33  | DELTA: instantiating (3) with fresh symbol all_76_0 gives:
% 18.38/3.34  |   (6)  a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 18.38/3.34  |        a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 18.38/3.34  |        use & a_select2(xinit_noise_defuse, n4) = use &
% 18.38/3.34  |        a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 18.38/3.34  |          n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 18.38/3.34  |        a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 18.38/3.34  |          n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 18.38/3.34  |        a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 18.38/3.34  |          n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 18.38/3.34  |        a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 18.38/3.34  |        use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 18.38/3.34  |        use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 18.38/3.34  |        use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 18.38/3.34  |        use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 18.38/3.34  |        use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 18.38/3.34  |        & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5,
% 18.38/3.34  |          n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(all_76_0) &  !
% 18.38/3.34  |        [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) |  ~ (leq(v0, n2)
% 18.38/3.34  |            = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] :  ?
% 18.38/3.34  |          [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 18.38/3.34  |            leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0) | v4 =
% 18.38/3.34  |              use))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0)
% 18.38/3.34  |          |  ~ (leq(v0, n2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ?
% 18.38/3.34  |          [v3: any] :  ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0,
% 18.38/3.34  |              v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0)
% 18.38/3.34  |              | v4 = use))) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2
% 18.38/3.34  |            = use) & a_select3(z_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 &
% 18.38/3.34  |          leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1)
% 18.38/3.34  |          & $i(v0) & ( ~ (v1 = pv5) |  ~ (v0 = n2)) & ( ~ (v1 = pv5) |  ~ (v0 =
% 18.38/3.34  |              n1)) & ( ~ (v1 = pv5) |  ~ (v0 = n0)))
% 18.38/3.34  | 
% 18.38/3.34  | ALPHA: (6) implies:
% 18.38/3.34  |   (7)  leq(n0, pv5) = 0
% 18.38/3.34  |   (8)  leq(pv5, n0) = 0
% 18.38/3.34  |   (9)   ! [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) |  ~ (leq(v0,
% 18.38/3.34  |              n2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : 
% 18.38/3.34  |          ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 18.38/3.34  |            leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0) | v4 =
% 18.38/3.34  |              use)))
% 18.38/3.34  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = use) &
% 18.38/3.34  |           a_select3(z_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 & leq(v0,
% 18.38/3.34  |             n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) &
% 18.38/3.34  |           $i(v0) & ( ~ (v1 = pv5) |  ~ (v0 = n2)) & ( ~ (v1 = pv5) |  ~ (v0 =
% 18.38/3.34  |               n1)) & ( ~ (v1 = pv5) |  ~ (v0 = n0)))
% 18.38/3.34  | 
% 18.38/3.34  | DELTA: instantiating (10) with fresh symbols all_79_0, all_79_1, all_79_2
% 18.38/3.34  |        gives:
% 18.38/3.34  |   (11)   ~ (all_79_0 = use) & a_select3(z_defuse, all_79_2, all_79_1) =
% 18.38/3.34  |         all_79_0 & leq(all_79_1, all_76_0) = 0 & leq(all_79_2, n2) = 0 &
% 18.38/3.34  |         leq(n0, all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) &
% 18.38/3.34  |         $i(all_79_1) & $i(all_79_2) & ( ~ (all_79_1 = pv5) |  ~ (all_79_2 =
% 18.38/3.34  |             n2)) & ( ~ (all_79_1 = pv5) |  ~ (all_79_2 = n1)) & ( ~ (all_79_1
% 18.38/3.34  |             = pv5) |  ~ (all_79_2 = n0))
% 18.38/3.34  | 
% 18.38/3.34  | ALPHA: (11) implies:
% 18.38/3.34  |   (12)   ~ (all_79_0 = use)
% 18.38/3.34  |   (13)  $i(all_79_2)
% 18.38/3.34  |   (14)  $i(all_79_1)
% 18.38/3.34  |   (15)  leq(n0, all_79_2) = 0
% 18.38/3.34  |   (16)  leq(n0, all_79_1) = 0
% 18.38/3.34  |   (17)  leq(all_79_2, n2) = 0
% 18.38/3.34  |   (18)  leq(all_79_1, all_76_0) = 0
% 18.38/3.34  |   (19)  a_select3(z_defuse, all_79_2, all_79_1) = all_79_0
% 18.38/3.34  | 
% 18.38/3.35  | GROUND_INST: instantiating (1) with pv5, simplifying with (2), (7) gives:
% 18.38/3.35  |   (20)  pv5 = n0 |  ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 18.38/3.35  | 
% 18.38/3.35  | GROUND_INST: instantiating (9) with all_79_2, all_79_1, simplifying with (13),
% 18.38/3.35  |              (14), (17), (18) gives:
% 18.38/3.35  |   (21)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (a_select3(z_defuse,
% 18.38/3.35  |             all_79_2, all_79_1) = v2 & leq(n0, all_79_1) = v1 & leq(n0,
% 18.38/3.35  |             all_79_2) = v0 & $i(v2) & ( ~ (v1 = 0) |  ~ (v0 = 0) | v2 = use))
% 18.38/3.35  | 
% 18.38/3.35  | DELTA: instantiating (21) with fresh symbols all_105_0, all_105_1, all_105_2
% 18.38/3.35  |        gives:
% 18.38/3.35  |   (22)  a_select3(z_defuse, all_79_2, all_79_1) = all_105_0 & leq(n0,
% 18.38/3.35  |           all_79_1) = all_105_1 & leq(n0, all_79_2) = all_105_2 &
% 18.38/3.35  |         $i(all_105_0) & ( ~ (all_105_1 = 0) |  ~ (all_105_2 = 0) | all_105_0 =
% 18.38/3.35  |           use)
% 18.38/3.35  | 
% 18.38/3.35  | ALPHA: (22) implies:
% 18.38/3.35  |   (23)  leq(n0, all_79_2) = all_105_2
% 18.38/3.35  |   (24)  leq(n0, all_79_1) = all_105_1
% 18.38/3.35  |   (25)  a_select3(z_defuse, all_79_2, all_79_1) = all_105_0
% 18.38/3.35  |   (26)   ~ (all_105_1 = 0) |  ~ (all_105_2 = 0) | all_105_0 = use
% 18.38/3.35  | 
% 18.38/3.35  | BETA: splitting (20) gives:
% 18.38/3.35  | 
% 18.38/3.35  | Case 1:
% 18.38/3.35  | | 
% 18.38/3.35  | | 
% 18.38/3.35  | | GROUND_INST: instantiating (4) with 0, all_105_2, all_79_2, n0, simplifying
% 18.38/3.35  | |              with (15), (23) gives:
% 18.38/3.35  | |   (27)  all_105_2 = 0
% 18.38/3.35  | | 
% 18.38/3.35  | | GROUND_INST: instantiating (4) with 0, all_105_1, all_79_1, n0, simplifying
% 18.38/3.35  | |              with (16), (24) gives:
% 18.38/3.35  | |   (28)  all_105_1 = 0
% 18.38/3.35  | | 
% 18.38/3.35  | | GROUND_INST: instantiating (5) with all_79_0, all_105_0, all_79_1, all_79_2,
% 18.38/3.35  | |              z_defuse, simplifying with (19), (25) gives:
% 18.38/3.35  | |   (29)  all_105_0 = all_79_0
% 18.38/3.35  | | 
% 18.38/3.35  | | BETA: splitting (26) gives:
% 18.38/3.35  | | 
% 18.38/3.35  | | Case 1:
% 18.38/3.35  | | | 
% 18.38/3.35  | | |   (30)   ~ (all_105_1 = 0)
% 18.38/3.35  | | | 
% 18.38/3.35  | | | REDUCE: (28), (30) imply:
% 18.38/3.35  | | |   (31)  $false
% 18.38/3.35  | | | 
% 18.38/3.35  | | | CLOSE: (31) is inconsistent.
% 18.38/3.35  | | | 
% 18.38/3.35  | | Case 2:
% 18.38/3.35  | | | 
% 18.38/3.35  | | |   (32)   ~ (all_105_2 = 0) | all_105_0 = use
% 18.38/3.35  | | | 
% 18.38/3.35  | | | BETA: splitting (32) gives:
% 18.38/3.35  | | | 
% 18.38/3.35  | | | Case 1:
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | |   (33)   ~ (all_105_2 = 0)
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | | REDUCE: (27), (33) imply:
% 18.38/3.35  | | | |   (34)  $false
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | | CLOSE: (34) is inconsistent.
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | Case 2:
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | |   (35)  all_105_0 = use
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | | COMBINE_EQS: (29), (35) imply:
% 18.38/3.35  | | | |   (36)  all_79_0 = use
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | | REDUCE: (12), (36) imply:
% 18.38/3.35  | | | |   (37)  $false
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | | CLOSE: (37) is inconsistent.
% 18.38/3.35  | | | | 
% 18.38/3.35  | | | End of split
% 18.38/3.35  | | | 
% 18.38/3.35  | | End of split
% 18.38/3.35  | | 
% 18.38/3.35  | Case 2:
% 18.38/3.35  | | 
% 18.38/3.35  | |   (38)   ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 18.38/3.35  | | 
% 18.38/3.35  | | DELTA: instantiating (38) with fresh symbol all_111_0 gives:
% 18.38/3.35  | |   (39)   ~ (all_111_0 = 0) & leq(pv5, n0) = all_111_0
% 18.38/3.35  | | 
% 18.38/3.35  | | ALPHA: (39) implies:
% 18.38/3.35  | |   (40)   ~ (all_111_0 = 0)
% 18.38/3.35  | |   (41)  leq(pv5, n0) = all_111_0
% 18.38/3.35  | | 
% 18.38/3.35  | | GROUND_INST: instantiating (4) with 0, all_111_0, n0, pv5, simplifying with
% 18.38/3.35  | |              (8), (41) gives:
% 18.38/3.35  | |   (42)  all_111_0 = 0
% 18.38/3.35  | | 
% 18.38/3.35  | | REDUCE: (40), (42) imply:
% 18.38/3.35  | |   (43)  $false
% 18.38/3.35  | | 
% 18.38/3.35  | | CLOSE: (43) is inconsistent.
% 18.38/3.35  | | 
% 18.38/3.35  | End of split
% 18.38/3.35  | 
% 18.38/3.35  End of proof
% 18.38/3.36  % SZS output end Proof for theBenchmark
% 18.38/3.36  
% 18.38/3.36  2763ms
%------------------------------------------------------------------------------