%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV398+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 22:56:10 EDT 2023

% Result   : Theorem 17.91s 3.16s
% Output   : Proof 21.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SWV398+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 08:09:40 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.63  Running up to 7 provers in parallel.
% 0.65/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.65/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.87/1.20  Prover 1: Preprocessing ...
% 3.49/1.21  Prover 4: Preprocessing ...
% 3.49/1.25  Prover 2: Preprocessing ...
% 3.49/1.25  Prover 5: Preprocessing ...
% 3.49/1.25  Prover 0: Preprocessing ...
% 3.49/1.25  Prover 6: Preprocessing ...
% 3.49/1.25  Prover 3: Preprocessing ...
% 7.27/1.76  Prover 1: Warning: ignoring some quantifiers
% 7.99/1.86  Prover 3: Warning: ignoring some quantifiers
% 7.99/1.87  Prover 1: Constructing countermodel ...
% 7.99/1.88  Prover 5: Proving ...
% 7.99/1.89  Prover 3: Constructing countermodel ...
% 7.99/1.89  Prover 6: Proving ...
% 8.71/1.92  Prover 0: Proving ...
% 8.93/1.94  Prover 4: Constructing countermodel ...
% 8.93/1.97  Prover 2: Proving ...
% 11.96/2.34  Prover 3: gave up
% 11.96/2.34  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.38/2.40  Prover 7: Preprocessing ...
% 13.69/2.62  Prover 7: Warning: ignoring some quantifiers
% 14.28/2.66  Prover 7: Constructing countermodel ...
% 16.60/2.95  Prover 7: gave up
% 16.60/2.96  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.85/3.02  Prover 8: Preprocessing ...
% 17.91/3.15  Prover 8: Warning: ignoring some quantifiers
% 17.91/3.16  Prover 0: proved (2525ms)
% 17.91/3.16  
% 17.91/3.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.91/3.16  
% 17.91/3.16  Prover 6: stopped
% 17.91/3.17  Prover 2: stopped
% 17.91/3.17  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.91/3.17  Prover 5: stopped
% 17.91/3.17  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.91/3.17  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 17.91/3.17  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.43/3.18  Prover 8: Constructing countermodel ...
% 18.43/3.21  Prover 11: Preprocessing ...
% 18.43/3.21  Prover 13: Preprocessing ...
% 18.43/3.22  Prover 10: Preprocessing ...
% 18.43/3.26  Prover 16: Preprocessing ...
% 19.52/3.36  Prover 10: Warning: ignoring some quantifiers
% 19.52/3.37  Prover 16: Warning: ignoring some quantifiers
% 19.52/3.37  Prover 10: Constructing countermodel ...
% 19.52/3.38  Prover 16: Constructing countermodel ...
% 20.20/3.45  Prover 11: Constructing countermodel ...
% 20.20/3.46  Prover 13: Warning: ignoring some quantifiers
% 20.20/3.46  Prover 4: Found proof (size 240)
% 20.20/3.46  Prover 4: proved (2827ms)
% 20.20/3.46  Prover 8: stopped
% 20.20/3.46  Prover 10: stopped
% 20.20/3.47  Prover 1: stopped
% 20.20/3.47  Prover 13: Constructing countermodel ...
% 20.20/3.47  Prover 11: stopped
% 20.20/3.47  Prover 16: stopped
% 20.20/3.48  Prover 13: stopped
% 20.20/3.48  
% 20.20/3.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.20/3.48  
% 20.68/3.50  % SZS output start Proof for theBenchmark
% 20.68/3.50  Assumptions after simplification:
% 20.68/3.50  ---------------------------------
% 20.68/3.50  
% 20.68/3.50    (ax36)
% 20.68/3.53    $i(create_slb) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (triple(v0,
% 20.68/3.53          create_slb, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | check_cpq(v2) = 0)
% 20.68/3.53  
% 20.68/3.53    (ax47)
% 20.68/3.53    $i(bad) & $i(create_slb) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 20.68/3.53      $i] :  ! [v4: $i] : (v1 = create_slb |  ~ (triple(v0, v1, v2) = v3) |  ~
% 20.68/3.53      (findmin_cpq_eff(v3) = v4) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i]
% 20.68/3.53      :  ? [v6: any] :  ? [v7: $i] :  ? [v8: $i] : (findmin_pqp_res(v0) = v5 &
% 20.68/3.53        triple(v0, v7, bad) = v8 & update_slb(v1, v5) = v7 & contains_slb(v1, v5)
% 20.68/3.53        = v6 & $i(v8) & $i(v7) & $i(v5) & (v8 = v4 | v6 = 0)))
% 20.68/3.53  
% 20.68/3.53    (ax48)
% 20.68/3.53    $i(bad) & $i(create_slb) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 20.68/3.53      $i] :  ! [v4: $i] : (v1 = create_slb |  ~ (triple(v0, v1, v2) = v3) |  ~
% 20.68/3.53      (findmin_cpq_eff(v3) = v4) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i]
% 20.68/3.53      :  ? [v6: any] :  ? [v7: $i] :  ? [v8: any] :  ? [v9: $i] :  ? [v10: $i] :
% 20.68/3.53      (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10 & update_slb(v1, v5) =
% 20.68/3.53        v9 & lookup_slb(v1, v5) = v7 & contains_slb(v1, v5) = v6 &
% 20.68/3.53        strictly_less_than(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~
% 20.68/3.53          (v8 = 0) |  ~ (v6 = 0) | v10 = v4)))
% 20.68/3.53  
% 20.68/3.53    (ax49)
% 20.68/3.54    $i(create_slb) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  !
% 20.68/3.54    [v4: $i] :  ! [v5: $i] : (v1 = create_slb |  ~ (findmin_pqp_res(v0) = v3) |  ~
% 20.68/3.54      (triple(v0, v4, v2) = v5) |  ~ (update_slb(v1, v3) = v4) |  ~ $i(v2) |  ~
% 20.68/3.54      $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7: $i] :  ? [v8: any] :  ? [v9: $i]
% 20.68/3.54      :  ? [v10: $i] : (triple(v0, v1, v2) = v9 & findmin_cpq_eff(v9) = v10 &
% 20.68/3.54        lookup_slb(v1, v3) = v7 & contains_slb(v1, v3) = v6 & less_than(v7, v3) =
% 20.68/3.54        v8 & $i(v10) & $i(v9) & $i(v7) & ( ~ (v8 = 0) |  ~ (v6 = 0) | v10 = v5)))
% 20.68/3.54    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 =
% 20.68/3.54      create_slb |  ~ (triple(v0, v1, v2) = v3) |  ~ (findmin_cpq_eff(v3) = v4) | 
% 20.68/3.54      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6: any] :  ? [v7: $i]
% 20.68/3.54      :  ? [v8: any] :  ? [v9: $i] :  ? [v10: $i] : (findmin_pqp_res(v0) = v5 &
% 20.68/3.54        triple(v0, v9, v2) = v10 & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) =
% 20.68/3.54        v7 & contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) & $i(v9)
% 20.68/3.54        & $i(v7) & $i(v5) & ( ~ (v8 = 0) |  ~ (v6 = 0) | v10 = v4)))
% 20.68/3.54  
% 20.68/3.54    (ax51)
% 20.68/3.54    $i(create_slb) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  !
% 20.68/3.54    [v4: $i] : (v1 = create_slb |  ~ (findmin_cpq_res(v3) = v4) |  ~ (triple(v0,
% 20.68/3.54          v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | (findmin_pqp_res(v0)
% 20.68/3.54        = v4 & $i(v4)))
% 20.68/3.54  
% 20.68/3.54    (ax52)
% 20.68/3.54     ! [v0: $i] :  ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) |  ~ $i(v0) |  ?
% 20.68/3.54      [v2: $i] :  ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) =
% 20.68/3.54        v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) &  ! [v0: $i] :  ! [v1:
% 20.68/3.54      $i] : ( ~ (removemin_cpq_eff(v0) = v1) |  ~ $i(v0) |  ? [v2: $i] :  ? [v3:
% 20.68/3.54        $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 &
% 20.68/3.54        remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) &  ! [v0: $i] :  !
% 20.68/3.54    [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) |  ~ $i(v0) |  ? [v2: $i] :  ? [v3:
% 20.68/3.54        $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 &
% 20.68/3.54        remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2)))
% 20.68/3.54  
% 20.68/3.54    (l24_co)
% 20.68/3.54     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: int] :  ? [v5:
% 20.68/3.54      $i] : ( ~ (v4 = 0) & triple(v0, v1, v2) = v3 & check_cpq(v5) = 0 &
% 20.68/3.54      check_cpq(v3) = v4 & findmin_cpq_eff(v3) = v5 & $i(v5) & $i(v3) & $i(v2) &
% 20.68/3.54      $i(v1) & $i(v0))
% 20.68/3.54  
% 20.68/3.54    (l26_li4142)
% 20.68/3.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 20.68/3.55      $i] :  ! [v6: int] : (v6 = 0 |  ~ (triple(v0, v1, v2) = v3) |  ~
% 20.68/3.55      (less_than(v5, v4) = v6) |  ~ $i(v5) |  ~ $i(v4) |  ~ $i(v2) |  ~ $i(v1) | 
% 20.68/3.55      ~ $i(v0) |  ? [v7: int] : (( ~ (v7 = 0) & check_cpq(v3) = v7) | ( ~ (v7 = 0)
% 20.68/3.55          & pair_in_list(v1, v4, v5) = v7))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.68/3.55      $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : ( ~ (triple(v0, v1, v2) =
% 20.68/3.55        v3) |  ~ (pair_in_list(v1, v4, v5) = 0) |  ~ $i(v5) |  ~ $i(v4) |  ~
% 20.68/3.55      $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: int] : ((v6 = 0 & less_than(v5, v4)
% 20.68/3.55          = 0) | ( ~ (v6 = 0) & check_cpq(v3) = v6))) &  ! [v0: $i] :  ! [v1: $i]
% 20.68/3.55    :  ! [v2: $i] :  ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) |  ~ $i(v2) |  ~
% 20.68/3.55      $i(v1) |  ~ $i(v0) |  ? [v4: int] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: int]
% 20.68/3.55      :  ? [v8: int] : ($i(v6) & $i(v5) & ((v7 = 0 &  ~ (v8 = 0) &
% 20.68/3.55            pair_in_list(v1, v5, v6) = 0 & less_than(v6, v5) = v8) | (v4 = 0 &
% 20.68/3.55            check_cpq(v3) = 0))))
% 20.68/3.55  
% 20.68/3.55    (l34_l35)
% 20.68/3.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 20.68/3.55      (update_slb(v0, v1) = v2) |  ~ (pair_in_list(v0, v3, v4) = 0) |  ~ $i(v4) | 
% 20.68/3.55      ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6: $i] :  ? [v7: int]
% 20.68/3.55      :  ? [v8: int] :  ? [v9: int] : ($i(v6) & $i(v5) & ((v8 = 0 & v7 = 0 &
% 20.68/3.55            pair_in_list(v2, v5, v6) = 0 & strictly_less_than(v5, v6) = 0) | ( ~
% 20.68/3.55            (v9 = 0) & strictly_less_than(v3, v4) = v9)))) &  ! [v0: $i] :  ! [v1:
% 20.68/3.55      $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~ (update_slb(v0, v1) =
% 20.68/3.55        v2) |  ~ (strictly_less_than(v3, v4) = 0) |  ~ $i(v4) |  ~ $i(v3) |  ~
% 20.68/3.55      $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6: $i] :  ? [v7: int] :  ? [v8: int]
% 20.68/3.55      :  ? [v9: int] : ($i(v6) & $i(v5) & ((v8 = 0 & v7 = 0 & pair_in_list(v2, v5,
% 20.68/3.55              v6) = 0 & strictly_less_than(v5, v6) = 0) | ( ~ (v9 = 0) &
% 20.68/3.55            pair_in_list(v0, v3, v4) = v9))))
% 20.68/3.55  
% 20.68/3.55    (stricly_smaller_definition)
% 20.68/3.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 20.68/3.55      (strictly_less_than(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] : 
% 20.68/3.55      ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 20.68/3.55            0) | v4 = 0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 | 
% 20.68/3.55      ~ (less_than(v1, v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4:
% 20.68/3.55        any] : (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3
% 20.68/3.55            = 0) | v4 = 0))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~
% 20.68/3.55      (less_than(v1, v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4:
% 20.68/3.55        any] : (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3
% 20.68/3.55            = 0) | (v4 = 0 &  ~ (v2 = 0))))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 20.68/3.55      any] : ( ~ (less_than(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :
% 20.68/3.55       ? [v4: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & (
% 20.68/3.55          ~ (v3 = 0) | (v2 = 0 &  ~ (v4 = 0))))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 20.68/3.55      (strictly_less_than(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: int] : (
% 20.68/3.55        ~ (v2 = 0) & less_than(v1, v0) = v2 & less_than(v0, v1) = 0)) &  ! [v0:
% 20.68/3.55      $i] :  ! [v1: $i] : ( ~ (less_than(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 20.68/3.55      [v2: any] :  ? [v3: any] : (strictly_less_than(v0, v1) = v3 & less_than(v1,
% 20.68/3.55          v0) = v2 & (v3 = 0 | v2 = 0)))
% 20.68/3.55  
% 20.68/3.55    (totality)
% 20.68/3.55     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (less_than(v1, v0) =
% 20.68/3.55        v2) |  ~ $i(v1) |  ~ $i(v0) | less_than(v0, v1) = 0) &  ! [v0: $i] :  !
% 20.68/3.55    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (less_than(v0, v1) = v2) |  ~ $i(v1) | 
% 20.68/3.55      ~ $i(v0) | less_than(v1, v0) = 0)
% 20.68/3.55  
% 20.68/3.55    (function-axioms)
% 20.68/3.56     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0
% 20.68/3.56      |  ~ (triple(v4, v3, v2) = v1) |  ~ (triple(v4, v3, v2) = v0)) &  ! [v0:
% 20.68/3.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 20.68/3.56    :  ! [v4: $i] : (v1 = v0 |  ~ (pair_in_list(v4, v3, v2) = v1) |  ~
% 20.68/3.56      (pair_in_list(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :
% 20.68/3.56     ! [v3: $i] : (v1 = v0 |  ~ (remove_pqp(v3, v2) = v1) |  ~ (remove_pqp(v3, v2)
% 20.68/3.56        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0
% 20.68/3.56      |  ~ (insert_pqp(v3, v2) = v1) |  ~ (insert_pqp(v3, v2) = v0)) &  ! [v0:
% 20.68/3.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 20.68/3.56    : (v1 = v0 |  ~ (contains_cpq(v3, v2) = v1) |  ~ (contains_cpq(v3, v2) = v0))
% 20.68/3.56    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 20.68/3.56      (remove_cpq(v3, v2) = v1) |  ~ (remove_cpq(v3, v2) = v0)) &  ! [v0: $i] :  !
% 20.68/3.56    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (insert_cpq(v3, v2) = v1)
% 20.68/3.56      |  ~ (insert_cpq(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 20.68/3.56      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (succ_cpq(v3,
% 20.68/3.56          v2) = v1) |  ~ (succ_cpq(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 20.68/3.56    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (update_slb(v3, v2) = v1) |  ~
% 20.68/3.56      (update_slb(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 20.68/3.56    [v3: $i] : (v1 = v0 |  ~ (lookup_slb(v3, v2) = v1) |  ~ (lookup_slb(v3, v2) =
% 20.68/3.56        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 20.68/3.56      ~ (remove_slb(v3, v2) = v1) |  ~ (remove_slb(v3, v2) = v0)) &  ! [v0:
% 20.68/3.56      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 20.68/3.56    : (v1 = v0 |  ~ (contains_slb(v3, v2) = v1) |  ~ (contains_slb(v3, v2) = v0))
% 20.68/3.56    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 20.68/3.56      (pair(v3, v2) = v1) |  ~ (pair(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 20.68/3.56    ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (insert_slb(v3, v2) = v1) |  ~
% 20.68/3.56      (insert_slb(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 20.68/3.56      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 20.68/3.56      (strictly_less_than(v3, v2) = v1) |  ~ (strictly_less_than(v3, v2) = v0)) & 
% 20.68/3.56    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 20.68/3.56      $i] : (v1 = v0 |  ~ (less_than(v3, v2) = v1) |  ~ (less_than(v3, v2) = v0))
% 20.68/3.56    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 20.68/3.56      (removemin_cpq_res(v2) = v1) |  ~ (removemin_cpq_res(v2) = v0)) &  ! [v0:
% 20.68/3.56      $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (findmin_cpq_res(v2) = v1) |
% 20.68/3.56       ~ (findmin_cpq_res(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :
% 20.68/3.56    (v1 = v0 |  ~ (findmin_pqp_res(v2) = v1) |  ~ (findmin_pqp_res(v2) = v0)) &  !
% 20.68/3.56    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0
% 20.68/3.56      |  ~ (ok(v2) = v1) |  ~ (ok(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 20.68/3.56    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (check_cpq(v2) = v1) | 
% 20.68/3.56      ~ (check_cpq(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0
% 20.68/3.56      |  ~ (removemin_cpq_eff(v2) = v1) |  ~ (removemin_cpq_eff(v2) = v0)) &  !
% 20.68/3.56    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (findmin_cpq_eff(v2) =
% 20.68/3.56        v1) |  ~ (findmin_cpq_eff(v2) = v0)) &  ! [v0: MultipleValueBool] :  !
% 20.68/3.56    [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (isnonempty_slb(v2) =
% 20.68/3.56        v1) |  ~ (isnonempty_slb(v2) = v0))
% 20.68/3.56  
% 20.68/3.56  Further assumptions not needed in the proof:
% 20.68/3.56  --------------------------------------------
% 20.68/3.56  ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 20.68/3.56  ax31, ax32, ax33, ax34, ax35, ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44,
% 20.68/3.56  ax45, ax46, ax50, ax53, bottom_smallest, reflexivity, transitivity
% 20.68/3.56  
% 20.68/3.56  Those formulas are unsatisfiable:
% 20.68/3.56  ---------------------------------
% 20.68/3.56  
% 20.68/3.56  Begin of proof
% 20.68/3.56  | 
% 20.68/3.56  | ALPHA: (totality) implies:
% 20.68/3.56  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (less_than(v1,
% 20.68/3.56  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) | less_than(v0, v1) = 0)
% 20.68/3.56  | 
% 20.68/3.56  | ALPHA: (stricly_smaller_definition) implies:
% 20.68/3.56  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (strictly_less_than(v0, v1) = 0) |  ~
% 20.68/3.56  |          $i(v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & less_than(v1, v0)
% 20.68/3.56  |            = v2 & less_than(v0, v1) = 0))
% 20.68/3.56  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (less_than(v0, v1) = v2)
% 20.68/3.56  |          |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 20.68/3.56  |          (strictly_less_than(v0, v1) = v3 & less_than(v1, v0) = v4 & ( ~ (v3 =
% 20.68/3.56  |                0) | (v2 = 0 &  ~ (v4 = 0)))))
% 20.68/3.56  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (less_than(v1, v0) = v2)
% 20.68/3.56  |          |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 20.68/3.56  |          (strictly_less_than(v0, v1) = v3 & less_than(v0, v1) = v4 & ( ~ (v3 =
% 20.68/3.56  |                0) | (v4 = 0 &  ~ (v2 = 0)))))
% 20.68/3.56  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (less_than(v1,
% 20.68/3.56  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :
% 20.68/3.56  |          (strictly_less_than(v0, v1) = v4 & less_than(v0, v1) = v3 & ( ~ (v3 =
% 20.68/3.56  |                0) | v4 = 0)))
% 20.68/3.56  |   (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 20.68/3.56  |          (strictly_less_than(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3:
% 20.68/3.56  |            any] :  ? [v4: any] : (less_than(v1, v0) = v4 & less_than(v0, v1) =
% 20.68/3.56  |            v3 & ( ~ (v3 = 0) | v4 = 0)))
% 20.68/3.56  | 
% 20.68/3.56  | ALPHA: (ax36) implies:
% 21.07/3.56  |   (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (triple(v0, create_slb,
% 21.07/3.56  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | check_cpq(v2) = 0)
% 21.07/3.56  | 
% 21.07/3.56  | ALPHA: (ax47) implies:
% 21.07/3.57  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 21.07/3.57  |        (v1 = create_slb |  ~ (triple(v0, v1, v2) = v3) |  ~
% 21.07/3.57  |          (findmin_cpq_eff(v3) = v4) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 21.07/3.57  |          [v5: $i] :  ? [v6: any] :  ? [v7: $i] :  ? [v8: $i] :
% 21.07/3.57  |          (findmin_pqp_res(v0) = v5 & triple(v0, v7, bad) = v8 & update_slb(v1,
% 21.07/3.57  |              v5) = v7 & contains_slb(v1, v5) = v6 & $i(v8) & $i(v7) & $i(v5) &
% 21.07/3.57  |            (v8 = v4 | v6 = 0)))
% 21.07/3.57  | 
% 21.07/3.57  | ALPHA: (ax48) implies:
% 21.07/3.57  |   (9)  $i(bad)
% 21.07/3.57  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 21.07/3.57  |         (v1 = create_slb |  ~ (triple(v0, v1, v2) = v3) |  ~
% 21.07/3.57  |           (findmin_cpq_eff(v3) = v4) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 21.07/3.57  |           [v5: $i] :  ? [v6: any] :  ? [v7: $i] :  ? [v8: any] :  ? [v9: $i] :
% 21.07/3.57  |            ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, bad) = v10
% 21.07/3.57  |             & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 &
% 21.07/3.57  |             contains_slb(v1, v5) = v6 & strictly_less_than(v5, v7) = v8 &
% 21.07/3.57  |             $i(v10) & $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) |  ~ (v6 = 0) |
% 21.07/3.57  |               v10 = v4)))
% 21.07/3.57  | 
% 21.07/3.57  | ALPHA: (ax49) implies:
% 21.07/3.57  |   (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 21.07/3.57  |         (v1 = create_slb |  ~ (triple(v0, v1, v2) = v3) |  ~
% 21.07/3.57  |           (findmin_cpq_eff(v3) = v4) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 21.07/3.57  |           [v5: $i] :  ? [v6: any] :  ? [v7: $i] :  ? [v8: any] :  ? [v9: $i] :
% 21.07/3.57  |            ? [v10: $i] : (findmin_pqp_res(v0) = v5 & triple(v0, v9, v2) = v10
% 21.07/3.57  |             & update_slb(v1, v5) = v9 & lookup_slb(v1, v5) = v7 &
% 21.07/3.57  |             contains_slb(v1, v5) = v6 & less_than(v7, v5) = v8 & $i(v10) &
% 21.07/3.57  |             $i(v9) & $i(v7) & $i(v5) & ( ~ (v8 = 0) |  ~ (v6 = 0) | v10 =
% 21.07/3.57  |               v4)))
% 21.07/3.57  |   (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : 
% 21.07/3.57  |         ! [v5: $i] : (v1 = create_slb |  ~ (findmin_pqp_res(v0) = v3) |  ~
% 21.07/3.57  |           (triple(v0, v4, v2) = v5) |  ~ (update_slb(v1, v3) = v4) |  ~ $i(v2)
% 21.07/3.57  |           |  ~ $i(v1) |  ~ $i(v0) |  ? [v6: any] :  ? [v7: $i] :  ? [v8: any]
% 21.07/3.57  |           :  ? [v9: $i] :  ? [v10: $i] : (triple(v0, v1, v2) = v9 &
% 21.07/3.57  |             findmin_cpq_eff(v9) = v10 & lookup_slb(v1, v3) = v7 &
% 21.07/3.57  |             contains_slb(v1, v3) = v6 & less_than(v7, v3) = v8 & $i(v10) &
% 21.07/3.57  |             $i(v9) & $i(v7) & ( ~ (v8 = 0) |  ~ (v6 = 0) | v10 = v5)))
% 21.07/3.57  | 
% 21.07/3.57  | ALPHA: (ax51) implies:
% 21.07/3.57  |   (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 21.07/3.57  |         (v1 = create_slb |  ~ (findmin_cpq_res(v3) = v4) |  ~ (triple(v0, v1,
% 21.07/3.57  |               v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 21.07/3.57  |           (findmin_pqp_res(v0) = v4 & $i(v4)))
% 21.07/3.57  | 
% 21.07/3.57  | ALPHA: (ax52) implies:
% 21.07/3.57  |   (14)   ! [v0: $i] :  ! [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) |  ~ $i(v0)
% 21.07/3.57  |           |  ? [v2: $i] :  ? [v3: $i] : (findmin_cpq_res(v0) = v3 &
% 21.07/3.57  |             removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2 & $i(v3) &
% 21.07/3.57  |             $i(v2)))
% 21.07/3.57  | 
% 21.07/3.57  | ALPHA: (l26_li4142) implies:
% 21.07/3.57  |   (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 21.07/3.57  |           (triple(v0, v1, v2) = v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ?
% 21.07/3.57  |           [v4: int] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: int] :  ? [v8: int]
% 21.07/3.57  |           : ($i(v6) & $i(v5) & ((v7 = 0 &  ~ (v8 = 0) & pair_in_list(v1, v5,
% 21.07/3.57  |                   v6) = 0 & less_than(v6, v5) = v8) | (v4 = 0 & check_cpq(v3)
% 21.07/3.57  |                 = 0))))
% 21.07/3.57  |   (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : 
% 21.07/3.57  |         ! [v5: $i] : ( ~ (triple(v0, v1, v2) = v3) |  ~ (pair_in_list(v1, v4,
% 21.07/3.57  |               v5) = 0) |  ~ $i(v5) |  ~ $i(v4) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 21.07/3.57  |           $i(v0) |  ? [v6: int] : ((v6 = 0 & less_than(v5, v4) = 0) | ( ~ (v6
% 21.07/3.57  |                 = 0) & check_cpq(v3) = v6)))
% 21.07/3.57  | 
% 21.07/3.57  | ALPHA: (l34_l35) implies:
% 21.07/3.57  |   (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 21.07/3.57  |         ( ~ (update_slb(v0, v1) = v2) |  ~ (strictly_less_than(v3, v4) = 0) | 
% 21.07/3.57  |           ~ $i(v4) |  ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6:
% 21.07/3.57  |             $i] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] : ($i(v6) &
% 21.07/3.57  |             $i(v5) & ((v8 = 0 & v7 = 0 & pair_in_list(v2, v5, v6) = 0 &
% 21.07/3.57  |                 strictly_less_than(v5, v6) = 0) | ( ~ (v9 = 0) &
% 21.07/3.57  |                 pair_in_list(v0, v3, v4) = v9))))
% 21.07/3.57  |   (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 21.07/3.58  |         ( ~ (update_slb(v0, v1) = v2) |  ~ (pair_in_list(v0, v3, v4) = 0) |  ~
% 21.07/3.58  |           $i(v4) |  ~ $i(v3) |  ~ $i(v1) |  ~ $i(v0) |  ? [v5: $i] :  ? [v6:
% 21.07/3.58  |             $i] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] : ($i(v6) &
% 21.07/3.58  |             $i(v5) & ((v8 = 0 & v7 = 0 & pair_in_list(v2, v5, v6) = 0 &
% 21.07/3.58  |                 strictly_less_than(v5, v6) = 0) | ( ~ (v9 = 0) &
% 21.07/3.58  |                 strictly_less_than(v3, v4) = v9))))
% 21.07/3.58  | 
% 21.07/3.58  | ALPHA: (function-axioms) implies:
% 21.07/3.58  |   (19)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.07/3.58  |         : (v1 = v0 |  ~ (check_cpq(v2) = v1) |  ~ (check_cpq(v2) = v0))
% 21.07/3.58  |   (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 21.07/3.58  |           (findmin_pqp_res(v2) = v1) |  ~ (findmin_pqp_res(v2) = v0))
% 21.07/3.58  |   (21)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.07/3.58  |         :  ! [v3: $i] : (v1 = v0 |  ~ (less_than(v3, v2) = v1) |  ~
% 21.07/3.58  |           (less_than(v3, v2) = v0))
% 21.07/3.58  |   (22)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.07/3.58  |         :  ! [v3: $i] : (v1 = v0 |  ~ (strictly_less_than(v3, v2) = v1) |  ~
% 21.07/3.58  |           (strictly_less_than(v3, v2) = v0))
% 21.07/3.58  |   (23)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.07/3.58  |         :  ! [v3: $i] : (v1 = v0 |  ~ (contains_slb(v3, v2) = v1) |  ~
% 21.07/3.58  |           (contains_slb(v3, v2) = v0))
% 21.07/3.58  |   (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 21.07/3.58  |           (lookup_slb(v3, v2) = v1) |  ~ (lookup_slb(v3, v2) = v0))
% 21.07/3.58  |   (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 21.07/3.58  |           (update_slb(v3, v2) = v1) |  ~ (update_slb(v3, v2) = v0))
% 21.07/3.58  |   (26)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i]
% 21.07/3.58  |         :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (pair_in_list(v4, v3, v2)
% 21.07/3.58  |             = v1) |  ~ (pair_in_list(v4, v3, v2) = v0))
% 21.07/3.58  |   (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 21.07/3.58  |         (v1 = v0 |  ~ (triple(v4, v3, v2) = v1) |  ~ (triple(v4, v3, v2) =
% 21.07/3.58  |             v0))
% 21.07/3.58  | 
% 21.14/3.58  | DELTA: instantiating (l24_co) with fresh symbols all_48_0, all_48_1, all_48_2,
% 21.14/3.58  |        all_48_3, all_48_4, all_48_5 gives:
% 21.14/3.58  |   (28)   ~ (all_48_1 = 0) & triple(all_48_5, all_48_4, all_48_3) = all_48_2 &
% 21.14/3.58  |         check_cpq(all_48_0) = 0 & check_cpq(all_48_2) = all_48_1 &
% 21.14/3.58  |         findmin_cpq_eff(all_48_2) = all_48_0 & $i(all_48_0) & $i(all_48_2) &
% 21.14/3.58  |         $i(all_48_3) & $i(all_48_4) & $i(all_48_5)
% 21.14/3.58  | 
% 21.14/3.58  | ALPHA: (28) implies:
% 21.14/3.58  |   (29)   ~ (all_48_1 = 0)
% 21.14/3.58  |   (30)  $i(all_48_5)
% 21.14/3.58  |   (31)  $i(all_48_4)
% 21.14/3.58  |   (32)  $i(all_48_3)
% 21.14/3.58  |   (33)  $i(all_48_2)
% 21.14/3.58  |   (34)  findmin_cpq_eff(all_48_2) = all_48_0
% 21.14/3.58  |   (35)  check_cpq(all_48_2) = all_48_1
% 21.14/3.58  |   (36)  check_cpq(all_48_0) = 0
% 21.14/3.58  |   (37)  triple(all_48_5, all_48_4, all_48_3) = all_48_2
% 21.14/3.58  | 
% 21.14/3.58  | GROUND_INST: instantiating (14) with all_48_2, all_48_0, simplifying with
% 21.14/3.58  |              (33), (34) gives:
% 21.14/3.58  |   (38)   ? [v0: $i] :  ? [v1: $i] : (findmin_cpq_res(all_48_2) = v1 &
% 21.14/3.58  |           removemin_cpq_eff(all_48_2) = v0 & remove_cpq(all_48_0, v1) = v0 &
% 21.14/3.58  |           $i(v1) & $i(v0))
% 21.14/3.58  | 
% 21.14/3.58  | GROUND_INST: instantiating (11) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.14/3.58  |              all_48_0, simplifying with (30), (31), (32), (34), (37) gives:
% 21.14/3.58  |   (39)  all_48_4 = create_slb |  ? [v0: $i] :  ? [v1: any] :  ? [v2: $i] :  ?
% 21.14/3.58  |         [v3: any] :  ? [v4: $i] :  ? [v5: $i] : (findmin_pqp_res(all_48_5) =
% 21.14/3.58  |           v0 & triple(all_48_5, v4, all_48_3) = v5 & update_slb(all_48_4, v0)
% 21.14/3.58  |           = v4 & lookup_slb(all_48_4, v0) = v2 & contains_slb(all_48_4, v0) =
% 21.14/3.58  |           v1 & less_than(v2, v0) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0) & (
% 21.14/3.58  |             ~ (v3 = 0) |  ~ (v1 = 0) | v5 = all_48_0))
% 21.14/3.58  | 
% 21.14/3.58  | GROUND_INST: instantiating (10) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.14/3.58  |              all_48_0, simplifying with (30), (31), (32), (34), (37) gives:
% 21.14/3.59  |   (40)  all_48_4 = create_slb |  ? [v0: $i] :  ? [v1: any] :  ? [v2: $i] :  ?
% 21.14/3.59  |         [v3: any] :  ? [v4: $i] :  ? [v5: $i] : (findmin_pqp_res(all_48_5) =
% 21.14/3.59  |           v0 & triple(all_48_5, v4, bad) = v5 & update_slb(all_48_4, v0) = v4
% 21.14/3.59  |           & lookup_slb(all_48_4, v0) = v2 & contains_slb(all_48_4, v0) = v1 &
% 21.14/3.59  |           strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v0)
% 21.14/3.59  |           & ( ~ (v3 = 0) |  ~ (v1 = 0) | v5 = all_48_0))
% 21.14/3.59  | 
% 21.14/3.59  | GROUND_INST: instantiating (8) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.14/3.59  |              all_48_0, simplifying with (30), (31), (32), (34), (37) gives:
% 21.14/3.59  |   (41)  all_48_4 = create_slb |  ? [v0: $i] :  ? [v1: any] :  ? [v2: $i] :  ?
% 21.14/3.59  |         [v3: $i] : (findmin_pqp_res(all_48_5) = v0 & triple(all_48_5, v2, bad)
% 21.14/3.59  |           = v3 & update_slb(all_48_4, v0) = v2 & contains_slb(all_48_4, v0) =
% 21.14/3.59  |           v1 & $i(v3) & $i(v2) & $i(v0) & (v3 = all_48_0 | v1 = 0))
% 21.14/3.59  | 
% 21.14/3.59  | GROUND_INST: instantiating (15) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.14/3.59  |              simplifying with (30), (31), (32), (37) gives:
% 21.14/3.59  |   (42)   ? [v0: int] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] :  ? [v4: int]
% 21.14/3.59  |         : ($i(v2) & $i(v1) & ((v3 = 0 &  ~ (v4 = 0) & pair_in_list(all_48_4,
% 21.14/3.59  |                 v1, v2) = 0 & less_than(v2, v1) = v4) | (v0 = 0 &
% 21.14/3.59  |               check_cpq(all_48_2) = 0)))
% 21.14/3.59  | 
% 21.14/3.59  | DELTA: instantiating (38) with fresh symbols all_55_0, all_55_1 gives:
% 21.14/3.59  |   (43)  findmin_cpq_res(all_48_2) = all_55_0 & removemin_cpq_eff(all_48_2) =
% 21.14/3.59  |         all_55_1 & remove_cpq(all_48_0, all_55_0) = all_55_1 & $i(all_55_0) &
% 21.14/3.59  |         $i(all_55_1)
% 21.14/3.59  | 
% 21.14/3.59  | ALPHA: (43) implies:
% 21.14/3.59  |   (44)  findmin_cpq_res(all_48_2) = all_55_0
% 21.14/3.59  | 
% 21.14/3.59  | DELTA: instantiating (42) with fresh symbols all_57_0, all_57_1, all_57_2,
% 21.14/3.59  |        all_57_3, all_57_4 gives:
% 21.14/3.59  |   (45)  $i(all_57_2) & $i(all_57_3) & ((all_57_1 = 0 &  ~ (all_57_0 = 0) &
% 21.14/3.59  |             pair_in_list(all_48_4, all_57_3, all_57_2) = 0 &
% 21.14/3.59  |             less_than(all_57_2, all_57_3) = all_57_0) | (all_57_4 = 0 &
% 21.14/3.59  |             check_cpq(all_48_2) = 0))
% 21.14/3.59  | 
% 21.14/3.59  | ALPHA: (45) implies:
% 21.14/3.59  |   (46)  $i(all_57_3)
% 21.14/3.59  |   (47)  $i(all_57_2)
% 21.14/3.59  |   (48)  (all_57_1 = 0 &  ~ (all_57_0 = 0) & pair_in_list(all_48_4, all_57_3,
% 21.14/3.59  |             all_57_2) = 0 & less_than(all_57_2, all_57_3) = all_57_0) |
% 21.14/3.59  |         (all_57_4 = 0 & check_cpq(all_48_2) = 0)
% 21.14/3.59  | 
% 21.14/3.59  | BETA: splitting (48) gives:
% 21.14/3.59  | 
% 21.14/3.59  | Case 1:
% 21.14/3.59  | | 
% 21.14/3.59  | |   (49)  all_57_1 = 0 &  ~ (all_57_0 = 0) & pair_in_list(all_48_4, all_57_3,
% 21.14/3.59  | |           all_57_2) = 0 & less_than(all_57_2, all_57_3) = all_57_0
% 21.14/3.59  | | 
% 21.14/3.59  | | ALPHA: (49) implies:
% 21.14/3.59  | |   (50)   ~ (all_57_0 = 0)
% 21.14/3.59  | |   (51)  less_than(all_57_2, all_57_3) = all_57_0
% 21.14/3.59  | |   (52)  pair_in_list(all_48_4, all_57_3, all_57_2) = 0
% 21.14/3.59  | | 
% 21.14/3.59  | | GROUND_INST: instantiating (1) with all_57_3, all_57_2, all_57_0,
% 21.14/3.59  | |              simplifying with (46), (47), (51) gives:
% 21.14/3.59  | |   (53)  all_57_0 = 0 | less_than(all_57_3, all_57_2) = 0
% 21.14/3.59  | | 
% 21.14/3.59  | | GROUND_INST: instantiating (5) with all_57_3, all_57_2, all_57_0,
% 21.14/3.59  | |              simplifying with (46), (47), (51) gives:
% 21.14/3.59  | |   (54)  all_57_0 = 0 |  ? [v0: any] :  ? [v1: any] :
% 21.14/3.59  | |         (strictly_less_than(all_57_3, all_57_2) = v1 & less_than(all_57_3,
% 21.14/3.59  | |             all_57_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 21.14/3.59  | | 
% 21.14/3.59  | | GROUND_INST: instantiating (4) with all_57_3, all_57_2, all_57_0,
% 21.14/3.59  | |              simplifying with (46), (47), (51) gives:
% 21.14/3.59  | |   (55)   ? [v0: any] :  ? [v1: any] : (strictly_less_than(all_57_3,
% 21.14/3.59  | |             all_57_2) = v0 & less_than(all_57_3, all_57_2) = v1 & ( ~ (v0 =
% 21.14/3.59  | |               0) | (v1 = 0 &  ~ (all_57_0 = 0))))
% 21.14/3.59  | | 
% 21.14/3.59  | | GROUND_INST: instantiating (3) with all_57_2, all_57_3, all_57_0,
% 21.14/3.59  | |              simplifying with (46), (47), (51) gives:
% 21.14/3.59  | |   (56)   ? [v0: any] :  ? [v1: any] : (strictly_less_than(all_57_2,
% 21.14/3.59  | |             all_57_3) = v0 & less_than(all_57_3, all_57_2) = v1 & ( ~ (v0 =
% 21.14/3.59  | |               0) | (all_57_0 = 0 &  ~ (v1 = 0))))
% 21.14/3.59  | | 
% 21.14/3.59  | | GROUND_INST: instantiating (13) with all_48_5, all_48_4, all_48_3, all_48_2,
% 21.14/3.59  | |              all_55_0, simplifying with (30), (31), (32), (37), (44) gives:
% 21.14/3.59  | |   (57)  all_48_4 = create_slb | (findmin_pqp_res(all_48_5) = all_55_0 &
% 21.14/3.59  | |           $i(all_55_0))
% 21.14/3.59  | | 
% 21.14/3.59  | | DELTA: instantiating (56) with fresh symbols all_69_0, all_69_1 gives:
% 21.14/3.59  | |   (58)  strictly_less_than(all_57_2, all_57_3) = all_69_1 &
% 21.14/3.59  | |         less_than(all_57_3, all_57_2) = all_69_0 & ( ~ (all_69_1 = 0) |
% 21.14/3.59  | |           (all_57_0 = 0 &  ~ (all_69_0 = 0)))
% 21.14/3.59  | | 
% 21.14/3.59  | | ALPHA: (58) implies:
% 21.14/3.59  | |   (59)  less_than(all_57_3, all_57_2) = all_69_0
% 21.14/3.59  | | 
% 21.14/3.59  | | DELTA: instantiating (55) with fresh symbols all_71_0, all_71_1 gives:
% 21.14/3.59  | |   (60)  strictly_less_than(all_57_3, all_57_2) = all_71_1 &
% 21.14/3.59  | |         less_than(all_57_3, all_57_2) = all_71_0 & ( ~ (all_71_1 = 0) |
% 21.14/3.59  | |           (all_71_0 = 0 &  ~ (all_57_0 = 0)))
% 21.14/3.59  | | 
% 21.14/3.59  | | ALPHA: (60) implies:
% 21.14/3.60  | |   (61)  less_than(all_57_3, all_57_2) = all_71_0
% 21.14/3.60  | |   (62)  strictly_less_than(all_57_3, all_57_2) = all_71_1
% 21.14/3.60  | | 
% 21.14/3.60  | | BETA: splitting (53) gives:
% 21.14/3.60  | | 
% 21.14/3.60  | | Case 1:
% 21.14/3.60  | | | 
% 21.14/3.60  | | |   (63)  less_than(all_57_3, all_57_2) = 0
% 21.14/3.60  | | | 
% 21.14/3.60  | | | GROUND_INST: instantiating (21) with all_69_0, all_71_0, all_57_2,
% 21.14/3.60  | | |              all_57_3, simplifying with (59), (61) gives:
% 21.14/3.60  | | |   (64)  all_71_0 = all_69_0
% 21.14/3.60  | | | 
% 21.14/3.60  | | | GROUND_INST: instantiating (21) with 0, all_71_0, all_57_2, all_57_3,
% 21.14/3.60  | | |              simplifying with (61), (63) gives:
% 21.14/3.60  | | |   (65)  all_71_0 = 0
% 21.14/3.60  | | | 
% 21.14/3.60  | | | COMBINE_EQS: (64), (65) imply:
% 21.14/3.60  | | |   (66)  all_69_0 = 0
% 21.14/3.60  | | | 
% 21.14/3.60  | | | SIMP: (66) implies:
% 21.14/3.60  | | |   (67)  all_69_0 = 0
% 21.14/3.60  | | | 
% 21.14/3.60  | | | BETA: splitting (54) gives:
% 21.14/3.60  | | | 
% 21.14/3.60  | | | Case 1:
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | |   (68)  all_57_0 = 0
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | REDUCE: (50), (68) imply:
% 21.14/3.60  | | | |   (69)  $false
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | CLOSE: (69) is inconsistent.
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | Case 2:
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | |   (70)   ? [v0: any] :  ? [v1: any] : (strictly_less_than(all_57_3,
% 21.14/3.60  | | | |             all_57_2) = v1 & less_than(all_57_3, all_57_2) = v0 & ( ~
% 21.14/3.60  | | | |             (v0 = 0) | v1 = 0))
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | DELTA: instantiating (70) with fresh symbols all_89_0, all_89_1 gives:
% 21.14/3.60  | | | |   (71)  strictly_less_than(all_57_3, all_57_2) = all_89_0 &
% 21.14/3.60  | | | |         less_than(all_57_3, all_57_2) = all_89_1 & ( ~ (all_89_1 = 0) |
% 21.14/3.60  | | | |           all_89_0 = 0)
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | ALPHA: (71) implies:
% 21.14/3.60  | | | |   (72)  less_than(all_57_3, all_57_2) = all_89_1
% 21.14/3.60  | | | |   (73)  strictly_less_than(all_57_3, all_57_2) = all_89_0
% 21.14/3.60  | | | |   (74)   ~ (all_89_1 = 0) | all_89_0 = 0
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | GROUND_INST: instantiating (21) with 0, all_89_1, all_57_2, all_57_3,
% 21.14/3.60  | | | |              simplifying with (63), (72) gives:
% 21.14/3.60  | | | |   (75)  all_89_1 = 0
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | GROUND_INST: instantiating (22) with all_71_1, all_89_0, all_57_2,
% 21.14/3.60  | | | |              all_57_3, simplifying with (62), (73) gives:
% 21.14/3.60  | | | |   (76)  all_89_0 = all_71_1
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | BETA: splitting (74) gives:
% 21.14/3.60  | | | | 
% 21.14/3.60  | | | | Case 1:
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | |   (77)   ~ (all_89_1 = 0)
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | | REDUCE: (75), (77) imply:
% 21.14/3.60  | | | | |   (78)  $false
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | | CLOSE: (78) is inconsistent.
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | Case 2:
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | |   (79)  all_89_0 = 0
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | | COMBINE_EQS: (76), (79) imply:
% 21.14/3.60  | | | | |   (80)  all_71_1 = 0
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | | REDUCE: (62), (80) imply:
% 21.14/3.60  | | | | |   (81)  strictly_less_than(all_57_3, all_57_2) = 0
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | | BETA: splitting (39) gives:
% 21.14/3.60  | | | | | 
% 21.14/3.60  | | | | | Case 1:
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | |   (82)  all_48_4 = create_slb
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | REDUCE: (37), (82) imply:
% 21.14/3.60  | | | | | |   (83)  triple(all_48_5, create_slb, all_48_3) = all_48_2
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | GROUND_INST: instantiating (7) with all_48_5, all_48_3, all_48_2,
% 21.14/3.60  | | | | | |              simplifying with (30), (32), (83) gives:
% 21.14/3.60  | | | | | |   (84)  check_cpq(all_48_2) = 0
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | GROUND_INST: instantiating (19) with all_48_1, 0, all_48_2,
% 21.14/3.60  | | | | | |              simplifying with (35), (84) gives:
% 21.14/3.60  | | | | | |   (85)  all_48_1 = 0
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | REDUCE: (29), (85) imply:
% 21.14/3.60  | | | | | |   (86)  $false
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | CLOSE: (86) is inconsistent.
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | Case 2:
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | |   (87)   ~ (all_48_4 = create_slb)
% 21.14/3.60  | | | | | |   (88)   ? [v0: $i] :  ? [v1: any] :  ? [v2: $i] :  ? [v3: any] :  ?
% 21.14/3.60  | | | | | |         [v4: $i] :  ? [v5: $i] : (findmin_pqp_res(all_48_5) = v0 &
% 21.14/3.60  | | | | | |           triple(all_48_5, v4, all_48_3) = v5 & update_slb(all_48_4,
% 21.14/3.60  | | | | | |             v0) = v4 & lookup_slb(all_48_4, v0) = v2 &
% 21.14/3.60  | | | | | |           contains_slb(all_48_4, v0) = v1 & less_than(v2, v0) = v3 &
% 21.14/3.60  | | | | | |           $i(v5) & $i(v4) & $i(v2) & $i(v0) & ( ~ (v3 = 0) |  ~ (v1
% 21.14/3.60  | | | | | |               = 0) | v5 = all_48_0))
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | DELTA: instantiating (88) with fresh symbols all_106_0, all_106_1,
% 21.14/3.60  | | | | | |        all_106_2, all_106_3, all_106_4, all_106_5 gives:
% 21.14/3.60  | | | | | |   (89)  findmin_pqp_res(all_48_5) = all_106_5 & triple(all_48_5,
% 21.14/3.60  | | | | | |           all_106_1, all_48_3) = all_106_0 & update_slb(all_48_4,
% 21.14/3.60  | | | | | |           all_106_5) = all_106_1 & lookup_slb(all_48_4, all_106_5) =
% 21.14/3.60  | | | | | |         all_106_3 & contains_slb(all_48_4, all_106_5) = all_106_4 &
% 21.14/3.60  | | | | | |         less_than(all_106_3, all_106_5) = all_106_2 & $i(all_106_0)
% 21.14/3.60  | | | | | |         & $i(all_106_1) & $i(all_106_3) & $i(all_106_5) & ( ~
% 21.14/3.60  | | | | | |           (all_106_2 = 0) |  ~ (all_106_4 = 0) | all_106_0 =
% 21.14/3.60  | | | | | |           all_48_0)
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | ALPHA: (89) implies:
% 21.14/3.60  | | | | | |   (90)  $i(all_106_5)
% 21.14/3.60  | | | | | |   (91)  less_than(all_106_3, all_106_5) = all_106_2
% 21.14/3.60  | | | | | |   (92)  contains_slb(all_48_4, all_106_5) = all_106_4
% 21.14/3.60  | | | | | |   (93)  lookup_slb(all_48_4, all_106_5) = all_106_3
% 21.14/3.60  | | | | | |   (94)  update_slb(all_48_4, all_106_5) = all_106_1
% 21.14/3.60  | | | | | |   (95)  triple(all_48_5, all_106_1, all_48_3) = all_106_0
% 21.14/3.60  | | | | | |   (96)  findmin_pqp_res(all_48_5) = all_106_5
% 21.14/3.60  | | | | | |   (97)   ~ (all_106_2 = 0) |  ~ (all_106_4 = 0) | all_106_0 =
% 21.14/3.60  | | | | | |         all_48_0
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | BETA: splitting (57) gives:
% 21.14/3.60  | | | | | | 
% 21.14/3.60  | | | | | | Case 1:
% 21.14/3.60  | | | | | | | 
% 21.14/3.60  | | | | | | |   (98)  all_48_4 = create_slb
% 21.14/3.60  | | | | | | | 
% 21.14/3.60  | | | | | | | REDUCE: (87), (98) imply:
% 21.14/3.60  | | | | | | |   (99)  $false
% 21.14/3.60  | | | | | | | 
% 21.14/3.60  | | | | | | | CLOSE: (99) is inconsistent.
% 21.14/3.60  | | | | | | | 
% 21.14/3.60  | | | | | | Case 2:
% 21.14/3.60  | | | | | | | 
% 21.14/3.60  | | | | | | |   (100)  findmin_pqp_res(all_48_5) = all_55_0 & $i(all_55_0)
% 21.14/3.60  | | | | | | | 
% 21.14/3.60  | | | | | | | ALPHA: (100) implies:
% 21.14/3.61  | | | | | | |   (101)  findmin_pqp_res(all_48_5) = all_55_0
% 21.14/3.61  | | | | | | | 
% 21.14/3.61  | | | | | | | BETA: splitting (41) gives:
% 21.14/3.61  | | | | | | | 
% 21.14/3.61  | | | | | | | Case 1:
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | |   (102)  all_48_4 = create_slb
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | | REDUCE: (87), (102) imply:
% 21.14/3.61  | | | | | | | |   (103)  $false
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | | CLOSE: (103) is inconsistent.
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | Case 2:
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | |   (104)   ? [v0: $i] :  ? [v1: any] :  ? [v2: $i] :  ? [v3: $i]
% 21.14/3.61  | | | | | | | |          : (findmin_pqp_res(all_48_5) = v0 & triple(all_48_5,
% 21.14/3.61  | | | | | | | |              v2, bad) = v3 & update_slb(all_48_4, v0) = v2 &
% 21.14/3.61  | | | | | | | |            contains_slb(all_48_4, v0) = v1 & $i(v3) & $i(v2) &
% 21.14/3.61  | | | | | | | |            $i(v0) & (v3 = all_48_0 | v1 = 0))
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | | DELTA: instantiating (104) with fresh symbols all_115_0,
% 21.14/3.61  | | | | | | | |        all_115_1, all_115_2, all_115_3 gives:
% 21.14/3.61  | | | | | | | |   (105)  findmin_pqp_res(all_48_5) = all_115_3 &
% 21.14/3.61  | | | | | | | |          triple(all_48_5, all_115_1, bad) = all_115_0 &
% 21.14/3.61  | | | | | | | |          update_slb(all_48_4, all_115_3) = all_115_1 &
% 21.14/3.61  | | | | | | | |          contains_slb(all_48_4, all_115_3) = all_115_2 &
% 21.14/3.61  | | | | | | | |          $i(all_115_0) & $i(all_115_1) & $i(all_115_3) &
% 21.14/3.61  | | | | | | | |          (all_115_0 = all_48_0 | all_115_2 = 0)
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | | ALPHA: (105) implies:
% 21.14/3.61  | | | | | | | |   (106)  $i(all_115_1)
% 21.14/3.61  | | | | | | | |   (107)  contains_slb(all_48_4, all_115_3) = all_115_2
% 21.14/3.61  | | | | | | | |   (108)  update_slb(all_48_4, all_115_3) = all_115_1
% 21.14/3.61  | | | | | | | |   (109)  triple(all_48_5, all_115_1, bad) = all_115_0
% 21.14/3.61  | | | | | | | |   (110)  findmin_pqp_res(all_48_5) = all_115_3
% 21.14/3.61  | | | | | | | |   (111)  all_115_0 = all_48_0 | all_115_2 = 0
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | | BETA: splitting (40) gives:
% 21.14/3.61  | | | | | | | | 
% 21.14/3.61  | | | | | | | | Case 1:
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | |   (112)  all_48_4 = create_slb
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (87), (112) imply:
% 21.14/3.61  | | | | | | | | |   (113)  $false
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | CLOSE: (113) is inconsistent.
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | Case 2:
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | |   (114)   ? [v0: $i] :  ? [v1: any] :  ? [v2: $i] :  ? [v3:
% 21.14/3.61  | | | | | | | | |            any] :  ? [v4: $i] :  ? [v5: $i] :
% 21.14/3.61  | | | | | | | | |          (findmin_pqp_res(all_48_5) = v0 & triple(all_48_5,
% 21.14/3.61  | | | | | | | | |              v4, bad) = v5 & update_slb(all_48_4, v0) = v4 &
% 21.14/3.61  | | | | | | | | |            lookup_slb(all_48_4, v0) = v2 &
% 21.14/3.61  | | | | | | | | |            contains_slb(all_48_4, v0) = v1 &
% 21.14/3.61  | | | | | | | | |            strictly_less_than(v0, v2) = v3 & $i(v5) & $i(v4) &
% 21.14/3.61  | | | | | | | | |            $i(v2) & $i(v0) & ( ~ (v3 = 0) |  ~ (v1 = 0) | v5 =
% 21.14/3.61  | | | | | | | | |              all_48_0))
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | DELTA: instantiating (114) with fresh symbols all_120_0,
% 21.14/3.61  | | | | | | | | |        all_120_1, all_120_2, all_120_3, all_120_4, all_120_5
% 21.14/3.61  | | | | | | | | |        gives:
% 21.14/3.61  | | | | | | | | |   (115)  findmin_pqp_res(all_48_5) = all_120_5 &
% 21.14/3.61  | | | | | | | | |          triple(all_48_5, all_120_1, bad) = all_120_0 &
% 21.14/3.61  | | | | | | | | |          update_slb(all_48_4, all_120_5) = all_120_1 &
% 21.14/3.61  | | | | | | | | |          lookup_slb(all_48_4, all_120_5) = all_120_3 &
% 21.14/3.61  | | | | | | | | |          contains_slb(all_48_4, all_120_5) = all_120_4 &
% 21.14/3.61  | | | | | | | | |          strictly_less_than(all_120_5, all_120_3) = all_120_2
% 21.14/3.61  | | | | | | | | |          & $i(all_120_0) & $i(all_120_1) & $i(all_120_3) &
% 21.14/3.61  | | | | | | | | |          $i(all_120_5) & ( ~ (all_120_2 = 0) |  ~ (all_120_4 =
% 21.14/3.61  | | | | | | | | |              0) | all_120_0 = all_48_0)
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | ALPHA: (115) implies:
% 21.14/3.61  | | | | | | | | |   (116)  $i(all_120_3)
% 21.14/3.61  | | | | | | | | |   (117)  strictly_less_than(all_120_5, all_120_3) = all_120_2
% 21.14/3.61  | | | | | | | | |   (118)  contains_slb(all_48_4, all_120_5) = all_120_4
% 21.14/3.61  | | | | | | | | |   (119)  lookup_slb(all_48_4, all_120_5) = all_120_3
% 21.14/3.61  | | | | | | | | |   (120)  update_slb(all_48_4, all_120_5) = all_120_1
% 21.14/3.61  | | | | | | | | |   (121)  triple(all_48_5, all_120_1, bad) = all_120_0
% 21.14/3.61  | | | | | | | | |   (122)  findmin_pqp_res(all_48_5) = all_120_5
% 21.14/3.61  | | | | | | | | |   (123)   ~ (all_120_2 = 0) |  ~ (all_120_4 = 0) | all_120_0 =
% 21.14/3.61  | | | | | | | | |          all_48_0
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (20) with all_106_5, all_115_3,
% 21.14/3.61  | | | | | | | | |              all_48_5, simplifying with (96), (110) gives:
% 21.14/3.61  | | | | | | | | |   (124)  all_115_3 = all_106_5
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (20) with all_115_3, all_120_5,
% 21.14/3.61  | | | | | | | | |              all_48_5, simplifying with (110), (122) gives:
% 21.14/3.61  | | | | | | | | |   (125)  all_120_5 = all_115_3
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (20) with all_55_0, all_120_5,
% 21.14/3.61  | | | | | | | | |              all_48_5, simplifying with (101), (122) gives:
% 21.14/3.61  | | | | | | | | |   (126)  all_120_5 = all_55_0
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | COMBINE_EQS: (125), (126) imply:
% 21.14/3.61  | | | | | | | | |   (127)  all_115_3 = all_55_0
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | SIMP: (127) implies:
% 21.14/3.61  | | | | | | | | |   (128)  all_115_3 = all_55_0
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | COMBINE_EQS: (124), (128) imply:
% 21.14/3.61  | | | | | | | | |   (129)  all_106_5 = all_55_0
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (120), (126) imply:
% 21.14/3.61  | | | | | | | | |   (130)  update_slb(all_48_4, all_55_0) = all_120_1
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (108), (128) imply:
% 21.14/3.61  | | | | | | | | |   (131)  update_slb(all_48_4, all_55_0) = all_115_1
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (94), (129) imply:
% 21.14/3.61  | | | | | | | | |   (132)  update_slb(all_48_4, all_55_0) = all_106_1
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (119), (126) imply:
% 21.14/3.61  | | | | | | | | |   (133)  lookup_slb(all_48_4, all_55_0) = all_120_3
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (93), (129) imply:
% 21.14/3.61  | | | | | | | | |   (134)  lookup_slb(all_48_4, all_55_0) = all_106_3
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (118), (126) imply:
% 21.14/3.61  | | | | | | | | |   (135)  contains_slb(all_48_4, all_55_0) = all_120_4
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (107), (128) imply:
% 21.14/3.61  | | | | | | | | |   (136)  contains_slb(all_48_4, all_55_0) = all_115_2
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (92), (129) imply:
% 21.14/3.61  | | | | | | | | |   (137)  contains_slb(all_48_4, all_55_0) = all_106_4
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (117), (126) imply:
% 21.14/3.61  | | | | | | | | |   (138)  strictly_less_than(all_55_0, all_120_3) = all_120_2
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (91), (129) imply:
% 21.14/3.61  | | | | | | | | |   (139)  less_than(all_106_3, all_55_0) = all_106_2
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (90), (129) imply:
% 21.14/3.61  | | | | | | | | |   (140)  $i(all_55_0)
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (23) with all_115_2, all_120_4,
% 21.14/3.61  | | | | | | | | |              all_55_0, all_48_4, simplifying with (135), (136)
% 21.14/3.61  | | | | | | | | |              gives:
% 21.14/3.61  | | | | | | | | |   (141)  all_120_4 = all_115_2
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (23) with all_106_4, all_120_4,
% 21.14/3.61  | | | | | | | | |              all_55_0, all_48_4, simplifying with (135), (137)
% 21.14/3.61  | | | | | | | | |              gives:
% 21.14/3.61  | | | | | | | | |   (142)  all_120_4 = all_106_4
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (24) with all_106_3, all_120_3,
% 21.14/3.61  | | | | | | | | |              all_55_0, all_48_4, simplifying with (133), (134)
% 21.14/3.61  | | | | | | | | |              gives:
% 21.14/3.61  | | | | | | | | |   (143)  all_120_3 = all_106_3
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (25) with all_115_1, all_120_1,
% 21.14/3.61  | | | | | | | | |              all_55_0, all_48_4, simplifying with (130), (131)
% 21.14/3.61  | | | | | | | | |              gives:
% 21.14/3.61  | | | | | | | | |   (144)  all_120_1 = all_115_1
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | GROUND_INST: instantiating (25) with all_106_1, all_120_1,
% 21.14/3.61  | | | | | | | | |              all_55_0, all_48_4, simplifying with (130), (132)
% 21.14/3.61  | | | | | | | | |              gives:
% 21.14/3.61  | | | | | | | | |   (145)  all_120_1 = all_106_1
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | COMBINE_EQS: (144), (145) imply:
% 21.14/3.61  | | | | | | | | |   (146)  all_115_1 = all_106_1
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | SIMP: (146) implies:
% 21.14/3.61  | | | | | | | | |   (147)  all_115_1 = all_106_1
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | COMBINE_EQS: (141), (142) imply:
% 21.14/3.61  | | | | | | | | |   (148)  all_115_2 = all_106_4
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | SIMP: (148) implies:
% 21.14/3.61  | | | | | | | | |   (149)  all_115_2 = all_106_4
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (121), (145) imply:
% 21.14/3.61  | | | | | | | | |   (150)  triple(all_48_5, all_106_1, bad) = all_120_0
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.61  | | | | | | | | | REDUCE: (109), (147) imply:
% 21.14/3.61  | | | | | | | | |   (151)  triple(all_48_5, all_106_1, bad) = all_115_0
% 21.14/3.61  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | REDUCE: (138), (143) imply:
% 21.14/3.62  | | | | | | | | |   (152)  strictly_less_than(all_55_0, all_106_3) = all_120_2
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | REDUCE: (116), (143) imply:
% 21.14/3.62  | | | | | | | | |   (153)  $i(all_106_3)
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | REDUCE: (106), (147) imply:
% 21.14/3.62  | | | | | | | | |   (154)  $i(all_106_1)
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | GROUND_INST: instantiating (27) with all_115_0, all_120_0, bad,
% 21.14/3.62  | | | | | | | | |              all_106_1, all_48_5, simplifying with (150), (151)
% 21.14/3.62  | | | | | | | | |              gives:
% 21.14/3.62  | | | | | | | | |   (155)  all_120_0 = all_115_0
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | GROUND_INST: instantiating (1) with all_55_0, all_106_3,
% 21.14/3.62  | | | | | | | | |              all_106_2, simplifying with (139), (140), (153)
% 21.14/3.62  | | | | | | | | |              gives:
% 21.14/3.62  | | | | | | | | |   (156)  all_106_2 = 0 | less_than(all_55_0, all_106_3) = 0
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | GROUND_INST: instantiating (5) with all_55_0, all_106_3,
% 21.14/3.62  | | | | | | | | |              all_106_2, simplifying with (139), (140), (153)
% 21.14/3.62  | | | | | | | | |              gives:
% 21.14/3.62  | | | | | | | | |   (157)  all_106_2 = 0 |  ? [v0: any] :  ? [v1: any] :
% 21.14/3.62  | | | | | | | | |          (strictly_less_than(all_55_0, all_106_3) = v1 &
% 21.14/3.62  | | | | | | | | |            less_than(all_55_0, all_106_3) = v0 & ( ~ (v0 = 0)
% 21.14/3.62  | | | | | | | | |              | v1 = 0))
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | GROUND_INST: instantiating (6) with all_55_0, all_106_3,
% 21.14/3.62  | | | | | | | | |              all_120_2, simplifying with (140), (152), (153)
% 21.14/3.62  | | | | | | | | |              gives:
% 21.14/3.62  | | | | | | | | |   (158)  all_120_2 = 0 |  ? [v0: any] :  ? [v1: any] :
% 21.14/3.62  | | | | | | | | |          (less_than(all_106_3, all_55_0) = v1 &
% 21.14/3.62  | | | | | | | | |            less_than(all_55_0, all_106_3) = v0 & ( ~ (v0 = 0)
% 21.14/3.62  | | | | | | | | |              | v1 = 0))
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | GROUND_INST: instantiating (18) with all_48_4, all_55_0,
% 21.14/3.62  | | | | | | | | |              all_106_1, all_57_3, all_57_2, simplifying with
% 21.14/3.62  | | | | | | | | |              (31), (46), (47), (52), (132), (140) gives:
% 21.14/3.62  | | | | | | | | |   (159)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] :  ? [v3:
% 21.14/3.62  | | | | | | | | |            int] :  ? [v4: int] : ($i(v1) & $i(v0) & ((v3 = 0 &
% 21.14/3.62  | | | | | | | | |                v2 = 0 & pair_in_list(all_106_1, v0, v1) = 0 &
% 21.14/3.62  | | | | | | | | |                strictly_less_than(v0, v1) = 0) | ( ~ (v4 = 0)
% 21.14/3.62  | | | | | | | | |                & strictly_less_than(all_57_3, all_57_2) =
% 21.14/3.62  | | | | | | | | |                v4)))
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | GROUND_INST: instantiating (17) with all_48_4, all_55_0,
% 21.14/3.62  | | | | | | | | |              all_106_1, all_57_3, all_57_2, simplifying with
% 21.14/3.62  | | | | | | | | |              (31), (46), (47), (81), (132), (140) gives:
% 21.14/3.62  | | | | | | | | |   (160)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: int] :  ? [v3:
% 21.14/3.62  | | | | | | | | |            int] :  ? [v4: int] : ($i(v1) & $i(v0) & ((v3 = 0 &
% 21.14/3.62  | | | | | | | | |                v2 = 0 & pair_in_list(all_106_1, v0, v1) = 0 &
% 21.14/3.62  | | | | | | | | |                strictly_less_than(v0, v1) = 0) | ( ~ (v4 = 0)
% 21.14/3.62  | | | | | | | | |                & pair_in_list(all_48_4, all_57_3, all_57_2) =
% 21.14/3.62  | | | | | | | | |                v4)))
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | GROUND_INST: instantiating (12) with all_48_5, all_48_4, bad,
% 21.14/3.62  | | | | | | | | |              all_55_0, all_106_1, all_115_0, simplifying with
% 21.14/3.62  | | | | | | | | |              (9), (30), (31), (101), (132), (151) gives:
% 21.14/3.62  | | | | | | | | |   (161)  all_48_4 = create_slb |  ? [v0: any] :  ? [v1: $i] : 
% 21.14/3.62  | | | | | | | | |          ? [v2: any] :  ? [v3: $i] :  ? [v4: $i] :
% 21.14/3.62  | | | | | | | | |          (triple(all_48_5, all_48_4, bad) = v3 &
% 21.14/3.62  | | | | | | | | |            findmin_cpq_eff(v3) = v4 & lookup_slb(all_48_4,
% 21.14/3.62  | | | | | | | | |              all_55_0) = v1 & contains_slb(all_48_4, all_55_0)
% 21.14/3.62  | | | | | | | | |            = v0 & less_than(v1, all_55_0) = v2 & $i(v4) &
% 21.14/3.62  | | | | | | | | |            $i(v3) & $i(v1) & ( ~ (v2 = 0) |  ~ (v0 = 0) | v4 =
% 21.14/3.62  | | | | | | | | |              all_115_0))
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | DELTA: instantiating (160) with fresh symbols all_147_0,
% 21.14/3.62  | | | | | | | | |        all_147_1, all_147_2, all_147_3, all_147_4 gives:
% 21.14/3.62  | | | | | | | | |   (162)  $i(all_147_3) & $i(all_147_4) & ((all_147_1 = 0 &
% 21.14/3.62  | | | | | | | | |              all_147_2 = 0 & pair_in_list(all_106_1,
% 21.14/3.62  | | | | | | | | |                all_147_4, all_147_3) = 0 &
% 21.14/3.62  | | | | | | | | |              strictly_less_than(all_147_4, all_147_3) = 0) | (
% 21.14/3.62  | | | | | | | | |              ~ (all_147_0 = 0) & pair_in_list(all_48_4,
% 21.14/3.62  | | | | | | | | |                all_57_3, all_57_2) = all_147_0))
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | ALPHA: (162) implies:
% 21.14/3.62  | | | | | | | | |   (163)  (all_147_1 = 0 & all_147_2 = 0 &
% 21.14/3.62  | | | | | | | | |            pair_in_list(all_106_1, all_147_4, all_147_3) = 0 &
% 21.14/3.62  | | | | | | | | |            strictly_less_than(all_147_4, all_147_3) = 0) | ( ~
% 21.14/3.62  | | | | | | | | |            (all_147_0 = 0) & pair_in_list(all_48_4, all_57_3,
% 21.14/3.62  | | | | | | | | |              all_57_2) = all_147_0)
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_149_0,
% 21.14/3.62  | | | | | | | | |        all_149_1, all_149_2, all_149_3, all_149_4 gives:
% 21.14/3.62  | | | | | | | | |   (164)  $i(all_149_3) & $i(all_149_4) & ((all_149_1 = 0 &
% 21.14/3.62  | | | | | | | | |              all_149_2 = 0 & pair_in_list(all_106_1,
% 21.14/3.62  | | | | | | | | |                all_149_4, all_149_3) = 0 &
% 21.14/3.62  | | | | | | | | |              strictly_less_than(all_149_4, all_149_3) = 0) | (
% 21.14/3.62  | | | | | | | | |              ~ (all_149_0 = 0) & strictly_less_than(all_57_3,
% 21.14/3.62  | | | | | | | | |                all_57_2) = all_149_0))
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | ALPHA: (164) implies:
% 21.14/3.62  | | | | | | | | |   (165)  $i(all_149_4)
% 21.14/3.62  | | | | | | | | |   (166)  $i(all_149_3)
% 21.14/3.62  | | | | | | | | |   (167)  (all_149_1 = 0 & all_149_2 = 0 &
% 21.14/3.62  | | | | | | | | |            pair_in_list(all_106_1, all_149_4, all_149_3) = 0 &
% 21.14/3.62  | | | | | | | | |            strictly_less_than(all_149_4, all_149_3) = 0) | ( ~
% 21.14/3.62  | | | | | | | | |            (all_149_0 = 0) & strictly_less_than(all_57_3,
% 21.14/3.62  | | | | | | | | |              all_57_2) = all_149_0)
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | BETA: splitting (167) gives:
% 21.14/3.62  | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | Case 1:
% 21.14/3.62  | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | |   (168)  all_149_1 = 0 & all_149_2 = 0 &
% 21.14/3.62  | | | | | | | | | |          pair_in_list(all_106_1, all_149_4, all_149_3) = 0 &
% 21.14/3.62  | | | | | | | | | |          strictly_less_than(all_149_4, all_149_3) = 0
% 21.14/3.62  | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | ALPHA: (168) implies:
% 21.14/3.62  | | | | | | | | | |   (169)  strictly_less_than(all_149_4, all_149_3) = 0
% 21.14/3.62  | | | | | | | | | |   (170)  pair_in_list(all_106_1, all_149_4, all_149_3) = 0
% 21.14/3.62  | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | BETA: splitting (161) gives:
% 21.14/3.62  | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | Case 1:
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | |   (171)  all_48_4 = create_slb
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | REDUCE: (87), (171) imply:
% 21.14/3.62  | | | | | | | | | | |   (172)  $false
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | Case 2:
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | |   (173)   ? [v0: any] :  ? [v1: $i] :  ? [v2: any] :  ?
% 21.14/3.62  | | | | | | | | | | |          [v3: $i] :  ? [v4: $i] : (triple(all_48_5,
% 21.14/3.62  | | | | | | | | | | |              all_48_4, bad) = v3 & findmin_cpq_eff(v3) = v4
% 21.14/3.62  | | | | | | | | | | |            & lookup_slb(all_48_4, all_55_0) = v1 &
% 21.14/3.62  | | | | | | | | | | |            contains_slb(all_48_4, all_55_0) = v0 &
% 21.14/3.62  | | | | | | | | | | |            less_than(v1, all_55_0) = v2 & $i(v4) & $i(v3) &
% 21.14/3.62  | | | | | | | | | | |            $i(v1) & ( ~ (v2 = 0) |  ~ (v0 = 0) | v4 =
% 21.14/3.62  | | | | | | | | | | |              all_115_0))
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | DELTA: instantiating (173) with fresh symbols all_160_0,
% 21.14/3.62  | | | | | | | | | | |        all_160_1, all_160_2, all_160_3, all_160_4 gives:
% 21.14/3.62  | | | | | | | | | | |   (174)  triple(all_48_5, all_48_4, bad) = all_160_1 &
% 21.14/3.62  | | | | | | | | | | |          findmin_cpq_eff(all_160_1) = all_160_0 &
% 21.14/3.62  | | | | | | | | | | |          lookup_slb(all_48_4, all_55_0) = all_160_3 &
% 21.14/3.62  | | | | | | | | | | |          contains_slb(all_48_4, all_55_0) = all_160_4 &
% 21.14/3.62  | | | | | | | | | | |          less_than(all_160_3, all_55_0) = all_160_2 &
% 21.14/3.62  | | | | | | | | | | |          $i(all_160_0) & $i(all_160_1) & $i(all_160_3) & (
% 21.14/3.62  | | | | | | | | | | |            ~ (all_160_2 = 0) |  ~ (all_160_4 = 0) |
% 21.14/3.62  | | | | | | | | | | |            all_160_0 = all_115_0)
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | ALPHA: (174) implies:
% 21.14/3.62  | | | | | | | | | | |   (175)  less_than(all_160_3, all_55_0) = all_160_2
% 21.14/3.62  | | | | | | | | | | |   (176)  lookup_slb(all_48_4, all_55_0) = all_160_3
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | BETA: splitting (163) gives:
% 21.14/3.62  | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | Case 1:
% 21.14/3.62  | | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_106_3, all_160_3,
% 21.14/3.62  | | | | | | | | | | | |              all_55_0, all_48_4, simplifying with (134), (176)
% 21.14/3.62  | | | | | | | | | | | |              gives:
% 21.14/3.62  | | | | | | | | | | | |   (177)  all_160_3 = all_106_3
% 21.14/3.62  | | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | | REDUCE: (175), (177) imply:
% 21.14/3.62  | | | | | | | | | | | |   (178)  less_than(all_106_3, all_55_0) = all_160_2
% 21.14/3.62  | | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_106_2, all_160_2,
% 21.14/3.62  | | | | | | | | | | | |              all_55_0, all_106_3, simplifying with (139), (178)
% 21.14/3.62  | | | | | | | | | | | |              gives:
% 21.14/3.62  | | | | | | | | | | | |   (179)  all_160_2 = all_106_2
% 21.14/3.62  | | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | | GROUND_INST: instantiating (2) with all_149_4, all_149_3,
% 21.14/3.62  | | | | | | | | | | | |              simplifying with (165), (166), (169) gives:
% 21.14/3.62  | | | | | | | | | | | |   (180)   ? [v0: int] : ( ~ (v0 = 0) & less_than(all_149_3,
% 21.14/3.62  | | | | | | | | | | | |              all_149_4) = v0 & less_than(all_149_4,
% 21.14/3.62  | | | | | | | | | | | |              all_149_3) = 0)
% 21.14/3.62  | | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_48_5, all_106_1,
% 21.14/3.62  | | | | | | | | | | | |              all_48_3, all_106_0, all_149_4, all_149_3,
% 21.14/3.62  | | | | | | | | | | | |              simplifying with (30), (32), (95), (154), (165),
% 21.14/3.62  | | | | | | | | | | | |              (166), (170) gives:
% 21.14/3.62  | | | | | | | | | | | |   (181)   ? [v0: int] : ((v0 = 0 & less_than(all_149_3,
% 21.14/3.62  | | | | | | | | | | | |                all_149_4) = 0) | ( ~ (v0 = 0) &
% 21.14/3.62  | | | | | | | | | | | |              check_cpq(all_106_0) = v0))
% 21.14/3.62  | | | | | | | | | | | | 
% 21.14/3.62  | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_48_5, all_106_1, bad,
% 21.14/3.62  | | | | | | | | | | | |              all_115_0, all_149_4, all_149_3, simplifying with
% 21.14/3.62  | | | | | | | | | | | |              (9), (30), (151), (154), (165), (166), (170)
% 21.14/3.63  | | | | | | | | | | | |              gives:
% 21.14/3.63  | | | | | | | | | | | |   (182)   ? [v0: int] : ((v0 = 0 & less_than(all_149_3,
% 21.14/3.63  | | | | | | | | | | | |                all_149_4) = 0) | ( ~ (v0 = 0) &
% 21.14/3.63  | | | | | | | | | | | |              check_cpq(all_115_0) = v0))
% 21.14/3.63  | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | DELTA: instantiating (180) with fresh symbol all_189_0
% 21.14/3.63  | | | | | | | | | | | |        gives:
% 21.14/3.63  | | | | | | | | | | | |   (183)   ~ (all_189_0 = 0) & less_than(all_149_3,
% 21.14/3.63  | | | | | | | | | | | |            all_149_4) = all_189_0 & less_than(all_149_4,
% 21.14/3.63  | | | | | | | | | | | |            all_149_3) = 0
% 21.14/3.63  | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | ALPHA: (183) implies:
% 21.14/3.63  | | | | | | | | | | | |   (184)   ~ (all_189_0 = 0)
% 21.14/3.63  | | | | | | | | | | | |   (185)  less_than(all_149_3, all_149_4) = all_189_0
% 21.14/3.63  | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | DELTA: instantiating (182) with fresh symbol all_193_0
% 21.14/3.63  | | | | | | | | | | | |        gives:
% 21.14/3.63  | | | | | | | | | | | |   (186)  (all_193_0 = 0 & less_than(all_149_3, all_149_4) =
% 21.14/3.63  | | | | | | | | | | | |            0) | ( ~ (all_193_0 = 0) & check_cpq(all_115_0)
% 21.14/3.63  | | | | | | | | | | | |            = all_193_0)
% 21.14/3.63  | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | DELTA: instantiating (181) with fresh symbol all_194_0
% 21.14/3.63  | | | | | | | | | | | |        gives:
% 21.14/3.63  | | | | | | | | | | | |   (187)  (all_194_0 = 0 & less_than(all_149_3, all_149_4) =
% 21.14/3.63  | | | | | | | | | | | |            0) | ( ~ (all_194_0 = 0) & check_cpq(all_106_0)
% 21.14/3.63  | | | | | | | | | | | |            = all_194_0)
% 21.14/3.63  | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | BETA: splitting (186) gives:
% 21.14/3.63  | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | |   (188)  all_193_0 = 0 & less_than(all_149_3, all_149_4) =
% 21.14/3.63  | | | | | | | | | | | | |          0
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | ALPHA: (188) implies:
% 21.14/3.63  | | | | | | | | | | | | |   (189)  less_than(all_149_3, all_149_4) = 0
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | REF_CLOSE: (21), (184), (185), (189) are inconsistent by
% 21.14/3.63  | | | | | | | | | | | | |            sub-proof #2.
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | |   (190)   ~ (all_193_0 = 0) & check_cpq(all_115_0) =
% 21.14/3.63  | | | | | | | | | | | | |          all_193_0
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | ALPHA: (190) implies:
% 21.14/3.63  | | | | | | | | | | | | |   (191)   ~ (all_193_0 = 0)
% 21.14/3.63  | | | | | | | | | | | | |   (192)  check_cpq(all_115_0) = all_193_0
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | BETA: splitting (187) gives:
% 21.14/3.63  | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | |   (193)  all_194_0 = 0 & less_than(all_149_3, all_149_4) =
% 21.14/3.63  | | | | | | | | | | | | | |          0
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | ALPHA: (193) implies:
% 21.14/3.63  | | | | | | | | | | | | | |   (194)  less_than(all_149_3, all_149_4) = 0
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | REF_CLOSE: (21), (184), (185), (194) are inconsistent by
% 21.14/3.63  | | | | | | | | | | | | | |            sub-proof #2.
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | |   (195)   ~ (all_194_0 = 0) & check_cpq(all_106_0) =
% 21.14/3.63  | | | | | | | | | | | | | |          all_194_0
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | ALPHA: (195) implies:
% 21.14/3.63  | | | | | | | | | | | | | |   (196)   ~ (all_194_0 = 0)
% 21.14/3.63  | | | | | | | | | | | | | |   (197)  check_cpq(all_106_0) = all_194_0
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 21.14/3.63  | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | |   (198)   ~ (all_106_2 = 0)
% 21.14/3.63  | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | |   (199)  less_than(all_55_0, all_106_3) = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (200)  all_106_2 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | REDUCE: (198), (200) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (201)  $false
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | CLOSE: (201) is inconsistent.
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (202)   ? [v0: any] :  ? [v1: any] :
% 21.14/3.63  | | | | | | | | | | | | | | | | |          (strictly_less_than(all_55_0, all_106_3) = v1 &
% 21.14/3.63  | | | | | | | | | | | | | | | | |            less_than(all_55_0, all_106_3) = v0 & ( ~ (v0 =
% 21.14/3.63  | | | | | | | | | | | | | | | | |                0) | v1 = 0))
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | DELTA: instantiating (202) with fresh symbols all_433_0,
% 21.14/3.63  | | | | | | | | | | | | | | | | |        all_433_1 gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (203)  strictly_less_than(all_55_0, all_106_3) =
% 21.14/3.63  | | | | | | | | | | | | | | | | |          all_433_0 & less_than(all_55_0, all_106_3) =
% 21.14/3.63  | | | | | | | | | | | | | | | | |          all_433_1 & ( ~ (all_433_1 = 0) | all_433_0 = 0)
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (204)  less_than(all_55_0, all_106_3) = all_433_1
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (205)  all_120_2 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (206)  all_115_2 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (206) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (207)  all_106_4 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (207) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (208)  all_120_4 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | |   (209)   ~ (all_120_2 = 0)
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | REDUCE: (205), (209) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | |   (210)  $false
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | |   (211)   ~ (all_120_4 = 0) | all_120_0 = all_48_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | |   (212)   ~ (all_120_4 = 0)
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (212) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | |   (213)  $false
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | |   (214)  all_120_0 = all_48_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (214) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | |   (215)  all_115_0 = all_48_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (215) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | |   (216)  check_cpq(all_48_0) = all_193_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (36), (191), (216) are inconsistent by
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1.
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | End of split
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | End of split
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (217)  all_115_0 = all_48_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | REDUCE: (192), (217) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (218)  check_cpq(all_48_0) = all_193_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (36), (191), (218) are inconsistent by
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |            sub-proof #1.
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | End of split
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (219)   ? [v0: any] :  ? [v1: any] :
% 21.14/3.63  | | | | | | | | | | | | | | | | | |          (less_than(all_106_3, all_55_0) = v1 &
% 21.14/3.63  | | | | | | | | | | | | | | | | | |            less_than(all_55_0, all_106_3) = v0 & ( ~ (v0 =
% 21.14/3.63  | | | | | | | | | | | | | | | | | |                0) | v1 = 0))
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | DELTA: instantiating (219) with fresh symbols all_439_0,
% 21.14/3.63  | | | | | | | | | | | | | | | | | |        all_439_1 gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (220)  less_than(all_106_3, all_55_0) = all_439_0 &
% 21.14/3.63  | | | | | | | | | | | | | | | | | |          less_than(all_55_0, all_106_3) = all_439_1 & ( ~
% 21.14/3.63  | | | | | | | | | | | | | | | | | |            (all_439_1 = 0) | all_439_0 = 0)
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (221)  less_than(all_55_0, all_106_3) = all_439_1
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (222)  less_than(all_106_3, all_55_0) = all_439_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (223)   ~ (all_439_1 = 0) | all_439_0 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_433_1, all_439_1,
% 21.14/3.63  | | | | | | | | | | | | | | | | | |              all_106_3, all_55_0, simplifying with (204), (221)
% 21.14/3.63  | | | | | | | | | | | | | | | | | |              gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (224)  all_439_1 = all_433_1
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with 0, all_439_1, all_106_3,
% 21.14/3.63  | | | | | | | | | | | | | | | | | |              all_55_0, simplifying with (199), (221) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (225)  all_439_1 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with all_106_2, all_439_0,
% 21.14/3.63  | | | | | | | | | | | | | | | | | |              all_55_0, all_106_3, simplifying with (139), (222)
% 21.14/3.63  | | | | | | | | | | | | | | | | | |              gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (226)  all_439_0 = all_106_2
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (225) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | |   (227)  all_433_1 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (228)   ~ (all_439_1 = 0)
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | REDUCE: (225), (228) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (229)  $false
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | CLOSE: (229) is inconsistent.
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (230)  all_439_0 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (230) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (231)  all_106_2 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | REDUCE: (198), (231) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | | | |   (232)  $false
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 21.14/3.63  | | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | | End of split
% 21.14/3.63  | | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | End of split
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | End of split
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | |   (233)  all_106_2 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | REDUCE: (198), (233) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | |   (234)  $false
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent.
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | End of split
% 21.14/3.63  | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | |   (235)   ~ (all_106_4 = 0) | all_106_0 = all_48_0
% 21.14/3.63  | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | |   (236)  all_115_2 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (236) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | |   (237)  all_106_4 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | SIMP: (237) implies:
% 21.14/3.63  | | | | | | | | | | | | | | | |   (238)  all_106_4 = 0
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 21.14/3.63  | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | Case 1:
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (239)   ~ (all_106_4 = 0)
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | REDUCE: (238), (239) imply:
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (240)  $false
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | Case 2:
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | |   (241)  all_106_0 = all_48_0
% 21.14/3.63  | | | | | | | | | | | | | | | | | 
% 21.14/3.63  | | | | | | | | | | | | | | | | | REDUCE: (197), (241) imply:
% 21.14/3.64  | | | | | | | | | | | | | | | | |   (242)  check_cpq(all_48_0) = all_194_0
% 21.14/3.64  | | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with 0, all_194_0, all_48_0,
% 21.14/3.64  | | | | | | | | | | | | | | | | |              simplifying with (36), (242) gives:
% 21.14/3.64  | | | | | | | | | | | | | | | | |   (243)  all_194_0 = 0
% 21.14/3.64  | | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | | | REDUCE: (196), (243) imply:
% 21.14/3.64  | | | | | | | | | | | | | | | | |   (244)  $false
% 21.14/3.64  | | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 21.14/3.64  | | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | Case 2:
% 21.14/3.64  | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | |   (245)  all_115_0 = all_48_0
% 21.14/3.64  | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | | REDUCE: (192), (245) imply:
% 21.14/3.64  | | | | | | | | | | | | | | | |   (246)  check_cpq(all_48_0) = all_193_0
% 21.14/3.64  | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | | REF_CLOSE: (19), (36), (191), (246) are inconsistent by
% 21.14/3.64  | | | | | | | | | | | | | | | |            sub-proof #1.
% 21.14/3.64  | | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | Case 2:
% 21.14/3.64  | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | |   (247)   ~ (all_147_0 = 0) & pair_in_list(all_48_4,
% 21.14/3.64  | | | | | | | | | | | |            all_57_3, all_57_2) = all_147_0
% 21.14/3.64  | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | ALPHA: (247) implies:
% 21.14/3.64  | | | | | | | | | | | |   (248)   ~ (all_147_0 = 0)
% 21.14/3.64  | | | | | | | | | | | |   (249)  pair_in_list(all_48_4, all_57_3, all_57_2) =
% 21.14/3.64  | | | | | | | | | | | |          all_147_0
% 21.14/3.64  | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_147_0, all_57_2,
% 21.14/3.64  | | | | | | | | | | | |              all_57_3, all_48_4, simplifying with (52), (249)
% 21.14/3.64  | | | | | | | | | | | |              gives:
% 21.14/3.64  | | | | | | | | | | | |   (250)  all_147_0 = 0
% 21.14/3.64  | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | REDUCE: (248), (250) imply:
% 21.14/3.64  | | | | | | | | | | | |   (251)  $false
% 21.14/3.64  | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | | CLOSE: (251) is inconsistent.
% 21.14/3.64  | | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | Case 2:
% 21.14/3.64  | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | |   (252)   ~ (all_149_0 = 0) & strictly_less_than(all_57_3,
% 21.14/3.64  | | | | | | | | | |            all_57_2) = all_149_0
% 21.14/3.64  | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | ALPHA: (252) implies:
% 21.14/3.64  | | | | | | | | | |   (253)   ~ (all_149_0 = 0)
% 21.14/3.64  | | | | | | | | | |   (254)  strictly_less_than(all_57_3, all_57_2) = all_149_0
% 21.14/3.64  | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_149_0, all_57_2,
% 21.14/3.64  | | | | | | | | | |              all_57_3, simplifying with (81), (254) gives:
% 21.14/3.64  | | | | | | | | | |   (255)  all_149_0 = 0
% 21.14/3.64  | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | REDUCE: (253), (255) imply:
% 21.14/3.64  | | | | | | | | | |   (256)  $false
% 21.14/3.64  | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | | CLOSE: (256) is inconsistent.
% 21.14/3.64  | | | | | | | | | | 
% 21.14/3.64  | | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | | 
% 21.14/3.64  | | | | | | | | End of split
% 21.14/3.64  | | | | | | | | 
% 21.14/3.64  | | | | | | | End of split
% 21.14/3.64  | | | | | | | 
% 21.14/3.64  | | | | | | End of split
% 21.14/3.64  | | | | | | 
% 21.14/3.64  | | | | | End of split
% 21.14/3.64  | | | | | 
% 21.14/3.64  | | | | End of split
% 21.14/3.64  | | | | 
% 21.14/3.64  | | | End of split
% 21.14/3.64  | | | 
% 21.14/3.64  | | Case 2:
% 21.14/3.64  | | | 
% 21.14/3.64  | | |   (257)  all_57_0 = 0
% 21.14/3.64  | | | 
% 21.14/3.64  | | | REDUCE: (50), (257) imply:
% 21.14/3.64  | | |   (258)  $false
% 21.14/3.64  | | | 
% 21.14/3.64  | | | CLOSE: (258) is inconsistent.
% 21.14/3.64  | | | 
% 21.14/3.64  | | End of split
% 21.14/3.64  | | 
% 21.14/3.64  | Case 2:
% 21.14/3.64  | | 
% 21.14/3.64  | |   (259)  all_57_4 = 0 & check_cpq(all_48_2) = 0
% 21.14/3.64  | | 
% 21.14/3.64  | | ALPHA: (259) implies:
% 21.14/3.64  | |   (260)  check_cpq(all_48_2) = 0
% 21.14/3.64  | | 
% 21.14/3.64  | | GROUND_INST: instantiating (19) with all_48_1, 0, all_48_2, simplifying with
% 21.14/3.64  | |              (35), (260) gives:
% 21.14/3.64  | |   (261)  all_48_1 = 0
% 21.14/3.64  | | 
% 21.14/3.64  | | REDUCE: (29), (261) imply:
% 21.14/3.64  | |   (262)  $false
% 21.14/3.64  | | 
% 21.14/3.64  | | CLOSE: (262) is inconsistent.
% 21.14/3.64  | | 
% 21.14/3.64  | End of split
% 21.14/3.64  | 
% 21.14/3.64  End of proof
% 21.14/3.64  
% 21.14/3.64  Sub-proof #1 shows that the following formulas are inconsistent:
% 21.14/3.64  ----------------------------------------------------------------
% 21.14/3.64    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 21.14/3.64         (v1 = v0 |  ~ (check_cpq(v2) = v1) |  ~ (check_cpq(v2) = v0))
% 21.14/3.64    (2)  check_cpq(all_48_0) = all_193_0
% 21.14/3.64    (3)  check_cpq(all_48_0) = 0
% 21.14/3.64    (4)   ~ (all_193_0 = 0)
% 21.14/3.64  
% 21.14/3.64  Begin of proof
% 21.14/3.64  | 
% 21.14/3.64  | GROUND_INST: instantiating (1) with 0, all_193_0, all_48_0, simplifying with
% 21.14/3.64  |              (2), (3) gives:
% 21.14/3.64  |   (5)  all_193_0 = 0
% 21.14/3.64  | 
% 21.14/3.64  | REDUCE: (4), (5) imply:
% 21.14/3.64  |   (6)  $false
% 21.14/3.64  | 
% 21.14/3.64  | CLOSE: (6) is inconsistent.
% 21.14/3.64  | 
% 21.14/3.64  End of proof
% 21.14/3.64  
% 21.14/3.64  Sub-proof #2 shows that the following formulas are inconsistent:
% 21.14/3.64  ----------------------------------------------------------------
% 21.14/3.64    (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : 
% 21.14/3.64         ! [v3: $i] : (v1 = v0 |  ~ (less_than(v3, v2) = v1) |  ~ (less_than(v3,
% 21.14/3.64               v2) = v0))
% 21.14/3.64    (2)  less_than(all_149_3, all_149_4) = all_189_0
% 21.14/3.64    (3)  less_than(all_149_3, all_149_4) = 0
% 21.14/3.64    (4)   ~ (all_189_0 = 0)
% 21.14/3.64  
% 21.14/3.64  Begin of proof
% 21.14/3.64  | 
% 21.14/3.64  | GROUND_INST: instantiating (1) with 0, all_189_0, all_149_4, all_149_3,
% 21.14/3.64  |              simplifying with (2), (3) gives:
% 21.14/3.64  |   (5)  all_189_0 = 0
% 21.14/3.64  | 
% 21.14/3.64  | REDUCE: (4), (5) imply:
% 21.14/3.64  |   (6)  $false
% 21.14/3.64  | 
% 21.14/3.64  | CLOSE: (6) is inconsistent.
% 21.14/3.64  | 
% 21.14/3.64  End of proof
% 21.14/3.64  % SZS output end Proof for theBenchmark
% 21.14/3.64  
% 21.14/3.64  3027ms
%------------------------------------------------------------------------------