TSTP Solution File: SWV094+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV094+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 : n010.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 22:54:53 EDT 2023

% Result   : Theorem 15.43s 2.91s
% Output   : Proof 19.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWV094+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.14/0.15  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Tue Aug 29 07:47:49 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.22/0.63  ________       _____
% 0.22/0.63  ___  __ \_________(_)________________________________
% 0.22/0.63  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.22/0.63  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.22/0.63  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63  
% 0.22/0.63  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63  (2023-06-19)
% 0.22/0.63  
% 0.22/0.63  (c) Philipp Rümmer, 2009-2023
% 0.22/0.63  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63                Amanda Stjerna.
% 0.22/0.63  Free software under BSD-3-Clause.
% 0.22/0.63  
% 0.22/0.63  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63  
% 0.22/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.64  Running up to 7 provers in parallel.
% 0.22/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.11/1.51  Prover 4: Preprocessing ...
% 5.11/1.53  Prover 1: Preprocessing ...
% 5.11/1.53  Prover 6: Preprocessing ...
% 5.11/1.53  Prover 5: Preprocessing ...
% 5.11/1.53  Prover 0: Preprocessing ...
% 5.11/1.53  Prover 3: Preprocessing ...
% 5.11/1.53  Prover 2: Preprocessing ...
% 12.15/2.42  Prover 1: Warning: ignoring some quantifiers
% 12.15/2.45  Prover 3: Warning: ignoring some quantifiers
% 12.54/2.46  Prover 6: Proving ...
% 12.54/2.49  Prover 4: Warning: ignoring some quantifiers
% 12.54/2.49  Prover 1: Constructing countermodel ...
% 12.54/2.49  Prover 3: Constructing countermodel ...
% 13.27/2.58  Prover 4: Constructing countermodel ...
% 13.57/2.66  Prover 5: Proving ...
% 13.57/2.69  Prover 2: Proving ...
% 13.57/2.69  Prover 0: Proving ...
% 15.43/2.90  Prover 3: proved (2252ms)
% 15.43/2.90  
% 15.43/2.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.43/2.91  
% 15.43/2.91  Prover 5: stopped
% 15.43/2.91  Prover 0: stopped
% 15.95/2.93  Prover 2: stopped
% 15.95/2.93  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.95/2.93  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.95/2.93  Prover 6: stopped
% 15.95/2.93  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.95/2.93  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.95/2.93  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.03/3.08  Prover 8: Preprocessing ...
% 17.03/3.10  Prover 11: Preprocessing ...
% 17.03/3.10  Prover 7: Preprocessing ...
% 17.03/3.10  Prover 13: Preprocessing ...
% 17.03/3.11  Prover 10: Preprocessing ...
% 17.03/3.12  Prover 1: Found proof (size 27)
% 17.03/3.12  Prover 1: proved (2478ms)
% 17.03/3.13  Prover 4: stopped
% 18.24/3.24  Prover 10: stopped
% 18.24/3.25  Prover 7: stopped
% 18.24/3.26  Prover 13: stopped
% 18.24/3.26  Prover 11: stopped
% 18.24/3.35  Prover 8: Warning: ignoring some quantifiers
% 18.62/3.37  Prover 8: Constructing countermodel ...
% 18.62/3.39  Prover 8: stopped
% 18.62/3.39  
% 18.62/3.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.62/3.39  
% 18.62/3.40  % SZS output start Proof for theBenchmark
% 18.62/3.40  Assumptions after simplification:
% 18.62/3.40  ---------------------------------
% 18.62/3.40  
% 18.62/3.40    (quaternion_ds1_inuse_0006)
% 18.62/3.43    $i(z_defuse) & $i(n6) & $i(n999) & $i(pv52) & $i(pv51) & $i(pv5) &
% 18.62/3.43    $i(xinit_noise_defuse) & $i(xinit_mean_defuse) & $i(xinit_defuse) &
% 18.62/3.43    $i(u_defuse) & $i(sigma_defuse) & $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) &
% 18.62/3.43    $i(n3) & $i(n2) & $i(n1) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 18.62/3.43    (minus(n6, n1) = v1 & minus(n999, n1) = v0 & minus(pv5, n1) = v2 &
% 18.62/3.43      a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 18.62/3.43      a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use
% 18.62/3.43      & a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse,
% 18.62/3.43        n3) = use & a_select2(xinit_noise_defuse, n2) = use &
% 18.62/3.43      a_select2(xinit_noise_defuse, n1) = use & a_select2(xinit_noise_defuse, n0)
% 18.62/3.43      = use & a_select2(xinit_mean_defuse, n5) = use &
% 18.62/3.43      a_select2(xinit_mean_defuse, n4) = use & a_select2(xinit_mean_defuse, n3) =
% 18.62/3.43      use & a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 18.62/3.43        n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 18.62/3.43      a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use &
% 18.62/3.43      a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use &
% 18.62/3.43      a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use &
% 18.62/3.43      a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use &
% 18.62/3.43      a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use &
% 18.62/3.43      a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use &
% 18.62/3.43      leq(pv52, v1) = 0 & leq(pv51, v1) = 0 & leq(pv5, v0) = 0 & leq(n0, pv52) = 0
% 18.62/3.43      & leq(n0, pv51) = 0 & leq(n0, pv5) = 0 & $i(v2) & $i(v1) & $i(v0) &  ! [v3:
% 18.62/3.43        $i] :  ! [v4: $i] : ( ~ (leq(v4, v2) = 0) |  ~ (leq(v3, n2) = 0) |  ~
% 18.62/3.43        $i(v4) |  ~ $i(v3) |  ? [v5: any] :  ? [v6: any] :  ? [v7: $i] :  ? [v8:
% 18.62/3.43          $i] : (a_select3(z_defuse, v3, v4) = v8 & a_select3(u_defuse, v3, v4) =
% 18.62/3.43          v7 & leq(n0, v4) = v6 & leq(n0, v3) = v5 & $i(v8) & $i(v7) & ( ~ (v6 =
% 18.62/3.43              0) |  ~ (v5 = 0) | (v8 = use & v7 = use)))) &  ? [v3: $i] :  ? [v4:
% 18.62/3.44        $i] :  ? [v5: $i] :  ? [v6: $i] : (a_select3(z_defuse, v3, v4) = v6 &
% 18.62/3.44        a_select3(u_defuse, v3, v4) = v5 & leq(v4, v2) = 0 & leq(v3, n2) = 0 &
% 18.62/3.44        leq(n0, v4) = 0 & leq(n0, v3) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & (
% 18.62/3.44          ~ (v6 = use) |  ~ (v5 = use))))
% 18.62/3.44  
% 18.62/3.44    (function-axioms)
% 19.32/3.44     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 19.32/3.44      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 19.32/3.44      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.32/3.44      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 19.32/3.44        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 19.32/3.44    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 19.32/3.44      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 19.32/3.44    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 19.32/3.44      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 19.32/3.44    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 19.32/3.44        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 19.32/3.44    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 19.32/3.44          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 19.32/3.44      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 19.32/3.44    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 19.32/3.44      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 19.32/3.44    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 19.32/3.44        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 19.32/3.44      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 19.32/3.44    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 19.32/3.44      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 19.32/3.44    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 19.32/3.44          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 19.32/3.44      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 19.32/3.44      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 19.32/3.44      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 19.32/3.44    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 19.32/3.44      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 19.32/3.44      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 19.32/3.44    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 19.32/3.44      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 19.32/3.44    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 19.32/3.44      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 19.32/3.44    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 19.32/3.44    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 19.32/3.44    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 19.32/3.44      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 19.32/3.44      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.32/3.44      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 19.32/3.44  
% 19.32/3.44  Further assumptions not needed in the proof:
% 19.32/3.44  --------------------------------------------
% 19.32/3.45  const_array1_select, const_array2_select, defuse, finite_domain_0,
% 19.32/3.45  finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 19.32/3.45  finite_domain_5, finite_domain_6, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1,
% 19.32/3.45  gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1,
% 19.32/3.45  gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2,
% 19.32/3.45  gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_6_0, gt_6_1, gt_6_2, gt_6_3, gt_6_4,
% 19.32/3.45  gt_6_5, gt_6_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, gt_999_3, gt_999_4,
% 19.32/3.45  gt_999_5, gt_999_6, gt_999_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq,
% 19.32/3.45  leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 19.32/3.45  leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 19.32/3.45  matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 19.32/3.45  matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 19.32/3.45  reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 19.32/3.45  sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 19.32/3.45  succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 19.32/3.45  succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 19.32/3.45  successor_2, successor_3, successor_4, successor_5, successor_6, sum_plus_base,
% 19.32/3.45  sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 19.32/3.45  uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 19.32/3.45  
% 19.32/3.45  Those formulas are unsatisfiable:
% 19.32/3.45  ---------------------------------
% 19.32/3.45  
% 19.32/3.45  Begin of proof
% 19.32/3.45  | 
% 19.32/3.45  | ALPHA: (quaternion_ds1_inuse_0006) implies:
% 19.32/3.45  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (minus(n6, n1) = v1 &
% 19.32/3.45  |          minus(n999, n1) = v0 & minus(pv5, n1) = v2 & a_select3(u_defuse, n2,
% 19.32/3.45  |            n0) = use & a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse,
% 19.32/3.45  |            n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use &
% 19.32/3.45  |          a_select2(xinit_noise_defuse, n4) = use &
% 19.32/3.45  |          a_select2(xinit_noise_defuse, n3) = use &
% 19.32/3.45  |          a_select2(xinit_noise_defuse, n2) = use &
% 19.32/3.45  |          a_select2(xinit_noise_defuse, n1) = use &
% 19.32/3.45  |          a_select2(xinit_noise_defuse, n0) = use &
% 19.32/3.45  |          a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 19.32/3.45  |            n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 19.32/3.45  |          a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 19.32/3.45  |            n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 19.32/3.45  |          a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 19.32/3.45  |          & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 19.32/3.45  |          use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 19.32/3.45  |          = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 19.32/3.45  |            n1) = use & a_select2(sigma_defuse, n0) = use &
% 19.32/3.45  |          a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 19.32/3.45  |          a_select2(rho_defuse, n0) = use & leq(pv52, v1) = 0 & leq(pv51, v1) =
% 19.32/3.45  |          0 & leq(pv5, v0) = 0 & leq(n0, pv52) = 0 & leq(n0, pv51) = 0 &
% 19.32/3.45  |          leq(n0, pv5) = 0 & $i(v2) & $i(v1) & $i(v0) &  ! [v3: $i] :  ! [v4:
% 19.32/3.45  |            $i] : ( ~ (leq(v4, v2) = 0) |  ~ (leq(v3, n2) = 0) |  ~ $i(v4) |  ~
% 19.32/3.45  |            $i(v3) |  ? [v5: any] :  ? [v6: any] :  ? [v7: $i] :  ? [v8: $i] :
% 19.32/3.45  |            (a_select3(z_defuse, v3, v4) = v8 & a_select3(u_defuse, v3, v4) =
% 19.32/3.45  |              v7 & leq(n0, v4) = v6 & leq(n0, v3) = v5 & $i(v8) & $i(v7) & ( ~
% 19.32/3.45  |                (v6 = 0) |  ~ (v5 = 0) | (v8 = use & v7 = use)))) &  ? [v3: $i]
% 19.32/3.45  |          :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] : (a_select3(z_defuse, v3,
% 19.32/3.45  |              v4) = v6 & a_select3(u_defuse, v3, v4) = v5 & leq(v4, v2) = 0 &
% 19.32/3.45  |            leq(v3, n2) = 0 & leq(n0, v4) = 0 & leq(n0, v3) = 0 & $i(v6) &
% 19.32/3.45  |            $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 = use) |  ~ (v5 = use))))
% 19.32/3.45  | 
% 19.32/3.45  | ALPHA: (function-axioms) implies:
% 19.32/3.45  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 19.32/3.45  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 19.32/3.45  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 19.32/3.45  |        (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2)
% 19.32/3.45  |            = v0))
% 19.32/3.45  | 
% 19.32/3.46  | DELTA: instantiating (1) with fresh symbols all_77_0, all_77_1, all_77_2
% 19.32/3.46  |        gives:
% 19.32/3.46  |   (4)  minus(n6, n1) = all_77_1 & minus(n999, n1) = all_77_2 & minus(pv5, n1)
% 19.32/3.46  |        = all_77_0 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 19.32/3.46  |          n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 19.32/3.46  |        a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse,
% 19.32/3.46  |          n4) = use & a_select2(xinit_noise_defuse, n3) = use &
% 19.32/3.46  |        a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse,
% 19.32/3.46  |          n1) = use & a_select2(xinit_noise_defuse, n0) = use &
% 19.32/3.46  |        a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 19.32/3.46  |          n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 19.32/3.46  |        a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 19.32/3.46  |          n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 19.32/3.46  |        a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use &
% 19.32/3.46  |        a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use &
% 19.32/3.46  |        a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use &
% 19.32/3.46  |        a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use &
% 19.32/3.46  |        a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use &
% 19.32/3.46  |        a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use &
% 19.32/3.46  |        leq(pv52, all_77_1) = 0 & leq(pv51, all_77_1) = 0 & leq(pv5, all_77_2)
% 19.32/3.46  |        = 0 & leq(n0, pv52) = 0 & leq(n0, pv51) = 0 & leq(n0, pv5) = 0 &
% 19.32/3.46  |        $i(all_77_0) & $i(all_77_1) & $i(all_77_2) &  ! [v0: $i] :  ! [v1: $i]
% 19.32/3.46  |        : ( ~ (leq(v1, all_77_0) = 0) |  ~ (leq(v0, n2) = 0) |  ~ $i(v1) |  ~
% 19.32/3.46  |          $i(v0) |  ? [v2: any] :  ? [v3: any] :  ? [v4: $i] :  ? [v5: $i] :
% 19.32/3.46  |          (a_select3(z_defuse, v0, v1) = v5 & a_select3(u_defuse, v0, v1) = v4
% 19.32/3.46  |            & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v5) & $i(v4) & ( ~ (v3 =
% 19.32/3.46  |                0) |  ~ (v2 = 0) | (v5 = use & v4 = use)))) &  ? [v0: $i] :  ?
% 19.32/3.46  |        [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (a_select3(z_defuse, v0, v1) =
% 19.32/3.46  |          v3 & a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_77_0) = 0 &
% 19.32/3.46  |          leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2)
% 19.32/3.46  |          & $i(v1) & $i(v0) & ( ~ (v3 = use) |  ~ (v2 = use)))
% 19.32/3.46  | 
% 19.32/3.46  | ALPHA: (4) implies:
% 19.32/3.46  |   (5)   ! [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_77_0) = 0) |  ~ (leq(v0,
% 19.32/3.46  |              n2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] : 
% 19.32/3.46  |          ? [v4: $i] :  ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 &
% 19.32/3.46  |            a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) =
% 19.32/3.46  |            v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0) | (v5 = use & v4
% 19.32/3.46  |                = use))))
% 19.32/3.46  |   (6)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :
% 19.32/3.46  |        (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 &
% 19.32/3.46  |          leq(v1, all_77_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0,
% 19.32/3.46  |            v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) |  ~
% 19.32/3.46  |            (v2 = use)))
% 19.32/3.46  | 
% 19.32/3.46  | DELTA: instantiating (6) with fresh symbols all_82_0, all_82_1, all_82_2,
% 19.32/3.46  |        all_82_3 gives:
% 19.32/3.46  |   (7)  a_select3(z_defuse, all_82_3, all_82_2) = all_82_0 &
% 19.32/3.46  |        a_select3(u_defuse, all_82_3, all_82_2) = all_82_1 & leq(all_82_2,
% 19.32/3.46  |          all_77_0) = 0 & leq(all_82_3, n2) = 0 & leq(n0, all_82_2) = 0 &
% 19.32/3.46  |        leq(n0, all_82_3) = 0 & $i(all_82_0) & $i(all_82_1) & $i(all_82_2) &
% 19.32/3.46  |        $i(all_82_3) & ( ~ (all_82_0 = use) |  ~ (all_82_1 = use))
% 19.32/3.46  | 
% 19.32/3.46  | ALPHA: (7) implies:
% 19.32/3.46  |   (8)  $i(all_82_3)
% 19.32/3.46  |   (9)  $i(all_82_2)
% 19.32/3.46  |   (10)  leq(n0, all_82_3) = 0
% 19.32/3.46  |   (11)  leq(n0, all_82_2) = 0
% 19.32/3.46  |   (12)  leq(all_82_3, n2) = 0
% 19.32/3.46  |   (13)  leq(all_82_2, all_77_0) = 0
% 19.32/3.46  |   (14)  a_select3(u_defuse, all_82_3, all_82_2) = all_82_1
% 19.32/3.46  |   (15)  a_select3(z_defuse, all_82_3, all_82_2) = all_82_0
% 19.32/3.46  |   (16)   ~ (all_82_0 = use) |  ~ (all_82_1 = use)
% 19.32/3.46  | 
% 19.48/3.47  | GROUND_INST: instantiating (5) with all_82_3, all_82_2, simplifying with (8),
% 19.48/3.47  |              (9), (12), (13) gives:
% 19.48/3.47  |   (17)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :  ? [v3: $i] :
% 19.48/3.47  |         (a_select3(z_defuse, all_82_3, all_82_2) = v3 & a_select3(u_defuse,
% 19.48/3.47  |             all_82_3, all_82_2) = v2 & leq(n0, all_82_2) = v1 & leq(n0,
% 19.48/3.47  |             all_82_3) = v0 & $i(v3) & $i(v2) & ( ~ (v1 = 0) |  ~ (v0 = 0) |
% 19.48/3.47  |             (v3 = use & v2 = use)))
% 19.48/3.47  | 
% 19.48/3.47  | DELTA: instantiating (17) with fresh symbols all_110_0, all_110_1, all_110_2,
% 19.48/3.47  |        all_110_3 gives:
% 19.48/3.47  |   (18)  a_select3(z_defuse, all_82_3, all_82_2) = all_110_0 &
% 19.48/3.47  |         a_select3(u_defuse, all_82_3, all_82_2) = all_110_1 & leq(n0,
% 19.48/3.47  |           all_82_2) = all_110_2 & leq(n0, all_82_3) = all_110_3 &
% 19.48/3.47  |         $i(all_110_0) & $i(all_110_1) & ( ~ (all_110_2 = 0) |  ~ (all_110_3 =
% 19.48/3.47  |             0) | (all_110_0 = use & all_110_1 = use))
% 19.48/3.47  | 
% 19.48/3.47  | ALPHA: (18) implies:
% 19.48/3.47  |   (19)  leq(n0, all_82_3) = all_110_3
% 19.48/3.47  |   (20)  leq(n0, all_82_2) = all_110_2
% 19.48/3.47  |   (21)  a_select3(u_defuse, all_82_3, all_82_2) = all_110_1
% 19.48/3.47  |   (22)  a_select3(z_defuse, all_82_3, all_82_2) = all_110_0
% 19.48/3.47  |   (23)   ~ (all_110_2 = 0) |  ~ (all_110_3 = 0) | (all_110_0 = use & all_110_1
% 19.48/3.47  |           = use)
% 19.48/3.47  | 
% 19.48/3.47  | GROUND_INST: instantiating (2) with 0, all_110_3, all_82_3, n0, simplifying
% 19.48/3.47  |              with (10), (19) gives:
% 19.48/3.47  |   (24)  all_110_3 = 0
% 19.48/3.47  | 
% 19.48/3.47  | GROUND_INST: instantiating (2) with 0, all_110_2, all_82_2, n0, simplifying
% 19.48/3.47  |              with (11), (20) gives:
% 19.48/3.47  |   (25)  all_110_2 = 0
% 19.48/3.47  | 
% 19.48/3.47  | GROUND_INST: instantiating (3) with all_82_1, all_110_1, all_82_2, all_82_3,
% 19.48/3.47  |              u_defuse, simplifying with (14), (21) gives:
% 19.48/3.47  |   (26)  all_110_1 = all_82_1
% 19.48/3.47  | 
% 19.48/3.47  | GROUND_INST: instantiating (3) with all_82_0, all_110_0, all_82_2, all_82_3,
% 19.48/3.47  |              z_defuse, simplifying with (15), (22) gives:
% 19.48/3.47  |   (27)  all_110_0 = all_82_0
% 19.48/3.47  | 
% 19.48/3.47  | BETA: splitting (23) gives:
% 19.48/3.47  | 
% 19.48/3.47  | Case 1:
% 19.48/3.47  | | 
% 19.48/3.47  | |   (28)   ~ (all_110_2 = 0)
% 19.48/3.47  | | 
% 19.48/3.47  | | REDUCE: (25), (28) imply:
% 19.48/3.47  | |   (29)  $false
% 19.48/3.47  | | 
% 19.48/3.47  | | CLOSE: (29) is inconsistent.
% 19.48/3.47  | | 
% 19.48/3.47  | Case 2:
% 19.48/3.47  | | 
% 19.48/3.47  | |   (30)   ~ (all_110_3 = 0) | (all_110_0 = use & all_110_1 = use)
% 19.48/3.47  | | 
% 19.48/3.47  | | BETA: splitting (30) gives:
% 19.48/3.47  | | 
% 19.48/3.47  | | Case 1:
% 19.48/3.47  | | | 
% 19.48/3.47  | | |   (31)   ~ (all_110_3 = 0)
% 19.48/3.47  | | | 
% 19.48/3.47  | | | REDUCE: (24), (31) imply:
% 19.48/3.47  | | |   (32)  $false
% 19.48/3.47  | | | 
% 19.48/3.47  | | | CLOSE: (32) is inconsistent.
% 19.48/3.47  | | | 
% 19.48/3.47  | | Case 2:
% 19.48/3.47  | | | 
% 19.48/3.47  | | |   (33)  all_110_0 = use & all_110_1 = use
% 19.48/3.47  | | | 
% 19.48/3.47  | | | ALPHA: (33) implies:
% 19.48/3.47  | | |   (34)  all_110_1 = use
% 19.48/3.47  | | |   (35)  all_110_0 = use
% 19.48/3.47  | | | 
% 19.48/3.47  | | | COMBINE_EQS: (27), (35) imply:
% 19.48/3.47  | | |   (36)  all_82_0 = use
% 19.48/3.47  | | | 
% 19.48/3.47  | | | COMBINE_EQS: (26), (34) imply:
% 19.48/3.47  | | |   (37)  all_82_1 = use
% 19.48/3.47  | | | 
% 19.48/3.47  | | | BETA: splitting (16) gives:
% 19.48/3.47  | | | 
% 19.48/3.47  | | | Case 1:
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | |   (38)   ~ (all_82_0 = use)
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | | REDUCE: (36), (38) imply:
% 19.48/3.47  | | | |   (39)  $false
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | | CLOSE: (39) is inconsistent.
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | Case 2:
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | |   (40)   ~ (all_82_1 = use)
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | | REDUCE: (37), (40) imply:
% 19.48/3.47  | | | |   (41)  $false
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | | CLOSE: (41) is inconsistent.
% 19.48/3.47  | | | | 
% 19.48/3.47  | | | End of split
% 19.48/3.47  | | | 
% 19.48/3.47  | | End of split
% 19.48/3.47  | | 
% 19.48/3.47  | End of split
% 19.48/3.47  | 
% 19.48/3.47  End of proof
% 19.48/3.47  % SZS output end Proof for theBenchmark
% 19.48/3.48  
% 19.48/3.48  2845ms
%------------------------------------------------------------------------------