TSTP Solution File: SWV198+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV198+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 22:55:19 EDT 2023

% Result   : Theorem 17.36s 3.09s
% Output   : Proof 23.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWV198+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue Aug 29 03:02:11 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.61  ________       _____
% 0.21/0.61  ___  __ \_________(_)________________________________
% 0.21/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61  
% 0.21/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61  (2023-06-19)
% 0.21/0.61  
% 0.21/0.61  (c) Philipp Rümmer, 2009-2023
% 0.21/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61                Amanda Stjerna.
% 0.21/0.61  Free software under BSD-3-Clause.
% 0.21/0.61  
% 0.21/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61  
% 0.21/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62  Running up to 7 provers in parallel.
% 0.21/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.87/1.42  Prover 1: Preprocessing ...
% 4.87/1.42  Prover 4: Preprocessing ...
% 5.22/1.46  Prover 3: Preprocessing ...
% 5.22/1.46  Prover 6: Preprocessing ...
% 5.22/1.46  Prover 0: Preprocessing ...
% 5.22/1.46  Prover 5: Preprocessing ...
% 5.22/1.46  Prover 2: Preprocessing ...
% 10.08/2.22  Prover 1: Warning: ignoring some quantifiers
% 11.61/2.29  Prover 1: Constructing countermodel ...
% 11.61/2.31  Prover 3: Warning: ignoring some quantifiers
% 11.61/2.33  Prover 6: Proving ...
% 11.61/2.33  Prover 3: Constructing countermodel ...
% 12.15/2.39  Prover 4: Warning: ignoring some quantifiers
% 12.73/2.48  Prover 4: Constructing countermodel ...
% 12.73/2.51  Prover 5: Proving ...
% 12.73/2.51  Prover 0: Proving ...
% 13.42/2.56  Prover 2: Proving ...
% 17.36/3.09  Prover 6: proved (2457ms)
% 17.36/3.09  
% 17.36/3.09  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.36/3.09  
% 17.36/3.10  Prover 2: stopped
% 17.74/3.11  Prover 5: stopped
% 17.74/3.11  Prover 0: stopped
% 17.74/3.11  Prover 3: stopped
% 17.74/3.13  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.74/3.13  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.74/3.13  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.74/3.13  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.74/3.13  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.12/3.33  Prover 7: Preprocessing ...
% 19.51/3.35  Prover 8: Preprocessing ...
% 19.51/3.39  Prover 10: Preprocessing ...
% 19.51/3.39  Prover 11: Preprocessing ...
% 19.51/3.40  Prover 13: Preprocessing ...
% 21.30/3.62  Prover 10: Warning: ignoring some quantifiers
% 21.30/3.64  Prover 10: Constructing countermodel ...
% 21.30/3.64  Prover 7: Warning: ignoring some quantifiers
% 21.74/3.66  Prover 8: Warning: ignoring some quantifiers
% 21.74/3.66  Prover 7: Constructing countermodel ...
% 21.74/3.69  Prover 8: Constructing countermodel ...
% 21.74/3.72  Prover 13: Warning: ignoring some quantifiers
% 21.74/3.74  Prover 1: Found proof (size 53)
% 21.74/3.74  Prover 1: proved (3111ms)
% 21.74/3.74  Prover 4: stopped
% 21.74/3.74  Prover 8: stopped
% 21.74/3.74  Prover 10: stopped
% 21.74/3.74  Prover 7: stopped
% 21.74/3.75  Prover 13: Constructing countermodel ...
% 22.43/3.77  Prover 13: stopped
% 22.43/3.78  Prover 11: Warning: ignoring some quantifiers
% 22.62/3.80  Prover 11: Constructing countermodel ...
% 22.62/3.82  Prover 11: stopped
% 22.62/3.82  
% 22.62/3.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.62/3.82  
% 22.62/3.82  % SZS output start Proof for theBenchmark
% 22.62/3.83  Assumptions after simplification:
% 22.62/3.83  ---------------------------------
% 22.62/3.83  
% 22.62/3.83    (finite_domain_0)
% 22.84/3.85    $i(n0) &  ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 22.84/3.85        int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 22.84/3.85  
% 22.84/3.85    (finite_domain_2)
% 22.84/3.85    $i(n2) & $i(n1) & $i(n0) &  ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~
% 22.84/3.85      (leq(v0, n2) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) =
% 22.84/3.85        v1))
% 22.84/3.85  
% 22.84/3.85    (quaternion_ds1_inuse_0009)
% 22.84/3.87    $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 22.84/3.87    $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 22.84/3.87    $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 22.84/3.87    &  ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 22.84/3.87        n0) = use & a_select3(u_defuse, n0, n0) = use &
% 22.84/3.87      a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 22.84/3.87      = use & a_select2(xinit_noise_defuse, n3) = use &
% 22.84/3.87      a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 22.84/3.87      = use & a_select2(xinit_noise_defuse, n0) = use &
% 22.84/3.87      a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 22.84/3.87      use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 22.84/3.87        n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 22.84/3.87      a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 22.84/3.87      a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 22.84/3.87      a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 22.84/3.87      a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 22.84/3.87      a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 22.84/3.87      a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 22.84/3.87      a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 &
% 22.84/3.87      leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) &  ! [v1: $i] :  ! [v2: $i] : (
% 22.84/3.87        ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ?
% 22.84/3.87        [v3: any] :  ? [v4: any] :  ? [v5: $i] : (a_select3(z_defuse, v1, v2) = v5
% 22.84/3.87          & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 =
% 22.84/3.87              0) | v5 = use))) &  ! [v1: $i] :  ! [v2: $i] : ( ~ (leq(v2, v0) = 0)
% 22.84/3.87        |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4:
% 22.84/3.87          any] :  ? [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) =
% 22.84/3.87          v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 =
% 22.84/3.87            use))) &  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = use) &
% 22.84/3.87        a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 & leq(v1, n2) = 0 &
% 22.84/3.87        leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1)))
% 22.84/3.87  
% 22.84/3.87    (function-axioms)
% 22.84/3.87     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 22.84/3.87      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 22.84/3.87      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 22.84/3.87      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 22.84/3.87        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 22.84/3.87    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 22.84/3.87      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 22.84/3.87    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 22.84/3.87      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 22.84/3.87    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 22.84/3.88        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 22.84/3.88    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 22.84/3.88          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 22.84/3.88      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 22.84/3.88    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 22.84/3.88      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 22.84/3.88    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 22.84/3.88        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 22.84/3.88      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 22.84/3.88    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 22.84/3.88      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 22.84/3.88    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 22.84/3.88          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 22.84/3.88      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 22.84/3.88      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 22.84/3.88      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 22.84/3.88    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 22.84/3.88      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 22.84/3.88      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 22.84/3.88    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 22.84/3.88      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 22.84/3.88    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 22.84/3.88      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 22.84/3.88    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 22.84/3.88    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 22.84/3.88    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 22.84/3.88      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 22.84/3.88      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 22.84/3.88      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 22.84/3.88  
% 22.84/3.88  Further assumptions not needed in the proof:
% 22.84/3.88  --------------------------------------------
% 22.84/3.88  const_array1_select, const_array2_select, defuse, finite_domain_1,
% 22.84/3.88  finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0,
% 22.84/3.88  gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 22.84/3.88  gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 22.84/3.88  gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2,
% 22.84/3.88  gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt,
% 22.84/3.88  leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 22.84/3.88  leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 22.84/3.88  matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 22.84/3.88  matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 22.84/3.88  reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 22.84/3.88  sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 22.84/3.88  succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 22.84/3.88  succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 22.84/3.88  successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 22.84/3.88  sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 22.84/3.88  uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 22.84/3.88  
% 22.84/3.88  Those formulas are unsatisfiable:
% 22.84/3.88  ---------------------------------
% 22.84/3.88  
% 22.84/3.88  Begin of proof
% 22.84/3.88  | 
% 22.84/3.88  | ALPHA: (finite_domain_0) implies:
% 22.84/3.88  |   (1)   ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 22.84/3.88  |            int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 22.84/3.88  | 
% 22.84/3.88  | ALPHA: (finite_domain_2) implies:
% 22.84/3.88  |   (2)   ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~ (leq(v0, n2) = 0) |  ~
% 22.84/3.88  |          $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 22.84/3.88  | 
% 22.84/3.88  | ALPHA: (quaternion_ds1_inuse_0009) implies:
% 22.84/3.88  |   (3)  $i(pv5)
% 22.84/3.89  |   (4)   ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 22.84/3.89  |            n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 22.84/3.89  |          a_select2(xinit_noise_defuse, n5) = use &
% 22.84/3.89  |          a_select2(xinit_noise_defuse, n4) = use &
% 22.84/3.89  |          a_select2(xinit_noise_defuse, n3) = use &
% 22.84/3.89  |          a_select2(xinit_noise_defuse, n2) = use &
% 22.84/3.89  |          a_select2(xinit_noise_defuse, n1) = use &
% 22.84/3.89  |          a_select2(xinit_noise_defuse, n0) = use &
% 22.84/3.89  |          a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 22.84/3.89  |            n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 22.84/3.89  |          a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 22.84/3.89  |            n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 22.84/3.89  |          a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 22.84/3.89  |          & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 22.84/3.89  |          use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 22.84/3.89  |          = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 22.84/3.89  |            n1) = use & a_select2(sigma_defuse, n0) = use &
% 22.84/3.89  |          a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 22.84/3.89  |          a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0
% 22.84/3.89  |          & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) &  ! [v1: $i] :  !
% 22.84/3.89  |          [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) |
% 22.84/3.89  |             ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] :
% 22.84/3.89  |            (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1)
% 22.84/3.89  |              = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = use))) &  !
% 22.84/3.89  |          [v1: $i] :  ! [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0)
% 22.84/3.89  |            |  ~ $i(v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i]
% 22.84/3.89  |            : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0,
% 22.84/3.89  |                v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = use))) & 
% 22.84/3.89  |          ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = use) &
% 22.84/3.89  |            a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 & leq(v1, n2) =
% 22.84/3.89  |            0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1)))
% 22.84/3.89  | 
% 22.84/3.89  | ALPHA: (function-axioms) implies:
% 22.84/3.89  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 22.84/3.89  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 22.84/3.89  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 22.84/3.89  |        (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2)
% 22.84/3.89  |            = v0))
% 22.84/3.89  | 
% 22.84/3.89  | DELTA: instantiating (4) with fresh symbol all_74_0 gives:
% 22.84/3.89  |   (7)  a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 22.84/3.89  |        a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 22.84/3.89  |        use & a_select2(xinit_noise_defuse, n4) = use &
% 22.84/3.89  |        a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 22.84/3.89  |          n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 22.84/3.89  |        a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 22.84/3.89  |          n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 22.84/3.89  |        a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 22.84/3.89  |          n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 22.84/3.89  |        a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 22.84/3.90  |        use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 22.84/3.90  |        use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 22.84/3.90  |        use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 22.84/3.90  |        use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 22.84/3.90  |        use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 22.84/3.90  |        & a_select2(rho_defuse, n0) = use & pred(pv5) = all_74_0 & leq(pv5,
% 22.84/3.90  |          n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(all_74_0) &  !
% 22.84/3.90  |        [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_74_0) = 0) |  ~ (leq(v0, n2)
% 22.84/3.90  |            = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ? [v3: any] :  ?
% 22.84/3.90  |          [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 22.84/3.90  |            leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0) | v4 =
% 22.84/3.90  |              use))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_74_0) = 0)
% 22.84/3.90  |          |  ~ (leq(v0, n2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ?
% 22.84/3.90  |          [v3: any] :  ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0,
% 22.84/3.90  |              v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0)
% 22.84/3.90  |              | v4 = use))) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2
% 22.84/3.90  |            = use) & a_select3(u_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 &
% 22.84/3.90  |          leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1)
% 22.84/3.90  |          & $i(v0))
% 22.84/3.90  | 
% 22.84/3.90  | ALPHA: (7) implies:
% 22.84/3.90  |   (8)  leq(n0, pv5) = 0
% 22.84/3.90  |   (9)  leq(pv5, n0) = 0
% 22.84/3.90  |   (10)  a_select3(u_defuse, n0, n0) = use
% 22.84/3.90  |   (11)  a_select3(u_defuse, n1, n0) = use
% 22.84/3.90  |   (12)  a_select3(u_defuse, n2, n0) = use
% 22.84/3.90  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = use) &
% 22.84/3.90  |           a_select3(u_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2) =
% 22.84/3.90  |           0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0))
% 22.84/3.90  | 
% 22.84/3.90  | DELTA: instantiating (13) with fresh symbols all_79_0, all_79_1, all_79_2
% 22.84/3.90  |        gives:
% 22.84/3.90  |   (14)   ~ (all_79_0 = use) & a_select3(u_defuse, all_79_2, all_79_1) =
% 22.84/3.90  |         all_79_0 & leq(all_79_1, pv5) = 0 & leq(all_79_2, n2) = 0 & leq(n0,
% 22.84/3.90  |           all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) & $i(all_79_1)
% 22.84/3.90  |         & $i(all_79_2)
% 22.84/3.90  | 
% 22.84/3.90  | ALPHA: (14) implies:
% 22.84/3.90  |   (15)   ~ (all_79_0 = use)
% 22.84/3.90  |   (16)  $i(all_79_2)
% 22.84/3.90  |   (17)  $i(all_79_1)
% 22.84/3.90  |   (18)  leq(n0, all_79_2) = 0
% 22.84/3.90  |   (19)  leq(n0, all_79_1) = 0
% 22.84/3.90  |   (20)  leq(all_79_2, n2) = 0
% 22.84/3.90  |   (21)  leq(all_79_1, pv5) = 0
% 22.84/3.90  |   (22)  a_select3(u_defuse, all_79_2, all_79_1) = all_79_0
% 22.84/3.90  | 
% 23.14/3.90  | GROUND_INST: instantiating (1) with pv5, simplifying with (3), (8) gives:
% 23.14/3.90  |   (23)  pv5 = n0 |  ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 23.14/3.90  | 
% 23.14/3.90  | GROUND_INST: instantiating (1) with all_79_2, simplifying with (16), (18)
% 23.14/3.90  |              gives:
% 23.14/3.90  |   (24)  all_79_2 = n0 |  ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_2, n0) = v0)
% 23.14/3.90  | 
% 23.14/3.90  | GROUND_INST: instantiating (1) with all_79_1, simplifying with (17), (19)
% 23.14/3.90  |              gives:
% 23.14/3.90  |   (25)  all_79_1 = n0 |  ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0)
% 23.14/3.90  | 
% 23.14/3.90  | GROUND_INST: instantiating (2) with all_79_2, simplifying with (16), (20)
% 23.14/3.90  |              gives:
% 23.14/3.91  |   (26)  all_79_2 = n2 | all_79_2 = n1 | all_79_2 = n0 |  ? [v0: int] : ( ~ (v0
% 23.14/3.91  |             = 0) & leq(n0, all_79_2) = v0)
% 23.14/3.91  | 
% 23.14/3.91  | BETA: splitting (23) gives:
% 23.14/3.91  | 
% 23.14/3.91  | Case 1:
% 23.14/3.91  | | 
% 23.14/3.91  | |   (27)  pv5 = n0
% 23.14/3.91  | | 
% 23.14/3.91  | | REDUCE: (21), (27) imply:
% 23.14/3.91  | |   (28)  leq(all_79_1, n0) = 0
% 23.14/3.91  | | 
% 23.14/3.91  | | BETA: splitting (25) gives:
% 23.14/3.91  | | 
% 23.14/3.91  | | Case 1:
% 23.14/3.91  | | | 
% 23.14/3.91  | | |   (29)  all_79_1 = n0
% 23.14/3.91  | | | 
% 23.14/3.91  | | | REDUCE: (22), (29) imply:
% 23.14/3.91  | | |   (30)  a_select3(u_defuse, all_79_2, n0) = all_79_0
% 23.14/3.91  | | | 
% 23.14/3.91  | | | BETA: splitting (24) gives:
% 23.14/3.91  | | | 
% 23.14/3.91  | | | Case 1:
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | |   (31)  all_79_2 = n0
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | | REDUCE: (30), (31) imply:
% 23.14/3.91  | | | |   (32)  a_select3(u_defuse, n0, n0) = all_79_0
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | | GROUND_INST: instantiating (6) with use, all_79_0, n0, n0, u_defuse,
% 23.14/3.91  | | | |              simplifying with (10), (32) gives:
% 23.14/3.91  | | | |   (33)  all_79_0 = use
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | | REDUCE: (15), (33) imply:
% 23.14/3.91  | | | |   (34)  $false
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | | CLOSE: (34) is inconsistent.
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | Case 2:
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | |   (35)   ~ (all_79_2 = n0)
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | | BETA: splitting (26) gives:
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | | Case 1:
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | |   (36)  all_79_2 = n0
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | | REDUCE: (35), (36) imply:
% 23.14/3.91  | | | | |   (37)  $false
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | | CLOSE: (37) is inconsistent.
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | Case 2:
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | |   (38)  all_79_2 = n2 | all_79_2 = n1 |  ? [v0: int] : ( ~ (v0 = 0) &
% 23.14/3.91  | | | | |           leq(n0, all_79_2) = v0)
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | | BETA: splitting (38) gives:
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | | Case 1:
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | |   (39)  all_79_2 = n2
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | | REDUCE: (30), (39) imply:
% 23.14/3.91  | | | | | |   (40)  a_select3(u_defuse, n2, n0) = all_79_0
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | | GROUND_INST: instantiating (6) with use, all_79_0, n0, n2, u_defuse,
% 23.14/3.91  | | | | | |              simplifying with (12), (40) gives:
% 23.14/3.91  | | | | | |   (41)  all_79_0 = use
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | | REDUCE: (15), (41) imply:
% 23.14/3.91  | | | | | |   (42)  $false
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | | CLOSE: (42) is inconsistent.
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | Case 2:
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | |   (43)  all_79_2 = n1 |  ? [v0: int] : ( ~ (v0 = 0) & leq(n0,
% 23.14/3.91  | | | | | |             all_79_2) = v0)
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | | BETA: splitting (43) gives:
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | | Case 1:
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | |   (44)  all_79_2 = n1
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | REDUCE: (30), (44) imply:
% 23.14/3.91  | | | | | | |   (45)  a_select3(u_defuse, n1, n0) = all_79_0
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | GROUND_INST: instantiating (6) with use, all_79_0, n0, n1,
% 23.14/3.91  | | | | | | |              u_defuse, simplifying with (11), (45) gives:
% 23.14/3.91  | | | | | | |   (46)  all_79_0 = use
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | REDUCE: (15), (46) imply:
% 23.14/3.91  | | | | | | |   (47)  $false
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | CLOSE: (47) is inconsistent.
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | Case 2:
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | |   (48)   ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_2) = v0)
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | DELTA: instantiating (48) with fresh symbol all_488_0 gives:
% 23.14/3.91  | | | | | | |   (49)   ~ (all_488_0 = 0) & leq(n0, all_79_2) = all_488_0
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | ALPHA: (49) implies:
% 23.14/3.91  | | | | | | |   (50)   ~ (all_488_0 = 0)
% 23.14/3.91  | | | | | | |   (51)  leq(n0, all_79_2) = all_488_0
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | GROUND_INST: instantiating (5) with 0, all_488_0, all_79_2, n0,
% 23.14/3.91  | | | | | | |              simplifying with (18), (51) gives:
% 23.14/3.91  | | | | | | |   (52)  all_488_0 = 0
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | REDUCE: (50), (52) imply:
% 23.14/3.91  | | | | | | |   (53)  $false
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | | CLOSE: (53) is inconsistent.
% 23.14/3.91  | | | | | | | 
% 23.14/3.91  | | | | | | End of split
% 23.14/3.91  | | | | | | 
% 23.14/3.91  | | | | | End of split
% 23.14/3.91  | | | | | 
% 23.14/3.91  | | | | End of split
% 23.14/3.91  | | | | 
% 23.14/3.91  | | | End of split
% 23.14/3.91  | | | 
% 23.14/3.91  | | Case 2:
% 23.14/3.91  | | | 
% 23.14/3.91  | | |   (54)   ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0)
% 23.14/3.91  | | | 
% 23.14/3.92  | | | DELTA: instantiating (54) with fresh symbol all_111_0 gives:
% 23.14/3.92  | | |   (55)   ~ (all_111_0 = 0) & leq(all_79_1, n0) = all_111_0
% 23.14/3.92  | | | 
% 23.14/3.92  | | | ALPHA: (55) implies:
% 23.14/3.92  | | |   (56)   ~ (all_111_0 = 0)
% 23.14/3.92  | | |   (57)  leq(all_79_1, n0) = all_111_0
% 23.14/3.92  | | | 
% 23.14/3.92  | | | GROUND_INST: instantiating (5) with 0, all_111_0, n0, all_79_1,
% 23.14/3.92  | | |              simplifying with (28), (57) gives:
% 23.14/3.92  | | |   (58)  all_111_0 = 0
% 23.14/3.92  | | | 
% 23.14/3.92  | | | REDUCE: (56), (58) imply:
% 23.14/3.92  | | |   (59)  $false
% 23.14/3.92  | | | 
% 23.14/3.92  | | | CLOSE: (59) is inconsistent.
% 23.14/3.92  | | | 
% 23.14/3.92  | | End of split
% 23.14/3.92  | | 
% 23.14/3.92  | Case 2:
% 23.14/3.92  | | 
% 23.14/3.92  | |   (60)   ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 23.14/3.92  | | 
% 23.14/3.92  | | DELTA: instantiating (60) with fresh symbol all_107_0 gives:
% 23.14/3.92  | |   (61)   ~ (all_107_0 = 0) & leq(pv5, n0) = all_107_0
% 23.14/3.92  | | 
% 23.14/3.92  | | ALPHA: (61) implies:
% 23.14/3.92  | |   (62)   ~ (all_107_0 = 0)
% 23.14/3.92  | |   (63)  leq(pv5, n0) = all_107_0
% 23.14/3.92  | | 
% 23.14/3.92  | | GROUND_INST: instantiating (5) with 0, all_107_0, n0, pv5, simplifying with
% 23.14/3.92  | |              (9), (63) gives:
% 23.14/3.92  | |   (64)  all_107_0 = 0
% 23.14/3.92  | | 
% 23.14/3.92  | | REDUCE: (62), (64) imply:
% 23.14/3.92  | |   (65)  $false
% 23.14/3.92  | | 
% 23.14/3.92  | | CLOSE: (65) is inconsistent.
% 23.14/3.92  | | 
% 23.14/3.92  | End of split
% 23.14/3.92  | 
% 23.14/3.92  End of proof
% 23.14/3.92  % SZS output end Proof for theBenchmark
% 23.14/3.92  
% 23.14/3.92  3311ms
%------------------------------------------------------------------------------