TSTP Solution File: MSC010+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : MSC010+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n023.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 09:26:45 EDT 2023

% Result   : Theorem 8.38s 1.89s
% Output   : Proof 13.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : MSC010+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n023.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 14:02:27 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.62/0.61  ________       _____
% 0.62/0.61  ___  __ \_________(_)________________________________
% 0.62/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.62/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.62/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.62/0.61  
% 0.62/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.61  (2023-06-19)
% 0.62/0.61  
% 0.62/0.61  (c) Philipp Rümmer, 2009-2023
% 0.62/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.61                Amanda Stjerna.
% 0.62/0.61  Free software under BSD-3-Clause.
% 0.62/0.61  
% 0.62/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.61  
% 0.62/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.62  Running up to 7 provers in parallel.
% 0.72/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.72/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.72/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.72/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.72/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.72/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.72/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.10/1.11  Prover 4: Preprocessing ...
% 3.10/1.11  Prover 1: Preprocessing ...
% 3.10/1.15  Prover 5: Preprocessing ...
% 3.10/1.15  Prover 6: Preprocessing ...
% 3.10/1.15  Prover 3: Preprocessing ...
% 3.10/1.15  Prover 2: Preprocessing ...
% 3.10/1.15  Prover 0: Preprocessing ...
% 6.28/1.57  Prover 3: Constructing countermodel ...
% 6.28/1.57  Prover 1: Constructing countermodel ...
% 6.28/1.58  Prover 2: Proving ...
% 6.28/1.58  Prover 6: Proving ...
% 6.28/1.59  Prover 5: Constructing countermodel ...
% 6.87/1.61  Prover 4: Constructing countermodel ...
% 6.87/1.62  Prover 0: Proving ...
% 8.38/1.89  Prover 3: proved (1245ms)
% 8.38/1.89  
% 8.38/1.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.38/1.89  
% 8.38/1.89  Prover 5: stopped
% 8.38/1.89  Prover 0: stopped
% 8.38/1.89  Prover 2: stopped
% 8.91/1.90  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.91/1.90  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.91/1.90  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.91/1.90  Prover 6: stopped
% 8.91/1.92  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.91/1.92  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.41/2.00  Prover 7: Preprocessing ...
% 9.41/2.01  Prover 13: Preprocessing ...
% 9.41/2.02  Prover 11: Preprocessing ...
% 9.41/2.02  Prover 8: Preprocessing ...
% 9.41/2.03  Prover 10: Preprocessing ...
% 10.35/2.12  Prover 7: Constructing countermodel ...
% 10.55/2.13  Prover 10: Constructing countermodel ...
% 10.55/2.18  Prover 13: Constructing countermodel ...
% 10.55/2.18  Prover 11: Constructing countermodel ...
% 10.55/2.20  Prover 8: Warning: ignoring some quantifiers
% 10.55/2.21  Prover 8: Constructing countermodel ...
% 11.78/2.36  Prover 10: Found proof (size 86)
% 11.78/2.36  Prover 10: proved (464ms)
% 11.78/2.36  Prover 1: stopped
% 11.78/2.36  Prover 8: stopped
% 11.78/2.36  Prover 7: stopped
% 11.78/2.36  Prover 13: stopped
% 11.78/2.37  Prover 4: stopped
% 11.78/2.37  Prover 11: stopped
% 11.78/2.37  
% 11.78/2.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.78/2.37  
% 11.78/2.37  % SZS output start Proof for theBenchmark
% 11.78/2.38  Assumptions after simplification:
% 11.78/2.38  ---------------------------------
% 11.78/2.38  
% 11.78/2.38    (n1)
% 12.60/2.41    $i(id_ds1_filter_init) & $i(pminus_ds1_filter_init) &
% 12.60/2.41    $i(xhatmin_ds1_filter_init) & $i(r_ds1_filter_init) & $i(q_ds1_filter_init) &
% 12.60/2.41    $i(dv_ds1_filter_init) & $i(phi_ds1_filter_init) & $i(init) &
% 12.60/2.41    $i(h_ds1_filter_init) & $i(n2) & $i(n5) & $i(n998) & $i(pv5) & $i(n0) &
% 12.60/2.41    $i(pv63) & $i(pv64) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : 
% 12.60/2.41    ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9:
% 12.60/2.41      $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 12.60/2.41      $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ? [v19:
% 12.60/2.41      $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i] :  ? [v24:
% 12.60/2.41      $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28: $i] :  ? [v29:
% 12.60/2.41      $i] :  ? [v30: $i] : ($i(v29) & $i(v28) & $i(v26) & $i(v25) & $i(v23) &
% 12.60/2.41      $i(v22) & $i(v20) & $i(v19) & $i(v17) & $i(v16) & $i(v14) & $i(v13) &
% 12.60/2.41      $i(v11) & $i(v10) & $i(v8) & $i(v7) & $i(v5) & $i(v4) & $i(v2) & $i(v1) &
% 12.60/2.41      (pv63 = pv64 |  ~ leq(pv5, n998) |  ~ leq(n0, pv5) |  ~ leq(n0, pv63) |  ~
% 12.60/2.41        leq(n0, pv64) |  ~ leq(pv63, n5) |  ~ leq(pv64, n5) |  ! [v31: $i] :  !
% 12.60/2.41        [v32: $i] : (v32 = init | v31 = pv64 |  ~ (a_select3(id_ds1_filter_init,
% 12.60/2.41              pv63, v31) = v32) |  ~ $i(v31) |  ~ leq(v31, n5) |  ~ leq(v31, pv64)
% 12.60/2.41          |  ~ leq(n0, v31)) | (v7 = pv63 &  ~ (v9 = init) &
% 12.60/2.41          a_select3(id_ds1_filter_init, pv63, v8) = v9 & $i(v9) & gt(pv64, v8) &
% 12.60/2.41          leq(v8, n5) & leq(n0, v8)) | ( ~ (v30 = init) &
% 12.60/2.41          a_select3(h_ds1_filter_init, v28, v29) = v30 & $i(v30) & leq(v29, n5) &
% 12.60/2.41          leq(v28, n2) & leq(n0, v29) & leq(n0, v28)) | ( ~ (v27 = init) &
% 12.60/2.41          a_select3(phi_ds1_filter_init, v25, v26) = v27 & $i(v27) & leq(v26, n5)
% 12.60/2.41          & leq(v25, n5) & leq(n0, v26) & leq(n0, v25)) | ( ~ (v24 = init) &
% 12.60/2.41          a_select3(dv_ds1_filter_init, v22, v23) = v24 & $i(v24) & leq(v23, n0) &
% 12.60/2.41          leq(v22, n5) & leq(n0, v23) & leq(n0, v22)) | ( ~ (v21 = init) &
% 12.60/2.41          a_select3(q_ds1_filter_init, v19, v20) = v21 & $i(v21) & leq(v20, n5) &
% 12.60/2.41          leq(v19, n5) & leq(n0, v20) & leq(n0, v19)) | ( ~ (v18 = init) &
% 12.60/2.41          a_select3(r_ds1_filter_init, v16, v17) = v18 & $i(v18) & leq(v17, n2) &
% 12.60/2.41          leq(v16, n2) & leq(n0, v17) & leq(n0, v16)) | ( ~ (v15 = init) &
% 12.60/2.41          a_select3(xhatmin_ds1_filter_init, v13, v14) = v15 & $i(v15) & leq(v14,
% 12.60/2.41            n0) & leq(v13, n5) & leq(n0, v14) & leq(n0, v13)) | ( ~ (v12 = init) &
% 12.60/2.41          a_select3(pminus_ds1_filter_init, v10, v11) = v12 & $i(v12) & leq(v11,
% 12.60/2.41            n5) & leq(v10, n5) & leq(n0, v11) & leq(n0, v10)) | ( ~ (v6 = init) &
% 12.60/2.41          a_select3(id_ds1_filter_init, v4, v5) = v6 & $i(v6) & gt(pv63, v4) &
% 12.60/2.41          leq(v5, n5) & leq(v4, n5) & leq(n0, v5) & leq(n0, v4)) | ( ~ (v3 = init)
% 12.60/2.41          & pred(pv63) = v0 & a_select3(id_ds1_filter_init, v1, v2) = v3 & $i(v3)
% 12.60/2.41          & $i(v0) & leq(v2, n5) & leq(v1, v0) & leq(n0, v2) & leq(n0, v1))))
% 12.60/2.41  
% 12.60/2.41    (n91)
% 12.60/2.42    $i(id_ds1_filter_init) & $i(pminus_ds1_filter_init) &
% 12.60/2.42    $i(xhatmin_ds1_filter_init) & $i(r_ds1_filter_init) & $i(q_ds1_filter_init) &
% 12.60/2.42    $i(dv_ds1_filter_init) & $i(phi_ds1_filter_init) & $i(init) &
% 12.60/2.42    $i(h_ds1_filter_init) & $i(n2) & $i(n5) & $i(n998) & $i(pv5) & $i(n0) &
% 12.60/2.42    $i(pv63) & $i(pv64) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 =
% 12.60/2.42        init) &  ~ (v1 = pv64) &  ~ (pv63 = pv64) & pred(pv63) = v0 &
% 12.60/2.42      a_select3(id_ds1_filter_init, pv63, v1) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 12.60/2.42      leq(v1, n5) & leq(v1, pv64) & leq(pv5, n998) & leq(n0, v1) & leq(n0, pv5) &
% 12.60/2.42      leq(n0, pv63) & leq(n0, pv64) & leq(pv63, n5) & leq(pv64, n5) &  ! [v3: $i]
% 12.60/2.42      :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~ (a_select3(id_ds1_filter_init,
% 12.60/2.42            v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~ gt(pv63, v3) |  ~ leq(v4,
% 12.60/2.42          n5) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3: $i] : 
% 12.60/2.42      ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~ (a_select3(id_ds1_filter_init,
% 12.60/2.42            v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~ leq(v4, n5) |  ~ leq(v3,
% 12.60/2.42          v0) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] :  !
% 12.60/2.42      [v5: $i] : (v5 = init |  ~ (a_select3(pminus_ds1_filter_init, v3, v4) = v5)
% 12.60/2.42        |  ~ $i(v4) |  ~ $i(v3) |  ~ leq(v4, n5) |  ~ leq(v3, n5) |  ~ leq(n0, v4)
% 12.60/2.42        |  ~ leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |
% 12.60/2.42         ~ (a_select3(xhatmin_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~
% 12.60/2.42        $i(v3) |  ~ leq(v4, n0) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~ leq(n0,
% 12.60/2.42          v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~
% 12.60/2.42        (a_select3(r_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~
% 12.60/2.42        leq(v4, n2) |  ~ leq(v3, n2) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3:
% 12.60/2.42        $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~
% 12.60/2.42        (a_select3(q_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~
% 12.60/2.42        leq(v4, n5) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3:
% 12.60/2.42        $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~
% 12.60/2.42        (a_select3(dv_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~
% 12.60/2.42        leq(v4, n0) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3:
% 12.60/2.42        $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~
% 12.60/2.42        (a_select3(phi_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~
% 12.60/2.42        leq(v4, n5) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3:
% 12.60/2.42        $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~
% 12.60/2.42        (a_select3(h_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~
% 12.60/2.42        leq(v4, n5) |  ~ leq(v3, n2) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3:
% 12.60/2.42        $i] :  ! [v4: $i] : (v4 = init |  ~ (a_select3(id_ds1_filter_init, pv63,
% 12.60/2.42            v3) = v4) |  ~ $i(v3) |  ~ gt(pv64, v3) |  ~ leq(v3, n5) |  ~ leq(n0,
% 12.60/2.42          v3)))
% 12.60/2.42  
% 12.60/2.42    (function-axioms)
% 12.60/2.42     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0
% 12.60/2.42      |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  !
% 12.60/2.42    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~
% 12.60/2.42      (pred(v2) = v0))
% 12.60/2.42  
% 12.60/2.42  Those formulas are unsatisfiable:
% 12.60/2.42  ---------------------------------
% 12.60/2.42  
% 12.60/2.42  Begin of proof
% 12.60/2.42  | 
% 12.60/2.42  | ALPHA: (n1) implies:
% 12.60/2.43  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 12.60/2.43  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 12.60/2.43  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 12.60/2.43  |         ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ? [v19:
% 12.60/2.43  |          $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i] :  ?
% 12.60/2.43  |        [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28: $i] :
% 12.60/2.43  |         ? [v29: $i] :  ? [v30: $i] : ($i(v29) & $i(v28) & $i(v26) & $i(v25) &
% 12.60/2.43  |          $i(v23) & $i(v22) & $i(v20) & $i(v19) & $i(v17) & $i(v16) & $i(v14) &
% 12.60/2.43  |          $i(v13) & $i(v11) & $i(v10) & $i(v8) & $i(v7) & $i(v5) & $i(v4) &
% 12.60/2.43  |          $i(v2) & $i(v1) & (pv63 = pv64 |  ~ leq(pv5, n998) |  ~ leq(n0, pv5)
% 12.60/2.43  |            |  ~ leq(n0, pv63) |  ~ leq(n0, pv64) |  ~ leq(pv63, n5) |  ~
% 12.60/2.43  |            leq(pv64, n5) |  ! [v31: $i] :  ! [v32: $i] : (v32 = init | v31 =
% 12.60/2.43  |              pv64 |  ~ (a_select3(id_ds1_filter_init, pv63, v31) = v32) |  ~
% 12.60/2.43  |              $i(v31) |  ~ leq(v31, n5) |  ~ leq(v31, pv64) |  ~ leq(n0, v31))
% 12.60/2.43  |            | (v7 = pv63 &  ~ (v9 = init) & a_select3(id_ds1_filter_init, pv63,
% 12.60/2.43  |                v8) = v9 & $i(v9) & gt(pv64, v8) & leq(v8, n5) & leq(n0, v8)) |
% 12.60/2.43  |            ( ~ (v30 = init) & a_select3(h_ds1_filter_init, v28, v29) = v30 &
% 12.60/2.43  |              $i(v30) & leq(v29, n5) & leq(v28, n2) & leq(n0, v29) & leq(n0,
% 12.60/2.43  |                v28)) | ( ~ (v27 = init) & a_select3(phi_ds1_filter_init, v25,
% 12.60/2.43  |                v26) = v27 & $i(v27) & leq(v26, n5) & leq(v25, n5) & leq(n0,
% 12.60/2.43  |                v26) & leq(n0, v25)) | ( ~ (v24 = init) &
% 12.60/2.43  |              a_select3(dv_ds1_filter_init, v22, v23) = v24 & $i(v24) &
% 12.60/2.43  |              leq(v23, n0) & leq(v22, n5) & leq(n0, v23) & leq(n0, v22)) | ( ~
% 12.60/2.43  |              (v21 = init) & a_select3(q_ds1_filter_init, v19, v20) = v21 &
% 12.60/2.43  |              $i(v21) & leq(v20, n5) & leq(v19, n5) & leq(n0, v20) & leq(n0,
% 12.60/2.43  |                v19)) | ( ~ (v18 = init) & a_select3(r_ds1_filter_init, v16,
% 12.60/2.43  |                v17) = v18 & $i(v18) & leq(v17, n2) & leq(v16, n2) & leq(n0,
% 12.60/2.43  |                v17) & leq(n0, v16)) | ( ~ (v15 = init) &
% 12.60/2.43  |              a_select3(xhatmin_ds1_filter_init, v13, v14) = v15 & $i(v15) &
% 12.60/2.43  |              leq(v14, n0) & leq(v13, n5) & leq(n0, v14) & leq(n0, v13)) | ( ~
% 12.60/2.43  |              (v12 = init) & a_select3(pminus_ds1_filter_init, v10, v11) = v12
% 12.60/2.43  |              & $i(v12) & leq(v11, n5) & leq(v10, n5) & leq(n0, v11) & leq(n0,
% 12.60/2.43  |                v10)) | ( ~ (v6 = init) & a_select3(id_ds1_filter_init, v4, v5)
% 12.60/2.43  |              = v6 & $i(v6) & gt(pv63, v4) & leq(v5, n5) & leq(v4, n5) &
% 12.60/2.43  |              leq(n0, v5) & leq(n0, v4)) | ( ~ (v3 = init) & pred(pv63) = v0 &
% 12.60/2.43  |              a_select3(id_ds1_filter_init, v1, v2) = v3 & $i(v3) & $i(v0) &
% 12.60/2.43  |              leq(v2, n5) & leq(v1, v0) & leq(n0, v2) & leq(n0, v1))))
% 12.60/2.43  | 
% 12.60/2.43  | ALPHA: (n91) implies:
% 12.60/2.43  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = init) &  ~ (v1 =
% 12.60/2.43  |            pv64) &  ~ (pv63 = pv64) & pred(pv63) = v0 &
% 12.60/2.43  |          a_select3(id_ds1_filter_init, pv63, v1) = v2 & $i(v2) & $i(v1) &
% 12.60/2.43  |          $i(v0) & leq(v1, n5) & leq(v1, pv64) & leq(pv5, n998) & leq(n0, v1) &
% 12.60/2.43  |          leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv63, n5) &
% 12.60/2.43  |          leq(pv64, n5) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init
% 12.60/2.43  |            |  ~ (a_select3(id_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~
% 12.60/2.43  |            $i(v3) |  ~ gt(pv63, v3) |  ~ leq(v4, n5) |  ~ leq(v3, n5) |  ~
% 12.60/2.43  |            leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 12.60/2.43  |            $i] : (v5 = init |  ~ (a_select3(id_ds1_filter_init, v3, v4) = v5)
% 12.60/2.43  |            |  ~ $i(v4) |  ~ $i(v3) |  ~ leq(v4, n5) |  ~ leq(v3, v0) |  ~
% 12.60/2.43  |            leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 12.60/2.43  |            $i] : (v5 = init |  ~ (a_select3(pminus_ds1_filter_init, v3, v4) =
% 12.60/2.43  |              v5) |  ~ $i(v4) |  ~ $i(v3) |  ~ leq(v4, n5) |  ~ leq(v3, n5) | 
% 12.60/2.43  |            ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] :  !
% 12.60/2.43  |          [v5: $i] : (v5 = init |  ~ (a_select3(xhatmin_ds1_filter_init, v3,
% 12.60/2.43  |                v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~ leq(v4, n0) |  ~ leq(v3,
% 12.60/2.43  |              n5) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3: $i] :  ! [v4:
% 12.60/2.43  |            $i] :  ! [v5: $i] : (v5 = init |  ~ (a_select3(r_ds1_filter_init,
% 12.60/2.43  |                v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3) |  ~ leq(v4, n2) |  ~
% 12.60/2.43  |            leq(v3, n2) |  ~ leq(n0, v4) |  ~ leq(n0, v3)) &  ! [v3: $i] :  !
% 12.60/2.43  |          [v4: $i] :  ! [v5: $i] : (v5 = init |  ~
% 12.60/2.43  |            (a_select3(q_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~ $i(v3)
% 12.60/2.43  |            |  ~ leq(v4, n5) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~ leq(n0,
% 12.60/2.43  |              v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init |  ~
% 12.60/2.43  |            (a_select3(dv_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~
% 12.60/2.43  |            $i(v3) |  ~ leq(v4, n0) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~
% 12.60/2.43  |            leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init
% 12.60/2.43  |            |  ~ (a_select3(phi_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~
% 12.60/2.43  |            $i(v3) |  ~ leq(v4, n5) |  ~ leq(v3, n5) |  ~ leq(n0, v4) |  ~
% 12.60/2.44  |            leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (v5 = init
% 12.60/2.44  |            |  ~ (a_select3(h_ds1_filter_init, v3, v4) = v5) |  ~ $i(v4) |  ~
% 12.60/2.44  |            $i(v3) |  ~ leq(v4, n5) |  ~ leq(v3, n2) |  ~ leq(n0, v4) |  ~
% 12.60/2.44  |            leq(n0, v3)) &  ! [v3: $i] :  ! [v4: $i] : (v4 = init |  ~
% 12.60/2.44  |            (a_select3(id_ds1_filter_init, pv63, v3) = v4) |  ~ $i(v3) |  ~
% 12.60/2.44  |            gt(pv64, v3) |  ~ leq(v3, n5) |  ~ leq(n0, v3)))
% 12.60/2.44  | 
% 12.60/2.44  | ALPHA: (function-axioms) implies:
% 12.60/2.44  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (pred(v2) = v1)
% 12.60/2.44  |          |  ~ (pred(v2) = v0))
% 12.60/2.44  | 
% 12.60/2.44  | DELTA: instantiating (2) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 12.60/2.44  |   (4)   ~ (all_4_0 = init) &  ~ (all_4_1 = pv64) &  ~ (pv63 = pv64) &
% 12.60/2.44  |        pred(pv63) = all_4_2 & a_select3(id_ds1_filter_init, pv63, all_4_1) =
% 12.60/2.44  |        all_4_0 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & leq(all_4_1, n5) &
% 12.60/2.44  |        leq(all_4_1, pv64) & leq(pv5, n998) & leq(n0, all_4_1) & leq(n0, pv5) &
% 12.60/2.44  |        leq(n0, pv63) & leq(n0, pv64) & leq(pv63, n5) & leq(pv64, n5) &  ! [v0:
% 12.60/2.44  |          $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.44  |          (a_select3(id_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 12.60/2.44  |          |  ~ gt(pv63, v0) |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1)
% 12.60/2.44  |          |  ~ leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 =
% 12.60/2.44  |          init |  ~ (a_select3(id_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) | 
% 12.60/2.44  |          ~ $i(v0) |  ~ leq(v1, n5) |  ~ leq(v0, all_4_2) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |
% 12.60/2.44  |           ~ (a_select3(pminus_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.44  |          $i(v0) |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |
% 12.60/2.44  |           ~ (a_select3(xhatmin_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.44  |          $i(v0) |  ~ leq(v1, n0) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |
% 12.60/2.44  |           ~ (a_select3(r_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.44  |          $i(v0) |  ~ leq(v1, n2) |  ~ leq(v0, n2) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |
% 12.60/2.44  |           ~ (a_select3(q_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.44  |          $i(v0) |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |
% 12.60/2.44  |           ~ (a_select3(dv_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.44  |          $i(v0) |  ~ leq(v1, n0) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |
% 12.60/2.44  |           ~ (a_select3(phi_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.44  |          $i(v0) |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |
% 12.60/2.44  |           ~ (a_select3(h_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.44  |          $i(v0) |  ~ leq(v1, n5) |  ~ leq(v0, n2) |  ~ leq(n0, v1) |  ~
% 12.60/2.44  |          leq(n0, v0)) &  ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 12.60/2.44  |          (a_select3(id_ds1_filter_init, pv63, v0) = v1) |  ~ $i(v0) |  ~
% 12.60/2.44  |          gt(pv64, v0) |  ~ leq(v0, n5) |  ~ leq(n0, v0))
% 12.60/2.44  | 
% 12.60/2.44  | ALPHA: (4) implies:
% 12.60/2.44  |   (5)   ~ (pv63 = pv64)
% 12.60/2.44  |   (6)   ~ (all_4_1 = pv64)
% 12.60/2.44  |   (7)   ~ (all_4_0 = init)
% 12.60/2.44  |   (8)  leq(pv64, n5)
% 12.60/2.44  |   (9)  leq(pv63, n5)
% 12.60/2.44  |   (10)  leq(n0, pv64)
% 12.60/2.44  |   (11)  leq(n0, pv63)
% 12.60/2.44  |   (12)  leq(n0, pv5)
% 12.60/2.44  |   (13)  leq(n0, all_4_1)
% 12.60/2.44  |   (14)  leq(pv5, n998)
% 12.60/2.44  |   (15)  leq(all_4_1, pv64)
% 12.60/2.44  |   (16)  leq(all_4_1, n5)
% 12.60/2.44  |   (17)  $i(all_4_1)
% 12.60/2.44  |   (18)  a_select3(id_ds1_filter_init, pv63, all_4_1) = all_4_0
% 12.60/2.44  |   (19)  pred(pv63) = all_4_2
% 12.60/2.45  |   (20)   ! [v0: $i] :  ! [v1: $i] : (v1 = init |  ~
% 12.60/2.45  |           (a_select3(id_ds1_filter_init, pv63, v0) = v1) |  ~ $i(v0) |  ~
% 12.60/2.45  |           gt(pv64, v0) |  ~ leq(v0, n5) |  ~ leq(n0, v0))
% 12.60/2.45  |   (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(h_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 12.60/2.45  |           |  ~ leq(v1, n5) |  ~ leq(v0, n2) |  ~ leq(n0, v1) |  ~ leq(n0, v0))
% 12.60/2.45  |   (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(phi_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.45  |           $i(v0) |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.45  |           leq(n0, v0))
% 12.60/2.45  |   (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(dv_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 12.60/2.45  |           |  ~ leq(v1, n0) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~ leq(n0, v0))
% 12.60/2.45  |   (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(q_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 12.60/2.45  |           |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~ leq(n0, v0))
% 12.60/2.45  |   (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(r_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 12.60/2.45  |           |  ~ leq(v1, n2) |  ~ leq(v0, n2) |  ~ leq(n0, v1) |  ~ leq(n0, v0))
% 12.60/2.45  |   (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(xhatmin_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.45  |           $i(v0) |  ~ leq(v1, n0) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.45  |           leq(n0, v0))
% 12.60/2.45  |   (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(pminus_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~
% 12.60/2.45  |           $i(v0) |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1) |  ~
% 12.60/2.45  |           leq(n0, v0))
% 12.60/2.45  |   (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(id_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 12.60/2.45  |           |  ~ leq(v1, n5) |  ~ leq(v0, all_4_2) |  ~ leq(n0, v1) |  ~ leq(n0,
% 12.60/2.45  |             v0))
% 12.60/2.45  |   (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = init |  ~
% 12.60/2.45  |           (a_select3(id_ds1_filter_init, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 12.60/2.45  |           |  ~ gt(pv63, v0) |  ~ leq(v1, n5) |  ~ leq(v0, n5) |  ~ leq(n0, v1)
% 12.60/2.45  |           |  ~ leq(n0, v0))
% 12.60/2.45  | 
% 12.60/2.45  | DELTA: instantiating (1) with fresh symbols all_7_0, all_7_1, all_7_2,
% 12.60/2.45  |        all_7_3, all_7_4, all_7_5, all_7_6, all_7_7, all_7_8, all_7_9,
% 12.60/2.45  |        all_7_10, all_7_11, all_7_12, all_7_13, all_7_14, all_7_15, all_7_16,
% 12.60/2.45  |        all_7_17, all_7_18, all_7_19, all_7_20, all_7_21, all_7_22, all_7_23,
% 12.60/2.45  |        all_7_24, all_7_25, all_7_26, all_7_27, all_7_28, all_7_29, all_7_30
% 12.60/2.45  |        gives:
% 12.60/2.46  |   (30)  $i(all_7_1) & $i(all_7_2) & $i(all_7_4) & $i(all_7_5) & $i(all_7_7) &
% 12.60/2.46  |         $i(all_7_8) & $i(all_7_10) & $i(all_7_11) & $i(all_7_13) &
% 12.60/2.46  |         $i(all_7_14) & $i(all_7_16) & $i(all_7_17) & $i(all_7_19) &
% 12.60/2.46  |         $i(all_7_20) & $i(all_7_22) & $i(all_7_23) & $i(all_7_25) &
% 12.60/2.46  |         $i(all_7_26) & $i(all_7_28) & $i(all_7_29) & (pv63 = pv64 |  ~
% 12.60/2.46  |           leq(pv5, n998) |  ~ leq(n0, pv5) |  ~ leq(n0, pv63) |  ~ leq(n0,
% 12.60/2.46  |             pv64) |  ~ leq(pv63, n5) |  ~ leq(pv64, n5) |  ! [v0: $i] :  !
% 12.60/2.46  |           [v1: $i] : (v1 = init | v0 = pv64 |  ~
% 12.60/2.46  |             (a_select3(id_ds1_filter_init, pv63, v0) = v1) |  ~ $i(v0) |  ~
% 12.60/2.46  |             leq(v0, n5) |  ~ leq(v0, pv64) |  ~ leq(n0, v0)) | (all_7_23 =
% 12.60/2.46  |             pv63 &  ~ (all_7_21 = init) & a_select3(id_ds1_filter_init, pv63,
% 12.60/2.46  |               all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) &
% 12.60/2.46  |             leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 = init) &
% 12.60/2.46  |             a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 &
% 12.60/2.46  |             $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0,
% 12.60/2.46  |               all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) &
% 12.60/2.46  |             a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 &
% 12.60/2.46  |             $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0,
% 12.60/2.46  |               all_7_4) & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.46  |             a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 &
% 12.60/2.46  |             $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0,
% 12.60/2.46  |               all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) &
% 12.60/2.46  |             a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 &
% 12.60/2.46  |             $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 12.60/2.46  |               all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) &
% 12.60/2.46  |             a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 &
% 12.60/2.46  |             $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0,
% 12.60/2.46  |               all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) &
% 12.60/2.46  |             a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = all_7_15
% 12.60/2.46  |             & $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0,
% 12.60/2.46  |               all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.46  |             a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = all_7_18 &
% 12.60/2.46  |             $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0,
% 12.60/2.46  |               all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init) &
% 12.60/2.46  |             a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 &
% 12.60/2.46  |             $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) &
% 12.60/2.46  |             leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~
% 12.60/2.46  |             (all_7_27 = init) & pred(pv63) = all_7_30 &
% 12.60/2.46  |             a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 &
% 12.60/2.46  |             $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29,
% 12.60/2.46  |               all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29)))
% 12.60/2.46  | 
% 12.60/2.46  | ALPHA: (30) implies:
% 12.60/2.46  |   (31)  $i(all_7_29)
% 12.60/2.46  |   (32)  $i(all_7_28)
% 12.60/2.46  |   (33)  $i(all_7_26)
% 12.60/2.46  |   (34)  $i(all_7_25)
% 12.60/2.46  |   (35)  $i(all_7_22)
% 12.60/2.46  |   (36)  $i(all_7_20)
% 12.60/2.46  |   (37)  $i(all_7_19)
% 12.60/2.46  |   (38)  $i(all_7_17)
% 12.60/2.46  |   (39)  $i(all_7_16)
% 12.60/2.46  |   (40)  $i(all_7_14)
% 12.60/2.46  |   (41)  $i(all_7_13)
% 12.60/2.46  |   (42)  $i(all_7_11)
% 12.60/2.46  |   (43)  $i(all_7_10)
% 12.60/2.46  |   (44)  $i(all_7_8)
% 12.60/2.46  |   (45)  $i(all_7_7)
% 12.60/2.46  |   (46)  $i(all_7_5)
% 12.60/2.46  |   (47)  $i(all_7_4)
% 12.60/2.46  |   (48)  $i(all_7_2)
% 12.60/2.46  |   (49)  $i(all_7_1)
% 12.60/2.46  |   (50)  pv63 = pv64 |  ~ leq(pv5, n998) |  ~ leq(n0, pv5) |  ~ leq(n0, pv63) |
% 12.60/2.46  |          ~ leq(n0, pv64) |  ~ leq(pv63, n5) |  ~ leq(pv64, n5) |  ! [v0: $i] :
% 12.60/2.46  |          ! [v1: $i] : (v1 = init | v0 = pv64 |  ~
% 12.60/2.46  |           (a_select3(id_ds1_filter_init, pv63, v0) = v1) |  ~ $i(v0) |  ~
% 12.60/2.46  |           leq(v0, n5) |  ~ leq(v0, pv64) |  ~ leq(n0, v0)) | (all_7_23 = pv63
% 12.60/2.46  |           &  ~ (all_7_21 = init) & a_select3(id_ds1_filter_init, pv63,
% 12.60/2.46  |             all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) &
% 12.60/2.46  |           leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 = init) &
% 12.60/2.46  |           a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 &
% 12.60/2.46  |           $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0, all_7_1)
% 12.60/2.46  |           & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) &
% 12.60/2.46  |           a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 &
% 12.60/2.46  |           $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0, all_7_4)
% 12.60/2.46  |           & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.46  |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 &
% 12.60/2.46  |           $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0, all_7_7)
% 12.60/2.46  |           & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) &
% 12.60/2.46  |           a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 &
% 12.60/2.46  |           $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 12.60/2.46  |             all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) &
% 12.60/2.46  |           a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 &
% 12.60/2.46  |           $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0,
% 12.60/2.46  |             all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) &
% 12.60/2.46  |           a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = all_7_15 &
% 12.60/2.46  |           $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0,
% 12.60/2.46  |             all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.46  |           a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = all_7_18 &
% 12.60/2.46  |           $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0,
% 12.60/2.46  |             all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init) &
% 12.60/2.46  |           a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 &
% 12.60/2.46  |           $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) &
% 12.60/2.46  |           leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~
% 12.60/2.46  |           (all_7_27 = init) & pred(pv63) = all_7_30 &
% 12.60/2.46  |           a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 &
% 12.60/2.46  |           $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29,
% 12.60/2.46  |             all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29))
% 12.60/2.46  | 
% 12.60/2.46  | BETA: splitting (50) gives:
% 12.60/2.46  | 
% 12.60/2.46  | Case 1:
% 12.60/2.46  | | 
% 12.60/2.46  | |   (51)   ~ leq(pv5, n998)
% 12.60/2.46  | | 
% 12.60/2.46  | | PRED_UNIFY: (14), (51) imply:
% 12.60/2.46  | |   (52)  $false
% 12.60/2.47  | | 
% 12.60/2.47  | | CLOSE: (52) is inconsistent.
% 12.60/2.47  | | 
% 12.60/2.47  | Case 2:
% 12.60/2.47  | | 
% 12.60/2.47  | |   (53)  pv63 = pv64 |  ~ leq(n0, pv5) |  ~ leq(n0, pv63) |  ~ leq(n0, pv64)
% 12.60/2.47  | |         |  ~ leq(pv63, n5) |  ~ leq(pv64, n5) |  ! [v0: $i] :  ! [v1: $i] :
% 12.60/2.47  | |         (v1 = init | v0 = pv64 |  ~ (a_select3(id_ds1_filter_init, pv63, v0)
% 12.60/2.47  | |             = v1) |  ~ $i(v0) |  ~ leq(v0, n5) |  ~ leq(v0, pv64) |  ~
% 12.60/2.47  | |           leq(n0, v0)) | (all_7_23 = pv63 &  ~ (all_7_21 = init) &
% 12.60/2.47  | |           a_select3(id_ds1_filter_init, pv63, all_7_22) = all_7_21 &
% 12.60/2.47  | |           $i(all_7_21) & gt(pv64, all_7_22) & leq(all_7_22, n5) & leq(n0,
% 12.60/2.47  | |             all_7_22)) | ( ~ (all_7_0 = init) & a_select3(h_ds1_filter_init,
% 12.60/2.47  | |             all_7_2, all_7_1) = all_7_0 & $i(all_7_0) & leq(all_7_1, n5) &
% 12.60/2.47  | |           leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0, all_7_2)) | ( ~
% 12.60/2.47  | |           (all_7_3 = init) & a_select3(phi_ds1_filter_init, all_7_5,
% 12.60/2.47  | |             all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) &
% 12.60/2.47  | |           leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, all_7_5)) | ( ~
% 12.60/2.47  | |           (all_7_6 = init) & a_select3(dv_ds1_filter_init, all_7_8, all_7_7)
% 12.60/2.47  | |           = all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) &
% 12.60/2.47  | |           leq(n0, all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) &
% 12.60/2.47  | |           a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 &
% 12.60/2.47  | |           $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 12.60/2.47  | |             all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) &
% 12.60/2.47  | |           a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 &
% 12.60/2.47  | |           $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0,
% 12.60/2.47  | |             all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) &
% 12.60/2.47  | |           a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) = all_7_15
% 12.60/2.47  | |           & $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0,
% 12.60/2.47  | |             all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.47  | |           a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) = all_7_18 &
% 12.60/2.47  | |           $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0,
% 12.60/2.47  | |             all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init) &
% 12.60/2.47  | |           a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 &
% 12.60/2.47  | |           $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) &
% 12.60/2.47  | |           leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~
% 12.60/2.47  | |           (all_7_27 = init) & pred(pv63) = all_7_30 &
% 12.60/2.47  | |           a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 &
% 12.60/2.47  | |           $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29,
% 12.60/2.47  | |             all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29))
% 12.60/2.47  | | 
% 12.60/2.47  | | BETA: splitting (53) gives:
% 12.60/2.47  | | 
% 12.60/2.47  | | Case 1:
% 12.60/2.47  | | | 
% 12.60/2.47  | | |   (54)   ~ leq(n0, pv5)
% 12.60/2.47  | | | 
% 12.60/2.47  | | | PRED_UNIFY: (12), (54) imply:
% 12.60/2.47  | | |   (55)  $false
% 12.60/2.47  | | | 
% 12.60/2.47  | | | CLOSE: (55) is inconsistent.
% 12.60/2.47  | | | 
% 12.60/2.47  | | Case 2:
% 12.60/2.47  | | | 
% 12.60/2.47  | | |   (56)  pv63 = pv64 |  ~ leq(n0, pv63) |  ~ leq(n0, pv64) |  ~ leq(pv63,
% 12.60/2.47  | | |           n5) |  ~ leq(pv64, n5) |  ! [v0: $i] :  ! [v1: $i] : (v1 = init
% 12.60/2.47  | | |           | v0 = pv64 |  ~ (a_select3(id_ds1_filter_init, pv63, v0) = v1)
% 12.60/2.47  | | |           |  ~ $i(v0) |  ~ leq(v0, n5) |  ~ leq(v0, pv64) |  ~ leq(n0,
% 12.60/2.47  | | |             v0)) | (all_7_23 = pv63 &  ~ (all_7_21 = init) &
% 12.60/2.47  | | |           a_select3(id_ds1_filter_init, pv63, all_7_22) = all_7_21 &
% 12.60/2.47  | | |           $i(all_7_21) & gt(pv64, all_7_22) & leq(all_7_22, n5) & leq(n0,
% 12.60/2.47  | | |             all_7_22)) | ( ~ (all_7_0 = init) &
% 12.60/2.47  | | |           a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 &
% 12.60/2.47  | | |           $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0,
% 12.60/2.47  | | |             all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) &
% 12.60/2.47  | | |           a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 &
% 12.60/2.47  | | |           $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0,
% 12.60/2.47  | | |             all_7_4) & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.47  | | |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 &
% 12.60/2.47  | | |           $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0,
% 12.60/2.47  | | |             all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) &
% 12.60/2.47  | | |           a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 &
% 12.60/2.47  | | |           $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 12.60/2.47  | | |             all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init) &
% 12.60/2.47  | | |           a_select3(r_ds1_filter_init, all_7_14, all_7_13) = all_7_12 &
% 12.60/2.47  | | |           $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0,
% 12.60/2.47  | | |             all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 = init) &
% 12.60/2.47  | | |           a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) =
% 12.60/2.47  | | |           all_7_15 & $i(all_7_15) & leq(all_7_16, n0) & leq(all_7_17, n5)
% 12.60/2.47  | | |           & leq(n0, all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 = init)
% 12.60/2.47  | | |           & a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) =
% 12.60/2.47  | | |           all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20, n5)
% 12.60/2.47  | | |           & leq(n0, all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 = init)
% 12.60/2.47  | | |           & a_select3(id_ds1_filter_init, all_7_26, all_7_25) = all_7_24 &
% 12.60/2.47  | | |           $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25, n5) &
% 12.60/2.47  | | |           leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~
% 12.60/2.47  | | |           (all_7_27 = init) & pred(pv63) = all_7_30 &
% 12.60/2.47  | | |           a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 &
% 12.60/2.47  | | |           $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29,
% 12.60/2.47  | | |             all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29))
% 12.60/2.47  | | | 
% 12.60/2.47  | | | BETA: splitting (56) gives:
% 12.60/2.47  | | | 
% 12.60/2.47  | | | Case 1:
% 12.60/2.47  | | | | 
% 12.60/2.47  | | | |   (57)   ~ leq(n0, pv63)
% 12.60/2.47  | | | | 
% 12.60/2.47  | | | | PRED_UNIFY: (11), (57) imply:
% 12.60/2.47  | | | |   (58)  $false
% 12.60/2.47  | | | | 
% 12.60/2.47  | | | | CLOSE: (58) is inconsistent.
% 12.60/2.47  | | | | 
% 12.60/2.47  | | | Case 2:
% 12.60/2.47  | | | | 
% 12.60/2.48  | | | |   (59)  pv63 = pv64 |  ~ leq(n0, pv64) |  ~ leq(pv63, n5) |  ~ leq(pv64,
% 12.60/2.48  | | | |           n5) |  ! [v0: $i] :  ! [v1: $i] : (v1 = init | v0 = pv64 |  ~
% 12.60/2.48  | | | |           (a_select3(id_ds1_filter_init, pv63, v0) = v1) |  ~ $i(v0) | 
% 12.60/2.48  | | | |           ~ leq(v0, n5) |  ~ leq(v0, pv64) |  ~ leq(n0, v0)) | (all_7_23
% 12.60/2.48  | | | |           = pv63 &  ~ (all_7_21 = init) & a_select3(id_ds1_filter_init,
% 12.60/2.48  | | | |             pv63, all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64,
% 12.60/2.48  | | | |             all_7_22) & leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~
% 12.60/2.48  | | | |           (all_7_0 = init) & a_select3(h_ds1_filter_init, all_7_2,
% 12.60/2.48  | | | |             all_7_1) = all_7_0 & $i(all_7_0) & leq(all_7_1, n5) &
% 12.60/2.48  | | | |           leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0, all_7_2)) | ( ~
% 12.60/2.48  | | | |           (all_7_3 = init) & a_select3(phi_ds1_filter_init, all_7_5,
% 12.60/2.48  | | | |             all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) &
% 12.60/2.48  | | | |           leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, all_7_5)) | ( ~
% 12.60/2.48  | | | |           (all_7_6 = init) & a_select3(dv_ds1_filter_init, all_7_8,
% 12.60/2.48  | | | |             all_7_7) = all_7_6 & $i(all_7_6) & leq(all_7_7, n0) &
% 12.60/2.48  | | | |           leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0, all_7_8)) | ( ~
% 12.60/2.48  | | | |           (all_7_9 = init) & a_select3(q_ds1_filter_init, all_7_11,
% 12.60/2.48  | | | |             all_7_10) = all_7_9 & $i(all_7_9) & leq(all_7_10, n5) &
% 12.60/2.48  | | | |           leq(all_7_11, n5) & leq(n0, all_7_10) & leq(n0, all_7_11)) | (
% 12.60/2.48  | | | |           ~ (all_7_12 = init) & a_select3(r_ds1_filter_init, all_7_14,
% 12.60/2.48  | | | |             all_7_13) = all_7_12 & $i(all_7_12) & leq(all_7_13, n2) &
% 12.60/2.48  | | | |           leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, all_7_14)) | (
% 12.60/2.48  | | | |           ~ (all_7_15 = init) & a_select3(xhatmin_ds1_filter_init,
% 12.60/2.48  | | | |             all_7_17, all_7_16) = all_7_15 & $i(all_7_15) &
% 12.60/2.48  | | | |           leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, all_7_16) &
% 12.60/2.48  | | | |           leq(n0, all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.48  | | | |           a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) =
% 12.60/2.48  | | | |           all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20,
% 12.60/2.48  | | | |             n5) & leq(n0, all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24
% 12.60/2.48  | | | |             = init) & a_select3(id_ds1_filter_init, all_7_26, all_7_25)
% 12.60/2.48  | | | |           = all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) & leq(all_7_25,
% 12.60/2.48  | | | |             n5) & leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0,
% 12.60/2.48  | | | |             all_7_26)) | ( ~ (all_7_27 = init) & pred(pv63) = all_7_30 &
% 12.60/2.48  | | | |           a_select3(id_ds1_filter_init, all_7_29, all_7_28) = all_7_27 &
% 12.60/2.48  | | | |           $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5) &
% 12.60/2.48  | | | |           leq(all_7_29, all_7_30) & leq(n0, all_7_28) & leq(n0,
% 12.60/2.48  | | | |             all_7_29))
% 12.60/2.48  | | | | 
% 12.60/2.48  | | | | BETA: splitting (59) gives:
% 12.60/2.48  | | | | 
% 12.60/2.48  | | | | Case 1:
% 12.60/2.48  | | | | | 
% 12.60/2.48  | | | | |   (60)   ~ leq(n0, pv64)
% 12.60/2.48  | | | | | 
% 12.60/2.48  | | | | | PRED_UNIFY: (10), (60) imply:
% 12.60/2.48  | | | | |   (61)  $false
% 12.60/2.48  | | | | | 
% 12.60/2.48  | | | | | CLOSE: (61) is inconsistent.
% 12.60/2.48  | | | | | 
% 12.60/2.48  | | | | Case 2:
% 12.60/2.48  | | | | | 
% 12.60/2.48  | | | | |   (62)  pv63 = pv64 |  ~ leq(pv63, n5) |  ~ leq(pv64, n5) |  ! [v0:
% 12.60/2.48  | | | | |           $i] :  ! [v1: $i] : (v1 = init | v0 = pv64 |  ~
% 12.60/2.48  | | | | |           (a_select3(id_ds1_filter_init, pv63, v0) = v1) |  ~ $i(v0) |
% 12.60/2.48  | | | | |            ~ leq(v0, n5) |  ~ leq(v0, pv64) |  ~ leq(n0, v0)) |
% 12.60/2.48  | | | | |         (all_7_23 = pv63 &  ~ (all_7_21 = init) &
% 12.60/2.48  | | | | |           a_select3(id_ds1_filter_init, pv63, all_7_22) = all_7_21 &
% 12.60/2.48  | | | | |           $i(all_7_21) & gt(pv64, all_7_22) & leq(all_7_22, n5) &
% 12.60/2.48  | | | | |           leq(n0, all_7_22)) | ( ~ (all_7_0 = init) &
% 12.60/2.48  | | | | |           a_select3(h_ds1_filter_init, all_7_2, all_7_1) = all_7_0 &
% 12.60/2.48  | | | | |           $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0,
% 12.60/2.48  | | | | |             all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 = init) &
% 12.60/2.48  | | | | |           a_select3(phi_ds1_filter_init, all_7_5, all_7_4) = all_7_3 &
% 12.60/2.48  | | | | |           $i(all_7_3) & leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0,
% 12.60/2.48  | | | | |             all_7_4) & leq(n0, all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.48  | | | | |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7) = all_7_6 &
% 12.60/2.48  | | | | |           $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8, n5) & leq(n0,
% 12.60/2.48  | | | | |             all_7_7) & leq(n0, all_7_8)) | ( ~ (all_7_9 = init) &
% 12.60/2.48  | | | | |           a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9 &
% 12.60/2.48  | | | | |           $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) &
% 12.60/2.48  | | | | |           leq(n0, all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 =
% 12.60/2.48  | | | | |             init) & a_select3(r_ds1_filter_init, all_7_14, all_7_13) =
% 12.60/2.48  | | | | |           all_7_12 & $i(all_7_12) & leq(all_7_13, n2) & leq(all_7_14,
% 12.60/2.48  | | | | |             n2) & leq(n0, all_7_13) & leq(n0, all_7_14)) | ( ~
% 12.60/2.48  | | | | |           (all_7_15 = init) & a_select3(xhatmin_ds1_filter_init,
% 12.60/2.48  | | | | |             all_7_17, all_7_16) = all_7_15 & $i(all_7_15) &
% 12.60/2.48  | | | | |           leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, all_7_16) &
% 12.60/2.48  | | | | |           leq(n0, all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.48  | | | | |           a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) =
% 12.60/2.48  | | | | |           all_7_18 & $i(all_7_18) & leq(all_7_19, n5) & leq(all_7_20,
% 12.60/2.48  | | | | |             n5) & leq(n0, all_7_19) & leq(n0, all_7_20)) | ( ~
% 12.60/2.48  | | | | |           (all_7_24 = init) & a_select3(id_ds1_filter_init, all_7_26,
% 12.60/2.48  | | | | |             all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) &
% 12.60/2.48  | | | | |           leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0, all_7_25) &
% 12.60/2.48  | | | | |           leq(n0, all_7_26)) | ( ~ (all_7_27 = init) & pred(pv63) =
% 12.60/2.48  | | | | |           all_7_30 & a_select3(id_ds1_filter_init, all_7_29, all_7_28)
% 12.60/2.48  | | | | |           = all_7_27 & $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5)
% 12.60/2.48  | | | | |           & leq(all_7_29, all_7_30) & leq(n0, all_7_28) & leq(n0,
% 12.60/2.48  | | | | |             all_7_29))
% 12.60/2.48  | | | | | 
% 12.60/2.48  | | | | | BETA: splitting (62) gives:
% 12.60/2.48  | | | | | 
% 12.60/2.48  | | | | | Case 1:
% 12.60/2.48  | | | | | | 
% 12.60/2.48  | | | | | |   (63)   ~ leq(pv63, n5)
% 12.60/2.48  | | | | | | 
% 12.60/2.48  | | | | | | PRED_UNIFY: (9), (63) imply:
% 12.60/2.48  | | | | | |   (64)  $false
% 12.60/2.48  | | | | | | 
% 12.60/2.48  | | | | | | CLOSE: (64) is inconsistent.
% 12.60/2.48  | | | | | | 
% 12.60/2.48  | | | | | Case 2:
% 12.60/2.48  | | | | | | 
% 12.60/2.48  | | | | | |   (65)  pv63 = pv64 |  ~ leq(pv64, n5) |  ! [v0: $i] :  ! [v1: $i] :
% 12.60/2.48  | | | | | |         (v1 = init | v0 = pv64 |  ~ (a_select3(id_ds1_filter_init,
% 12.60/2.48  | | | | | |               pv63, v0) = v1) |  ~ $i(v0) |  ~ leq(v0, n5) |  ~
% 12.60/2.48  | | | | | |           leq(v0, pv64) |  ~ leq(n0, v0)) | (all_7_23 = pv63 &  ~
% 12.60/2.48  | | | | | |           (all_7_21 = init) & a_select3(id_ds1_filter_init, pv63,
% 12.60/2.48  | | | | | |             all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64, all_7_22)
% 12.60/2.48  | | | | | |           & leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 =
% 12.60/2.48  | | | | | |             init) & a_select3(h_ds1_filter_init, all_7_2, all_7_1) =
% 12.60/2.48  | | | | | |           all_7_0 & $i(all_7_0) & leq(all_7_1, n5) & leq(all_7_2,
% 12.60/2.48  | | | | | |             n2) & leq(n0, all_7_1) & leq(n0, all_7_2)) | ( ~
% 12.60/2.48  | | | | | |           (all_7_3 = init) & a_select3(phi_ds1_filter_init, all_7_5,
% 12.60/2.48  | | | | | |             all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) &
% 12.60/2.48  | | | | | |           leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0, all_7_5)) |
% 12.60/2.48  | | | | | |         ( ~ (all_7_6 = init) & a_select3(dv_ds1_filter_init,
% 12.60/2.48  | | | | | |             all_7_8, all_7_7) = all_7_6 & $i(all_7_6) & leq(all_7_7,
% 12.60/2.48  | | | | | |             n0) & leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0,
% 12.60/2.48  | | | | | |             all_7_8)) | ( ~ (all_7_9 = init) &
% 12.60/2.48  | | | | | |           a_select3(q_ds1_filter_init, all_7_11, all_7_10) = all_7_9
% 12.60/2.48  | | | | | |           & $i(all_7_9) & leq(all_7_10, n5) & leq(all_7_11, n5) &
% 12.60/2.48  | | | | | |           leq(n0, all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 =
% 12.60/2.48  | | | | | |             init) & a_select3(r_ds1_filter_init, all_7_14, all_7_13)
% 12.60/2.48  | | | | | |           = all_7_12 & $i(all_7_12) & leq(all_7_13, n2) &
% 12.60/2.48  | | | | | |           leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0, all_7_14))
% 12.60/2.48  | | | | | |         | ( ~ (all_7_15 = init) & a_select3(xhatmin_ds1_filter_init,
% 12.60/2.48  | | | | | |             all_7_17, all_7_16) = all_7_15 & $i(all_7_15) &
% 12.60/2.48  | | | | | |           leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0, all_7_16)
% 12.60/2.48  | | | | | |           & leq(n0, all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.48  | | | | | |           a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) =
% 12.60/2.48  | | | | | |           all_7_18 & $i(all_7_18) & leq(all_7_19, n5) &
% 12.60/2.48  | | | | | |           leq(all_7_20, n5) & leq(n0, all_7_19) & leq(n0, all_7_20))
% 12.60/2.48  | | | | | |         | ( ~ (all_7_24 = init) & a_select3(id_ds1_filter_init,
% 12.60/2.48  | | | | | |             all_7_26, all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63,
% 12.60/2.48  | | | | | |             all_7_26) & leq(all_7_25, n5) & leq(all_7_26, n5) &
% 12.60/2.48  | | | | | |           leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~ (all_7_27 =
% 12.60/2.48  | | | | | |             init) & pred(pv63) = all_7_30 &
% 12.60/2.48  | | | | | |           a_select3(id_ds1_filter_init, all_7_29, all_7_28) =
% 12.60/2.48  | | | | | |           all_7_27 & $i(all_7_27) & $i(all_7_30) & leq(all_7_28, n5)
% 12.60/2.48  | | | | | |           & leq(all_7_29, all_7_30) & leq(n0, all_7_28) & leq(n0,
% 12.60/2.48  | | | | | |             all_7_29))
% 12.60/2.48  | | | | | | 
% 12.60/2.48  | | | | | | BETA: splitting (65) gives:
% 12.60/2.48  | | | | | | 
% 12.60/2.48  | | | | | | Case 1:
% 12.60/2.48  | | | | | | | 
% 12.60/2.48  | | | | | | |   (66)   ~ leq(pv64, n5)
% 12.60/2.48  | | | | | | | 
% 12.60/2.48  | | | | | | | PRED_UNIFY: (8), (66) imply:
% 12.60/2.48  | | | | | | |   (67)  $false
% 12.60/2.48  | | | | | | | 
% 12.60/2.48  | | | | | | | CLOSE: (67) is inconsistent.
% 12.60/2.48  | | | | | | | 
% 12.60/2.48  | | | | | | Case 2:
% 12.60/2.48  | | | | | | | 
% 12.60/2.49  | | | | | | |   (68)  pv63 = pv64 |  ! [v0: $i] :  ! [v1: $i] : (v1 = init | v0
% 12.60/2.49  | | | | | | |           = pv64 |  ~ (a_select3(id_ds1_filter_init, pv63, v0) =
% 12.60/2.49  | | | | | | |             v1) |  ~ $i(v0) |  ~ leq(v0, n5) |  ~ leq(v0, pv64) | 
% 12.60/2.49  | | | | | | |           ~ leq(n0, v0)) | (all_7_23 = pv63 &  ~ (all_7_21 = init)
% 12.60/2.49  | | | | | | |           & a_select3(id_ds1_filter_init, pv63, all_7_22) =
% 12.60/2.49  | | | | | | |           all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) &
% 12.60/2.49  | | | | | | |           leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0 =
% 12.60/2.49  | | | | | | |             init) & a_select3(h_ds1_filter_init, all_7_2, all_7_1)
% 12.60/2.49  | | | | | | |           = all_7_0 & $i(all_7_0) & leq(all_7_1, n5) &
% 12.60/2.49  | | | | | | |           leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0, all_7_2))
% 12.60/2.49  | | | | | | |         | ( ~ (all_7_3 = init) & a_select3(phi_ds1_filter_init,
% 12.60/2.49  | | | | | | |             all_7_5, all_7_4) = all_7_3 & $i(all_7_3) &
% 12.60/2.49  | | | | | | |           leq(all_7_4, n5) & leq(all_7_5, n5) & leq(n0, all_7_4) &
% 12.60/2.49  | | | | | | |           leq(n0, all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.49  | | | | | | |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7) =
% 12.60/2.49  | | | | | | |           all_7_6 & $i(all_7_6) & leq(all_7_7, n0) & leq(all_7_8,
% 12.60/2.49  | | | | | | |             n5) & leq(n0, all_7_7) & leq(n0, all_7_8)) | ( ~
% 12.60/2.49  | | | | | | |           (all_7_9 = init) & a_select3(q_ds1_filter_init,
% 12.60/2.49  | | | | | | |             all_7_11, all_7_10) = all_7_9 & $i(all_7_9) &
% 12.60/2.49  | | | | | | |           leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 12.60/2.49  | | | | | | |             all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 = init)
% 12.60/2.49  | | | | | | |           & a_select3(r_ds1_filter_init, all_7_14, all_7_13) =
% 12.60/2.49  | | | | | | |           all_7_12 & $i(all_7_12) & leq(all_7_13, n2) &
% 12.60/2.49  | | | | | | |           leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0,
% 12.60/2.49  | | | | | | |             all_7_14)) | ( ~ (all_7_15 = init) &
% 12.60/2.49  | | | | | | |           a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16) =
% 12.60/2.49  | | | | | | |           all_7_15 & $i(all_7_15) & leq(all_7_16, n0) &
% 12.60/2.49  | | | | | | |           leq(all_7_17, n5) & leq(n0, all_7_16) & leq(n0,
% 12.60/2.49  | | | | | | |             all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.49  | | | | | | |           a_select3(pminus_ds1_filter_init, all_7_20, all_7_19) =
% 12.60/2.49  | | | | | | |           all_7_18 & $i(all_7_18) & leq(all_7_19, n5) &
% 12.60/2.49  | | | | | | |           leq(all_7_20, n5) & leq(n0, all_7_19) & leq(n0,
% 12.60/2.49  | | | | | | |             all_7_20)) | ( ~ (all_7_24 = init) &
% 12.60/2.49  | | | | | | |           a_select3(id_ds1_filter_init, all_7_26, all_7_25) =
% 12.60/2.49  | | | | | | |           all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) &
% 12.60/2.49  | | | | | | |           leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0,
% 12.60/2.49  | | | | | | |             all_7_25) & leq(n0, all_7_26)) | ( ~ (all_7_27 = init)
% 12.60/2.49  | | | | | | |           & pred(pv63) = all_7_30 & a_select3(id_ds1_filter_init,
% 12.60/2.49  | | | | | | |             all_7_29, all_7_28) = all_7_27 & $i(all_7_27) &
% 12.60/2.49  | | | | | | |           $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29,
% 12.60/2.49  | | | | | | |             all_7_30) & leq(n0, all_7_28) & leq(n0, all_7_29))
% 12.60/2.49  | | | | | | | 
% 12.60/2.49  | | | | | | | BETA: splitting (68) gives:
% 12.60/2.49  | | | | | | | 
% 12.60/2.49  | | | | | | | Case 1:
% 12.60/2.49  | | | | | | | | 
% 12.60/2.49  | | | | | | | |   (69)  pv63 = pv64
% 12.60/2.49  | | | | | | | | 
% 12.60/2.49  | | | | | | | | REDUCE: (5), (69) imply:
% 12.60/2.49  | | | | | | | |   (70)  $false
% 12.60/2.49  | | | | | | | | 
% 12.60/2.49  | | | | | | | | CLOSE: (70) is inconsistent.
% 12.60/2.49  | | | | | | | | 
% 12.60/2.49  | | | | | | | Case 2:
% 12.60/2.49  | | | | | | | | 
% 12.60/2.49  | | | | | | | |   (71)   ! [v0: $i] :  ! [v1: $i] : (v1 = init | v0 = pv64 |  ~
% 12.60/2.49  | | | | | | | |           (a_select3(id_ds1_filter_init, pv63, v0) = v1) |  ~
% 12.60/2.49  | | | | | | | |           $i(v0) |  ~ leq(v0, n5) |  ~ leq(v0, pv64) |  ~
% 12.60/2.49  | | | | | | | |           leq(n0, v0)) | (all_7_23 = pv63 &  ~ (all_7_21 = init)
% 12.60/2.49  | | | | | | | |           & a_select3(id_ds1_filter_init, pv63, all_7_22) =
% 12.60/2.49  | | | | | | | |           all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) &
% 12.60/2.49  | | | | | | | |           leq(all_7_22, n5) & leq(n0, all_7_22)) | ( ~ (all_7_0
% 12.60/2.49  | | | | | | | |             = init) & a_select3(h_ds1_filter_init, all_7_2,
% 12.60/2.49  | | | | | | | |             all_7_1) = all_7_0 & $i(all_7_0) & leq(all_7_1, n5)
% 12.60/2.49  | | | | | | | |           & leq(all_7_2, n2) & leq(n0, all_7_1) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_2)) | ( ~ (all_7_3 = init) &
% 12.60/2.49  | | | | | | | |           a_select3(phi_ds1_filter_init, all_7_5, all_7_4) =
% 12.60/2.49  | | | | | | | |           all_7_3 & $i(all_7_3) & leq(all_7_4, n5) &
% 12.60/2.49  | | | | | | | |           leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.49  | | | | | | | |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7) =
% 12.60/2.49  | | | | | | | |           all_7_6 & $i(all_7_6) & leq(all_7_7, n0) &
% 12.60/2.49  | | | | | | | |           leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_8)) | ( ~ (all_7_9 = init) &
% 12.60/2.49  | | | | | | | |           a_select3(q_ds1_filter_init, all_7_11, all_7_10) =
% 12.60/2.49  | | | | | | | |           all_7_9 & $i(all_7_9) & leq(all_7_10, n5) &
% 12.60/2.49  | | | | | | | |           leq(all_7_11, n5) & leq(n0, all_7_10) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_11)) | ( ~ (all_7_12 = init) &
% 12.60/2.49  | | | | | | | |           a_select3(r_ds1_filter_init, all_7_14, all_7_13) =
% 12.60/2.49  | | | | | | | |           all_7_12 & $i(all_7_12) & leq(all_7_13, n2) &
% 12.60/2.49  | | | | | | | |           leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_14)) | ( ~ (all_7_15 = init) &
% 12.60/2.49  | | | | | | | |           a_select3(xhatmin_ds1_filter_init, all_7_17, all_7_16)
% 12.60/2.49  | | | | | | | |           = all_7_15 & $i(all_7_15) & leq(all_7_16, n0) &
% 12.60/2.49  | | | | | | | |           leq(all_7_17, n5) & leq(n0, all_7_16) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_17)) | ( ~ (all_7_18 = init) &
% 12.60/2.49  | | | | | | | |           a_select3(pminus_ds1_filter_init, all_7_20, all_7_19)
% 12.60/2.49  | | | | | | | |           = all_7_18 & $i(all_7_18) & leq(all_7_19, n5) &
% 12.60/2.49  | | | | | | | |           leq(all_7_20, n5) & leq(n0, all_7_19) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_20)) | ( ~ (all_7_24 = init) &
% 12.60/2.49  | | | | | | | |           a_select3(id_ds1_filter_init, all_7_26, all_7_25) =
% 12.60/2.49  | | | | | | | |           all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) &
% 12.60/2.49  | | | | | | | |           leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0,
% 12.60/2.49  | | | | | | | |             all_7_25) & leq(n0, all_7_26)) | ( ~ (all_7_27 =
% 12.60/2.49  | | | | | | | |             init) & pred(pv63) = all_7_30 &
% 12.60/2.49  | | | | | | | |           a_select3(id_ds1_filter_init, all_7_29, all_7_28) =
% 12.60/2.49  | | | | | | | |           all_7_27 & $i(all_7_27) & $i(all_7_30) & leq(all_7_28,
% 12.60/2.49  | | | | | | | |             n5) & leq(all_7_29, all_7_30) & leq(n0, all_7_28) &
% 12.60/2.49  | | | | | | | |           leq(n0, all_7_29))
% 12.60/2.49  | | | | | | | | 
% 12.60/2.49  | | | | | | | | BETA: splitting (71) gives:
% 12.60/2.49  | | | | | | | | 
% 12.60/2.49  | | | | | | | | Case 1:
% 12.60/2.49  | | | | | | | | | 
% 12.60/2.49  | | | | | | | | |   (72)   ! [v0: $i] :  ! [v1: $i] : (v1 = init | v0 = pv64 | 
% 12.60/2.49  | | | | | | | | |           ~ (a_select3(id_ds1_filter_init, pv63, v0) = v1) | 
% 12.60/2.49  | | | | | | | | |           ~ $i(v0) |  ~ leq(v0, n5) |  ~ leq(v0, pv64) |  ~
% 12.60/2.49  | | | | | | | | |           leq(n0, v0)) | (all_7_23 = pv63 &  ~ (all_7_21 =
% 12.60/2.49  | | | | | | | | |             init) & a_select3(id_ds1_filter_init, pv63,
% 12.60/2.49  | | | | | | | | |             all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64,
% 12.60/2.49  | | | | | | | | |             all_7_22) & leq(all_7_22, n5) & leq(n0, all_7_22))
% 12.60/2.49  | | | | | | | | |         | ( ~ (all_7_0 = init) & a_select3(h_ds1_filter_init,
% 12.60/2.49  | | | | | | | | |             all_7_2, all_7_1) = all_7_0 & $i(all_7_0) &
% 12.60/2.49  | | | | | | | | |           leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0,
% 12.60/2.49  | | | | | | | | |             all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 =
% 12.60/2.49  | | | | | | | | |             init) & a_select3(phi_ds1_filter_init, all_7_5,
% 12.60/2.49  | | | | | | | | |             all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4,
% 12.60/2.49  | | | | | | | | |             n5) & leq(all_7_5, n5) & leq(n0, all_7_4) &
% 12.60/2.49  | | | | | | | | |           leq(n0, all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.49  | | | | | | | | |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7) =
% 12.60/2.49  | | | | | | | | |           all_7_6 & $i(all_7_6) & leq(all_7_7, n0) &
% 12.60/2.49  | | | | | | | | |           leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0,
% 12.60/2.49  | | | | | | | | |             all_7_8))
% 12.60/2.49  | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | BETA: splitting (72) gives:
% 12.60/2.49  | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | Case 1:
% 12.60/2.49  | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | |   (73)   ! [v0: $i] :  ! [v1: $i] : (v1 = init | v0 = pv64 |
% 12.60/2.49  | | | | | | | | | |            ~ (a_select3(id_ds1_filter_init, pv63, v0) = v1)
% 12.60/2.49  | | | | | | | | | |           |  ~ $i(v0) |  ~ leq(v0, n5) |  ~ leq(v0, pv64) | 
% 12.60/2.49  | | | | | | | | | |           ~ leq(n0, v0)) | (all_7_23 = pv63 &  ~ (all_7_21 =
% 12.60/2.49  | | | | | | | | | |             init) & a_select3(id_ds1_filter_init, pv63,
% 12.60/2.49  | | | | | | | | | |             all_7_22) = all_7_21 & $i(all_7_21) & gt(pv64,
% 12.60/2.49  | | | | | | | | | |             all_7_22) & leq(all_7_22, n5) & leq(n0,
% 12.60/2.49  | | | | | | | | | |             all_7_22))
% 12.60/2.49  | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | BETA: splitting (73) gives:
% 12.60/2.49  | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | Case 1:
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | |   (74)   ! [v0: $i] :  ! [v1: $i] : (v1 = init | v0 = pv64
% 12.60/2.49  | | | | | | | | | | |           |  ~ (a_select3(id_ds1_filter_init, pv63, v0) =
% 12.60/2.49  | | | | | | | | | | |             v1) |  ~ $i(v0) |  ~ leq(v0, n5) |  ~ leq(v0,
% 12.60/2.49  | | | | | | | | | | |             pv64) |  ~ leq(n0, v0))
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | GROUND_INST: instantiating (74) with all_4_1, all_4_0,
% 12.60/2.49  | | | | | | | | | | |              simplifying with (13), (15), (16), (17), (18)
% 12.60/2.49  | | | | | | | | | | |              gives:
% 12.60/2.49  | | | | | | | | | | |   (75)  all_4_0 = init | all_4_1 = pv64
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | BETA: splitting (75) gives:
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | Case 1:
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | |   (76)  all_4_0 = init
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | | REDUCE: (7), (76) imply:
% 12.60/2.49  | | | | | | | | | | | |   (77)  $false
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | | CLOSE: (77) is inconsistent.
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | Case 2:
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | |   (78)  all_4_1 = pv64
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | | REDUCE: (6), (78) imply:
% 12.60/2.49  | | | | | | | | | | | |   (79)  $false
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | | CLOSE: (79) is inconsistent.
% 12.60/2.49  | | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | End of split
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | Case 2:
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | |   (80)  all_7_23 = pv63 &  ~ (all_7_21 = init) &
% 12.60/2.49  | | | | | | | | | | |         a_select3(id_ds1_filter_init, pv63, all_7_22) =
% 12.60/2.49  | | | | | | | | | | |         all_7_21 & $i(all_7_21) & gt(pv64, all_7_22) &
% 12.60/2.49  | | | | | | | | | | |         leq(all_7_22, n5) & leq(n0, all_7_22)
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | ALPHA: (80) implies:
% 12.60/2.49  | | | | | | | | | | |   (81)   ~ (all_7_21 = init)
% 12.60/2.49  | | | | | | | | | | |   (82)  leq(n0, all_7_22)
% 12.60/2.49  | | | | | | | | | | |   (83)  leq(all_7_22, n5)
% 12.60/2.49  | | | | | | | | | | |   (84)  gt(pv64, all_7_22)
% 12.60/2.49  | | | | | | | | | | |   (85)  a_select3(id_ds1_filter_init, pv63, all_7_22) =
% 12.60/2.49  | | | | | | | | | | |         all_7_21
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | GROUND_INST: instantiating (20) with all_7_22, all_7_21,
% 12.60/2.49  | | | | | | | | | | |              simplifying with (35), (82), (83), (84), (85)
% 12.60/2.49  | | | | | | | | | | |              gives:
% 12.60/2.49  | | | | | | | | | | |   (86)  all_7_21 = init
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | REDUCE: (81), (86) imply:
% 12.60/2.49  | | | | | | | | | | |   (87)  $false
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | | CLOSE: (87) is inconsistent.
% 12.60/2.49  | | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | | End of split
% 12.60/2.49  | | | | | | | | | | 
% 12.60/2.49  | | | | | | | | | Case 2:
% 12.60/2.49  | | | | | | | | | | 
% 12.60/2.50  | | | | | | | | | |   (88)  ( ~ (all_7_0 = init) & a_select3(h_ds1_filter_init,
% 12.60/2.50  | | | | | | | | | |             all_7_2, all_7_1) = all_7_0 & $i(all_7_0) &
% 12.60/2.50  | | | | | | | | | |           leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0,
% 12.60/2.50  | | | | | | | | | |             all_7_1) & leq(n0, all_7_2)) | ( ~ (all_7_3 =
% 12.60/2.50  | | | | | | | | | |             init) & a_select3(phi_ds1_filter_init, all_7_5,
% 12.60/2.50  | | | | | | | | | |             all_7_4) = all_7_3 & $i(all_7_3) & leq(all_7_4,
% 12.60/2.50  | | | | | | | | | |             n5) & leq(all_7_5, n5) & leq(n0, all_7_4) &
% 12.60/2.50  | | | | | | | | | |           leq(n0, all_7_5)) | ( ~ (all_7_6 = init) &
% 12.60/2.50  | | | | | | | | | |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7) =
% 12.60/2.50  | | | | | | | | | |           all_7_6 & $i(all_7_6) & leq(all_7_7, n0) &
% 12.60/2.50  | | | | | | | | | |           leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0,
% 12.60/2.50  | | | | | | | | | |             all_7_8))
% 12.60/2.50  | | | | | | | | | | 
% 12.60/2.50  | | | | | | | | | | BETA: splitting (88) gives:
% 12.60/2.50  | | | | | | | | | | 
% 12.60/2.50  | | | | | | | | | | Case 1:
% 12.60/2.50  | | | | | | | | | | | 
% 12.60/2.50  | | | | | | | | | | |   (89)   ~ (all_7_0 = init) & a_select3(h_ds1_filter_init,
% 12.60/2.50  | | | | | | | | | | |           all_7_2, all_7_1) = all_7_0 & $i(all_7_0) &
% 12.60/2.50  | | | | | | | | | | |         leq(all_7_1, n5) & leq(all_7_2, n2) & leq(n0,
% 12.60/2.50  | | | | | | | | | | |           all_7_1) & leq(n0, all_7_2)
% 12.60/2.50  | | | | | | | | | | | 
% 12.60/2.50  | | | | | | | | | | | ALPHA: (89) implies:
% 12.60/2.50  | | | | | | | | | | |   (90)   ~ (all_7_0 = init)
% 12.60/2.50  | | | | | | | | | | |   (91)  leq(n0, all_7_2)
% 12.60/2.50  | | | | | | | | | | |   (92)  leq(n0, all_7_1)
% 12.60/2.50  | | | | | | | | | | |   (93)  leq(all_7_2, n2)
% 12.60/2.50  | | | | | | | | | | |   (94)  leq(all_7_1, n5)
% 12.60/2.50  | | | | | | | | | | |   (95)  a_select3(h_ds1_filter_init, all_7_2, all_7_1) =
% 12.60/2.50  | | | | | | | | | | |         all_7_0
% 12.60/2.50  | | | | | | | | | | | 
% 12.60/2.50  | | | | | | | | | | | GROUND_INST: instantiating (21) with all_7_2, all_7_1, all_7_0,
% 12.60/2.50  | | | | | | | | | | |              simplifying with (48), (49), (91), (92), (93),
% 12.60/2.50  | | | | | | | | | | |              (94), (95) gives:
% 13.02/2.50  | | | | | | | | | | |   (96)  all_7_0 = init
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | REDUCE: (90), (96) imply:
% 13.02/2.50  | | | | | | | | | | |   (97)  $false
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | CLOSE: (97) is inconsistent.
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | Case 2:
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | |   (98)  ( ~ (all_7_3 = init) &
% 13.02/2.50  | | | | | | | | | | |           a_select3(phi_ds1_filter_init, all_7_5, all_7_4)
% 13.02/2.50  | | | | | | | | | | |           = all_7_3 & $i(all_7_3) & leq(all_7_4, n5) &
% 13.02/2.50  | | | | | | | | | | |           leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0,
% 13.02/2.50  | | | | | | | | | | |             all_7_5)) | ( ~ (all_7_6 = init) &
% 13.02/2.50  | | | | | | | | | | |           a_select3(dv_ds1_filter_init, all_7_8, all_7_7)
% 13.02/2.50  | | | | | | | | | | |           = all_7_6 & $i(all_7_6) & leq(all_7_7, n0) &
% 13.02/2.50  | | | | | | | | | | |           leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0,
% 13.02/2.50  | | | | | | | | | | |             all_7_8))
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | BETA: splitting (98) gives:
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | Case 1:
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | |   (99)   ~ (all_7_3 = init) &
% 13.02/2.50  | | | | | | | | | | | |         a_select3(phi_ds1_filter_init, all_7_5, all_7_4) =
% 13.02/2.50  | | | | | | | | | | | |         all_7_3 & $i(all_7_3) & leq(all_7_4, n5) &
% 13.02/2.50  | | | | | | | | | | | |         leq(all_7_5, n5) & leq(n0, all_7_4) & leq(n0,
% 13.02/2.50  | | | | | | | | | | | |           all_7_5)
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | ALPHA: (99) implies:
% 13.02/2.50  | | | | | | | | | | | |   (100)   ~ (all_7_3 = init)
% 13.02/2.50  | | | | | | | | | | | |   (101)  leq(n0, all_7_5)
% 13.02/2.50  | | | | | | | | | | | |   (102)  leq(n0, all_7_4)
% 13.02/2.50  | | | | | | | | | | | |   (103)  leq(all_7_5, n5)
% 13.02/2.50  | | | | | | | | | | | |   (104)  leq(all_7_4, n5)
% 13.02/2.50  | | | | | | | | | | | |   (105)  a_select3(phi_ds1_filter_init, all_7_5, all_7_4) =
% 13.02/2.50  | | | | | | | | | | | |          all_7_3
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | GROUND_INST: instantiating (22) with all_7_5, all_7_4, all_7_3,
% 13.02/2.50  | | | | | | | | | | | |              simplifying with (46), (47), (101), (102), (103),
% 13.02/2.50  | | | | | | | | | | | |              (104), (105) gives:
% 13.02/2.50  | | | | | | | | | | | |   (106)  all_7_3 = init
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | REDUCE: (100), (106) imply:
% 13.02/2.50  | | | | | | | | | | | |   (107)  $false
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | CLOSE: (107) is inconsistent.
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | Case 2:
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | |   (108)   ~ (all_7_6 = init) &
% 13.02/2.50  | | | | | | | | | | | |          a_select3(dv_ds1_filter_init, all_7_8, all_7_7) =
% 13.02/2.50  | | | | | | | | | | | |          all_7_6 & $i(all_7_6) & leq(all_7_7, n0) &
% 13.02/2.50  | | | | | | | | | | | |          leq(all_7_8, n5) & leq(n0, all_7_7) & leq(n0,
% 13.02/2.50  | | | | | | | | | | | |            all_7_8)
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | ALPHA: (108) implies:
% 13.02/2.50  | | | | | | | | | | | |   (109)   ~ (all_7_6 = init)
% 13.02/2.50  | | | | | | | | | | | |   (110)  leq(n0, all_7_8)
% 13.02/2.50  | | | | | | | | | | | |   (111)  leq(n0, all_7_7)
% 13.02/2.50  | | | | | | | | | | | |   (112)  leq(all_7_8, n5)
% 13.02/2.50  | | | | | | | | | | | |   (113)  leq(all_7_7, n0)
% 13.02/2.50  | | | | | | | | | | | |   (114)  a_select3(dv_ds1_filter_init, all_7_8, all_7_7) =
% 13.02/2.50  | | | | | | | | | | | |          all_7_6
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_7_8, all_7_7, all_7_6,
% 13.02/2.50  | | | | | | | | | | | |              simplifying with (44), (45), (110), (111), (112),
% 13.02/2.50  | | | | | | | | | | | |              (113), (114) gives:
% 13.02/2.50  | | | | | | | | | | | |   (115)  all_7_6 = init
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | REDUCE: (109), (115) imply:
% 13.02/2.50  | | | | | | | | | | | |   (116)  $false
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | | CLOSE: (116) is inconsistent.
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | End of split
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | End of split
% 13.02/2.50  | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | End of split
% 13.02/2.50  | | | | | | | | | 
% 13.02/2.50  | | | | | | | | Case 2:
% 13.02/2.50  | | | | | | | | | 
% 13.02/2.50  | | | | | | | | |   (117)  ( ~ (all_7_9 = init) & a_select3(q_ds1_filter_init,
% 13.02/2.50  | | | | | | | | |              all_7_11, all_7_10) = all_7_9 & $i(all_7_9) &
% 13.02/2.50  | | | | | | | | |            leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 13.02/2.50  | | | | | | | | |              all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12 =
% 13.02/2.50  | | | | | | | | |              init) & a_select3(r_ds1_filter_init, all_7_14,
% 13.02/2.50  | | | | | | | | |              all_7_13) = all_7_12 & $i(all_7_12) &
% 13.02/2.50  | | | | | | | | |            leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0,
% 13.02/2.50  | | | | | | | | |              all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15 =
% 13.02/2.50  | | | | | | | | |              init) & a_select3(xhatmin_ds1_filter_init,
% 13.02/2.50  | | | | | | | | |              all_7_17, all_7_16) = all_7_15 & $i(all_7_15) &
% 13.02/2.50  | | | | | | | | |            leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0,
% 13.02/2.50  | | | | | | | | |              all_7_16) & leq(n0, all_7_17)) | ( ~ (all_7_18 =
% 13.02/2.50  | | | | | | | | |              init) & a_select3(pminus_ds1_filter_init,
% 13.02/2.50  | | | | | | | | |              all_7_20, all_7_19) = all_7_18 & $i(all_7_18) &
% 13.02/2.50  | | | | | | | | |            leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0,
% 13.02/2.50  | | | | | | | | |              all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24 =
% 13.02/2.50  | | | | | | | | |              init) & a_select3(id_ds1_filter_init, all_7_26,
% 13.02/2.50  | | | | | | | | |              all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63,
% 13.02/2.50  | | | | | | | | |              all_7_26) & leq(all_7_25, n5) & leq(all_7_26, n5)
% 13.02/2.50  | | | | | | | | |            & leq(n0, all_7_25) & leq(n0, all_7_26)) | ( ~
% 13.02/2.50  | | | | | | | | |            (all_7_27 = init) & pred(pv63) = all_7_30 &
% 13.02/2.50  | | | | | | | | |            a_select3(id_ds1_filter_init, all_7_29, all_7_28) =
% 13.02/2.50  | | | | | | | | |            all_7_27 & $i(all_7_27) & $i(all_7_30) &
% 13.02/2.50  | | | | | | | | |            leq(all_7_28, n5) & leq(all_7_29, all_7_30) &
% 13.02/2.50  | | | | | | | | |            leq(n0, all_7_28) & leq(n0, all_7_29))
% 13.02/2.50  | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | BETA: splitting (117) gives:
% 13.02/2.50  | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | Case 1:
% 13.02/2.50  | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | |   (118)  ( ~ (all_7_9 = init) & a_select3(q_ds1_filter_init,
% 13.02/2.50  | | | | | | | | | |              all_7_11, all_7_10) = all_7_9 & $i(all_7_9) &
% 13.02/2.50  | | | | | | | | | |            leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 13.02/2.50  | | | | | | | | | |              all_7_10) & leq(n0, all_7_11)) | ( ~ (all_7_12
% 13.02/2.50  | | | | | | | | | |              = init) & a_select3(r_ds1_filter_init,
% 13.02/2.50  | | | | | | | | | |              all_7_14, all_7_13) = all_7_12 & $i(all_7_12) &
% 13.02/2.50  | | | | | | | | | |            leq(all_7_13, n2) & leq(all_7_14, n2) & leq(n0,
% 13.02/2.50  | | | | | | | | | |              all_7_13) & leq(n0, all_7_14)) | ( ~ (all_7_15
% 13.02/2.50  | | | | | | | | | |              = init) & a_select3(xhatmin_ds1_filter_init,
% 13.02/2.50  | | | | | | | | | |              all_7_17, all_7_16) = all_7_15 & $i(all_7_15) &
% 13.02/2.50  | | | | | | | | | |            leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0,
% 13.02/2.50  | | | | | | | | | |              all_7_16) & leq(n0, all_7_17))
% 13.02/2.50  | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | BETA: splitting (118) gives:
% 13.02/2.50  | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | Case 1:
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | |   (119)   ~ (all_7_9 = init) & a_select3(q_ds1_filter_init,
% 13.02/2.50  | | | | | | | | | | |            all_7_11, all_7_10) = all_7_9 & $i(all_7_9) &
% 13.02/2.50  | | | | | | | | | | |          leq(all_7_10, n5) & leq(all_7_11, n5) & leq(n0,
% 13.02/2.50  | | | | | | | | | | |            all_7_10) & leq(n0, all_7_11)
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | ALPHA: (119) implies:
% 13.02/2.50  | | | | | | | | | | |   (120)   ~ (all_7_9 = init)
% 13.02/2.50  | | | | | | | | | | |   (121)  leq(n0, all_7_11)
% 13.02/2.50  | | | | | | | | | | |   (122)  leq(n0, all_7_10)
% 13.02/2.50  | | | | | | | | | | |   (123)  leq(all_7_11, n5)
% 13.02/2.50  | | | | | | | | | | |   (124)  leq(all_7_10, n5)
% 13.02/2.50  | | | | | | | | | | |   (125)  a_select3(q_ds1_filter_init, all_7_11, all_7_10) =
% 13.02/2.50  | | | | | | | | | | |          all_7_9
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | GROUND_INST: instantiating (24) with all_7_11, all_7_10,
% 13.02/2.50  | | | | | | | | | | |              all_7_9, simplifying with (42), (43), (121),
% 13.02/2.50  | | | | | | | | | | |              (122), (123), (124), (125) gives:
% 13.02/2.50  | | | | | | | | | | |   (126)  all_7_9 = init
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | REDUCE: (120), (126) imply:
% 13.02/2.50  | | | | | | | | | | |   (127)  $false
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | Case 2:
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | |   (128)  ( ~ (all_7_12 = init) &
% 13.02/2.50  | | | | | | | | | | |            a_select3(r_ds1_filter_init, all_7_14, all_7_13)
% 13.02/2.50  | | | | | | | | | | |            = all_7_12 & $i(all_7_12) & leq(all_7_13, n2) &
% 13.02/2.50  | | | | | | | | | | |            leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0,
% 13.02/2.50  | | | | | | | | | | |              all_7_14)) | ( ~ (all_7_15 = init) &
% 13.02/2.50  | | | | | | | | | | |            a_select3(xhatmin_ds1_filter_init, all_7_17,
% 13.02/2.50  | | | | | | | | | | |              all_7_16) = all_7_15 & $i(all_7_15) &
% 13.02/2.50  | | | | | | | | | | |            leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0,
% 13.02/2.50  | | | | | | | | | | |              all_7_16) & leq(n0, all_7_17))
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | BETA: splitting (128) gives:
% 13.02/2.50  | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | Case 1:
% 13.02/2.50  | | | | | | | | | | | | 
% 13.02/2.50  | | | | | | | | | | | |   (129)   ~ (all_7_12 = init) &
% 13.02/2.50  | | | | | | | | | | | |          a_select3(r_ds1_filter_init, all_7_14, all_7_13) =
% 13.02/2.50  | | | | | | | | | | | |          all_7_12 & $i(all_7_12) & leq(all_7_13, n2) &
% 13.02/2.50  | | | | | | | | | | | |          leq(all_7_14, n2) & leq(n0, all_7_13) & leq(n0,
% 13.02/2.50  | | | | | | | | | | | |            all_7_14)
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | ALPHA: (129) implies:
% 13.02/2.51  | | | | | | | | | | | |   (130)   ~ (all_7_12 = init)
% 13.02/2.51  | | | | | | | | | | | |   (131)  leq(n0, all_7_14)
% 13.02/2.51  | | | | | | | | | | | |   (132)  leq(n0, all_7_13)
% 13.02/2.51  | | | | | | | | | | | |   (133)  leq(all_7_14, n2)
% 13.02/2.51  | | | | | | | | | | | |   (134)  leq(all_7_13, n2)
% 13.02/2.51  | | | | | | | | | | | |   (135)  a_select3(r_ds1_filter_init, all_7_14, all_7_13) =
% 13.02/2.51  | | | | | | | | | | | |          all_7_12
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_7_14, all_7_13,
% 13.02/2.51  | | | | | | | | | | | |              all_7_12, simplifying with (40), (41), (131),
% 13.02/2.51  | | | | | | | | | | | |              (132), (133), (134), (135) gives:
% 13.02/2.51  | | | | | | | | | | | |   (136)  all_7_12 = init
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | REDUCE: (130), (136) imply:
% 13.02/2.51  | | | | | | | | | | | |   (137)  $false
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | CLOSE: (137) is inconsistent.
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | Case 2:
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | |   (138)   ~ (all_7_15 = init) &
% 13.02/2.51  | | | | | | | | | | | |          a_select3(xhatmin_ds1_filter_init, all_7_17,
% 13.02/2.51  | | | | | | | | | | | |            all_7_16) = all_7_15 & $i(all_7_15) &
% 13.02/2.51  | | | | | | | | | | | |          leq(all_7_16, n0) & leq(all_7_17, n5) & leq(n0,
% 13.02/2.51  | | | | | | | | | | | |            all_7_16) & leq(n0, all_7_17)
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | ALPHA: (138) implies:
% 13.02/2.51  | | | | | | | | | | | |   (139)   ~ (all_7_15 = init)
% 13.02/2.51  | | | | | | | | | | | |   (140)  leq(n0, all_7_17)
% 13.02/2.51  | | | | | | | | | | | |   (141)  leq(n0, all_7_16)
% 13.02/2.51  | | | | | | | | | | | |   (142)  leq(all_7_17, n5)
% 13.02/2.51  | | | | | | | | | | | |   (143)  leq(all_7_16, n0)
% 13.02/2.51  | | | | | | | | | | | |   (144)  a_select3(xhatmin_ds1_filter_init, all_7_17,
% 13.02/2.51  | | | | | | | | | | | |            all_7_16) = all_7_15
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_7_17, all_7_16,
% 13.02/2.51  | | | | | | | | | | | |              all_7_15, simplifying with (38), (39), (140),
% 13.02/2.51  | | | | | | | | | | | |              (141), (142), (143), (144) gives:
% 13.02/2.51  | | | | | | | | | | | |   (145)  all_7_15 = init
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | REDUCE: (139), (145) imply:
% 13.02/2.51  | | | | | | | | | | | |   (146)  $false
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | End of split
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | End of split
% 13.02/2.51  | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | Case 2:
% 13.02/2.51  | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | |   (147)  ( ~ (all_7_18 = init) &
% 13.02/2.51  | | | | | | | | | |            a_select3(pminus_ds1_filter_init, all_7_20,
% 13.02/2.51  | | | | | | | | | |              all_7_19) = all_7_18 & $i(all_7_18) &
% 13.02/2.51  | | | | | | | | | |            leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0,
% 13.02/2.51  | | | | | | | | | |              all_7_19) & leq(n0, all_7_20)) | ( ~ (all_7_24
% 13.02/2.51  | | | | | | | | | |              = init) & a_select3(id_ds1_filter_init,
% 13.02/2.51  | | | | | | | | | |              all_7_26, all_7_25) = all_7_24 & $i(all_7_24) &
% 13.02/2.51  | | | | | | | | | |            gt(pv63, all_7_26) & leq(all_7_25, n5) &
% 13.02/2.51  | | | | | | | | | |            leq(all_7_26, n5) & leq(n0, all_7_25) & leq(n0,
% 13.02/2.51  | | | | | | | | | |              all_7_26)) | ( ~ (all_7_27 = init) & pred(pv63)
% 13.02/2.51  | | | | | | | | | |            = all_7_30 & a_select3(id_ds1_filter_init,
% 13.02/2.51  | | | | | | | | | |              all_7_29, all_7_28) = all_7_27 & $i(all_7_27) &
% 13.02/2.51  | | | | | | | | | |            $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29,
% 13.02/2.51  | | | | | | | | | |              all_7_30) & leq(n0, all_7_28) & leq(n0,
% 13.02/2.51  | | | | | | | | | |              all_7_29))
% 13.02/2.51  | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | BETA: splitting (147) gives:
% 13.02/2.51  | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | Case 1:
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | |   (148)   ~ (all_7_18 = init) &
% 13.02/2.51  | | | | | | | | | | |          a_select3(pminus_ds1_filter_init, all_7_20,
% 13.02/2.51  | | | | | | | | | | |            all_7_19) = all_7_18 & $i(all_7_18) &
% 13.02/2.51  | | | | | | | | | | |          leq(all_7_19, n5) & leq(all_7_20, n5) & leq(n0,
% 13.02/2.51  | | | | | | | | | | |            all_7_19) & leq(n0, all_7_20)
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | ALPHA: (148) implies:
% 13.02/2.51  | | | | | | | | | | |   (149)   ~ (all_7_18 = init)
% 13.02/2.51  | | | | | | | | | | |   (150)  leq(n0, all_7_20)
% 13.02/2.51  | | | | | | | | | | |   (151)  leq(n0, all_7_19)
% 13.02/2.51  | | | | | | | | | | |   (152)  leq(all_7_20, n5)
% 13.02/2.51  | | | | | | | | | | |   (153)  leq(all_7_19, n5)
% 13.02/2.51  | | | | | | | | | | |   (154)  a_select3(pminus_ds1_filter_init, all_7_20,
% 13.02/2.51  | | | | | | | | | | |            all_7_19) = all_7_18
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | GROUND_INST: instantiating (27) with all_7_20, all_7_19,
% 13.02/2.51  | | | | | | | | | | |              all_7_18, simplifying with (36), (37), (150),
% 13.02/2.51  | | | | | | | | | | |              (151), (152), (153), (154) gives:
% 13.02/2.51  | | | | | | | | | | |   (155)  all_7_18 = init
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | REDUCE: (149), (155) imply:
% 13.02/2.51  | | | | | | | | | | |   (156)  $false
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | Case 2:
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | |   (157)  ( ~ (all_7_24 = init) &
% 13.02/2.51  | | | | | | | | | | |            a_select3(id_ds1_filter_init, all_7_26,
% 13.02/2.51  | | | | | | | | | | |              all_7_25) = all_7_24 & $i(all_7_24) & gt(pv63,
% 13.02/2.51  | | | | | | | | | | |              all_7_26) & leq(all_7_25, n5) & leq(all_7_26,
% 13.02/2.51  | | | | | | | | | | |              n5) & leq(n0, all_7_25) & leq(n0, all_7_26)) |
% 13.02/2.51  | | | | | | | | | | |          ( ~ (all_7_27 = init) & pred(pv63) = all_7_30 &
% 13.02/2.51  | | | | | | | | | | |            a_select3(id_ds1_filter_init, all_7_29,
% 13.02/2.51  | | | | | | | | | | |              all_7_28) = all_7_27 & $i(all_7_27) &
% 13.02/2.51  | | | | | | | | | | |            $i(all_7_30) & leq(all_7_28, n5) & leq(all_7_29,
% 13.02/2.51  | | | | | | | | | | |              all_7_30) & leq(n0, all_7_28) & leq(n0,
% 13.02/2.51  | | | | | | | | | | |              all_7_29))
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | BETA: splitting (157) gives:
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | Case 1:
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | |   (158)   ~ (all_7_24 = init) &
% 13.02/2.51  | | | | | | | | | | | |          a_select3(id_ds1_filter_init, all_7_26, all_7_25)
% 13.02/2.51  | | | | | | | | | | | |          = all_7_24 & $i(all_7_24) & gt(pv63, all_7_26) &
% 13.02/2.51  | | | | | | | | | | | |          leq(all_7_25, n5) & leq(all_7_26, n5) & leq(n0,
% 13.02/2.51  | | | | | | | | | | | |            all_7_25) & leq(n0, all_7_26)
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | ALPHA: (158) implies:
% 13.02/2.51  | | | | | | | | | | | |   (159)   ~ (all_7_24 = init)
% 13.02/2.51  | | | | | | | | | | | |   (160)  leq(n0, all_7_26)
% 13.02/2.51  | | | | | | | | | | | |   (161)  leq(n0, all_7_25)
% 13.02/2.51  | | | | | | | | | | | |   (162)  leq(all_7_26, n5)
% 13.02/2.51  | | | | | | | | | | | |   (163)  leq(all_7_25, n5)
% 13.02/2.51  | | | | | | | | | | | |   (164)  gt(pv63, all_7_26)
% 13.02/2.51  | | | | | | | | | | | |   (165)  a_select3(id_ds1_filter_init, all_7_26, all_7_25)
% 13.02/2.51  | | | | | | | | | | | |          = all_7_24
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_7_26, all_7_25,
% 13.02/2.51  | | | | | | | | | | | |              all_7_24, simplifying with (33), (34), (160),
% 13.02/2.51  | | | | | | | | | | | |              (161), (162), (163), (164), (165) gives:
% 13.02/2.51  | | | | | | | | | | | |   (166)  all_7_24 = init
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | REDUCE: (159), (166) imply:
% 13.02/2.51  | | | | | | | | | | | |   (167)  $false
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | Case 2:
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | |   (168)   ~ (all_7_27 = init) & pred(pv63) = all_7_30 &
% 13.02/2.51  | | | | | | | | | | | |          a_select3(id_ds1_filter_init, all_7_29, all_7_28)
% 13.02/2.51  | | | | | | | | | | | |          = all_7_27 & $i(all_7_27) & $i(all_7_30) &
% 13.02/2.51  | | | | | | | | | | | |          leq(all_7_28, n5) & leq(all_7_29, all_7_30) &
% 13.02/2.51  | | | | | | | | | | | |          leq(n0, all_7_28) & leq(n0, all_7_29)
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | ALPHA: (168) implies:
% 13.02/2.51  | | | | | | | | | | | |   (169)   ~ (all_7_27 = init)
% 13.02/2.51  | | | | | | | | | | | |   (170)  leq(n0, all_7_29)
% 13.02/2.51  | | | | | | | | | | | |   (171)  leq(n0, all_7_28)
% 13.02/2.51  | | | | | | | | | | | |   (172)  leq(all_7_29, all_7_30)
% 13.02/2.51  | | | | | | | | | | | |   (173)  leq(all_7_28, n5)
% 13.02/2.51  | | | | | | | | | | | |   (174)  a_select3(id_ds1_filter_init, all_7_29, all_7_28)
% 13.02/2.51  | | | | | | | | | | | |          = all_7_27
% 13.02/2.51  | | | | | | | | | | | |   (175)  pred(pv63) = all_7_30
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_4_2, all_7_30, pv63,
% 13.02/2.51  | | | | | | | | | | | |              simplifying with (19), (175) gives:
% 13.02/2.51  | | | | | | | | | | | |   (176)  all_7_30 = all_4_2
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | REDUCE: (172), (176) imply:
% 13.02/2.51  | | | | | | | | | | | |   (177)  leq(all_7_29, all_4_2)
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | GROUND_INST: instantiating (28) with all_7_29, all_7_28,
% 13.02/2.51  | | | | | | | | | | | |              all_7_27, simplifying with (31), (32), (170),
% 13.02/2.51  | | | | | | | | | | | |              (171), (173), (174), (177) gives:
% 13.02/2.51  | | | | | | | | | | | |   (178)  all_7_27 = init
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | REDUCE: (169), (178) imply:
% 13.02/2.51  | | | | | | | | | | | |   (179)  $false
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 13.02/2.51  | | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | | End of split
% 13.02/2.51  | | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | | End of split
% 13.02/2.51  | | | | | | | | | | 
% 13.02/2.51  | | | | | | | | | End of split
% 13.02/2.51  | | | | | | | | | 
% 13.02/2.51  | | | | | | | | End of split
% 13.02/2.51  | | | | | | | | 
% 13.02/2.51  | | | | | | | End of split
% 13.02/2.51  | | | | | | | 
% 13.02/2.51  | | | | | | End of split
% 13.02/2.51  | | | | | | 
% 13.02/2.51  | | | | | End of split
% 13.02/2.51  | | | | | 
% 13.02/2.51  | | | | End of split
% 13.02/2.51  | | | | 
% 13.02/2.51  | | | End of split
% 13.02/2.51  | | | 
% 13.02/2.51  | | End of split
% 13.02/2.51  | | 
% 13.02/2.51  | End of split
% 13.02/2.51  | 
% 13.02/2.51  End of proof
% 13.02/2.51  % SZS output end Proof for theBenchmark
% 13.02/2.51  
% 13.02/2.51  1902ms
%------------------------------------------------------------------------------