TSTP Solution File: SWV196+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV196+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 22:55:18 EDT 2023

% Result   : Theorem 16.19s 2.88s
% Output   : Proof 19.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWV196+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n007.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 06:49:13 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.65/0.61  ________       _____
% 0.65/0.61  ___  __ \_________(_)________________________________
% 0.65/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.65/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.65/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.65/0.61  
% 0.65/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.65/0.61  (2023-06-19)
% 0.65/0.61  
% 0.65/0.61  (c) Philipp Rümmer, 2009-2023
% 0.65/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.65/0.61                Amanda Stjerna.
% 0.65/0.61  Free software under BSD-3-Clause.
% 0.65/0.61  
% 0.65/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.65/0.61  
% 0.65/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.63  Running up to 7 provers in parallel.
% 0.70/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.70/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.60/1.46  Prover 4: Preprocessing ...
% 5.65/1.47  Prover 1: Preprocessing ...
% 5.92/1.52  Prover 5: Preprocessing ...
% 5.92/1.52  Prover 2: Preprocessing ...
% 5.92/1.52  Prover 3: Preprocessing ...
% 5.92/1.52  Prover 6: Preprocessing ...
% 5.92/1.52  Prover 0: Preprocessing ...
% 12.78/2.47  Prover 1: Warning: ignoring some quantifiers
% 12.78/2.48  Prover 3: Warning: ignoring some quantifiers
% 13.32/2.51  Prover 3: Constructing countermodel ...
% 13.32/2.53  Prover 6: Proving ...
% 13.32/2.53  Prover 1: Constructing countermodel ...
% 13.32/2.53  Prover 4: Warning: ignoring some quantifiers
% 13.87/2.61  Prover 4: Constructing countermodel ...
% 13.87/2.62  Prover 0: Proving ...
% 14.58/2.67  Prover 5: Proving ...
% 14.97/2.74  Prover 2: Proving ...
% 15.63/2.88  Prover 3: proved (2242ms)
% 15.63/2.88  
% 16.19/2.88  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.19/2.88  
% 16.19/2.89  Prover 0: stopped
% 16.19/2.90  Prover 5: stopped
% 16.19/2.90  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.19/2.90  Prover 6: stopped
% 16.19/2.92  Prover 2: stopped
% 16.19/2.92  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.19/2.92  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.19/2.92  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.19/2.93  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.20/3.05  Prover 10: Preprocessing ...
% 17.20/3.09  Prover 8: Preprocessing ...
% 17.20/3.09  Prover 11: Preprocessing ...
% 17.20/3.10  Prover 7: Preprocessing ...
% 17.85/3.13  Prover 13: Preprocessing ...
% 17.85/3.15  Prover 1: Found proof (size 50)
% 17.85/3.15  Prover 1: proved (2518ms)
% 17.85/3.16  Prover 10: stopped
% 17.85/3.16  Prover 4: stopped
% 17.85/3.17  Prover 7: stopped
% 18.50/3.20  Prover 11: stopped
% 18.50/3.23  Prover 13: stopped
% 19.08/3.30  Prover 8: Warning: ignoring some quantifiers
% 19.16/3.32  Prover 8: Constructing countermodel ...
% 19.22/3.34  Prover 8: stopped
% 19.22/3.34  
% 19.22/3.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.22/3.34  
% 19.22/3.34  % SZS output start Proof for theBenchmark
% 19.22/3.35  Assumptions after simplification:
% 19.22/3.35  ---------------------------------
% 19.22/3.35  
% 19.22/3.35    (finite_domain_0)
% 19.22/3.37    $i(n0) &  ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 19.22/3.37        int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 19.22/3.37  
% 19.22/3.37    (finite_domain_2)
% 19.22/3.37    $i(n2) & $i(n1) & $i(n0) &  ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~
% 19.22/3.37      (leq(v0, n2) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) =
% 19.22/3.37        v1))
% 19.22/3.37  
% 19.22/3.37    (quaternion_ds1_inuse_0007)
% 19.22/3.38    $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 19.22/3.38    $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 19.22/3.38    $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 19.22/3.38    &  ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 19.22/3.38        n0) = use & a_select3(u_defuse, n0, n0) = use &
% 19.22/3.38      a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 19.22/3.38      = use & a_select2(xinit_noise_defuse, n3) = use &
% 19.22/3.38      a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 19.22/3.38      = use & a_select2(xinit_noise_defuse, n0) = use &
% 19.22/3.38      a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 19.22/3.38      use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 19.22/3.38        n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 19.22/3.38      a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 19.22/3.38      a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 19.22/3.38      a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 19.22/3.38      a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 19.22/3.38      a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 19.22/3.38      a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 19.22/3.38      a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 &
% 19.22/3.38      leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) &  ! [v1: $i]
% 19.22/3.38      :  ! [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) | 
% 19.22/3.38        ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] :
% 19.22/3.38        (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 &
% 19.22/3.38          $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = use))) &  ! [v1: $i] :  !
% 19.22/3.38      [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0) |  ~ $i(v2) |  ~
% 19.22/3.38        $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i] : (a_select3(u_defuse,
% 19.22/3.38            v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4
% 19.22/3.38              = 0) |  ~ (v3 = 0) | v5 = use))) &  ? [v1: $i] :  ? [v2: $i] :  ?
% 19.22/3.38      [v3: $i] : ( ~ (v3 = use) & a_select3(z_defuse, v1, v2) = v3 & leq(v2, pv5)
% 19.22/3.38        = 0 & leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) &
% 19.22/3.38        $i(v2) & $i(v1) & ( ~ (v2 = pv5) |  ~ (v1 = n2)) & ( ~ (v2 = pv5) |  ~ (v1
% 19.22/3.38            = n1)) & ( ~ (v2 = pv5) |  ~ (v1 = n0))))
% 19.22/3.38  
% 19.22/3.38    (function-axioms)
% 19.22/3.39     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 19.22/3.39      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 19.22/3.39      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.22/3.39      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 19.22/3.39        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 19.22/3.39    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 19.22/3.39      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 19.22/3.39    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 19.22/3.39      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 19.22/3.39    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 19.22/3.39        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 19.22/3.39    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 19.22/3.39          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 19.22/3.39      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 19.22/3.39    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 19.22/3.39      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 19.22/3.39    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 19.22/3.39        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 19.22/3.39      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 19.22/3.39    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 19.22/3.39      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 19.22/3.39    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 19.22/3.39          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 19.22/3.39      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 19.22/3.39      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 19.22/3.39      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 19.22/3.39    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 19.22/3.39      $i] : (v1 = v0 |  ~ (geq(v3, v2) = v1) |  ~ (geq(v3, v2) = v0)) &  ! [v0:
% 19.22/3.39      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 19.22/3.39    : (v1 = v0 |  ~ (lt(v3, v2) = v1) |  ~ (lt(v3, v2) = v0)) &  ! [v0:
% 19.22/3.39      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 19.22/3.39    : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 19.22/3.39      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 19.22/3.39    : (v1 = v0 |  ~ (gt(v3, v2) = v1) |  ~ (gt(v3, v2) = v0)) &  ! [v0: $i] :  !
% 19.22/3.39    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~ (inv(v2) = v0)) & 
% 19.22/3.39    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (trans(v2) = v1) |  ~
% 19.22/3.39      (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 19.22/3.39      (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 19.22/3.39      $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) = v0))
% 19.22/3.39  
% 19.22/3.39  Further assumptions not needed in the proof:
% 19.22/3.39  --------------------------------------------
% 19.22/3.39  const_array1_select, const_array2_select, defuse, finite_domain_1,
% 19.22/3.39  finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0,
% 19.22/3.39  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,
% 19.22/3.39  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,
% 19.22/3.39  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,
% 19.22/3.39  gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt,
% 19.22/3.39  leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 19.22/3.39  leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 19.22/3.39  matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 19.22/3.39  matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 19.22/3.39  reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 19.22/3.39  sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 19.22/3.39  succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 19.22/3.39  succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 19.22/3.39  successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 19.22/3.39  sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 19.22/3.39  uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 19.22/3.39  
% 19.22/3.39  Those formulas are unsatisfiable:
% 19.22/3.39  ---------------------------------
% 19.22/3.39  
% 19.22/3.39  Begin of proof
% 19.22/3.39  | 
% 19.22/3.39  | ALPHA: (finite_domain_0) implies:
% 19.22/3.39  |   (1)   ! [v0: $i] : (v0 = n0 |  ~ (leq(n0, v0) = 0) |  ~ $i(v0) |  ? [v1:
% 19.22/3.39  |            int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 19.22/3.39  | 
% 19.22/3.39  | ALPHA: (finite_domain_2) implies:
% 19.22/3.39  |   (2)   ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~ (leq(v0, n2) = 0) |  ~
% 19.22/3.39  |          $i(v0) |  ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 19.22/3.39  | 
% 19.22/3.39  | ALPHA: (quaternion_ds1_inuse_0007) implies:
% 19.22/3.40  |   (3)  $i(pv5)
% 19.22/3.40  |   (4)   ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 19.22/3.40  |            n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 19.22/3.40  |          a_select2(xinit_noise_defuse, n5) = use &
% 19.22/3.40  |          a_select2(xinit_noise_defuse, n4) = use &
% 19.22/3.40  |          a_select2(xinit_noise_defuse, n3) = use &
% 19.22/3.40  |          a_select2(xinit_noise_defuse, n2) = use &
% 19.22/3.40  |          a_select2(xinit_noise_defuse, n1) = use &
% 19.22/3.40  |          a_select2(xinit_noise_defuse, n0) = use &
% 19.22/3.40  |          a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 19.22/3.40  |            n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 19.22/3.40  |          a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 19.22/3.40  |            n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 19.22/3.40  |          a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 19.22/3.40  |          & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 19.22/3.40  |          use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 19.22/3.40  |          = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 19.22/3.40  |            n1) = use & a_select2(sigma_defuse, n0) = use &
% 19.22/3.40  |          a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 19.22/3.40  |          a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0
% 19.22/3.40  |          & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) &  !
% 19.22/3.40  |          [v1: $i] :  ! [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) = 0)
% 19.22/3.40  |            |  ~ $i(v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ? [v5: $i]
% 19.22/3.40  |            : (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0,
% 19.22/3.40  |                v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = use))) & 
% 19.22/3.40  |          ! [v1: $i] :  ! [v2: $i] : ( ~ (leq(v2, v0) = 0) |  ~ (leq(v1, n2) =
% 19.22/3.40  |              0) |  ~ $i(v2) |  ~ $i(v1) |  ? [v3: any] :  ? [v4: any] :  ?
% 19.22/3.40  |            [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 &
% 19.22/3.40  |              leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 =
% 19.22/3.40  |                use))) &  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 =
% 19.22/3.40  |              use) & a_select3(z_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 &
% 19.22/3.40  |            leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) &
% 19.22/3.40  |            $i(v2) & $i(v1) & ( ~ (v2 = pv5) |  ~ (v1 = n2)) & ( ~ (v2 = pv5) |
% 19.22/3.40  |               ~ (v1 = n1)) & ( ~ (v2 = pv5) |  ~ (v1 = n0))))
% 19.22/3.40  | 
% 19.22/3.40  | ALPHA: (function-axioms) implies:
% 19.22/3.40  |   (5)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 19.22/3.40  |         ! [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0))
% 19.22/3.40  | 
% 19.22/3.40  | DELTA: instantiating (4) with fresh symbol all_76_0 gives:
% 19.22/3.41  |   (6)  a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 19.22/3.41  |        a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 19.22/3.41  |        use & a_select2(xinit_noise_defuse, n4) = use &
% 19.22/3.41  |        a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 19.22/3.41  |          n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 19.22/3.41  |        a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 19.22/3.41  |          n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 19.22/3.41  |        a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 19.22/3.41  |          n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 19.22/3.41  |        a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 19.22/3.41  |        use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 19.22/3.41  |        use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 19.22/3.41  |        use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 19.22/3.41  |        use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 19.22/3.41  |        use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 19.22/3.41  |        & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5,
% 19.22/3.41  |          n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 &
% 19.22/3.41  |        $i(all_76_0) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0)
% 19.22/3.41  |          |  ~ (leq(v0, n2) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: any] :  ?
% 19.22/3.41  |          [v3: any] :  ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0,
% 19.22/3.41  |              v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0)
% 19.22/3.41  |              | v4 = use))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (leq(v1,
% 19.22/3.41  |              all_76_0) = 0) |  ~ (leq(v0, n2) = 0) |  ~ $i(v1) |  ~ $i(v0) | 
% 19.22/3.41  |          ? [v2: any] :  ? [v3: any] :  ? [v4: $i] : (a_select3(u_defuse, v0,
% 19.22/3.41  |              v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3
% 19.22/3.41  |                = 0) |  ~ (v2 = 0) | v4 = use))) &  ? [v0: $i] :  ? [v1: $i] : 
% 19.22/3.41  |        ? [v2: $i] : ( ~ (v2 = use) & a_select3(z_defuse, v0, v1) = v2 &
% 19.22/3.41  |          leq(v1, pv5) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) =
% 19.22/3.41  |          0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v1 = pv5) |  ~ (v0 = n2)) & ( ~
% 19.22/3.41  |            (v1 = pv5) |  ~ (v0 = n1)) & ( ~ (v1 = pv5) |  ~ (v0 = n0)))
% 19.22/3.41  | 
% 19.22/3.41  | ALPHA: (6) implies:
% 19.22/3.41  |   (7)  leq(n0, pv5) = 0
% 19.22/3.41  |   (8)  leq(pv5, n0) = 0
% 19.22/3.41  |   (9)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = use) &
% 19.22/3.41  |          a_select3(z_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2) = 0
% 19.22/3.41  |          & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0) & ( ~
% 19.22/3.41  |            (v1 = pv5) |  ~ (v0 = n2)) & ( ~ (v1 = pv5) |  ~ (v0 = n1)) & ( ~
% 19.22/3.41  |            (v1 = pv5) |  ~ (v0 = n0)))
% 19.22/3.41  | 
% 19.22/3.41  | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1, all_79_2
% 19.22/3.41  |        gives:
% 19.22/3.41  |   (10)   ~ (all_79_0 = use) & a_select3(z_defuse, all_79_2, all_79_1) =
% 19.22/3.41  |         all_79_0 & leq(all_79_1, pv5) = 0 & leq(all_79_2, n2) = 0 & leq(n0,
% 19.22/3.41  |           all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) & $i(all_79_1)
% 19.22/3.41  |         & $i(all_79_2) & ( ~ (all_79_1 = pv5) |  ~ (all_79_2 = n2)) & ( ~
% 19.22/3.41  |           (all_79_1 = pv5) |  ~ (all_79_2 = n1)) & ( ~ (all_79_1 = pv5) |  ~
% 19.22/3.41  |           (all_79_2 = n0))
% 19.22/3.41  | 
% 19.22/3.41  | ALPHA: (10) implies:
% 19.22/3.41  |   (11)  $i(all_79_2)
% 19.22/3.41  |   (12)  $i(all_79_1)
% 19.22/3.41  |   (13)  leq(n0, all_79_2) = 0
% 19.22/3.41  |   (14)  leq(n0, all_79_1) = 0
% 19.22/3.41  |   (15)  leq(all_79_2, n2) = 0
% 19.66/3.41  |   (16)  leq(all_79_1, pv5) = 0
% 19.66/3.41  |   (17)   ~ (all_79_1 = pv5) |  ~ (all_79_2 = n0)
% 19.66/3.41  |   (18)   ~ (all_79_1 = pv5) |  ~ (all_79_2 = n1)
% 19.66/3.41  |   (19)   ~ (all_79_1 = pv5) |  ~ (all_79_2 = n2)
% 19.66/3.41  | 
% 19.66/3.41  | GROUND_INST: instantiating (1) with pv5, simplifying with (3), (7) gives:
% 19.66/3.41  |   (20)  pv5 = n0 |  ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 19.66/3.41  | 
% 19.66/3.41  | GROUND_INST: instantiating (1) with all_79_1, simplifying with (12), (14)
% 19.66/3.41  |              gives:
% 19.66/3.41  |   (21)  all_79_1 = n0 |  ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0)
% 19.66/3.41  | 
% 19.66/3.41  | GROUND_INST: instantiating (2) with all_79_2, simplifying with (11), (15)
% 19.66/3.41  |              gives:
% 19.66/3.41  |   (22)  all_79_2 = n2 | all_79_2 = n1 | all_79_2 = n0 |  ? [v0: int] : ( ~ (v0
% 19.66/3.41  |             = 0) & leq(n0, all_79_2) = v0)
% 19.66/3.41  | 
% 19.66/3.41  | BETA: splitting (20) gives:
% 19.66/3.41  | 
% 19.66/3.41  | Case 1:
% 19.66/3.41  | | 
% 19.66/3.41  | |   (23)  pv5 = n0
% 19.66/3.41  | | 
% 19.66/3.41  | | REDUCE: (16), (23) imply:
% 19.66/3.41  | |   (24)  leq(all_79_1, n0) = 0
% 19.66/3.41  | | 
% 19.66/3.41  | | BETA: splitting (21) gives:
% 19.66/3.41  | | 
% 19.66/3.41  | | Case 1:
% 19.66/3.41  | | | 
% 19.66/3.41  | | |   (25)  all_79_1 = n0
% 19.66/3.41  | | | 
% 19.66/3.41  | | | BETA: splitting (19) gives:
% 19.66/3.41  | | | 
% 19.66/3.41  | | | Case 1:
% 19.66/3.41  | | | | 
% 19.66/3.41  | | | |   (26)   ~ (all_79_1 = pv5)
% 19.66/3.41  | | | | 
% 19.66/3.41  | | | | REDUCE: (23), (25), (26) imply:
% 19.66/3.42  | | | |   (27)  $false
% 19.66/3.42  | | | | 
% 19.66/3.42  | | | | CLOSE: (27) is inconsistent.
% 19.66/3.42  | | | | 
% 19.66/3.42  | | | Case 2:
% 19.66/3.42  | | | | 
% 19.66/3.42  | | | |   (28)  all_79_1 = pv5
% 19.66/3.42  | | | |   (29)   ~ (all_79_2 = n2)
% 19.66/3.42  | | | | 
% 19.66/3.42  | | | | COMBINE_EQS: (25), (28) imply:
% 19.66/3.42  | | | |   (30)  pv5 = n0
% 19.66/3.42  | | | | 
% 19.66/3.42  | | | | BETA: splitting (17) gives:
% 19.66/3.42  | | | | 
% 19.66/3.42  | | | | Case 1:
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | |   (31)   ~ (all_79_2 = n0)
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | | BETA: splitting (22) gives:
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | | Case 1:
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | |   (32)  all_79_2 = n0
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | | REDUCE: (31), (32) imply:
% 19.66/3.42  | | | | | |   (33)  $false
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | | CLOSE: (33) is inconsistent.
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | Case 2:
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | |   (34)  all_79_2 = n2 | all_79_2 = n1 |  ? [v0: int] : ( ~ (v0 = 0)
% 19.66/3.42  | | | | | |           & leq(n0, all_79_2) = v0)
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | | BETA: splitting (34) gives:
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | | Case 1:
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | |   (35)  all_79_2 = n2
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | | REDUCE: (29), (35) imply:
% 19.66/3.42  | | | | | | |   (36)  $false
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | | CLOSE: (36) is inconsistent.
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | Case 2:
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | |   (37)  all_79_2 = n1 |  ? [v0: int] : ( ~ (v0 = 0) & leq(n0,
% 19.66/3.42  | | | | | | |             all_79_2) = v0)
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | | BETA: splitting (37) gives:
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | | Case 1:
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | |   (38)  all_79_2 = n1
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | | BETA: splitting (18) gives:
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | | Case 1:
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | |   (39)   ~ (all_79_1 = pv5)
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | | REDUCE: (23), (25), (39) imply:
% 19.66/3.42  | | | | | | | | |   (40)  $false
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | | CLOSE: (40) is inconsistent.
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | Case 2:
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | |   (41)   ~ (all_79_2 = n1)
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | | REDUCE: (38), (41) imply:
% 19.66/3.42  | | | | | | | | |   (42)  $false
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | | CLOSE: (42) is inconsistent.
% 19.66/3.42  | | | | | | | | | 
% 19.66/3.42  | | | | | | | | End of split
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | Case 2:
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | |   (43)   ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_2) = v0)
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | | DELTA: instantiating (43) with fresh symbol all_131_0 gives:
% 19.66/3.42  | | | | | | | |   (44)   ~ (all_131_0 = 0) & leq(n0, all_79_2) = all_131_0
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | | ALPHA: (44) implies:
% 19.66/3.42  | | | | | | | |   (45)   ~ (all_131_0 = 0)
% 19.66/3.42  | | | | | | | |   (46)  leq(n0, all_79_2) = all_131_0
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | | GROUND_INST: instantiating (5) with 0, all_131_0, all_79_2, n0,
% 19.66/3.42  | | | | | | | |              simplifying with (13), (46) gives:
% 19.66/3.42  | | | | | | | |   (47)  all_131_0 = 0
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | | REDUCE: (45), (47) imply:
% 19.66/3.42  | | | | | | | |   (48)  $false
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | | CLOSE: (48) is inconsistent.
% 19.66/3.42  | | | | | | | | 
% 19.66/3.42  | | | | | | | End of split
% 19.66/3.42  | | | | | | | 
% 19.66/3.42  | | | | | | End of split
% 19.66/3.42  | | | | | | 
% 19.66/3.42  | | | | | End of split
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | Case 2:
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | |   (49)   ~ (all_79_1 = pv5)
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | | REDUCE: (23), (25), (49) imply:
% 19.66/3.42  | | | | |   (50)  $false
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | | CLOSE: (50) is inconsistent.
% 19.66/3.42  | | | | | 
% 19.66/3.42  | | | | End of split
% 19.66/3.42  | | | | 
% 19.66/3.42  | | | End of split
% 19.66/3.42  | | | 
% 19.66/3.42  | | Case 2:
% 19.66/3.42  | | | 
% 19.66/3.42  | | |   (51)   ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0)
% 19.66/3.42  | | | 
% 19.66/3.42  | | | DELTA: instantiating (51) with fresh symbol all_111_0 gives:
% 19.66/3.42  | | |   (52)   ~ (all_111_0 = 0) & leq(all_79_1, n0) = all_111_0
% 19.66/3.42  | | | 
% 19.66/3.42  | | | ALPHA: (52) implies:
% 19.66/3.42  | | |   (53)   ~ (all_111_0 = 0)
% 19.66/3.42  | | |   (54)  leq(all_79_1, n0) = all_111_0
% 19.66/3.42  | | | 
% 19.66/3.42  | | | GROUND_INST: instantiating (5) with 0, all_111_0, n0, all_79_1,
% 19.66/3.42  | | |              simplifying with (24), (54) gives:
% 19.66/3.42  | | |   (55)  all_111_0 = 0
% 19.66/3.42  | | | 
% 19.66/3.42  | | | REDUCE: (53), (55) imply:
% 19.66/3.42  | | |   (56)  $false
% 19.66/3.42  | | | 
% 19.66/3.42  | | | CLOSE: (56) is inconsistent.
% 19.66/3.42  | | | 
% 19.66/3.42  | | End of split
% 19.66/3.42  | | 
% 19.66/3.42  | Case 2:
% 19.66/3.42  | | 
% 19.66/3.42  | |   (57)   ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 19.66/3.42  | | 
% 19.66/3.42  | | DELTA: instantiating (57) with fresh symbol all_107_0 gives:
% 19.66/3.42  | |   (58)   ~ (all_107_0 = 0) & leq(pv5, n0) = all_107_0
% 19.66/3.42  | | 
% 19.66/3.42  | | ALPHA: (58) implies:
% 19.66/3.42  | |   (59)   ~ (all_107_0 = 0)
% 19.66/3.43  | |   (60)  leq(pv5, n0) = all_107_0
% 19.66/3.43  | | 
% 19.66/3.43  | | GROUND_INST: instantiating (5) with 0, all_107_0, n0, pv5, simplifying with
% 19.66/3.43  | |              (8), (60) gives:
% 19.66/3.43  | |   (61)  all_107_0 = 0
% 19.66/3.43  | | 
% 19.66/3.43  | | REDUCE: (59), (61) imply:
% 19.66/3.43  | |   (62)  $false
% 19.66/3.43  | | 
% 19.66/3.43  | | CLOSE: (62) is inconsistent.
% 19.66/3.43  | | 
% 19.66/3.43  | End of split
% 19.66/3.43  | 
% 19.66/3.43  End of proof
% 19.66/3.43  % SZS output end Proof for theBenchmark
% 19.66/3.43  
% 19.66/3.43  2811ms
%------------------------------------------------------------------------------