%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWV109+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 22:54:56 EDT 2023

% Result   : Theorem 127.34s 17.36s
% Output   : Proof 248.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SWV109+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.02/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.31  % Computer : n032.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue Aug 29 03:42:31 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.14/0.56  ________       _____
% 0.14/0.56  ___  __ \_________(_)________________________________
% 0.14/0.56  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.14/0.56  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.14/0.56  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.14/0.56  
% 0.14/0.56  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.56  (2023-06-19)
% 0.14/0.56  
% 0.14/0.56  (c) Philipp Rümmer, 2009-2023
% 0.14/0.56  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.56                Amanda Stjerna.
% 0.14/0.56  Free software under BSD-3-Clause.
% 0.14/0.56  
% 0.14/0.56  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.56  
% 0.14/0.56  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.58  Running up to 7 provers in parallel.
% 0.14/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.61  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.12/1.43  Prover 1: Preprocessing ...
% 5.12/1.44  Prover 4: Preprocessing ...
% 5.51/1.49  Prover 5: Preprocessing ...
% 5.51/1.49  Prover 3: Preprocessing ...
% 5.51/1.49  Prover 6: Preprocessing ...
% 5.51/1.49  Prover 2: Preprocessing ...
% 5.51/1.49  Prover 0: Preprocessing ...
% 13.63/2.67  Prover 1: Warning: ignoring some quantifiers
% 15.30/2.78  Prover 3: Warning: ignoring some quantifiers
% 15.30/2.80  Prover 1: Constructing countermodel ...
% 15.30/2.81  Prover 6: Proving ...
% 15.30/2.86  Prover 3: Constructing countermodel ...
% 15.90/2.88  Prover 4: Warning: ignoring some quantifiers
% 17.35/3.08  Prover 4: Constructing countermodel ...
% 17.35/3.14  Prover 2: Proving ...
% 18.06/3.17  Prover 5: Proving ...
% 18.06/3.18  Prover 0: Proving ...
% 72.94/10.37  Prover 2: stopped
% 72.94/10.38  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 75.34/10.61  Prover 7: Preprocessing ...
% 78.37/11.04  Prover 7: Warning: ignoring some quantifiers
% 78.88/11.10  Prover 7: Constructing countermodel ...
% 100.71/13.93  Prover 5: stopped
% 100.71/13.94  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.15/14.03  Prover 8: Preprocessing ...
% 102.26/14.23  Prover 8: Warning: ignoring some quantifiers
% 103.31/14.27  Prover 8: Constructing countermodel ...
% 116.13/15.93  Prover 1: stopped
% 116.13/15.93  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.31/16.04  Prover 9: Preprocessing ...
% 119.32/16.31  Prover 9: Warning: ignoring some quantifiers
% 119.51/16.32  Prover 9: Constructing countermodel ...
% 127.34/17.36  Prover 3: proved (16753ms)
% 127.34/17.36  
% 127.34/17.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 127.34/17.36  
% 127.34/17.36  Prover 9: stopped
% 127.34/17.36  Prover 0: stopped
% 127.34/17.37  Prover 6: stopped
% 127.34/17.37  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 127.34/17.37  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 127.34/17.37  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 127.34/17.37  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 128.07/17.49  Prover 10: Preprocessing ...
% 128.52/17.50  Prover 13: Preprocessing ...
% 128.52/17.51  Prover 11: Preprocessing ...
% 128.52/17.51  Prover 16: Preprocessing ...
% 129.05/17.57  Prover 10: Warning: ignoring some quantifiers
% 129.05/17.59  Prover 10: Constructing countermodel ...
% 129.05/17.65  Prover 16: Warning: ignoring some quantifiers
% 129.05/17.66  Prover 13: Warning: ignoring some quantifiers
% 129.05/17.67  Prover 16: Constructing countermodel ...
% 129.05/17.68  Prover 11: Warning: ignoring some quantifiers
% 129.50/17.68  Prover 13: Constructing countermodel ...
% 129.50/17.69  Prover 11: Constructing countermodel ...
% 154.71/20.99  Prover 13: stopped
% 154.71/21.01  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 155.32/21.14  Prover 19: Preprocessing ...
% 157.85/21.35  Prover 19: Warning: ignoring some quantifiers
% 157.85/21.36  Prover 19: Constructing countermodel ...
% 159.65/21.57  Prover 16: stopped
% 177.64/24.17  Prover 19: stopped
% 197.59/27.92  Prover 4: stopped
% 206.92/30.13  Prover 7: stopped
% 245.80/41.34  Prover 10: Found proof (size 8341)
% 245.80/41.34  Prover 10: proved (23982ms)
% 245.80/41.36  Prover 11: stopped
% 245.80/41.36  Prover 8: stopped
% 245.80/41.36  
% 245.80/41.36  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 245.80/41.36  
% 245.95/41.48  % SZS output start Proof for theBenchmark
% 245.95/41.49  Assumptions after simplification:
% 245.95/41.49  ---------------------------------
% 245.95/41.49  
% 245.95/41.49    (finite_domain_1)
% 245.95/41.50    $i(n1) & $i(n0) &  ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0,
% 245.95/41.50        n1) |  ~ leq(n0, v0))
% 245.95/41.50  
% 245.95/41.50    (finite_domain_2)
% 245.95/41.50    $i(n2) & $i(n1) & $i(n0) &  ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~
% 245.95/41.50      $i(v0) |  ~ leq(v0, n2) |  ~ leq(n0, v0))
% 245.95/41.50  
% 245.95/41.50    (finite_domain_5)
% 245.95/41.50    $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0) &  ! [v0: $i] : (v0 = n5 |
% 245.95/41.50      v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n5)
% 245.95/41.50      |  ~ leq(n0, v0))
% 245.95/41.50  
% 245.95/41.50    (irreflexivity_gt)
% 245.95/41.50     ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 245.95/41.50  
% 245.95/41.50    (leq_gt2)
% 245.95/41.50     ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v0, v1)
% 245.95/41.50      | gt(v1, v0))
% 245.95/41.50  
% 245.95/41.50    (leq_gt_pred)
% 246.40/41.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~ $i(v1) |  ~
% 246.40/41.53      $i(v0) |  ~ leq(v0, v2) | gt(v1, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 246.40/41.53      $i] : ( ~ (pred(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0,
% 246.40/41.53        v2))
% 246.40/41.53  
% 246.40/41.53    (pred_minus_1)
% 246.40/41.53    $i(n1) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (minus(v0, n1) = v1) |  ~ $i(v0) |
% 246.40/41.53      (pred(v0) = v1 & $i(v1)))
% 246.40/41.53  
% 246.40/41.53    (pred_succ)
% 246.40/41.53     ! [v0: $i] :  ! [v1: $i] : ( ~ (succ(v0) = v1) |  ~ $i(v0) | pred(v1) = v0)
% 246.40/41.53  
% 246.40/41.53    (quaternion_ds1_symm_0002)
% 246.40/41.54    $i(id_ds1_filter) & $i(pminus_ds1_filter) & $i(r_ds1_filter) &
% 246.40/41.54    $i(q_ds1_filter) & $i(n6) & $i(n999) & $i(pv47) & $i(pv5) & $i(n3) & $i(n1) &
% 246.40/41.54    $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :
% 246.40/41.54     ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ? [v10:
% 246.40/41.54      $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :  ? [v15:
% 246.40/41.54      $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ? [v19: $i] :  ? [v20:
% 246.40/41.54      $i] :  ? [v21: $i] :  ? [v22: $i] : (minus(n6, n1) = v1 & minus(n999, n1) =
% 246.40/41.54      v0 & minus(n3, n1) = v2 & $i(v20) & $i(v19) & $i(v16) & $i(v15) & $i(v12) &
% 246.40/41.54      $i(v11) & $i(v8) & $i(v7) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 246.40/41.54      leq(pv47, v1) & leq(pv5, v0) & leq(n0, pv47) & leq(n0, pv5) &  ! [v23: $i] :
% 246.40/41.54       ! [v24: $i] :  ! [v25: $i] : ( ~ (a_select3(id_ds1_filter, v23, v24) = v25)
% 246.40/41.54        |  ~ $i(v24) |  ~ $i(v23) |  ~ leq(v24, v1) |  ~ leq(v23, v1) |  ~ leq(n0,
% 246.40/41.54          v24) |  ~ leq(n0, v23) | (a_select3(id_ds1_filter, v24, v23) = v25 &
% 246.40/41.54          $i(v25))) &  ! [v23: $i] :  ! [v24: $i] :  ! [v25: $i] : ( ~
% 246.40/41.54        (a_select3(pminus_ds1_filter, v23, v24) = v25) |  ~ $i(v24) |  ~ $i(v23) |
% 246.40/41.54         ~ leq(v24, v1) |  ~ leq(v23, v1) |  ~ leq(n0, v24) |  ~ leq(n0, v23) |
% 246.40/41.54        (a_select3(pminus_ds1_filter, v24, v23) = v25 & $i(v25))) &  ! [v23: $i] :
% 246.40/41.54       ! [v24: $i] :  ! [v25: $i] : ( ~ (a_select3(r_ds1_filter, v23, v24) = v25)
% 246.40/41.54        |  ~ $i(v24) |  ~ $i(v23) |  ~ leq(v24, v2) |  ~ leq(v23, v2) |  ~ leq(n0,
% 246.40/41.54          v24) |  ~ leq(n0, v23) | (a_select3(r_ds1_filter, v24, v23) = v25 &
% 246.40/41.54          $i(v25))) &  ! [v23: $i] :  ! [v24: $i] :  ! [v25: $i] : ( ~
% 246.40/41.54        (a_select3(q_ds1_filter, v23, v24) = v25) |  ~ $i(v24) |  ~ $i(v23) |  ~
% 246.40/41.54        leq(v24, v1) |  ~ leq(v23, v1) |  ~ leq(n0, v24) |  ~ leq(n0, v23) |
% 246.40/41.54        (a_select3(q_ds1_filter, v24, v23) = v25 & $i(v25))) & (( ~ (v22 = v21) &
% 246.40/41.54          a_select3(q_ds1_filter, v20, v19) = v22 & a_select3(q_ds1_filter, v19,
% 246.40/41.54            v20) = v21 & $i(v22) & $i(v21) & leq(v20, v1) & leq(v19, v1) & leq(n0,
% 246.40/41.54            v20) & leq(n0, v19)) | ( ~ (v18 = v17) & a_select3(r_ds1_filter, v16,
% 246.40/41.54            v15) = v18 & a_select3(r_ds1_filter, v15, v16) = v17 & $i(v18) &
% 246.40/41.54          $i(v17) & leq(v16, v2) & leq(v15, v2) & leq(n0, v16) & leq(n0, v15)) | (
% 246.40/41.54          ~ (v14 = v13) & a_select3(pminus_ds1_filter, v12, v11) = v14 &
% 246.40/41.54          a_select3(pminus_ds1_filter, v11, v12) = v13 & $i(v14) & $i(v13) &
% 246.40/41.54          leq(v12, v1) & leq(v11, v1) & leq(n0, v12) & leq(n0, v11)) | ( ~ (v10 =
% 246.40/41.54            v9) & a_select3(pminus_ds1_filter, v8, v7) = v10 &
% 246.40/41.54          a_select3(pminus_ds1_filter, v7, v8) = v9 & $i(v10) & $i(v9) & leq(v8,
% 246.40/41.54            v1) & leq(v7, v1) & leq(n0, v8) & leq(n0, v7)) | ( ~ (v6 = v5) &
% 246.40/41.54          a_select3(id_ds1_filter, v4, v3) = v6 & a_select3(id_ds1_filter, v3, v4)
% 246.40/41.54          = v5 & $i(v6) & $i(v5) & leq(v4, v1) & leq(v3, v1) & leq(n0, v4) &
% 246.40/41.55          leq(n0, v3))))
% 246.40/41.55  
% 246.40/41.55    (successor_1)
% 246.40/41.55    succ(n0) = n1 & $i(n1) & $i(n0)
% 246.40/41.55  
% 246.40/41.55    (successor_2)
% 246.40/41.55    $i(n2) & $i(n0) &  ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 246.40/41.55  
% 246.40/41.55    (successor_3)
% 246.40/41.55    $i(n3) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 246.40/41.55      succ(n0) = v0 & $i(v1) & $i(v0))
% 246.40/41.55  
% 246.40/41.55    (successor_4)
% 246.40/41.55    $i(n4) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (succ(v2) = n4 &
% 246.40/41.55      succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 246.40/41.55  
% 246.40/41.55    (successor_5)
% 246.40/41.55    $i(n5) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :
% 246.40/41.55    (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 246.40/41.55      & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 246.40/41.55  
% 246.40/41.55    (successor_6)
% 246.40/41.55    $i(n6) & $i(n0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ?
% 246.40/41.55    [v4: $i] : (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 &
% 246.40/41.55      succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 246.40/41.55  
% 246.40/41.55    (function-axioms)
% 246.40/41.56     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 246.40/41.56      $i] : (v1 = v0 |  ~ (tptp_update3(v5, v4, v3, v2) = v1) |  ~
% 246.40/41.56      (tptp_update3(v5, v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 246.40/41.56      $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_update2(v4, v3, v2) =
% 246.40/41.56        v1) |  ~ (tptp_update2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 246.40/41.56    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (sum(v4, v3, v2) = v1) | 
% 246.40/41.56      ~ (sum(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 246.40/41.56    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (tptp_const_array2(v4, v3, v2) = v1) | 
% 246.40/41.56      ~ (tptp_const_array2(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 246.59/41.56    [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (a_select3(v4, v3, v2) =
% 246.59/41.56        v1) |  ~ (a_select3(v4, v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 246.59/41.56    [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (minus(v3, v2) = v1) |  ~ (minus(v3,
% 246.59/41.56          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 246.59/41.56      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: $i] :  !
% 246.59/41.56    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (tptp_mmul(v3, v2) = v1)
% 246.59/41.56      |  ~ (tptp_mmul(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : 
% 246.59/41.56    ! [v3: $i] : (v1 = v0 |  ~ (tptp_msub(v3, v2) = v1) |  ~ (tptp_msub(v3, v2) =
% 246.59/41.56        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 246.59/41.56      ~ (tptp_madd(v3, v2) = v1) |  ~ (tptp_madd(v3, v2) = v0)) &  ! [v0: $i] :  !
% 246.59/41.56    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (dim(v3, v2) = v1) |  ~
% 246.59/41.56      (dim(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 246.59/41.56    : (v1 = v0 |  ~ (tptp_const_array1(v3, v2) = v1) |  ~ (tptp_const_array1(v3,
% 246.59/41.56          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1
% 246.59/41.56      = v0 |  ~ (a_select2(v3, v2) = v1) |  ~ (a_select2(v3, v2) = v0)) &  ! [v0:
% 246.59/41.56      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 246.59/41.56      (uniform_int_rnd(v3, v2) = v1) |  ~ (uniform_int_rnd(v3, v2) = v0)) &  !
% 246.59/41.56    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (inv(v2) = v1) |  ~
% 246.59/41.56      (inv(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 246.59/41.56      (trans(v2) = v1) |  ~ (trans(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 246.59/41.56    [v2: $i] : (v1 = v0 |  ~ (succ(v2) = v1) |  ~ (succ(v2) = v0)) &  ! [v0: $i] :
% 246.59/41.56     ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (pred(v2) = v1) |  ~ (pred(v2) =
% 246.59/41.56        v0))
% 246.59/41.56  
% 246.59/41.56  Further assumptions not needed in the proof:
% 246.59/41.56  --------------------------------------------
% 246.59/41.56  const_array1_select, const_array2_select, defuse, finite_domain_0,
% 246.59/41.56  finite_domain_3, finite_domain_4, finite_domain_6, gt_0_tptp_minus_1, gt_1_0,
% 246.59/41.56  gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 246.59/41.56  gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 246.59/41.56  gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_6_0, gt_6_1, gt_6_2,
% 246.59/41.56  gt_6_3, gt_6_4, gt_6_5, gt_6_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2,
% 246.59/41.56  gt_999_3, gt_999_4, gt_999_5, gt_999_6, gt_999_tptp_minus_1, gt_succ, leq_geq,
% 246.59/41.56  leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ,
% 246.59/41.56  lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 246.59/41.56  matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 246.59/41.56  matrix_symm_update_diagonal, reflexivity_leq, sel2_update_1, sel2_update_2,
% 246.59/41.56  sel2_update_3, sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l,
% 246.59/41.56  succ_plus_1_r, succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r,
% 246.59/41.56  succ_plus_4_l, succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred,
% 246.59/41.56  succ_tptp_minus_1, sum_plus_base, sum_plus_base_float, totality,
% 246.59/41.56  transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 246.59/41.56  uniform_int_rand_ranges_lo
% 246.59/41.56  
% 246.59/41.56  Those formulas are unsatisfiable:
% 246.59/41.56  ---------------------------------
% 246.59/41.56  
% 246.59/41.56  Begin of proof
% 246.59/41.56  | 
% 246.59/41.56  | ALPHA: (leq_gt_pred) implies:
% 246.59/41.56  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 246.59/41.56  |          $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 246.59/41.56  | 
% 246.59/41.56  | ALPHA: (pred_minus_1) implies:
% 246.59/41.57  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (minus(v0, n1) = v1) |  ~ $i(v0) |
% 246.59/41.57  |          (pred(v0) = v1 & $i(v1)))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (finite_domain_5) implies:
% 246.59/41.57  |   (3)   ! [v0: $i] : (v0 = n5 | v0 = n4 | v0 = n3 | v0 = n2 | v0 = n1 | v0 =
% 246.59/41.57  |          n0 |  ~ $i(v0) |  ~ leq(v0, n5) |  ~ leq(n0, v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (finite_domain_1) implies:
% 246.59/41.57  |   (4)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 246.59/41.57  |          leq(n0, v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (finite_domain_2) implies:
% 246.59/41.57  |   (5)   ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n2)
% 246.59/41.57  |          |  ~ leq(n0, v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (successor_4) implies:
% 246.59/41.57  |   (6)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 246.59/41.57  |          v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (successor_5) implies:
% 246.59/41.57  |   (7)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : (succ(v3) = n5
% 246.59/41.57  |          & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 246.59/41.57  |          $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (successor_6) implies:
% 246.59/41.57  |   (8)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :
% 246.59/41.57  |        (succ(v4) = n6 & succ(v3) = v4 & succ(v2) = v3 & succ(v1) = v2 &
% 246.59/41.57  |          succ(v0) = v1 & succ(n0) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 246.59/41.57  |          $i(v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (successor_1) implies:
% 246.59/41.57  |   (9)  succ(n0) = n1
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (successor_2) implies:
% 246.59/41.57  |   (10)   ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (successor_3) implies:
% 246.59/41.57  |   (11)   ? [v0: $i] :  ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0)
% 246.59/41.57  |           = v0 & $i(v1) & $i(v0))
% 246.59/41.57  | 
% 246.59/41.57  | ALPHA: (quaternion_ds1_symm_0002) implies:
% 246.59/41.57  |   (12)  $i(n0)
% 246.59/41.57  |   (13)  $i(n6)
% 246.59/41.58  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 246.59/41.58  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 246.59/41.58  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 246.59/41.58  |           $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ?
% 246.59/41.58  |         [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] : (minus(n6,
% 246.59/41.58  |             n1) = v1 & minus(n999, n1) = v0 & minus(n3, n1) = v2 & $i(v20) &
% 246.59/41.58  |           $i(v19) & $i(v16) & $i(v15) & $i(v12) & $i(v11) & $i(v8) & $i(v7) &
% 246.59/41.58  |           $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(pv47, v1) &
% 246.59/41.58  |           leq(pv5, v0) & leq(n0, pv47) & leq(n0, pv5) &  ! [v23: $i] :  !
% 246.59/41.58  |           [v24: $i] :  ! [v25: $i] : ( ~ (a_select3(id_ds1_filter, v23, v24) =
% 246.59/41.58  |               v25) |  ~ $i(v24) |  ~ $i(v23) |  ~ leq(v24, v1) |  ~ leq(v23,
% 246.59/41.58  |               v1) |  ~ leq(n0, v24) |  ~ leq(n0, v23) |
% 246.59/41.58  |             (a_select3(id_ds1_filter, v24, v23) = v25 & $i(v25))) &  ! [v23:
% 246.59/41.58  |             $i] :  ! [v24: $i] :  ! [v25: $i] : ( ~
% 246.59/41.58  |             (a_select3(pminus_ds1_filter, v23, v24) = v25) |  ~ $i(v24) |  ~
% 246.59/41.58  |             $i(v23) |  ~ leq(v24, v1) |  ~ leq(v23, v1) |  ~ leq(n0, v24) |  ~
% 246.59/41.58  |             leq(n0, v23) | (a_select3(pminus_ds1_filter, v24, v23) = v25 &
% 246.59/41.58  |               $i(v25))) &  ! [v23: $i] :  ! [v24: $i] :  ! [v25: $i] : ( ~
% 246.59/41.58  |             (a_select3(r_ds1_filter, v23, v24) = v25) |  ~ $i(v24) |  ~
% 246.59/41.58  |             $i(v23) |  ~ leq(v24, v2) |  ~ leq(v23, v2) |  ~ leq(n0, v24) |  ~
% 246.59/41.58  |             leq(n0, v23) | (a_select3(r_ds1_filter, v24, v23) = v25 &
% 246.59/41.58  |               $i(v25))) &  ! [v23: $i] :  ! [v24: $i] :  ! [v25: $i] : ( ~
% 246.59/41.58  |             (a_select3(q_ds1_filter, v23, v24) = v25) |  ~ $i(v24) |  ~
% 246.59/41.58  |             $i(v23) |  ~ leq(v24, v1) |  ~ leq(v23, v1) |  ~ leq(n0, v24) |  ~
% 246.59/41.58  |             leq(n0, v23) | (a_select3(q_ds1_filter, v24, v23) = v25 &
% 246.59/41.58  |               $i(v25))) & (( ~ (v22 = v21) & a_select3(q_ds1_filter, v20, v19)
% 246.59/41.58  |               = v22 & a_select3(q_ds1_filter, v19, v20) = v21 & $i(v22) &
% 246.59/41.58  |               $i(v21) & leq(v20, v1) & leq(v19, v1) & leq(n0, v20) & leq(n0,
% 246.59/41.58  |                 v19)) | ( ~ (v18 = v17) & a_select3(r_ds1_filter, v16, v15) =
% 246.59/41.58  |               v18 & a_select3(r_ds1_filter, v15, v16) = v17 & $i(v18) &
% 246.59/41.58  |               $i(v17) & leq(v16, v2) & leq(v15, v2) & leq(n0, v16) & leq(n0,
% 246.59/41.58  |                 v15)) | ( ~ (v14 = v13) & a_select3(pminus_ds1_filter, v12,
% 246.59/41.58  |                 v11) = v14 & a_select3(pminus_ds1_filter, v11, v12) = v13 &
% 246.59/41.58  |               $i(v14) & $i(v13) & leq(v12, v1) & leq(v11, v1) & leq(n0, v12) &
% 246.59/41.58  |               leq(n0, v11)) | ( ~ (v10 = v9) & a_select3(pminus_ds1_filter,
% 246.59/41.58  |                 v8, v7) = v10 & a_select3(pminus_ds1_filter, v7, v8) = v9 &
% 246.59/41.58  |               $i(v10) & $i(v9) & leq(v8, v1) & leq(v7, v1) & leq(n0, v8) &
% 246.59/41.58  |               leq(n0, v7)) | ( ~ (v6 = v5) & a_select3(id_ds1_filter, v4, v3)
% 246.59/41.58  |               = v6 & a_select3(id_ds1_filter, v3, v4) = v5 & $i(v6) & $i(v5) &
% 246.59/41.58  |               leq(v4, v1) & leq(v3, v1) & leq(n0, v4) & leq(n0, v3))))
% 246.59/41.58  | 
% 246.59/41.58  | ALPHA: (function-axioms) implies:
% 246.59/41.58  |   (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (pred(v2) =
% 246.59/41.58  |             v1) |  ~ (pred(v2) = v0))
% 246.59/41.58  |   (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (succ(v2) =
% 246.59/41.58  |             v1) |  ~ (succ(v2) = v0))
% 246.59/41.58  |   (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 246.59/41.58  |         (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2)
% 246.59/41.58  |             = v0))
% 246.59/41.58  | 
% 246.59/41.58  | DELTA: instantiating (10) with fresh symbol all_55_0 gives:
% 246.59/41.58  |   (18)  succ(all_55_0) = n2 & succ(n0) = all_55_0 & $i(all_55_0)
% 246.59/41.58  | 
% 246.59/41.58  | ALPHA: (18) implies:
% 246.59/41.58  |   (19)  $i(all_55_0)
% 246.59/41.58  |   (20)  succ(n0) = all_55_0
% 246.59/41.58  |   (21)  succ(all_55_0) = n2
% 246.59/41.58  | 
% 246.59/41.58  | DELTA: instantiating (11) with fresh symbols all_57_0, all_57_1 gives:
% 246.59/41.58  |   (22)  succ(all_57_0) = n3 & succ(all_57_1) = all_57_0 & succ(n0) = all_57_1
% 246.59/41.58  |         & $i(all_57_0) & $i(all_57_1)
% 246.59/41.58  | 
% 246.59/41.58  | ALPHA: (22) implies:
% 246.59/41.59  |   (23)  $i(all_57_0)
% 246.59/41.59  |   (24)  succ(n0) = all_57_1
% 246.59/41.59  |   (25)  succ(all_57_1) = all_57_0
% 246.59/41.59  |   (26)  succ(all_57_0) = n3
% 246.59/41.59  | 
% 246.59/41.59  | DELTA: instantiating (6) with fresh symbols all_60_0, all_60_1, all_60_2
% 246.59/41.59  |        gives:
% 246.59/41.59  |   (27)  succ(all_60_0) = n4 & succ(all_60_1) = all_60_0 & succ(all_60_2) =
% 246.59/41.59  |         all_60_1 & succ(n0) = all_60_2 & $i(all_60_0) & $i(all_60_1) &
% 246.59/41.59  |         $i(all_60_2)
% 246.59/41.59  | 
% 246.59/41.59  | ALPHA: (27) implies:
% 246.59/41.59  |   (28)  $i(all_60_0)
% 246.59/41.59  |   (29)  succ(n0) = all_60_2
% 246.59/41.59  |   (30)  succ(all_60_2) = all_60_1
% 246.59/41.59  |   (31)  succ(all_60_1) = all_60_0
% 246.59/41.59  |   (32)  succ(all_60_0) = n4
% 246.59/41.59  | 
% 246.59/41.59  | DELTA: instantiating (7) with fresh symbols all_62_0, all_62_1, all_62_2,
% 246.59/41.59  |        all_62_3 gives:
% 246.59/41.59  |   (33)  succ(all_62_0) = n5 & succ(all_62_1) = all_62_0 & succ(all_62_2) =
% 246.59/41.59  |         all_62_1 & succ(all_62_3) = all_62_2 & succ(n0) = all_62_3 &
% 246.59/41.59  |         $i(all_62_0) & $i(all_62_1) & $i(all_62_2) & $i(all_62_3)
% 246.59/41.59  | 
% 246.59/41.59  | ALPHA: (33) implies:
% 246.59/41.59  |   (34)  $i(all_62_0)
% 246.59/41.59  |   (35)  succ(n0) = all_62_3
% 246.59/41.59  |   (36)  succ(all_62_3) = all_62_2
% 246.59/41.59  |   (37)  succ(all_62_2) = all_62_1
% 246.59/41.59  |   (38)  succ(all_62_1) = all_62_0
% 246.59/41.59  |   (39)  succ(all_62_0) = n5
% 246.59/41.59  | 
% 246.59/41.59  | DELTA: instantiating (8) with fresh symbols all_64_0, all_64_1, all_64_2,
% 246.59/41.59  |        all_64_3, all_64_4 gives:
% 246.59/41.59  |   (40)  succ(all_64_0) = n6 & succ(all_64_1) = all_64_0 & succ(all_64_2) =
% 246.59/41.59  |         all_64_1 & succ(all_64_3) = all_64_2 & succ(all_64_4) = all_64_3 &
% 246.59/41.59  |         succ(n0) = all_64_4 & $i(all_64_0) & $i(all_64_1) & $i(all_64_2) &
% 246.59/41.59  |         $i(all_64_3) & $i(all_64_4)
% 246.59/41.59  | 
% 246.59/41.59  | ALPHA: (40) implies:
% 246.59/41.59  |   (41)  $i(all_64_0)
% 246.59/41.59  |   (42)  succ(n0) = all_64_4
% 246.59/41.59  |   (43)  succ(all_64_4) = all_64_3
% 246.59/41.59  |   (44)  succ(all_64_3) = all_64_2
% 246.59/41.59  |   (45)  succ(all_64_2) = all_64_1
% 246.59/41.59  |   (46)  succ(all_64_1) = all_64_0
% 246.59/41.59  |   (47)  succ(all_64_0) = n6
% 246.59/41.59  | 
% 246.59/41.59  | DELTA: instantiating (14) with fresh symbols all_74_0, all_74_1, all_74_2,
% 246.59/41.59  |        all_74_3, all_74_4, all_74_5, all_74_6, all_74_7, all_74_8, all_74_9,
% 246.59/41.59  |        all_74_10, all_74_11, all_74_12, all_74_13, all_74_14, all_74_15,
% 246.59/41.59  |        all_74_16, all_74_17, all_74_18, all_74_19, all_74_20, all_74_21,
% 246.59/41.59  |        all_74_22 gives:
% 246.59/41.60  |   (48)  minus(n6, n1) = all_74_21 & minus(n999, n1) = all_74_22 & minus(n3,
% 246.59/41.60  |           n1) = all_74_20 & $i(all_74_2) & $i(all_74_3) & $i(all_74_6) &
% 246.59/41.60  |         $i(all_74_7) & $i(all_74_10) & $i(all_74_11) & $i(all_74_14) &
% 246.59/41.60  |         $i(all_74_15) & $i(all_74_18) & $i(all_74_19) & $i(all_74_20) &
% 246.59/41.60  |         $i(all_74_21) & $i(all_74_22) & leq(pv47, all_74_21) & leq(pv5,
% 246.59/41.60  |           all_74_22) & leq(n0, pv47) & leq(n0, pv5) &  ! [v0: $i] :  ! [v1:
% 246.59/41.60  |           $i] :  ! [v2: $i] : ( ~ (a_select3(id_ds1_filter, v0, v1) = v2) |  ~
% 246.59/41.60  |           $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |
% 246.59/41.60  |            ~ leq(n0, v1) |  ~ leq(n0, v0) | (a_select3(id_ds1_filter, v1, v0)
% 246.59/41.60  |             = v2 & $i(v2))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 246.59/41.60  |           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 246.59/41.60  |           |  ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) | 
% 246.59/41.60  |           ~ leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 &
% 246.59/41.60  |             $i(v2))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 246.59/41.60  |           (a_select3(r_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 246.59/41.60  |           leq(v1, all_74_20) |  ~ leq(v0, all_74_20) |  ~ leq(n0, v1) |  ~
% 246.59/41.60  |           leq(n0, v0) | (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2))) &  !
% 246.59/41.60  |         [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(q_ds1_filter,
% 246.59/41.60  |               v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_21) | 
% 246.59/41.60  |           ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 246.59/41.60  |           (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2))) & (( ~ (all_74_0 =
% 246.59/41.60  |               all_74_1) & a_select3(q_ds1_filter, all_74_2, all_74_3) =
% 246.59/41.60  |             all_74_0 & a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1
% 246.59/41.60  |             & $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_21) &
% 246.59/41.60  |             leq(all_74_3, all_74_21) & leq(n0, all_74_2) & leq(n0, all_74_3))
% 246.59/41.60  |           | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6,
% 246.59/41.60  |               all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7,
% 246.59/41.60  |               all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) &
% 246.59/41.60  |             leq(all_74_6, all_74_20) & leq(all_74_7, all_74_20) & leq(n0,
% 246.59/41.60  |               all_74_6) & leq(n0, all_74_7)) | ( ~ (all_74_8 = all_74_9) &
% 246.59/41.60  |             a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8 &
% 246.59/41.60  |             a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9 &
% 246.59/41.60  |             $i(all_74_8) & $i(all_74_9) & leq(all_74_10, all_74_21) &
% 246.59/41.60  |             leq(all_74_11, all_74_21) & leq(n0, all_74_10) & leq(n0,
% 246.59/41.60  |               all_74_11)) | ( ~ (all_74_12 = all_74_13) &
% 246.59/41.60  |             a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 &
% 246.59/41.60  |             a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 &
% 246.59/41.60  |             $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) &
% 246.59/41.60  |             leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0,
% 246.59/41.60  |               all_74_15)) | ( ~ (all_74_16 = all_74_17) &
% 246.59/41.60  |             a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 &
% 246.59/41.60  |             a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 &
% 246.59/41.60  |             $i(all_74_16) & $i(all_74_17) & leq(all_74_18, all_74_21) &
% 246.59/41.60  |             leq(all_74_19, all_74_21) & leq(n0, all_74_18) & leq(n0,
% 246.59/41.60  |               all_74_19)))
% 246.59/41.60  | 
% 246.59/41.60  | ALPHA: (48) implies:
% 246.59/41.60  |   (49)  $i(all_74_19)
% 246.59/41.60  |   (50)  $i(all_74_18)
% 246.59/41.60  |   (51)  $i(all_74_15)
% 246.59/41.60  |   (52)  $i(all_74_14)
% 246.59/41.60  |   (53)  $i(all_74_11)
% 246.59/41.60  |   (54)  $i(all_74_10)
% 246.59/41.60  |   (55)  $i(all_74_7)
% 246.59/41.60  |   (56)  $i(all_74_6)
% 246.59/41.60  |   (57)  $i(all_74_3)
% 246.59/41.60  |   (58)  $i(all_74_2)
% 246.59/41.60  |   (59)  minus(n3, n1) = all_74_20
% 246.59/41.60  |   (60)  minus(n6, n1) = all_74_21
% 246.59/41.60  |   (61)  ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2,
% 246.59/41.60  |             all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3, all_74_2)
% 246.59/41.60  |           = all_74_1 & $i(all_74_0) & $i(all_74_1) & leq(all_74_2, all_74_21)
% 246.59/41.60  |           & leq(all_74_3, all_74_21) & leq(n0, all_74_2) & leq(n0, all_74_3))
% 246.59/41.60  |         | ( ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6,
% 246.59/41.60  |             all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7, all_74_6)
% 246.59/41.60  |           = all_74_5 & $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_20)
% 246.59/41.60  |           & leq(all_74_7, all_74_20) & leq(n0, all_74_6) & leq(n0, all_74_7))
% 246.59/41.60  |         | ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10,
% 246.59/41.60  |             all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11,
% 246.59/41.60  |             all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) &
% 246.59/41.60  |           leq(all_74_10, all_74_21) & leq(all_74_11, all_74_21) & leq(n0,
% 246.59/41.60  |             all_74_10) & leq(n0, all_74_11)) | ( ~ (all_74_12 = all_74_13) &
% 246.59/41.60  |           a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12 &
% 246.59/41.60  |           a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13 &
% 246.59/41.60  |           $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) &
% 246.59/41.60  |           leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0, all_74_15))
% 246.59/41.60  |         | ( ~ (all_74_16 = all_74_17) & a_select3(id_ds1_filter, all_74_18,
% 246.59/41.60  |             all_74_19) = all_74_16 & a_select3(id_ds1_filter, all_74_19,
% 246.59/41.60  |             all_74_18) = all_74_17 & $i(all_74_16) & $i(all_74_17) &
% 246.59/41.60  |           leq(all_74_18, all_74_21) & leq(all_74_19, all_74_21) & leq(n0,
% 246.59/41.60  |             all_74_18) & leq(n0, all_74_19))
% 246.59/41.61  |   (62)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(q_ds1_filter,
% 246.59/41.61  |               v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_21) | 
% 246.59/41.61  |           ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 246.59/41.61  |           (a_select3(q_ds1_filter, v1, v0) = v2 & $i(v2)))
% 246.59/41.61  |   (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 246.59/41.61  |               v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_20) | 
% 246.59/41.61  |           ~ leq(v0, all_74_20) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 246.59/41.61  |           (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 246.59/41.61  |   (64)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 246.59/41.61  |           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0)
% 246.59/41.61  |           |  ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) | 
% 246.59/41.61  |           ~ leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 &
% 246.59/41.61  |             $i(v2)))
% 246.59/41.61  |   (65)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 246.59/41.61  |           (a_select3(id_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 246.59/41.61  |           leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 246.59/41.61  |           leq(n0, v0) | (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 246.59/41.61  | 
% 246.59/41.61  | GROUND_INST: instantiating (16) with all_60_2, all_62_3, n0, simplifying with
% 246.59/41.61  |              (29), (35) gives:
% 246.59/41.61  |   (66)  all_62_3 = all_60_2
% 246.59/41.61  | 
% 246.59/41.61  | GROUND_INST: instantiating (16) with all_57_1, all_62_3, n0, simplifying with
% 246.59/41.61  |              (24), (35) gives:
% 246.59/41.61  |   (67)  all_62_3 = all_57_1
% 246.59/41.61  | 
% 246.59/41.61  | GROUND_INST: instantiating (16) with all_55_0, all_62_3, n0, simplifying with
% 246.59/41.61  |              (20), (35) gives:
% 246.59/41.61  |   (68)  all_62_3 = all_55_0
% 246.59/41.61  | 
% 246.59/41.61  | GROUND_INST: instantiating (16) with all_57_1, all_64_4, n0, simplifying with
% 246.59/41.61  |              (24), (42) gives:
% 246.59/41.61  |   (69)  all_64_4 = all_57_1
% 246.59/41.61  | 
% 246.59/41.61  | GROUND_INST: instantiating (16) with n1, all_64_4, n0, simplifying with (9),
% 246.59/41.61  |              (42) gives:
% 246.59/41.61  |   (70)  all_64_4 = n1
% 246.59/41.61  | 
% 246.59/41.61  | COMBINE_EQS: (69), (70) imply:
% 246.59/41.61  |   (71)  all_57_1 = n1
% 246.59/41.61  | 
% 246.59/41.61  | SIMP: (71) implies:
% 246.59/41.61  |   (72)  all_57_1 = n1
% 246.59/41.61  | 
% 246.59/41.61  | COMBINE_EQS: (66), (68) imply:
% 246.59/41.61  |   (73)  all_60_2 = all_55_0
% 246.59/41.61  | 
% 246.59/41.61  | COMBINE_EQS: (66), (67) imply:
% 246.59/41.61  |   (74)  all_60_2 = all_57_1
% 246.59/41.61  | 
% 246.59/41.61  | COMBINE_EQS: (73), (74) imply:
% 246.59/41.61  |   (75)  all_57_1 = all_55_0
% 246.59/41.61  | 
% 246.59/41.61  | SIMP: (75) implies:
% 246.59/41.61  |   (76)  all_57_1 = all_55_0
% 246.59/41.61  | 
% 246.59/41.61  | COMBINE_EQS: (72), (76) imply:
% 246.59/41.61  |   (77)  all_55_0 = n1
% 246.59/41.61  | 
% 246.59/41.61  | COMBINE_EQS: (73), (77) imply:
% 246.59/41.61  |   (78)  all_60_2 = n1
% 246.59/41.61  | 
% 246.59/41.61  | COMBINE_EQS: (66), (78) imply:
% 246.59/41.61  |   (79)  all_62_3 = n1
% 246.59/41.61  | 
% 246.59/41.61  | REDUCE: (43), (70) imply:
% 246.59/41.61  |   (80)  succ(n1) = all_64_3
% 246.59/41.61  | 
% 246.59/41.61  | REDUCE: (36), (79) imply:
% 246.59/41.61  |   (81)  succ(n1) = all_62_2
% 246.59/41.61  | 
% 246.59/41.61  | REDUCE: (30), (78) imply:
% 246.59/41.61  |   (82)  succ(n1) = all_60_1
% 246.59/41.61  | 
% 246.59/41.61  | REDUCE: (25), (72) imply:
% 246.59/41.61  |   (83)  succ(n1) = all_57_0
% 246.59/41.61  | 
% 246.59/41.61  | REDUCE: (21), (77) imply:
% 246.59/41.61  |   (84)  succ(n1) = n2
% 246.59/41.61  | 
% 246.59/41.61  | REDUCE: (19), (77) imply:
% 246.59/41.62  |   (85)  $i(n1)
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with all_60_1, all_62_2, n1, simplifying with
% 246.59/41.62  |              (81), (82) gives:
% 246.59/41.62  |   (86)  all_62_2 = all_60_1
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with all_57_0, all_62_2, n1, simplifying with
% 246.59/41.62  |              (81), (83) gives:
% 246.59/41.62  |   (87)  all_62_2 = all_57_0
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with all_60_1, all_64_3, n1, simplifying with
% 246.59/41.62  |              (80), (82) gives:
% 246.59/41.62  |   (88)  all_64_3 = all_60_1
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with n2, all_64_3, n1, simplifying with (80),
% 246.59/41.62  |              (84) gives:
% 246.59/41.62  |   (89)  all_64_3 = n2
% 246.59/41.62  | 
% 246.59/41.62  | COMBINE_EQS: (88), (89) imply:
% 246.59/41.62  |   (90)  all_60_1 = n2
% 246.59/41.62  | 
% 246.59/41.62  | SIMP: (90) implies:
% 246.59/41.62  |   (91)  all_60_1 = n2
% 246.59/41.62  | 
% 246.59/41.62  | COMBINE_EQS: (86), (87) imply:
% 246.59/41.62  |   (92)  all_60_1 = all_57_0
% 246.59/41.62  | 
% 246.59/41.62  | SIMP: (92) implies:
% 246.59/41.62  |   (93)  all_60_1 = all_57_0
% 246.59/41.62  | 
% 246.59/41.62  | COMBINE_EQS: (91), (93) imply:
% 246.59/41.62  |   (94)  all_57_0 = n2
% 246.59/41.62  | 
% 246.59/41.62  | SIMP: (94) implies:
% 246.59/41.62  |   (95)  all_57_0 = n2
% 246.59/41.62  | 
% 246.59/41.62  | COMBINE_EQS: (87), (95) imply:
% 246.59/41.62  |   (96)  all_62_2 = n2
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (44), (89) imply:
% 246.59/41.62  |   (97)  succ(n2) = all_64_2
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (37), (96) imply:
% 246.59/41.62  |   (98)  succ(n2) = all_62_1
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (31), (91) imply:
% 246.59/41.62  |   (99)  succ(n2) = all_60_0
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (26), (95) imply:
% 246.59/41.62  |   (100)  succ(n2) = n3
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (23), (95) imply:
% 246.59/41.62  |   (101)  $i(n2)
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with all_60_0, all_62_1, n2, simplifying with
% 246.59/41.62  |              (98), (99) gives:
% 246.59/41.62  |   (102)  all_62_1 = all_60_0
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with all_62_1, all_64_2, n2, simplifying with
% 246.59/41.62  |              (97), (98) gives:
% 246.59/41.62  |   (103)  all_64_2 = all_62_1
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with n3, all_64_2, n2, simplifying with (97),
% 246.59/41.62  |              (100) gives:
% 246.59/41.62  |   (104)  all_64_2 = n3
% 246.59/41.62  | 
% 246.59/41.62  | COMBINE_EQS: (103), (104) imply:
% 246.59/41.62  |   (105)  all_62_1 = n3
% 246.59/41.62  | 
% 246.59/41.62  | SIMP: (105) implies:
% 246.59/41.62  |   (106)  all_62_1 = n3
% 246.59/41.62  | 
% 246.59/41.62  | COMBINE_EQS: (102), (106) imply:
% 246.59/41.62  |   (107)  all_60_0 = n3
% 246.59/41.62  | 
% 246.59/41.62  | SIMP: (107) implies:
% 246.59/41.62  |   (108)  all_60_0 = n3
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (45), (104) imply:
% 246.59/41.62  |   (109)  succ(n3) = all_64_1
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (38), (106) imply:
% 246.59/41.62  |   (110)  succ(n3) = all_62_0
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (32), (108) imply:
% 246.59/41.62  |   (111)  succ(n3) = n4
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (28), (108) imply:
% 246.59/41.62  |   (112)  $i(n3)
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with all_62_0, all_64_1, n3, simplifying with
% 246.59/41.62  |              (109), (110) gives:
% 246.59/41.62  |   (113)  all_64_1 = all_62_0
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with n4, all_64_1, n3, simplifying with (109),
% 246.59/41.62  |              (111) gives:
% 246.59/41.62  |   (114)  all_64_1 = n4
% 246.59/41.62  | 
% 246.59/41.62  | COMBINE_EQS: (113), (114) imply:
% 246.59/41.62  |   (115)  all_62_0 = n4
% 246.59/41.62  | 
% 246.59/41.62  | SIMP: (115) implies:
% 246.59/41.62  |   (116)  all_62_0 = n4
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (46), (114) imply:
% 246.59/41.62  |   (117)  succ(n4) = all_64_0
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (39), (116) imply:
% 246.59/41.62  |   (118)  succ(n4) = n5
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (34), (116) imply:
% 246.59/41.62  |   (119)  $i(n4)
% 246.59/41.62  | 
% 246.59/41.62  | GROUND_INST: instantiating (16) with n5, all_64_0, n4, simplifying with (117),
% 246.59/41.62  |              (118) gives:
% 246.59/41.62  |   (120)  all_64_0 = n5
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (47), (120) imply:
% 246.59/41.62  |   (121)  succ(n5) = n6
% 246.59/41.62  | 
% 246.59/41.62  | REDUCE: (41), (120) imply:
% 246.59/41.62  |   (122)  $i(n5)
% 246.59/41.62  | 
% 246.59/41.63  | GROUND_INST: instantiating (pred_succ) with n1, n2, simplifying with (84),
% 246.59/41.63  |              (85) gives:
% 246.59/41.63  |   (123)  pred(n2) = n1
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (pred_succ) with n2, n3, simplifying with (100),
% 246.59/41.63  |              (101) gives:
% 246.59/41.63  |   (124)  pred(n3) = n2
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (pred_succ) with n3, n4, simplifying with (111),
% 246.59/41.63  |              (112) gives:
% 246.59/41.63  |   (125)  pred(n4) = n3
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (118),
% 246.59/41.63  |              (119) gives:
% 246.59/41.63  |   (126)  pred(n5) = n4
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (pred_succ) with n5, n6, simplifying with (121),
% 246.59/41.63  |              (122) gives:
% 246.59/41.63  |   (127)  pred(n6) = n5
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (2) with n3, all_74_20, simplifying with (59),
% 246.59/41.63  |              (112) gives:
% 246.59/41.63  |   (128)  pred(n3) = all_74_20 & $i(all_74_20)
% 246.59/41.63  | 
% 246.59/41.63  | ALPHA: (128) implies:
% 246.59/41.63  |   (129)  $i(all_74_20)
% 246.59/41.63  |   (130)  pred(n3) = all_74_20
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (2) with n6, all_74_21, simplifying with (13), (60)
% 246.59/41.63  |              gives:
% 246.59/41.63  |   (131)  pred(n6) = all_74_21 & $i(all_74_21)
% 246.59/41.63  | 
% 246.59/41.63  | ALPHA: (131) implies:
% 246.59/41.63  |   (132)  $i(all_74_21)
% 246.59/41.63  |   (133)  pred(n6) = all_74_21
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (15) with n2, all_74_20, n3, simplifying with
% 246.59/41.63  |              (124), (130) gives:
% 246.59/41.63  |   (134)  all_74_20 = n2
% 246.59/41.63  | 
% 246.59/41.63  | GROUND_INST: instantiating (15) with n5, all_74_21, n6, simplifying with
% 246.59/41.63  |              (127), (133) gives:
% 246.59/41.63  |   (135)  all_74_21 = n5
% 246.59/41.63  | 
% 246.59/41.63  | BETA: splitting (61) gives:
% 246.59/41.63  | 
% 246.59/41.63  | Case 1:
% 246.59/41.63  | | 
% 246.59/41.63  | |   (136)  ( ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2,
% 246.59/41.63  | |              all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3,
% 246.59/41.63  | |              all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) &
% 246.59/41.63  | |            leq(all_74_2, all_74_21) & leq(all_74_3, all_74_21) & leq(n0,
% 246.59/41.63  | |              all_74_2) & leq(n0, all_74_3)) | ( ~ (all_74_4 = all_74_5) &
% 246.59/41.63  | |            a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4 &
% 246.59/41.63  | |            a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5 &
% 246.59/41.63  | |            $i(all_74_4) & $i(all_74_5) & leq(all_74_6, all_74_20) &
% 246.59/41.63  | |            leq(all_74_7, all_74_20) & leq(n0, all_74_6) & leq(n0, all_74_7))
% 246.59/41.63  | | 
% 246.59/41.63  | | BETA: splitting (136) gives:
% 246.59/41.63  | | 
% 246.59/41.63  | | Case 1:
% 246.59/41.63  | | | 
% 246.59/41.63  | | |   (137)   ~ (all_74_0 = all_74_1) & a_select3(q_ds1_filter, all_74_2,
% 246.59/41.63  | | |            all_74_3) = all_74_0 & a_select3(q_ds1_filter, all_74_3,
% 246.59/41.63  | | |            all_74_2) = all_74_1 & $i(all_74_0) & $i(all_74_1) &
% 246.59/41.63  | | |          leq(all_74_2, all_74_21) & leq(all_74_3, all_74_21) & leq(n0,
% 246.59/41.63  | | |            all_74_2) & leq(n0, all_74_3)
% 246.59/41.63  | | | 
% 246.59/41.63  | | | ALPHA: (137) implies:
% 246.59/41.63  | | |   (138)   ~ (all_74_0 = all_74_1)
% 246.59/41.63  | | |   (139)  leq(n0, all_74_3)
% 246.59/41.63  | | |   (140)  leq(n0, all_74_2)
% 246.59/41.63  | | |   (141)  leq(all_74_3, all_74_21)
% 246.59/41.63  | | |   (142)  leq(all_74_2, all_74_21)
% 246.59/41.63  | | |   (143)  a_select3(q_ds1_filter, all_74_3, all_74_2) = all_74_1
% 246.59/41.63  | | |   (144)  a_select3(q_ds1_filter, all_74_2, all_74_3) = all_74_0
% 246.59/41.63  | | | 
% 246.59/41.63  | | | REDUCE: (135), (142) imply:
% 246.59/41.63  | | |   (145)  leq(all_74_2, n5)
% 246.59/41.63  | | | 
% 246.59/41.63  | | | REDUCE: (135), (141) imply:
% 246.59/41.63  | | |   (146)  leq(all_74_3, n5)
% 246.59/41.63  | | | 
% 246.59/41.63  | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_3, simplifying with
% 246.59/41.63  | | |              (12), (57), (139) gives:
% 246.59/41.63  | | |   (147)  all_74_3 = n0 | gt(all_74_3, n0)
% 246.59/41.63  | | | 
% 246.59/41.63  | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_2, simplifying with
% 246.59/41.63  | | |              (12), (58), (140) gives:
% 246.59/41.63  | | |   (148)  all_74_2 = n0 | gt(all_74_2, n0)
% 246.59/41.63  | | | 
% 246.97/41.64  | | | GROUND_INST: instantiating (3) with all_74_3, simplifying with (57),
% 246.97/41.64  | | |              (139), (146) gives:
% 246.97/41.64  | | |   (149)  all_74_3 = n5 | all_74_3 = n4 | all_74_3 = n3 | all_74_3 = n2 |
% 246.97/41.64  | | |          all_74_3 = n1 | all_74_3 = n0
% 246.97/41.64  | | | 
% 246.97/41.64  | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n5, simplifying with
% 246.97/41.64  | | |              (57), (122), (146) gives:
% 246.97/41.64  | | |   (150)  all_74_3 = n5 | gt(n5, all_74_3)
% 246.97/41.64  | | | 
% 246.97/41.64  | | | GROUND_INST: instantiating (3) with all_74_2, simplifying with (58),
% 246.97/41.64  | | |              (140), (145) gives:
% 246.97/41.64  | | |   (151)  all_74_2 = n5 | all_74_2 = n4 | all_74_2 = n3 | all_74_2 = n2 |
% 246.97/41.64  | | |          all_74_2 = n1 | all_74_2 = n0
% 246.97/41.64  | | | 
% 246.97/41.64  | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n5, simplifying with
% 246.97/41.64  | | |              (58), (122), (145) gives:
% 246.97/41.64  | | |   (152)  all_74_2 = n5 | gt(n5, all_74_2)
% 246.97/41.64  | | | 
% 246.97/41.64  | | | BETA: splitting (148) gives:
% 246.97/41.64  | | | 
% 246.97/41.64  | | | Case 1:
% 246.97/41.64  | | | | 
% 246.97/41.64  | | | |   (153)  gt(all_74_2, n0)
% 246.97/41.64  | | | | 
% 246.97/41.64  | | | | BETA: splitting (147) gives:
% 246.97/41.64  | | | | 
% 246.97/41.64  | | | | Case 1:
% 246.97/41.64  | | | | | 
% 246.97/41.64  | | | | |   (154)  gt(all_74_3, n0)
% 246.97/41.64  | | | | | 
% 246.97/41.64  | | | | | BETA: splitting (152) gives:
% 246.97/41.64  | | | | | 
% 246.97/41.64  | | | | | Case 1:
% 246.97/41.64  | | | | | | 
% 246.97/41.64  | | | | | |   (155)  gt(n5, all_74_2)
% 246.97/41.64  | | | | | | 
% 246.97/41.64  | | | | | | BETA: splitting (150) gives:
% 246.97/41.64  | | | | | | 
% 246.97/41.64  | | | | | | Case 1:
% 246.97/41.64  | | | | | | | 
% 246.97/41.64  | | | | | | |   (156)  gt(n5, all_74_3)
% 246.97/41.64  | | | | | | | 
% 246.97/41.64  | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying
% 246.97/41.64  | | | | | | |              with (57), (122), (126), (156) gives:
% 246.97/41.64  | | | | | | |   (157)  leq(all_74_3, n4)
% 246.97/41.64  | | | | | | | 
% 246.97/41.64  | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying
% 246.97/41.64  | | | | | | |              with (58), (122), (126), (155) gives:
% 246.97/41.64  | | | | | | |   (158)  leq(all_74_2, n4)
% 246.97/41.64  | | | | | | | 
% 246.97/41.64  | | | | | | | BETA: splitting (151) gives:
% 246.97/41.64  | | | | | | | 
% 246.97/41.64  | | | | | | | Case 1:
% 246.97/41.64  | | | | | | | | 
% 246.97/41.64  | | | | | | | |   (159)  all_74_2 = n0
% 246.97/41.64  | | | | | | | | 
% 246.97/41.64  | | | | | | | | REF_CLOSE: (58), (153), (159), (irreflexivity_gt) are
% 246.97/41.64  | | | | | | | |            inconsistent by sub-proof #59.
% 246.97/41.64  | | | | | | | | 
% 246.97/41.64  | | | | | | | Case 2:
% 246.97/41.64  | | | | | | | | 
% 246.97/41.64  | | | | | | | |   (160)   ~ (all_74_2 = n0)
% 246.97/41.64  | | | | | | | | 
% 246.97/41.64  | | | | | | | | BETA: splitting (149) gives:
% 246.97/41.64  | | | | | | | | 
% 246.97/41.64  | | | | | | | | Case 1:
% 246.97/41.64  | | | | | | | | | 
% 246.97/41.64  | | | | | | | | |   (161)  all_74_3 = n0
% 246.97/41.64  | | | | | | | | | 
% 246.97/41.64  | | | | | | | | | REF_CLOSE: (57), (154), (161), (irreflexivity_gt) are
% 246.97/41.64  | | | | | | | | |            inconsistent by sub-proof #58.
% 246.97/41.64  | | | | | | | | | 
% 246.97/41.64  | | | | | | | | Case 2:
% 246.97/41.64  | | | | | | | | | 
% 246.97/41.64  | | | | | | | | |   (162)   ~ (all_74_3 = n0)
% 246.97/41.64  | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4,
% 246.97/41.65  | | | | | | | | |              simplifying with (57), (119), (157) gives:
% 246.97/41.65  | | | | | | | | |   (163)  all_74_3 = n4 | gt(n4, all_74_3)
% 246.97/41.65  | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4,
% 246.97/41.65  | | | | | | | | |              simplifying with (58), (119), (158) gives:
% 246.97/41.65  | | | | | | | | |   (164)  all_74_2 = n4 | gt(n4, all_74_2)
% 246.97/41.65  | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | BETA: splitting (163) gives:
% 246.97/41.65  | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | Case 1:
% 246.97/41.65  | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | |   (165)  gt(n4, all_74_3)
% 246.97/41.65  | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3,
% 246.97/41.65  | | | | | | | | | |              simplifying with (57), (119), (125), (165) gives:
% 246.97/41.65  | | | | | | | | | |   (166)  leq(all_74_3, n3)
% 246.97/41.65  | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3,
% 246.97/41.65  | | | | | | | | | |              simplifying with (57), (112), (166) gives:
% 246.97/41.65  | | | | | | | | | |   (167)  all_74_3 = n3 | gt(n3, all_74_3)
% 246.97/41.65  | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | BETA: splitting (164) gives:
% 246.97/41.65  | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | Case 1:
% 246.97/41.65  | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | |   (168)  gt(n4, all_74_2)
% 246.97/41.65  | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 246.97/41.65  | | | | | | | | | | |              simplifying with (58), (119), (125), (168) gives:
% 246.97/41.65  | | | | | | | | | | |   (169)  leq(all_74_2, n3)
% 246.97/41.65  | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 246.97/41.65  | | | | | | | | | | |              simplifying with (58), (112), (169) gives:
% 246.97/41.65  | | | | | | | | | | |   (170)  all_74_2 = n3 | gt(n3, all_74_2)
% 246.97/41.65  | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | BETA: splitting (167) gives:
% 246.97/41.65  | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | Case 1:
% 246.97/41.65  | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | |   (171)  gt(n3, all_74_3)
% 246.97/41.65  | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 246.97/41.65  | | | | | | | | | | | |              simplifying with (57), (112), (124), (171) gives:
% 246.97/41.65  | | | | | | | | | | | |   (172)  leq(all_74_3, n2)
% 246.97/41.65  | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 246.97/41.65  | | | | | | | | | | | |              simplifying with (57), (101), (172) gives:
% 246.97/41.65  | | | | | | | | | | | |   (173)  all_74_3 = n2 | gt(n2, all_74_3)
% 246.97/41.65  | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | BETA: splitting (170) gives:
% 246.97/41.65  | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | Case 1:
% 246.97/41.65  | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | |   (174)  gt(n3, all_74_2)
% 246.97/41.65  | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 246.97/41.65  | | | | | | | | | | | | |              simplifying with (58), (112), (124), (174) gives:
% 246.97/41.65  | | | | | | | | | | | | |   (175)  leq(all_74_2, n2)
% 246.97/41.65  | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 246.97/41.65  | | | | | | | | | | | | |              simplifying with (58), (101), (175) gives:
% 246.97/41.65  | | | | | | | | | | | | |   (176)  all_74_2 = n2 | gt(n2, all_74_2)
% 246.97/41.65  | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | BETA: splitting (173) gives:
% 246.97/41.65  | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | Case 1:
% 246.97/41.65  | | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | |   (177)  gt(n2, all_74_3)
% 246.97/41.65  | | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 246.97/41.65  | | | | | | | | | | | | | |              simplifying with (57), (101), (123), (177) gives:
% 246.97/41.65  | | | | | | | | | | | | | |   (178)  leq(all_74_3, n1)
% 246.97/41.65  | | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with
% 246.97/41.65  | | | | | | | | | | | | | |              (57), (139), (178) gives:
% 246.97/41.65  | | | | | | | | | | | | | |   (179)  all_74_3 = n1 | all_74_3 = n0
% 246.97/41.65  | | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 246.97/41.65  | | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | | Case 1:
% 246.97/41.65  | | | | | | | | | | | | | | | 
% 246.97/41.65  | | | | | | | | | | | | | | |   (180)  all_74_3 = n0
% 246.97/41.65  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | REDUCE: (162), (180) imply:
% 246.97/41.66  | | | | | | | | | | | | | | |   (181)  $false
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | Case 2:
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | |   (182)  all_74_3 = n1
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | REDUCE: (144), (182) imply:
% 246.97/41.66  | | | | | | | | | | | | | | |   (183)  a_select3(q_ds1_filter, all_74_2, n1) = all_74_0
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | REDUCE: (143), (182) imply:
% 246.97/41.66  | | | | | | | | | | | | | | |   (184)  a_select3(q_ds1_filter, n1, all_74_2) = all_74_1
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | REDUCE: (146), (182) imply:
% 246.97/41.66  | | | | | | | | | | | | | | |   (185)  leq(n1, n5)
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | REDUCE: (139), (182) imply:
% 246.97/41.66  | | | | | | | | | | | | | | |   (186)  leq(n0, n1)
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 246.97/41.66  | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | Case 1:
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | |   (187)  gt(n2, all_74_2)
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 246.97/41.66  | | | | | | | | | | | | | | | |              simplifying with (58), (101), (123), (187) gives:
% 246.97/41.66  | | | | | | | | | | | | | | | |   (188)  leq(all_74_2, n1)
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with
% 246.97/41.66  | | | | | | | | | | | | | | | |              (58), (140), (188) gives:
% 246.97/41.66  | | | | | | | | | | | | | | | |   (189)  all_74_2 = n1 | all_74_2 = n0
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | Case 1:
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (190)  all_74_2 = n0
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | REDUCE: (160), (190) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (191)  $false
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | Case 2:
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (192)  all_74_2 = n1
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | REDUCE: (183), (192) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (193)  a_select3(q_ds1_filter, n1, n1) = all_74_0
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | REDUCE: (184), (192) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (194)  a_select3(q_ds1_filter, n1, n1) = all_74_1
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n1,
% 246.97/41.66  | | | | | | | | | | | | | | | | |              n1, q_ds1_filter, simplifying with (193), (194)
% 246.97/41.66  | | | | | | | | | | | | | | | | |              gives:
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (195)  all_74_0 = all_74_1
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | REDUCE: (138), (195) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (196)  $false
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | End of split
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | Case 2:
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | |   (197)  all_74_2 = n2
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | REDUCE: (183), (197) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | |   (198)  a_select3(q_ds1_filter, n2, n1) = all_74_0
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | REDUCE: (184), (197) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | |   (199)  a_select3(q_ds1_filter, n1, n2) = all_74_1
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | REDUCE: (145), (197) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | |   (200)  leq(n2, n5)
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | REDUCE: (140), (197) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | |   (201)  leq(n0, n2)
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n2, all_74_1,
% 246.97/41.66  | | | | | | | | | | | | | | | |              simplifying with (85), (101), (186), (199), (201)
% 246.97/41.66  | | | | | | | | | | | | | | | |              gives:
% 246.97/41.66  | | | | | | | | | | | | | | | |   (202)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 246.97/41.66  | | | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n2, n1) = all_74_1 &
% 246.97/41.66  | | | | | | | | | | | | | | | |            $i(all_74_1))
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 246.97/41.66  | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | Case 1:
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (203)   ~ leq(n2, all_74_21)
% 246.97/41.66  | | | | | | | | | | | | | | | | | 
% 246.97/41.66  | | | | | | | | | | | | | | | | | REDUCE: (135), (203) imply:
% 246.97/41.66  | | | | | | | | | | | | | | | | |   (204)   ~ leq(n2, n5)
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | PRED_UNIFY: (200), (204) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | | |   (205)  $false
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | Case 2:
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | |   (206)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 246.97/41.67  | | | | | | | | | | | | | | | | |              n2, n1) = all_74_1 & $i(all_74_1))
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | Case 1:
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | |   (207)   ~ leq(n1, all_74_21)
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | | REDUCE: (135), (207) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | | | |   (208)   ~ leq(n1, n5)
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | | PRED_UNIFY: (185), (208) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | | | |   (209)  $false
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | Case 2:
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | |   (210)  a_select3(q_ds1_filter, n2, n1) = all_74_1 &
% 246.97/41.67  | | | | | | | | | | | | | | | | | |          $i(all_74_1)
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 246.97/41.67  | | | | | | | | | | | | | | | | | |   (211)  a_select3(q_ds1_filter, n2, n1) = all_74_1
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n1,
% 246.97/41.67  | | | | | | | | | | | | | | | | | |              n2, q_ds1_filter, simplifying with (198), (211)
% 246.97/41.67  | | | | | | | | | | | | | | | | | |              gives:
% 246.97/41.67  | | | | | | | | | | | | | | | | | |   (212)  all_74_0 = all_74_1
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | | REDUCE: (138), (212) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | | | |   (213)  $false
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 246.97/41.67  | | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | End of split
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | End of split
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | End of split
% 246.97/41.67  | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | End of split
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | Case 2:
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | |   (214)  all_74_3 = n2
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | REDUCE: (144), (214) imply:
% 246.97/41.67  | | | | | | | | | | | | | |   (215)  a_select3(q_ds1_filter, all_74_2, n2) = all_74_0
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | REDUCE: (143), (214) imply:
% 246.97/41.67  | | | | | | | | | | | | | |   (216)  a_select3(q_ds1_filter, n2, all_74_2) = all_74_1
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | REDUCE: (146), (214) imply:
% 246.97/41.67  | | | | | | | | | | | | | |   (217)  leq(n2, n5)
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | REDUCE: (139), (214) imply:
% 246.97/41.67  | | | | | | | | | | | | | |   (218)  leq(n0, n2)
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 246.97/41.67  | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | Case 1:
% 246.97/41.67  | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | |   (219)  gt(n2, all_74_2)
% 246.97/41.67  | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 246.97/41.67  | | | | | | | | | | | | | | |              simplifying with (58), (101), (123), (219) gives:
% 246.97/41.67  | | | | | | | | | | | | | | |   (220)  leq(all_74_2, n1)
% 246.97/41.67  | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with
% 246.97/41.67  | | | | | | | | | | | | | | |              (58), (140), (220) gives:
% 246.97/41.67  | | | | | | | | | | | | | | |   (221)  all_74_2 = n1 | all_74_2 = n0
% 246.97/41.67  | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 246.97/41.67  | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | Case 1:
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | |   (222)  all_74_2 = n0
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | REDUCE: (160), (222) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | |   (223)  $false
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | Case 2:
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | |   (224)  all_74_2 = n1
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | REDUCE: (215), (224) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | |   (225)  a_select3(q_ds1_filter, n1, n2) = all_74_0
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | REDUCE: (216), (224) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | |   (226)  a_select3(q_ds1_filter, n2, n1) = all_74_1
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | REDUCE: (145), (224) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | |   (227)  leq(n1, n5)
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | REDUCE: (140), (224) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | |   (228)  leq(n0, n1)
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n2, all_74_0,
% 246.97/41.67  | | | | | | | | | | | | | | | |              simplifying with (85), (101), (218), (225), (228)
% 246.97/41.67  | | | | | | | | | | | | | | | |              gives:
% 246.97/41.67  | | | | | | | | | | | | | | | |   (229)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 246.97/41.67  | | | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n2, n1) = all_74_0 &
% 246.97/41.67  | | | | | | | | | | | | | | | |            $i(all_74_0))
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 246.97/41.67  | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | Case 1:
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | |   (230)   ~ leq(n2, all_74_21)
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | REDUCE: (135), (230) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | | |   (231)   ~ leq(n2, n5)
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 246.97/41.67  | | | | | | | | | | | | | | | | | PRED_UNIFY: (217), (231) imply:
% 246.97/41.67  | | | | | | | | | | | | | | | | |   (232)  $false
% 246.97/41.67  | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 247.14/41.67  | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | Case 2:
% 247.14/41.67  | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | |   (233)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.67  | | | | | | | | | | | | | | | | |              n2, n1) = all_74_0 & $i(all_74_0))
% 247.14/41.67  | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 247.14/41.67  | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | Case 1:
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | |   (234)   ~ leq(n1, all_74_21)
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | | REDUCE: (135), (234) imply:
% 247.14/41.67  | | | | | | | | | | | | | | | | | |   (235)   ~ leq(n1, n5)
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | | PRED_UNIFY: (227), (235) imply:
% 247.14/41.67  | | | | | | | | | | | | | | | | | |   (236)  $false
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | Case 2:
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | |   (237)  a_select3(q_ds1_filter, n2, n1) = all_74_0 &
% 247.14/41.67  | | | | | | | | | | | | | | | | | |          $i(all_74_0)
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 247.14/41.67  | | | | | | | | | | | | | | | | | |   (238)  a_select3(q_ds1_filter, n2, n1) = all_74_0
% 247.14/41.67  | | | | | | | | | | | | | | | | | | 
% 247.14/41.67  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n1,
% 247.14/41.67  | | | | | | | | | | | | | | | | | |              n2, q_ds1_filter, simplifying with (226), (238)
% 247.14/41.67  | | | | | | | | | | | | | | | | | |              gives:
% 247.14/41.68  | | | | | | | | | | | | | | | | | |   (239)  all_74_0 = all_74_1
% 247.14/41.68  | | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | | REDUCE: (138), (239) imply:
% 247.14/41.68  | | | | | | | | | | | | | | | | | |   (240)  $false
% 247.14/41.68  | | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 247.14/41.68  | | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | Case 2:
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | |   (241)  all_74_2 = n2
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (215), (241) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (242)  a_select3(q_ds1_filter, n2, n2) = all_74_0
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (216), (241) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (243)  a_select3(q_ds1_filter, n2, n2) = all_74_1
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n2,
% 247.14/41.68  | | | | | | | | | | | | | | |              n2, q_ds1_filter, simplifying with (242), (243)
% 247.14/41.68  | | | | | | | | | | | | | | |              gives:
% 247.14/41.68  | | | | | | | | | | | | | | |   (244)  all_74_0 = all_74_1
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (138), (244) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (245)  $false
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | Case 2:
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | |   (246)  all_74_2 = n3
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | REDUCE: (144), (246) imply:
% 247.14/41.68  | | | | | | | | | | | | |   (247)  a_select3(q_ds1_filter, n3, all_74_3) = all_74_0
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | REDUCE: (143), (246) imply:
% 247.14/41.68  | | | | | | | | | | | | |   (248)  a_select3(q_ds1_filter, all_74_3, n3) = all_74_1
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | REDUCE: (145), (246) imply:
% 247.14/41.68  | | | | | | | | | | | | |   (249)  leq(n3, n5)
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | REDUCE: (140), (246) imply:
% 247.14/41.68  | | | | | | | | | | | | |   (250)  leq(n0, n3)
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | BETA: splitting (173) gives:
% 247.14/41.68  | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | Case 1:
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | |   (251)  gt(n2, all_74_3)
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 247.14/41.68  | | | | | | | | | | | | | |              simplifying with (57), (101), (123), (251) gives:
% 247.14/41.68  | | | | | | | | | | | | | |   (252)  leq(all_74_3, n1)
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with
% 247.14/41.68  | | | | | | | | | | | | | |              (57), (139), (252) gives:
% 247.14/41.68  | | | | | | | | | | | | | |   (253)  all_74_3 = n1 | all_74_3 = n0
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | Case 1:
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | |   (254)  all_74_3 = n0
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (162), (254) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (255)  $false
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | CLOSE: (255) is inconsistent.
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | Case 2:
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | |   (256)  all_74_3 = n1
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (248), (256) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (257)  a_select3(q_ds1_filter, n1, n3) = all_74_1
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (247), (256) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (258)  a_select3(q_ds1_filter, n3, n1) = all_74_0
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (146), (256) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (259)  leq(n1, n5)
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (139), (256) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (260)  leq(n0, n1)
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n3, all_74_1,
% 247.14/41.68  | | | | | | | | | | | | | | |              simplifying with (85), (112), (250), (257), (260)
% 247.14/41.68  | | | | | | | | | | | | | | |              gives:
% 247.14/41.68  | | | | | | | | | | | | | | |   (261)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.14/41.68  | | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n3, n1) = all_74_1 &
% 247.14/41.68  | | | | | | | | | | | | | | |            $i(all_74_1))
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | Case 1:
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | |   (262)   ~ leq(n3, all_74_21)
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | REDUCE: (135), (262) imply:
% 247.14/41.68  | | | | | | | | | | | | | | | |   (263)   ~ leq(n3, n5)
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | PRED_UNIFY: (249), (263) imply:
% 247.14/41.68  | | | | | | | | | | | | | | | |   (264)  $false
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent.
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | Case 2:
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | |   (265)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.68  | | | | | | | | | | | | | | | |              n3, n1) = all_74_1 & $i(all_74_1))
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | Case 1:
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | |   (266)   ~ leq(n1, all_74_21)
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | REDUCE: (135), (266) imply:
% 247.14/41.68  | | | | | | | | | | | | | | | | |   (267)   ~ leq(n1, n5)
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | PRED_UNIFY: (259), (267) imply:
% 247.14/41.68  | | | | | | | | | | | | | | | | |   (268)  $false
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent.
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | Case 2:
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | |   (269)  a_select3(q_ds1_filter, n3, n1) = all_74_1 &
% 247.14/41.68  | | | | | | | | | | | | | | | | |          $i(all_74_1)
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 247.14/41.68  | | | | | | | | | | | | | | | | |   (270)  a_select3(q_ds1_filter, n3, n1) = all_74_1
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (258), (270) are inconsistent by
% 247.14/41.68  | | | | | | | | | | | | | | | | |            sub-proof #57.
% 247.14/41.68  | | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | End of split
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | Case 2:
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | |   (271)  all_74_3 = n2
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | REDUCE: (248), (271) imply:
% 247.14/41.68  | | | | | | | | | | | | | |   (272)  a_select3(q_ds1_filter, n2, n3) = all_74_1
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | REDUCE: (247), (271) imply:
% 247.14/41.68  | | | | | | | | | | | | | |   (273)  a_select3(q_ds1_filter, n3, n2) = all_74_0
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | REDUCE: (146), (271) imply:
% 247.14/41.68  | | | | | | | | | | | | | |   (274)  leq(n2, n5)
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | REDUCE: (139), (271) imply:
% 247.14/41.68  | | | | | | | | | | | | | |   (275)  leq(n0, n2)
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n3, all_74_1,
% 247.14/41.68  | | | | | | | | | | | | | |              simplifying with (101), (112), (250), (272), (275)
% 247.14/41.68  | | | | | | | | | | | | | |              gives:
% 247.14/41.68  | | | | | | | | | | | | | |   (276)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.14/41.68  | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n3, n2) = all_74_1 &
% 247.14/41.68  | | | | | | | | | | | | | |            $i(all_74_1))
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 247.14/41.68  | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | Case 1:
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | |   (277)   ~ leq(n3, all_74_21)
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | REDUCE: (135), (277) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (278)   ~ leq(n3, n5)
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | PRED_UNIFY: (249), (278) imply:
% 247.14/41.68  | | | | | | | | | | | | | | |   (279)  $false
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | CLOSE: (279) is inconsistent.
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | Case 2:
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | |   (280)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.68  | | | | | | | | | | | | | | |              n3, n2) = all_74_1 & $i(all_74_1))
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 247.14/41.68  | | | | | | | | | | | | | | | 
% 247.14/41.68  | | | | | | | | | | | | | | | Case 1:
% 247.14/41.68  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | |   (281)   ~ leq(n2, all_74_21)
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | REDUCE: (135), (281) imply:
% 247.14/41.69  | | | | | | | | | | | | | | | |   (282)   ~ leq(n2, n5)
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | PRED_UNIFY: (274), (282) imply:
% 247.14/41.69  | | | | | | | | | | | | | | | |   (283)  $false
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent.
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | Case 2:
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | |   (284)  a_select3(q_ds1_filter, n3, n2) = all_74_1 &
% 247.14/41.69  | | | | | | | | | | | | | | | |          $i(all_74_1)
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 247.14/41.69  | | | | | | | | | | | | | | | |   (285)  a_select3(q_ds1_filter, n3, n2) = all_74_1
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n2,
% 247.14/41.69  | | | | | | | | | | | | | | | |              n3, q_ds1_filter, simplifying with (273), (285)
% 247.14/41.69  | | | | | | | | | | | | | | | |              gives:
% 247.14/41.69  | | | | | | | | | | | | | | | |   (286)  all_74_0 = all_74_1
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | REDUCE: (138), (286) imply:
% 247.14/41.69  | | | | | | | | | | | | | | | |   (287)  $false
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | End of split
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | End of split
% 247.14/41.69  | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | End of split
% 247.14/41.69  | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | End of split
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | Case 2:
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | |   (288)  all_74_3 = n3
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | REDUCE: (144), (288) imply:
% 247.14/41.69  | | | | | | | | | | | |   (289)  a_select3(q_ds1_filter, all_74_2, n3) = all_74_0
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | REDUCE: (143), (288) imply:
% 247.14/41.69  | | | | | | | | | | | |   (290)  a_select3(q_ds1_filter, n3, all_74_2) = all_74_1
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | REDUCE: (146), (288) imply:
% 247.14/41.69  | | | | | | | | | | | |   (291)  leq(n3, n5)
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | REDUCE: (139), (288) imply:
% 247.14/41.69  | | | | | | | | | | | |   (292)  leq(n0, n3)
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | BETA: splitting (170) gives:
% 247.14/41.69  | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | Case 1:
% 247.14/41.69  | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | |   (293)  gt(n3, all_74_2)
% 247.14/41.69  | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 247.14/41.69  | | | | | | | | | | | | |              simplifying with (58), (112), (124), (293) gives:
% 247.14/41.69  | | | | | | | | | | | | |   (294)  leq(all_74_2, n2)
% 247.14/41.69  | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 247.14/41.69  | | | | | | | | | | | | |              simplifying with (58), (101), (294) gives:
% 247.14/41.69  | | | | | | | | | | | | |   (295)  all_74_2 = n2 | gt(n2, all_74_2)
% 247.14/41.69  | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | BETA: splitting (295) gives:
% 247.14/41.69  | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | Case 1:
% 247.14/41.69  | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | |   (296)  gt(n2, all_74_2)
% 247.14/41.69  | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 247.14/41.69  | | | | | | | | | | | | | |              simplifying with (58), (101), (123), (296) gives:
% 247.14/41.69  | | | | | | | | | | | | | |   (297)  leq(all_74_2, n1)
% 247.14/41.69  | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with
% 247.14/41.69  | | | | | | | | | | | | | |              (58), (140), (297) gives:
% 247.14/41.69  | | | | | | | | | | | | | |   (298)  all_74_2 = n1 | all_74_2 = n0
% 247.14/41.69  | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 247.14/41.69  | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | Case 1:
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | |   (299)  all_74_2 = n0
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | REDUCE: (160), (299) imply:
% 247.14/41.69  | | | | | | | | | | | | | | |   (300)  $false
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | CLOSE: (300) is inconsistent.
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | Case 2:
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | |   (301)  all_74_2 = n1
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | REDUCE: (289), (301) imply:
% 247.14/41.69  | | | | | | | | | | | | | | |   (302)  a_select3(q_ds1_filter, n1, n3) = all_74_0
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | REDUCE: (290), (301) imply:
% 247.14/41.69  | | | | | | | | | | | | | | |   (303)  a_select3(q_ds1_filter, n3, n1) = all_74_1
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | REDUCE: (145), (301) imply:
% 247.14/41.69  | | | | | | | | | | | | | | |   (304)  leq(n1, n5)
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | REDUCE: (140), (301) imply:
% 247.14/41.69  | | | | | | | | | | | | | | |   (305)  leq(n0, n1)
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n3, all_74_0,
% 247.14/41.69  | | | | | | | | | | | | | | |              simplifying with (85), (112), (292), (302), (305)
% 247.14/41.69  | | | | | | | | | | | | | | |              gives:
% 247.14/41.69  | | | | | | | | | | | | | | |   (306)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.14/41.69  | | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n3, n1) = all_74_0 &
% 247.14/41.69  | | | | | | | | | | | | | | |            $i(all_74_0))
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 247.14/41.69  | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | Case 1:
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | |   (307)   ~ leq(n3, all_74_21)
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | REDUCE: (135), (307) imply:
% 247.14/41.69  | | | | | | | | | | | | | | | |   (308)   ~ leq(n3, n5)
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | PRED_UNIFY: (291), (308) imply:
% 247.14/41.69  | | | | | | | | | | | | | | | |   (309)  $false
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | CLOSE: (309) is inconsistent.
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | Case 2:
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | |   (310)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.69  | | | | | | | | | | | | | | | |              n3, n1) = all_74_0 & $i(all_74_0))
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 247.14/41.69  | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | Case 1:
% 247.14/41.69  | | | | | | | | | | | | | | | | | 
% 247.14/41.69  | | | | | | | | | | | | | | | | |   (311)   ~ leq(n1, all_74_21)
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | | REDUCE: (135), (311) imply:
% 247.14/41.70  | | | | | | | | | | | | | | | | |   (312)   ~ leq(n1, n5)
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | | PRED_UNIFY: (304), (312) imply:
% 247.14/41.70  | | | | | | | | | | | | | | | | |   (313)  $false
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | | CLOSE: (313) is inconsistent.
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | Case 2:
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | |   (314)  a_select3(q_ds1_filter, n3, n1) = all_74_0 &
% 247.14/41.70  | | | | | | | | | | | | | | | | |          $i(all_74_0)
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 247.14/41.70  | | | | | | | | | | | | | | | | |   (315)  a_select3(q_ds1_filter, n3, n1) = all_74_0
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (303), (315) are inconsistent by
% 247.14/41.70  | | | | | | | | | | | | | | | | |            sub-proof #57.
% 247.14/41.70  | | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | Case 2:
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | |   (316)  all_74_2 = n2
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | REDUCE: (289), (316) imply:
% 247.14/41.70  | | | | | | | | | | | | | |   (317)  a_select3(q_ds1_filter, n2, n3) = all_74_0
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | REDUCE: (290), (316) imply:
% 247.14/41.70  | | | | | | | | | | | | | |   (318)  a_select3(q_ds1_filter, n3, n2) = all_74_1
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | REDUCE: (145), (316) imply:
% 247.14/41.70  | | | | | | | | | | | | | |   (319)  leq(n2, n5)
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | REDUCE: (140), (316) imply:
% 247.14/41.70  | | | | | | | | | | | | | |   (320)  leq(n0, n2)
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n3, all_74_0,
% 247.14/41.70  | | | | | | | | | | | | | |              simplifying with (101), (112), (292), (317), (320)
% 247.14/41.70  | | | | | | | | | | | | | |              gives:
% 247.14/41.70  | | | | | | | | | | | | | |   (321)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.14/41.70  | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n3, n2) = all_74_0 &
% 247.14/41.70  | | | | | | | | | | | | | |            $i(all_74_0))
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | Case 1:
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | |   (322)   ~ leq(n3, all_74_21)
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | REDUCE: (135), (322) imply:
% 247.14/41.70  | | | | | | | | | | | | | | |   (323)   ~ leq(n3, n5)
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | PRED_UNIFY: (291), (323) imply:
% 247.14/41.70  | | | | | | | | | | | | | | |   (324)  $false
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent.
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | Case 2:
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | |   (325)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.70  | | | | | | | | | | | | | | |              n3, n2) = all_74_0 & $i(all_74_0))
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | BETA: splitting (325) gives:
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | Case 1:
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | |   (326)   ~ leq(n2, all_74_21)
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | REDUCE: (135), (326) imply:
% 247.14/41.70  | | | | | | | | | | | | | | | |   (327)   ~ leq(n2, n5)
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | PRED_UNIFY: (319), (327) imply:
% 247.14/41.70  | | | | | | | | | | | | | | | |   (328)  $false
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | CLOSE: (328) is inconsistent.
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | Case 2:
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | |   (329)  a_select3(q_ds1_filter, n3, n2) = all_74_0 &
% 247.14/41.70  | | | | | | | | | | | | | | | |          $i(all_74_0)
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 247.14/41.70  | | | | | | | | | | | | | | | |   (330)  a_select3(q_ds1_filter, n3, n2) = all_74_0
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n2,
% 247.14/41.70  | | | | | | | | | | | | | | | |              n3, q_ds1_filter, simplifying with (318), (330)
% 247.14/41.70  | | | | | | | | | | | | | | | |              gives:
% 247.14/41.70  | | | | | | | | | | | | | | | |   (331)  all_74_0 = all_74_1
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | REDUCE: (138), (331) imply:
% 247.14/41.70  | | | | | | | | | | | | | | | |   (332)  $false
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent.
% 247.14/41.70  | | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | Case 2:
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | |   (333)  all_74_2 = n3
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | REDUCE: (289), (333) imply:
% 247.14/41.70  | | | | | | | | | | | | |   (334)  a_select3(q_ds1_filter, n3, n3) = all_74_0
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | REDUCE: (290), (333) imply:
% 247.14/41.70  | | | | | | | | | | | | |   (335)  a_select3(q_ds1_filter, n3, n3) = all_74_1
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n3,
% 247.14/41.70  | | | | | | | | | | | | |              n3, q_ds1_filter, simplifying with (334), (335)
% 247.14/41.70  | | | | | | | | | | | | |              gives:
% 247.14/41.70  | | | | | | | | | | | | |   (336)  all_74_0 = all_74_1
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | REDUCE: (138), (336) imply:
% 247.14/41.70  | | | | | | | | | | | | |   (337)  $false
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | CLOSE: (337) is inconsistent.
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | End of split
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | Case 2:
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | |   (338)  all_74_2 = n4
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | REDUCE: (144), (338) imply:
% 247.14/41.70  | | | | | | | | | | |   (339)  a_select3(q_ds1_filter, n4, all_74_3) = all_74_0
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | REDUCE: (143), (338) imply:
% 247.14/41.70  | | | | | | | | | | |   (340)  a_select3(q_ds1_filter, all_74_3, n4) = all_74_1
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | REDUCE: (145), (338) imply:
% 247.14/41.70  | | | | | | | | | | |   (341)  leq(n4, n5)
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | REDUCE: (140), (338) imply:
% 247.14/41.70  | | | | | | | | | | |   (342)  leq(n0, n4)
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | BETA: splitting (167) gives:
% 247.14/41.70  | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | Case 1:
% 247.14/41.70  | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | |   (343)  gt(n3, all_74_3)
% 247.14/41.70  | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 247.14/41.70  | | | | | | | | | | | |              simplifying with (57), (112), (124), (343) gives:
% 247.14/41.70  | | | | | | | | | | | |   (344)  leq(all_74_3, n2)
% 247.14/41.70  | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 247.14/41.70  | | | | | | | | | | | |              simplifying with (57), (101), (344) gives:
% 247.14/41.70  | | | | | | | | | | | |   (345)  all_74_3 = n2 | gt(n2, all_74_3)
% 247.14/41.70  | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | BETA: splitting (345) gives:
% 247.14/41.70  | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | Case 1:
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | |   (346)  gt(n2, all_74_3)
% 247.14/41.70  | | | | | | | | | | | | | 
% 247.14/41.70  | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 247.14/41.70  | | | | | | | | | | | | |              simplifying with (57), (101), (123), (346) gives:
% 247.14/41.71  | | | | | | | | | | | | |   (347)  leq(all_74_3, n1)
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with
% 247.14/41.71  | | | | | | | | | | | | |              (57), (139), (347) gives:
% 247.14/41.71  | | | | | | | | | | | | |   (348)  all_74_3 = n1 | all_74_3 = n0
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | BETA: splitting (348) gives:
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | Case 1:
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | |   (349)  all_74_3 = n0
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | REDUCE: (162), (349) imply:
% 247.14/41.71  | | | | | | | | | | | | | |   (350)  $false
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | CLOSE: (350) is inconsistent.
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | Case 2:
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | |   (351)  all_74_3 = n1
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | REDUCE: (340), (351) imply:
% 247.14/41.71  | | | | | | | | | | | | | |   (352)  a_select3(q_ds1_filter, n1, n4) = all_74_1
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | REDUCE: (339), (351) imply:
% 247.14/41.71  | | | | | | | | | | | | | |   (353)  a_select3(q_ds1_filter, n4, n1) = all_74_0
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | REDUCE: (146), (351) imply:
% 247.14/41.71  | | | | | | | | | | | | | |   (354)  leq(n1, n5)
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | REDUCE: (139), (351) imply:
% 247.14/41.71  | | | | | | | | | | | | | |   (355)  leq(n0, n1)
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n4, all_74_1,
% 247.14/41.71  | | | | | | | | | | | | | |              simplifying with (85), (119), (342), (352), (355)
% 247.14/41.71  | | | | | | | | | | | | | |              gives:
% 247.14/41.71  | | | | | | | | | | | | | |   (356)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.14/41.71  | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n4, n1) = all_74_1 &
% 247.14/41.71  | | | | | | | | | | | | | |            $i(all_74_1))
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | BETA: splitting (356) gives:
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | Case 1:
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | |   (357)   ~ leq(n4, all_74_21)
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | REDUCE: (135), (357) imply:
% 247.14/41.71  | | | | | | | | | | | | | | |   (358)   ~ leq(n4, n5)
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | PRED_UNIFY: (341), (358) imply:
% 247.14/41.71  | | | | | | | | | | | | | | |   (359)  $false
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | CLOSE: (359) is inconsistent.
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | Case 2:
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | |   (360)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.71  | | | | | | | | | | | | | | |              n4, n1) = all_74_1 & $i(all_74_1))
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | BETA: splitting (360) gives:
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | Case 1:
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | |   (361)   ~ leq(n1, all_74_21)
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | | REDUCE: (135), (361) imply:
% 247.14/41.71  | | | | | | | | | | | | | | | |   (362)   ~ leq(n1, n5)
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | | PRED_UNIFY: (354), (362) imply:
% 247.14/41.71  | | | | | | | | | | | | | | | |   (363)  $false
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | | CLOSE: (363) is inconsistent.
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | Case 2:
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | |   (364)  a_select3(q_ds1_filter, n4, n1) = all_74_1 &
% 247.14/41.71  | | | | | | | | | | | | | | | |          $i(all_74_1)
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | | ALPHA: (364) implies:
% 247.14/41.71  | | | | | | | | | | | | | | | |   (365)  a_select3(q_ds1_filter, n4, n1) = all_74_1
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n1,
% 247.14/41.71  | | | | | | | | | | | | | | | |              n4, q_ds1_filter, simplifying with (353), (365)
% 247.14/41.71  | | | | | | | | | | | | | | | |              gives:
% 247.14/41.71  | | | | | | | | | | | | | | | |   (366)  all_74_0 = all_74_1
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | | REDUCE: (138), (366) imply:
% 247.14/41.71  | | | | | | | | | | | | | | | |   (367)  $false
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | | CLOSE: (367) is inconsistent.
% 247.14/41.71  | | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | End of split
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | End of split
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | End of split
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | Case 2:
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | |   (368)  all_74_3 = n2
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | REDUCE: (340), (368) imply:
% 247.14/41.71  | | | | | | | | | | | | |   (369)  a_select3(q_ds1_filter, n2, n4) = all_74_1
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | REDUCE: (339), (368) imply:
% 247.14/41.71  | | | | | | | | | | | | |   (370)  a_select3(q_ds1_filter, n4, n2) = all_74_0
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | REDUCE: (146), (368) imply:
% 247.14/41.71  | | | | | | | | | | | | |   (371)  leq(n2, n5)
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | REDUCE: (139), (368) imply:
% 247.14/41.71  | | | | | | | | | | | | |   (372)  leq(n0, n2)
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n4, all_74_1,
% 247.14/41.71  | | | | | | | | | | | | |              simplifying with (101), (119), (342), (369), (372)
% 247.14/41.71  | | | | | | | | | | | | |              gives:
% 247.14/41.71  | | | | | | | | | | | | |   (373)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.14/41.71  | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n4, n2) = all_74_1 &
% 247.14/41.71  | | | | | | | | | | | | |            $i(all_74_1))
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | BETA: splitting (373) gives:
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | Case 1:
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | |   (374)   ~ leq(n4, all_74_21)
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | REDUCE: (135), (374) imply:
% 247.14/41.71  | | | | | | | | | | | | | |   (375)   ~ leq(n4, n5)
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | PRED_UNIFY: (341), (375) imply:
% 247.14/41.71  | | | | | | | | | | | | | |   (376)  $false
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | CLOSE: (376) is inconsistent.
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | Case 2:
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | |   (377)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.71  | | | | | | | | | | | | | |              n4, n2) = all_74_1 & $i(all_74_1))
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | Case 1:
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | |   (378)   ~ leq(n2, all_74_21)
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | REDUCE: (135), (378) imply:
% 247.14/41.71  | | | | | | | | | | | | | | |   (379)   ~ leq(n2, n5)
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | PRED_UNIFY: (371), (379) imply:
% 247.14/41.71  | | | | | | | | | | | | | | |   (380)  $false
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | CLOSE: (380) is inconsistent.
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | Case 2:
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | |   (381)  a_select3(q_ds1_filter, n4, n2) = all_74_1 &
% 247.14/41.71  | | | | | | | | | | | | | | |          $i(all_74_1)
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | ALPHA: (381) implies:
% 247.14/41.71  | | | | | | | | | | | | | | |   (382)  a_select3(q_ds1_filter, n4, n2) = all_74_1
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (370), (382) are inconsistent by
% 247.14/41.71  | | | | | | | | | | | | | | |            sub-proof #56.
% 247.14/41.71  | | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | | End of split
% 247.14/41.71  | | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | | End of split
% 247.14/41.71  | | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | | End of split
% 247.14/41.71  | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | Case 2:
% 247.14/41.71  | | | | | | | | | | | | 
% 247.14/41.71  | | | | | | | | | | | |   (383)  all_74_3 = n3
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | REDUCE: (340), (383) imply:
% 247.14/41.72  | | | | | | | | | | | |   (384)  a_select3(q_ds1_filter, n3, n4) = all_74_1
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | REDUCE: (339), (383) imply:
% 247.14/41.72  | | | | | | | | | | | |   (385)  a_select3(q_ds1_filter, n4, n3) = all_74_0
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | REDUCE: (146), (383) imply:
% 247.14/41.72  | | | | | | | | | | | |   (386)  leq(n3, n5)
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | REDUCE: (139), (383) imply:
% 247.14/41.72  | | | | | | | | | | | |   (387)  leq(n0, n3)
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | GROUND_INST: instantiating (62) with n3, n4, all_74_1,
% 247.14/41.72  | | | | | | | | | | | |              simplifying with (112), (119), (342), (384), (387)
% 247.14/41.72  | | | | | | | | | | | |              gives:
% 247.14/41.72  | | | | | | | | | | | |   (388)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 247.14/41.72  | | | | | | | | | | | |          (a_select3(q_ds1_filter, n4, n3) = all_74_1 &
% 247.14/41.72  | | | | | | | | | | | |            $i(all_74_1))
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | BETA: splitting (388) gives:
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | Case 1:
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | |   (389)   ~ leq(n4, all_74_21)
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | REDUCE: (135), (389) imply:
% 247.14/41.72  | | | | | | | | | | | | |   (390)   ~ leq(n4, n5)
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | PRED_UNIFY: (341), (390) imply:
% 247.14/41.72  | | | | | | | | | | | | |   (391)  $false
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | CLOSE: (391) is inconsistent.
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | Case 2:
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | |   (392)   ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.72  | | | | | | | | | | | | |              n4, n3) = all_74_1 & $i(all_74_1))
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | BETA: splitting (392) gives:
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | Case 1:
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | |   (393)   ~ leq(n3, all_74_21)
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | REDUCE: (135), (393) imply:
% 247.14/41.72  | | | | | | | | | | | | | |   (394)   ~ leq(n3, n5)
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | PRED_UNIFY: (386), (394) imply:
% 247.14/41.72  | | | | | | | | | | | | | |   (395)  $false
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | CLOSE: (395) is inconsistent.
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | Case 2:
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | |   (396)  a_select3(q_ds1_filter, n4, n3) = all_74_1 &
% 247.14/41.72  | | | | | | | | | | | | | |          $i(all_74_1)
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | ALPHA: (396) implies:
% 247.14/41.72  | | | | | | | | | | | | | |   (397)  a_select3(q_ds1_filter, n4, n3) = all_74_1
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (385), (397) are inconsistent by
% 247.14/41.72  | | | | | | | | | | | | | |            sub-proof #55.
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | End of split
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | End of split
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | End of split
% 247.14/41.72  | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | End of split
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | Case 2:
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | |   (398)  all_74_3 = n4
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | REDUCE: (144), (398) imply:
% 247.14/41.72  | | | | | | | | | |   (399)  a_select3(q_ds1_filter, all_74_2, n4) = all_74_0
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | REDUCE: (143), (398) imply:
% 247.14/41.72  | | | | | | | | | |   (400)  a_select3(q_ds1_filter, n4, all_74_2) = all_74_1
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | REDUCE: (146), (398) imply:
% 247.14/41.72  | | | | | | | | | |   (401)  leq(n4, n5)
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | REDUCE: (139), (398) imply:
% 247.14/41.72  | | | | | | | | | |   (402)  leq(n0, n4)
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | BETA: splitting (164) gives:
% 247.14/41.72  | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | Case 1:
% 247.14/41.72  | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | |   (403)  gt(n4, all_74_2)
% 247.14/41.72  | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 247.14/41.72  | | | | | | | | | | |              simplifying with (58), (119), (125), (403) gives:
% 247.14/41.72  | | | | | | | | | | |   (404)  leq(all_74_2, n3)
% 247.14/41.72  | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 247.14/41.72  | | | | | | | | | | |              simplifying with (58), (112), (404) gives:
% 247.14/41.72  | | | | | | | | | | |   (405)  all_74_2 = n3 | gt(n3, all_74_2)
% 247.14/41.72  | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | BETA: splitting (405) gives:
% 247.14/41.72  | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | Case 1:
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | |   (406)  gt(n3, all_74_2)
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 247.14/41.72  | | | | | | | | | | | |              simplifying with (58), (112), (124), (406) gives:
% 247.14/41.72  | | | | | | | | | | | |   (407)  leq(all_74_2, n2)
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 247.14/41.72  | | | | | | | | | | | |              simplifying with (58), (101), (407) gives:
% 247.14/41.72  | | | | | | | | | | | |   (408)  all_74_2 = n2 | gt(n2, all_74_2)
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | BETA: splitting (408) gives:
% 247.14/41.72  | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | Case 1:
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | |   (409)  gt(n2, all_74_2)
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 247.14/41.72  | | | | | | | | | | | | |              simplifying with (58), (101), (123), (409) gives:
% 247.14/41.72  | | | | | | | | | | | | |   (410)  leq(all_74_2, n1)
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with
% 247.14/41.72  | | | | | | | | | | | | |              (58), (140), (410) gives:
% 247.14/41.72  | | | | | | | | | | | | |   (411)  all_74_2 = n1 | all_74_2 = n0
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | BETA: splitting (411) gives:
% 247.14/41.72  | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | Case 1:
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | |   (412)  all_74_2 = n0
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | REDUCE: (160), (412) imply:
% 247.14/41.72  | | | | | | | | | | | | | |   (413)  $false
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | CLOSE: (413) is inconsistent.
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | Case 2:
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | |   (414)  all_74_2 = n1
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | REDUCE: (399), (414) imply:
% 247.14/41.72  | | | | | | | | | | | | | |   (415)  a_select3(q_ds1_filter, n1, n4) = all_74_0
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | REDUCE: (400), (414) imply:
% 247.14/41.72  | | | | | | | | | | | | | |   (416)  a_select3(q_ds1_filter, n4, n1) = all_74_1
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | REDUCE: (145), (414) imply:
% 247.14/41.72  | | | | | | | | | | | | | |   (417)  leq(n1, n5)
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | REDUCE: (140), (414) imply:
% 247.14/41.72  | | | | | | | | | | | | | |   (418)  leq(n0, n1)
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n4, all_74_0,
% 247.14/41.72  | | | | | | | | | | | | | |              simplifying with (85), (119), (402), (415), (418)
% 247.14/41.72  | | | | | | | | | | | | | |              gives:
% 247.14/41.72  | | | | | | | | | | | | | |   (419)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.14/41.72  | | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n4, n1) = all_74_0 &
% 247.14/41.72  | | | | | | | | | | | | | |            $i(all_74_0))
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | BETA: splitting (419) gives:
% 247.14/41.72  | | | | | | | | | | | | | | 
% 247.14/41.72  | | | | | | | | | | | | | | Case 1:
% 247.14/41.72  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | |   (420)   ~ leq(n4, all_74_21)
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | REDUCE: (135), (420) imply:
% 247.14/41.73  | | | | | | | | | | | | | | |   (421)   ~ leq(n4, n5)
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | PRED_UNIFY: (401), (421) imply:
% 247.14/41.73  | | | | | | | | | | | | | | |   (422)  $false
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | CLOSE: (422) is inconsistent.
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | |   (423)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.73  | | | | | | | | | | | | | | |              n4, n1) = all_74_0 & $i(all_74_0))
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | BETA: splitting (423) gives:
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | Case 1:
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | |   (424)   ~ leq(n1, all_74_21)
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | | REDUCE: (135), (424) imply:
% 247.14/41.73  | | | | | | | | | | | | | | | |   (425)   ~ leq(n1, n5)
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | | PRED_UNIFY: (417), (425) imply:
% 247.14/41.73  | | | | | | | | | | | | | | | |   (426)  $false
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | | CLOSE: (426) is inconsistent.
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | |   (427)  a_select3(q_ds1_filter, n4, n1) = all_74_0 &
% 247.14/41.73  | | | | | | | | | | | | | | | |          $i(all_74_0)
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | | ALPHA: (427) implies:
% 247.14/41.73  | | | | | | | | | | | | | | | |   (428)  a_select3(q_ds1_filter, n4, n1) = all_74_0
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n1,
% 247.14/41.73  | | | | | | | | | | | | | | | |              n4, q_ds1_filter, simplifying with (416), (428)
% 247.14/41.73  | | | | | | | | | | | | | | | |              gives:
% 247.14/41.73  | | | | | | | | | | | | | | | |   (429)  all_74_0 = all_74_1
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | | REDUCE: (138), (429) imply:
% 247.14/41.73  | | | | | | | | | | | | | | | |   (430)  $false
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | | CLOSE: (430) is inconsistent.
% 247.14/41.73  | | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | |   (431)  all_74_2 = n2
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | REDUCE: (399), (431) imply:
% 247.14/41.73  | | | | | | | | | | | | |   (432)  a_select3(q_ds1_filter, n2, n4) = all_74_0
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | REDUCE: (400), (431) imply:
% 247.14/41.73  | | | | | | | | | | | | |   (433)  a_select3(q_ds1_filter, n4, n2) = all_74_1
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | REDUCE: (145), (431) imply:
% 247.14/41.73  | | | | | | | | | | | | |   (434)  leq(n2, n5)
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | REDUCE: (140), (431) imply:
% 247.14/41.73  | | | | | | | | | | | | |   (435)  leq(n0, n2)
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n4, all_74_0,
% 247.14/41.73  | | | | | | | | | | | | |              simplifying with (101), (119), (402), (432), (435)
% 247.14/41.73  | | | | | | | | | | | | |              gives:
% 247.14/41.73  | | | | | | | | | | | | |   (436)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.14/41.73  | | | | | | | | | | | | |          (a_select3(q_ds1_filter, n4, n2) = all_74_0 &
% 247.14/41.73  | | | | | | | | | | | | |            $i(all_74_0))
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | BETA: splitting (436) gives:
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | Case 1:
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | |   (437)   ~ leq(n4, all_74_21)
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | REDUCE: (135), (437) imply:
% 247.14/41.73  | | | | | | | | | | | | | |   (438)   ~ leq(n4, n5)
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | PRED_UNIFY: (401), (438) imply:
% 247.14/41.73  | | | | | | | | | | | | | |   (439)  $false
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | CLOSE: (439) is inconsistent.
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | |   (440)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.73  | | | | | | | | | | | | | |              n4, n2) = all_74_0 & $i(all_74_0))
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | BETA: splitting (440) gives:
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | Case 1:
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | |   (441)   ~ leq(n2, all_74_21)
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | REDUCE: (135), (441) imply:
% 247.14/41.73  | | | | | | | | | | | | | | |   (442)   ~ leq(n2, n5)
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | PRED_UNIFY: (434), (442) imply:
% 247.14/41.73  | | | | | | | | | | | | | | |   (443)  $false
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | CLOSE: (443) is inconsistent.
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | |   (444)  a_select3(q_ds1_filter, n4, n2) = all_74_0 &
% 247.14/41.73  | | | | | | | | | | | | | | |          $i(all_74_0)
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | ALPHA: (444) implies:
% 247.14/41.73  | | | | | | | | | | | | | | |   (445)  a_select3(q_ds1_filter, n4, n2) = all_74_0
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (433), (445) are inconsistent by
% 247.14/41.73  | | | | | | | | | | | | | | |            sub-proof #56.
% 247.14/41.73  | | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | |   (446)  all_74_2 = n3
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | REDUCE: (399), (446) imply:
% 247.14/41.73  | | | | | | | | | | | |   (447)  a_select3(q_ds1_filter, n3, n4) = all_74_0
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | REDUCE: (400), (446) imply:
% 247.14/41.73  | | | | | | | | | | | |   (448)  a_select3(q_ds1_filter, n4, n3) = all_74_1
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | REDUCE: (145), (446) imply:
% 247.14/41.73  | | | | | | | | | | | |   (449)  leq(n3, n5)
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | REDUCE: (140), (446) imply:
% 247.14/41.73  | | | | | | | | | | | |   (450)  leq(n0, n3)
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | GROUND_INST: instantiating (62) with n3, n4, all_74_0,
% 247.14/41.73  | | | | | | | | | | | |              simplifying with (112), (119), (402), (447), (450)
% 247.14/41.73  | | | | | | | | | | | |              gives:
% 247.14/41.73  | | | | | | | | | | | |   (451)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 247.14/41.73  | | | | | | | | | | | |          (a_select3(q_ds1_filter, n4, n3) = all_74_0 &
% 247.14/41.73  | | | | | | | | | | | |            $i(all_74_0))
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | BETA: splitting (451) gives:
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | Case 1:
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | |   (452)   ~ leq(n4, all_74_21)
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | REDUCE: (135), (452) imply:
% 247.14/41.73  | | | | | | | | | | | | |   (453)   ~ leq(n4, n5)
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | PRED_UNIFY: (401), (453) imply:
% 247.14/41.73  | | | | | | | | | | | | |   (454)  $false
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | CLOSE: (454) is inconsistent.
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | |   (455)   ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter,
% 247.14/41.73  | | | | | | | | | | | | |              n4, n3) = all_74_0 & $i(all_74_0))
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | BETA: splitting (455) gives:
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | Case 1:
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | |   (456)   ~ leq(n3, all_74_21)
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | REDUCE: (135), (456) imply:
% 247.14/41.73  | | | | | | | | | | | | | |   (457)   ~ leq(n3, n5)
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | PRED_UNIFY: (449), (457) imply:
% 247.14/41.73  | | | | | | | | | | | | | |   (458)  $false
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | CLOSE: (458) is inconsistent.
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | |   (459)  a_select3(q_ds1_filter, n4, n3) = all_74_0 &
% 247.14/41.73  | | | | | | | | | | | | | |          $i(all_74_0)
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | ALPHA: (459) implies:
% 247.14/41.73  | | | | | | | | | | | | | |   (460)  a_select3(q_ds1_filter, n4, n3) = all_74_0
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | | REF_CLOSE: (17), (138), (448), (460) are inconsistent by
% 247.14/41.73  | | | | | | | | | | | | | |            sub-proof #55.
% 247.14/41.73  | | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | End of split
% 247.14/41.73  | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | Case 2:
% 247.14/41.73  | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | |   (461)  all_74_2 = n4
% 247.14/41.73  | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | REDUCE: (399), (461) imply:
% 247.14/41.73  | | | | | | | | | | |   (462)  a_select3(q_ds1_filter, n4, n4) = all_74_0
% 247.14/41.73  | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | REDUCE: (400), (461) imply:
% 247.14/41.73  | | | | | | | | | | |   (463)  a_select3(q_ds1_filter, n4, n4) = all_74_1
% 247.14/41.73  | | | | | | | | | | | 
% 247.14/41.73  | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n4,
% 247.14/41.73  | | | | | | | | | | |              n4, q_ds1_filter, simplifying with (462), (463)
% 247.14/41.73  | | | | | | | | | | |              gives:
% 247.40/41.73  | | | | | | | | | | |   (464)  all_74_0 = all_74_1
% 247.40/41.73  | | | | | | | | | | | 
% 247.40/41.73  | | | | | | | | | | | REDUCE: (138), (464) imply:
% 247.40/41.73  | | | | | | | | | | |   (465)  $false
% 247.40/41.73  | | | | | | | | | | | 
% 247.40/41.73  | | | | | | | | | | | CLOSE: (465) is inconsistent.
% 247.40/41.73  | | | | | | | | | | | 
% 247.40/41.73  | | | | | | | | | | End of split
% 247.40/41.73  | | | | | | | | | | 
% 247.40/41.73  | | | | | | | | | End of split
% 247.40/41.73  | | | | | | | | | 
% 247.40/41.73  | | | | | | | | End of split
% 247.40/41.73  | | | | | | | | 
% 247.40/41.73  | | | | | | | End of split
% 247.40/41.73  | | | | | | | 
% 247.40/41.73  | | | | | | Case 2:
% 247.40/41.73  | | | | | | | 
% 247.40/41.73  | | | | | | |   (466)  all_74_3 = n5
% 247.40/41.73  | | | | | | | 
% 247.40/41.73  | | | | | | | REDUCE: (144), (466) imply:
% 247.40/41.74  | | | | | | |   (467)  a_select3(q_ds1_filter, all_74_2, n5) = all_74_0
% 247.40/41.74  | | | | | | | 
% 247.40/41.74  | | | | | | | REDUCE: (143), (466) imply:
% 247.40/41.74  | | | | | | |   (468)  a_select3(q_ds1_filter, n5, all_74_2) = all_74_1
% 247.40/41.74  | | | | | | | 
% 247.40/41.74  | | | | | | | REDUCE: (146), (466) imply:
% 247.40/41.74  | | | | | | |   (469)  leq(n5, n5)
% 247.40/41.74  | | | | | | | 
% 247.40/41.74  | | | | | | | REDUCE: (139), (466) imply:
% 247.40/41.74  | | | | | | |   (470)  leq(n0, n5)
% 247.40/41.74  | | | | | | | 
% 247.40/41.74  | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying
% 247.40/41.74  | | | | | | |              with (58), (122), (126), (155) gives:
% 247.40/41.74  | | | | | | |   (471)  leq(all_74_2, n4)
% 247.40/41.74  | | | | | | | 
% 247.40/41.74  | | | | | | | BETA: splitting (151) gives:
% 247.40/41.74  | | | | | | | 
% 247.40/41.74  | | | | | | | Case 1:
% 247.40/41.74  | | | | | | | | 
% 247.40/41.74  | | | | | | | |   (472)  all_74_2 = n0
% 247.40/41.74  | | | | | | | | 
% 247.40/41.74  | | | | | | | | REF_CLOSE: (58), (153), (472), (irreflexivity_gt) are
% 247.40/41.74  | | | | | | | |            inconsistent by sub-proof #59.
% 247.40/41.74  | | | | | | | | 
% 247.40/41.74  | | | | | | | Case 2:
% 247.40/41.74  | | | | | | | | 
% 247.40/41.74  | | | | | | | |   (473)   ~ (all_74_2 = n0)
% 247.40/41.74  | | | | | | | | 
% 247.40/41.74  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4,
% 247.40/41.74  | | | | | | | |              simplifying with (58), (119), (471) gives:
% 247.40/41.74  | | | | | | | |   (474)  all_74_2 = n4 | gt(n4, all_74_2)
% 247.40/41.74  | | | | | | | | 
% 247.40/41.74  | | | | | | | | BETA: splitting (474) gives:
% 247.40/41.74  | | | | | | | | 
% 247.40/41.74  | | | | | | | | Case 1:
% 247.40/41.74  | | | | | | | | | 
% 247.40/41.74  | | | | | | | | |   (475)  gt(n4, all_74_2)
% 247.40/41.74  | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 247.40/41.74  | | | | | | | | |              simplifying with (58), (119), (125), (475) gives:
% 247.40/41.74  | | | | | | | | |   (476)  leq(all_74_2, n3)
% 247.40/41.74  | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 247.40/41.74  | | | | | | | | |              simplifying with (58), (112), (476) gives:
% 247.40/41.74  | | | | | | | | |   (477)  all_74_2 = n3 | gt(n3, all_74_2)
% 247.40/41.74  | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | BETA: splitting (477) gives:
% 247.40/41.74  | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | Case 1:
% 247.40/41.74  | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | |   (478)  gt(n3, all_74_2)
% 247.40/41.74  | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 247.40/41.74  | | | | | | | | | |              simplifying with (58), (112), (124), (478) gives:
% 247.40/41.74  | | | | | | | | | |   (479)  leq(all_74_2, n2)
% 247.40/41.74  | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 247.40/41.74  | | | | | | | | | |              simplifying with (58), (101), (479) gives:
% 247.40/41.74  | | | | | | | | | |   (480)  all_74_2 = n2 | gt(n2, all_74_2)
% 247.40/41.74  | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | BETA: splitting (480) gives:
% 247.40/41.74  | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | Case 1:
% 247.40/41.74  | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | |   (481)  gt(n2, all_74_2)
% 247.40/41.74  | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 247.40/41.74  | | | | | | | | | | |              simplifying with (58), (101), (123), (481) gives:
% 247.40/41.74  | | | | | | | | | | |   (482)  leq(all_74_2, n1)
% 247.40/41.74  | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with
% 247.40/41.74  | | | | | | | | | | |              (58), (140), (482) gives:
% 247.40/41.74  | | | | | | | | | | |   (483)  all_74_2 = n1 | all_74_2 = n0
% 247.40/41.74  | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | BETA: splitting (483) gives:
% 247.40/41.74  | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | Case 1:
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | |   (484)  all_74_2 = n0
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | REDUCE: (473), (484) imply:
% 247.40/41.74  | | | | | | | | | | | |   (485)  $false
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | CLOSE: (485) is inconsistent.
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | Case 2:
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | |   (486)  all_74_2 = n1
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | REDUCE: (467), (486) imply:
% 247.40/41.74  | | | | | | | | | | | |   (487)  a_select3(q_ds1_filter, n1, n5) = all_74_0
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | REDUCE: (468), (486) imply:
% 247.40/41.74  | | | | | | | | | | | |   (488)  a_select3(q_ds1_filter, n5, n1) = all_74_1
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | REDUCE: (145), (486) imply:
% 247.40/41.74  | | | | | | | | | | | |   (489)  leq(n1, n5)
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | REDUCE: (140), (486) imply:
% 247.40/41.74  | | | | | | | | | | | |   (490)  leq(n0, n1)
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n5, all_74_0,
% 247.40/41.74  | | | | | | | | | | | |              simplifying with (85), (122), (470), (487), (490)
% 247.40/41.74  | | | | | | | | | | | |              gives:
% 247.40/41.74  | | | | | | | | | | | |   (491)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.40/41.74  | | | | | | | | | | | |          (a_select3(q_ds1_filter, n5, n1) = all_74_0 &
% 247.40/41.74  | | | | | | | | | | | |            $i(all_74_0))
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | BETA: splitting (491) gives:
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | Case 1:
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | |   (492)   ~ leq(n5, all_74_21)
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | REDUCE: (135), (492) imply:
% 247.40/41.74  | | | | | | | | | | | | |   (493)   ~ leq(n5, n5)
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | PRED_UNIFY: (469), (493) imply:
% 247.40/41.74  | | | | | | | | | | | | |   (494)  $false
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | CLOSE: (494) is inconsistent.
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | Case 2:
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | |   (495)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.40/41.74  | | | | | | | | | | | | |              n5, n1) = all_74_0 & $i(all_74_0))
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | BETA: splitting (495) gives:
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | Case 1:
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | |   (496)   ~ leq(n1, all_74_21)
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | | REDUCE: (135), (496) imply:
% 247.40/41.74  | | | | | | | | | | | | | |   (497)   ~ leq(n1, n5)
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | | PRED_UNIFY: (489), (497) imply:
% 247.40/41.74  | | | | | | | | | | | | | |   (498)  $false
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | | CLOSE: (498) is inconsistent.
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | Case 2:
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | |   (499)  a_select3(q_ds1_filter, n5, n1) = all_74_0 &
% 247.40/41.74  | | | | | | | | | | | | | |          $i(all_74_0)
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | | ALPHA: (499) implies:
% 247.40/41.74  | | | | | | | | | | | | | |   (500)  a_select3(q_ds1_filter, n5, n1) = all_74_0
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n1,
% 247.40/41.74  | | | | | | | | | | | | | |              n5, q_ds1_filter, simplifying with (488), (500)
% 247.40/41.74  | | | | | | | | | | | | | |              gives:
% 247.40/41.74  | | | | | | | | | | | | | |   (501)  all_74_0 = all_74_1
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | | REDUCE: (138), (501) imply:
% 247.40/41.74  | | | | | | | | | | | | | |   (502)  $false
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | | CLOSE: (502) is inconsistent.
% 247.40/41.74  | | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | | End of split
% 247.40/41.74  | | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | | End of split
% 247.40/41.74  | | | | | | | | | | | | 
% 247.40/41.74  | | | | | | | | | | | End of split
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | Case 2:
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | |   (503)  all_74_2 = n2
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | REDUCE: (467), (503) imply:
% 247.40/41.75  | | | | | | | | | | |   (504)  a_select3(q_ds1_filter, n2, n5) = all_74_0
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | REDUCE: (468), (503) imply:
% 247.40/41.75  | | | | | | | | | | |   (505)  a_select3(q_ds1_filter, n5, n2) = all_74_1
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | REDUCE: (145), (503) imply:
% 247.40/41.75  | | | | | | | | | | |   (506)  leq(n2, n5)
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | REDUCE: (140), (503) imply:
% 247.40/41.75  | | | | | | | | | | |   (507)  leq(n0, n2)
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n5, all_74_0,
% 247.40/41.75  | | | | | | | | | | |              simplifying with (101), (122), (470), (504), (507)
% 247.40/41.75  | | | | | | | | | | |              gives:
% 247.40/41.75  | | | | | | | | | | |   (508)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.40/41.75  | | | | | | | | | | |          (a_select3(q_ds1_filter, n5, n2) = all_74_0 &
% 247.40/41.75  | | | | | | | | | | |            $i(all_74_0))
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | BETA: splitting (508) gives:
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | Case 1:
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | |   (509)   ~ leq(n5, all_74_21)
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | REDUCE: (135), (509) imply:
% 247.40/41.75  | | | | | | | | | | | |   (510)   ~ leq(n5, n5)
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | PRED_UNIFY: (469), (510) imply:
% 247.40/41.75  | | | | | | | | | | | |   (511)  $false
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | CLOSE: (511) is inconsistent.
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | Case 2:
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | |   (512)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.40/41.75  | | | | | | | | | | | |              n5, n2) = all_74_0 & $i(all_74_0))
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | BETA: splitting (512) gives:
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | Case 1:
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | |   (513)   ~ leq(n2, all_74_21)
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | | REDUCE: (135), (513) imply:
% 247.40/41.75  | | | | | | | | | | | | |   (514)   ~ leq(n2, n5)
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | | PRED_UNIFY: (506), (514) imply:
% 247.40/41.75  | | | | | | | | | | | | |   (515)  $false
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | | CLOSE: (515) is inconsistent.
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | Case 2:
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | |   (516)  a_select3(q_ds1_filter, n5, n2) = all_74_0 &
% 247.40/41.75  | | | | | | | | | | | | |          $i(all_74_0)
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | | ALPHA: (516) implies:
% 247.40/41.75  | | | | | | | | | | | | |   (517)  a_select3(q_ds1_filter, n5, n2) = all_74_0
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n2,
% 247.40/41.75  | | | | | | | | | | | | |              n5, q_ds1_filter, simplifying with (505), (517)
% 247.40/41.75  | | | | | | | | | | | | |              gives:
% 247.40/41.75  | | | | | | | | | | | | |   (518)  all_74_0 = all_74_1
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | | REDUCE: (138), (518) imply:
% 247.40/41.75  | | | | | | | | | | | | |   (519)  $false
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | | CLOSE: (519) is inconsistent.
% 247.40/41.75  | | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | End of split
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | End of split
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | End of split
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | Case 2:
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | |   (520)  all_74_2 = n3
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | REDUCE: (467), (520) imply:
% 247.40/41.75  | | | | | | | | | |   (521)  a_select3(q_ds1_filter, n3, n5) = all_74_0
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | REDUCE: (468), (520) imply:
% 247.40/41.75  | | | | | | | | | |   (522)  a_select3(q_ds1_filter, n5, n3) = all_74_1
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | REDUCE: (145), (520) imply:
% 247.40/41.75  | | | | | | | | | |   (523)  leq(n3, n5)
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | REDUCE: (140), (520) imply:
% 247.40/41.75  | | | | | | | | | |   (524)  leq(n0, n3)
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | GROUND_INST: instantiating (62) with n3, n5, all_74_0,
% 247.40/41.75  | | | | | | | | | |              simplifying with (112), (122), (470), (521), (524)
% 247.40/41.75  | | | | | | | | | |              gives:
% 247.40/41.75  | | | | | | | | | |   (525)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 247.40/41.75  | | | | | | | | | |          (a_select3(q_ds1_filter, n5, n3) = all_74_0 &
% 247.40/41.75  | | | | | | | | | |            $i(all_74_0))
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | BETA: splitting (525) gives:
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | Case 1:
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | |   (526)   ~ leq(n5, all_74_21)
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | REDUCE: (135), (526) imply:
% 247.40/41.75  | | | | | | | | | | |   (527)   ~ leq(n5, n5)
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | PRED_UNIFY: (469), (527) imply:
% 247.40/41.75  | | | | | | | | | | |   (528)  $false
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | CLOSE: (528) is inconsistent.
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | Case 2:
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | |   (529)   ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter,
% 247.40/41.75  | | | | | | | | | | |              n5, n3) = all_74_0 & $i(all_74_0))
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | BETA: splitting (529) gives:
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | Case 1:
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | |   (530)   ~ leq(n3, all_74_21)
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | REDUCE: (135), (530) imply:
% 247.40/41.75  | | | | | | | | | | | |   (531)   ~ leq(n3, n5)
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | PRED_UNIFY: (523), (531) imply:
% 247.40/41.75  | | | | | | | | | | | |   (532)  $false
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | CLOSE: (532) is inconsistent.
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | Case 2:
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | |   (533)  a_select3(q_ds1_filter, n5, n3) = all_74_0 &
% 247.40/41.75  | | | | | | | | | | | |          $i(all_74_0)
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | ALPHA: (533) implies:
% 247.40/41.75  | | | | | | | | | | | |   (534)  a_select3(q_ds1_filter, n5, n3) = all_74_0
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | | REF_CLOSE: (17), (138), (522), (534) are inconsistent by
% 247.40/41.75  | | | | | | | | | | | |            sub-proof #54.
% 247.40/41.75  | | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | | End of split
% 247.40/41.75  | | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | | End of split
% 247.40/41.75  | | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | End of split
% 247.40/41.75  | | | | | | | | | 
% 247.40/41.75  | | | | | | | | Case 2:
% 247.40/41.75  | | | | | | | | | 
% 247.40/41.75  | | | | | | | | |   (535)  all_74_2 = n4
% 247.40/41.75  | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | REDUCE: (467), (535) imply:
% 247.40/41.75  | | | | | | | | |   (536)  a_select3(q_ds1_filter, n4, n5) = all_74_0
% 247.40/41.75  | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | REDUCE: (468), (535) imply:
% 247.40/41.75  | | | | | | | | |   (537)  a_select3(q_ds1_filter, n5, n4) = all_74_1
% 247.40/41.75  | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | REDUCE: (145), (535) imply:
% 247.40/41.75  | | | | | | | | |   (538)  leq(n4, n5)
% 247.40/41.75  | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | REDUCE: (140), (535) imply:
% 247.40/41.75  | | | | | | | | |   (539)  leq(n0, n4)
% 247.40/41.75  | | | | | | | | | 
% 247.40/41.75  | | | | | | | | | GROUND_INST: instantiating (62) with n4, n5, all_74_0,
% 247.40/41.75  | | | | | | | | |              simplifying with (119), (122), (470), (536), (539)
% 247.40/41.75  | | | | | | | | |              gives:
% 247.40/41.76  | | | | | | | | |   (540)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 247.40/41.76  | | | | | | | | |          (a_select3(q_ds1_filter, n5, n4) = all_74_0 &
% 247.40/41.76  | | | | | | | | |            $i(all_74_0))
% 247.40/41.76  | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | BETA: splitting (540) gives:
% 247.40/41.76  | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | Case 1:
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | |   (541)   ~ leq(n5, all_74_21)
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | REDUCE: (135), (541) imply:
% 247.40/41.76  | | | | | | | | | |   (542)   ~ leq(n5, n5)
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | PRED_UNIFY: (469), (542) imply:
% 247.40/41.76  | | | | | | | | | |   (543)  $false
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | CLOSE: (543) is inconsistent.
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | Case 2:
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | |   (544)   ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter,
% 247.40/41.76  | | | | | | | | | |              n5, n4) = all_74_0 & $i(all_74_0))
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | BETA: splitting (544) gives:
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | Case 1:
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | |   (545)   ~ leq(n4, all_74_21)
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | | REDUCE: (135), (545) imply:
% 247.40/41.76  | | | | | | | | | | |   (546)   ~ leq(n4, n5)
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | | PRED_UNIFY: (538), (546) imply:
% 247.40/41.76  | | | | | | | | | | |   (547)  $false
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | | CLOSE: (547) is inconsistent.
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | Case 2:
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | |   (548)  a_select3(q_ds1_filter, n5, n4) = all_74_0 &
% 247.40/41.76  | | | | | | | | | | |          $i(all_74_0)
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | | ALPHA: (548) implies:
% 247.40/41.76  | | | | | | | | | | |   (549)  a_select3(q_ds1_filter, n5, n4) = all_74_0
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | | REF_CLOSE: (17), (138), (537), (549) are inconsistent by
% 247.40/41.76  | | | | | | | | | | |            sub-proof #53.
% 247.40/41.76  | | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | | End of split
% 247.40/41.76  | | | | | | | | | | 
% 247.40/41.76  | | | | | | | | | End of split
% 247.40/41.76  | | | | | | | | | 
% 247.40/41.76  | | | | | | | | End of split
% 247.40/41.76  | | | | | | | | 
% 247.40/41.76  | | | | | | | End of split
% 247.40/41.76  | | | | | | | 
% 247.40/41.76  | | | | | | End of split
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | Case 2:
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | |   (550)  all_74_2 = n5
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | | REDUCE: (144), (550) imply:
% 247.40/41.76  | | | | | |   (551)  a_select3(q_ds1_filter, n5, all_74_3) = all_74_0
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | | REDUCE: (143), (550) imply:
% 247.40/41.76  | | | | | |   (552)  a_select3(q_ds1_filter, all_74_3, n5) = all_74_1
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | | REDUCE: (145), (550) imply:
% 247.40/41.76  | | | | | |   (553)  leq(n5, n5)
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | | REDUCE: (140), (550) imply:
% 247.40/41.76  | | | | | |   (554)  leq(n0, n5)
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | | BETA: splitting (150) gives:
% 247.40/41.76  | | | | | | 
% 247.40/41.76  | | | | | | Case 1:
% 247.40/41.76  | | | | | | | 
% 247.40/41.76  | | | | | | |   (555)  gt(n5, all_74_3)
% 247.40/41.76  | | | | | | | 
% 247.40/41.76  | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying
% 247.40/41.76  | | | | | | |              with (57), (122), (126), (555) gives:
% 247.40/41.76  | | | | | | |   (556)  leq(all_74_3, n4)
% 247.40/41.76  | | | | | | | 
% 247.40/41.76  | | | | | | | BETA: splitting (149) gives:
% 247.40/41.76  | | | | | | | 
% 247.40/41.76  | | | | | | | Case 1:
% 247.40/41.76  | | | | | | | | 
% 247.40/41.76  | | | | | | | |   (557)  all_74_3 = n0
% 247.40/41.76  | | | | | | | | 
% 247.40/41.76  | | | | | | | | REF_CLOSE: (57), (154), (557), (irreflexivity_gt) are
% 247.40/41.76  | | | | | | | |            inconsistent by sub-proof #58.
% 247.40/41.76  | | | | | | | | 
% 247.40/41.76  | | | | | | | Case 2:
% 247.40/41.76  | | | | | | | | 
% 247.40/41.76  | | | | | | | |   (558)   ~ (all_74_3 = n0)
% 247.40/41.76  | | | | | | | | 
% 247.40/41.76  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4,
% 247.40/41.76  | | | | | | | |              simplifying with (57), (119), (556) gives:
% 247.51/41.76  | | | | | | | |   (559)  all_74_3 = n4 | gt(n4, all_74_3)
% 247.51/41.76  | | | | | | | | 
% 247.51/41.76  | | | | | | | | BETA: splitting (559) gives:
% 247.51/41.76  | | | | | | | | 
% 247.51/41.76  | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | 
% 247.51/41.76  | | | | | | | | |   (560)  gt(n4, all_74_3)
% 247.51/41.76  | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3,
% 247.51/41.76  | | | | | | | | |              simplifying with (57), (119), (125), (560) gives:
% 247.51/41.76  | | | | | | | | |   (561)  leq(all_74_3, n3)
% 247.51/41.76  | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3,
% 247.51/41.76  | | | | | | | | |              simplifying with (57), (112), (561) gives:
% 247.51/41.76  | | | | | | | | |   (562)  all_74_3 = n3 | gt(n3, all_74_3)
% 247.51/41.76  | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | BETA: splitting (562) gives:
% 247.51/41.76  | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | |   (563)  gt(n3, all_74_3)
% 247.51/41.76  | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 247.51/41.76  | | | | | | | | | |              simplifying with (57), (112), (124), (563) gives:
% 247.51/41.76  | | | | | | | | | |   (564)  leq(all_74_3, n2)
% 247.51/41.76  | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 247.51/41.76  | | | | | | | | | |              simplifying with (57), (101), (564) gives:
% 247.51/41.76  | | | | | | | | | |   (565)  all_74_3 = n2 | gt(n2, all_74_3)
% 247.51/41.76  | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | BETA: splitting (565) gives:
% 247.51/41.76  | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | |   (566)  gt(n2, all_74_3)
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 247.51/41.76  | | | | | | | | | | |              simplifying with (57), (101), (123), (566) gives:
% 247.51/41.76  | | | | | | | | | | |   (567)  leq(all_74_3, n1)
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with
% 247.51/41.76  | | | | | | | | | | |              (57), (139), (567) gives:
% 247.51/41.76  | | | | | | | | | | |   (568)  all_74_3 = n1 | all_74_3 = n0
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | BETA: splitting (568) gives:
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | |   (569)  all_74_3 = n0
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | REDUCE: (558), (569) imply:
% 247.51/41.76  | | | | | | | | | | | |   (570)  $false
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | CLOSE: (570) is inconsistent.
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | Case 2:
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | |   (571)  all_74_3 = n1
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | REDUCE: (552), (571) imply:
% 247.51/41.76  | | | | | | | | | | | |   (572)  a_select3(q_ds1_filter, n1, n5) = all_74_1
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | REDUCE: (551), (571) imply:
% 247.51/41.76  | | | | | | | | | | | |   (573)  a_select3(q_ds1_filter, n5, n1) = all_74_0
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | REDUCE: (146), (571) imply:
% 247.51/41.76  | | | | | | | | | | | |   (574)  leq(n1, n5)
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | REDUCE: (139), (571) imply:
% 247.51/41.76  | | | | | | | | | | | |   (575)  leq(n0, n1)
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | GROUND_INST: instantiating (62) with n1, n5, all_74_1,
% 247.51/41.76  | | | | | | | | | | | |              simplifying with (85), (122), (554), (572), (575)
% 247.51/41.76  | | | | | | | | | | | |              gives:
% 247.51/41.76  | | | | | | | | | | | |   (576)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.51/41.76  | | | | | | | | | | | |          (a_select3(q_ds1_filter, n5, n1) = all_74_1 &
% 247.51/41.76  | | | | | | | | | | | |            $i(all_74_1))
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | BETA: splitting (576) gives:
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | |   (577)   ~ leq(n5, all_74_21)
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | REDUCE: (135), (577) imply:
% 247.51/41.76  | | | | | | | | | | | | |   (578)   ~ leq(n5, n5)
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | PRED_UNIFY: (553), (578) imply:
% 247.51/41.76  | | | | | | | | | | | | |   (579)  $false
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | CLOSE: (579) is inconsistent.
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | Case 2:
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | |   (580)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.76  | | | | | | | | | | | | |              n5, n1) = all_74_1 & $i(all_74_1))
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | BETA: splitting (580) gives:
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | |   (581)   ~ leq(n1, all_74_21)
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | | REDUCE: (135), (581) imply:
% 247.51/41.76  | | | | | | | | | | | | | |   (582)   ~ leq(n1, n5)
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | | PRED_UNIFY: (574), (582) imply:
% 247.51/41.76  | | | | | | | | | | | | | |   (583)  $false
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | | CLOSE: (583) is inconsistent.
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | Case 2:
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | |   (584)  a_select3(q_ds1_filter, n5, n1) = all_74_1 &
% 247.51/41.76  | | | | | | | | | | | | | |          $i(all_74_1)
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | | ALPHA: (584) implies:
% 247.51/41.76  | | | | | | | | | | | | | |   (585)  a_select3(q_ds1_filter, n5, n1) = all_74_1
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n1,
% 247.51/41.76  | | | | | | | | | | | | | |              n5, q_ds1_filter, simplifying with (573), (585)
% 247.51/41.76  | | | | | | | | | | | | | |              gives:
% 247.51/41.76  | | | | | | | | | | | | | |   (586)  all_74_0 = all_74_1
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | | REDUCE: (138), (586) imply:
% 247.51/41.76  | | | | | | | | | | | | | |   (587)  $false
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | | CLOSE: (587) is inconsistent.
% 247.51/41.76  | | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | End of split
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | End of split
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | End of split
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | Case 2:
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | |   (588)  all_74_3 = n2
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | REDUCE: (552), (588) imply:
% 247.51/41.76  | | | | | | | | | | |   (589)  a_select3(q_ds1_filter, n2, n5) = all_74_1
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | REDUCE: (551), (588) imply:
% 247.51/41.76  | | | | | | | | | | |   (590)  a_select3(q_ds1_filter, n5, n2) = all_74_0
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | REDUCE: (146), (588) imply:
% 247.51/41.76  | | | | | | | | | | |   (591)  leq(n2, n5)
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | REDUCE: (139), (588) imply:
% 247.51/41.76  | | | | | | | | | | |   (592)  leq(n0, n2)
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | GROUND_INST: instantiating (62) with n2, n5, all_74_1,
% 247.51/41.76  | | | | | | | | | | |              simplifying with (101), (122), (554), (589), (592)
% 247.51/41.76  | | | | | | | | | | |              gives:
% 247.51/41.76  | | | | | | | | | | |   (593)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.51/41.76  | | | | | | | | | | |          (a_select3(q_ds1_filter, n5, n2) = all_74_1 &
% 247.51/41.76  | | | | | | | | | | |            $i(all_74_1))
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | BETA: splitting (593) gives:
% 247.51/41.76  | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | |   (594)   ~ leq(n5, all_74_21)
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | REDUCE: (135), (594) imply:
% 247.51/41.76  | | | | | | | | | | | |   (595)   ~ leq(n5, n5)
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | PRED_UNIFY: (553), (595) imply:
% 247.51/41.76  | | | | | | | | | | | |   (596)  $false
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | CLOSE: (596) is inconsistent.
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | Case 2:
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | |   (597)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.76  | | | | | | | | | | | |              n5, n2) = all_74_1 & $i(all_74_1))
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | BETA: splitting (597) gives:
% 247.51/41.76  | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | Case 1:
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | |   (598)   ~ leq(n2, all_74_21)
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | REDUCE: (135), (598) imply:
% 247.51/41.76  | | | | | | | | | | | | |   (599)   ~ leq(n2, n5)
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | PRED_UNIFY: (591), (599) imply:
% 247.51/41.76  | | | | | | | | | | | | |   (600)  $false
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | CLOSE: (600) is inconsistent.
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | Case 2:
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | |   (601)  a_select3(q_ds1_filter, n5, n2) = all_74_1 &
% 247.51/41.76  | | | | | | | | | | | | |          $i(all_74_1)
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | ALPHA: (601) implies:
% 247.51/41.76  | | | | | | | | | | | | |   (602)  a_select3(q_ds1_filter, n5, n2) = all_74_1
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n2,
% 247.51/41.76  | | | | | | | | | | | | |              n5, q_ds1_filter, simplifying with (590), (602)
% 247.51/41.76  | | | | | | | | | | | | |              gives:
% 247.51/41.76  | | | | | | | | | | | | |   (603)  all_74_0 = all_74_1
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.76  | | | | | | | | | | | | | REDUCE: (138), (603) imply:
% 247.51/41.76  | | | | | | | | | | | | |   (604)  $false
% 247.51/41.76  | | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | | CLOSE: (604) is inconsistent.
% 247.51/41.77  | | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | |   (605)  all_74_3 = n3
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | REDUCE: (552), (605) imply:
% 247.51/41.77  | | | | | | | | | |   (606)  a_select3(q_ds1_filter, n3, n5) = all_74_1
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | REDUCE: (551), (605) imply:
% 247.51/41.77  | | | | | | | | | |   (607)  a_select3(q_ds1_filter, n5, n3) = all_74_0
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | REDUCE: (146), (605) imply:
% 247.51/41.77  | | | | | | | | | |   (608)  leq(n3, n5)
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | REDUCE: (139), (605) imply:
% 247.51/41.77  | | | | | | | | | |   (609)  leq(n0, n3)
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | GROUND_INST: instantiating (62) with n3, n5, all_74_1,
% 247.51/41.77  | | | | | | | | | |              simplifying with (112), (122), (554), (606), (609)
% 247.51/41.77  | | | | | | | | | |              gives:
% 247.51/41.77  | | | | | | | | | |   (610)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 247.51/41.77  | | | | | | | | | |          (a_select3(q_ds1_filter, n5, n3) = all_74_1 &
% 247.51/41.77  | | | | | | | | | |            $i(all_74_1))
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | BETA: splitting (610) gives:
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | |   (611)   ~ leq(n5, all_74_21)
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REDUCE: (135), (611) imply:
% 247.51/41.77  | | | | | | | | | | |   (612)   ~ leq(n5, n5)
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | PRED_UNIFY: (553), (612) imply:
% 247.51/41.77  | | | | | | | | | | |   (613)  $false
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | CLOSE: (613) is inconsistent.
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | |   (614)   ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.77  | | | | | | | | | | |              n5, n3) = all_74_1 & $i(all_74_1))
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | BETA: splitting (614) gives:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | |   (615)   ~ leq(n3, all_74_21)
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | REDUCE: (135), (615) imply:
% 247.51/41.77  | | | | | | | | | | | |   (616)   ~ leq(n3, n5)
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | PRED_UNIFY: (608), (616) imply:
% 247.51/41.77  | | | | | | | | | | | |   (617)  $false
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | CLOSE: (617) is inconsistent.
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | |   (618)  a_select3(q_ds1_filter, n5, n3) = all_74_1 &
% 247.51/41.77  | | | | | | | | | | | |          $i(all_74_1)
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | ALPHA: (618) implies:
% 247.51/41.77  | | | | | | | | | | | |   (619)  a_select3(q_ds1_filter, n5, n3) = all_74_1
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | REF_CLOSE: (17), (138), (607), (619) are inconsistent by
% 247.51/41.77  | | | | | | | | | | | |            sub-proof #54.
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | |   (620)  all_74_3 = n4
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | REDUCE: (552), (620) imply:
% 247.51/41.77  | | | | | | | | |   (621)  a_select3(q_ds1_filter, n4, n5) = all_74_1
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | REDUCE: (551), (620) imply:
% 247.51/41.77  | | | | | | | | |   (622)  a_select3(q_ds1_filter, n5, n4) = all_74_0
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | REDUCE: (146), (620) imply:
% 247.51/41.77  | | | | | | | | |   (623)  leq(n4, n5)
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | REDUCE: (139), (620) imply:
% 247.51/41.77  | | | | | | | | |   (624)  leq(n0, n4)
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | GROUND_INST: instantiating (62) with n4, n5, all_74_1,
% 247.51/41.77  | | | | | | | | |              simplifying with (119), (122), (554), (621), (624)
% 247.51/41.77  | | | | | | | | |              gives:
% 247.51/41.77  | | | | | | | | |   (625)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 247.51/41.77  | | | | | | | | |          (a_select3(q_ds1_filter, n5, n4) = all_74_1 &
% 247.51/41.77  | | | | | | | | |            $i(all_74_1))
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | BETA: splitting (625) gives:
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | |   (626)   ~ leq(n5, all_74_21)
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | REDUCE: (135), (626) imply:
% 247.51/41.77  | | | | | | | | | |   (627)   ~ leq(n5, n5)
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | PRED_UNIFY: (553), (627) imply:
% 247.51/41.77  | | | | | | | | | |   (628)  $false
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | CLOSE: (628) is inconsistent.
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | |   (629)   ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.77  | | | | | | | | | |              n5, n4) = all_74_1 & $i(all_74_1))
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | BETA: splitting (629) gives:
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | |   (630)   ~ leq(n4, all_74_21)
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REDUCE: (135), (630) imply:
% 247.51/41.77  | | | | | | | | | | |   (631)   ~ leq(n4, n5)
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | PRED_UNIFY: (623), (631) imply:
% 247.51/41.77  | | | | | | | | | | |   (632)  $false
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | CLOSE: (632) is inconsistent.
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | |   (633)  a_select3(q_ds1_filter, n5, n4) = all_74_1 &
% 247.51/41.77  | | | | | | | | | | |          $i(all_74_1)
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | ALPHA: (633) implies:
% 247.51/41.77  | | | | | | | | | | |   (634)  a_select3(q_ds1_filter, n5, n4) = all_74_1
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REF_CLOSE: (17), (138), (622), (634) are inconsistent by
% 247.51/41.77  | | | | | | | | | | |            sub-proof #53.
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | End of split
% 247.51/41.77  | | | | | | | | 
% 247.51/41.77  | | | | | | | End of split
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | Case 2:
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | |   (635)  all_74_3 = n5
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | REDUCE: (552), (635) imply:
% 247.51/41.77  | | | | | | |   (636)  a_select3(q_ds1_filter, n5, n5) = all_74_1
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | REDUCE: (551), (635) imply:
% 247.51/41.77  | | | | | | |   (637)  a_select3(q_ds1_filter, n5, n5) = all_74_0
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n5, n5,
% 247.51/41.77  | | | | | | |              q_ds1_filter, simplifying with (636), (637) gives:
% 247.51/41.77  | | | | | | |   (638)  all_74_0 = all_74_1
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | REDUCE: (138), (638) imply:
% 247.51/41.77  | | | | | | |   (639)  $false
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | CLOSE: (639) is inconsistent.
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | End of split
% 247.51/41.77  | | | | | | 
% 247.51/41.77  | | | | | End of split
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | Case 2:
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | |   (640)  all_74_3 = n0
% 247.51/41.77  | | | | |   (641)   ~ gt(all_74_3, n0)
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | | REDUCE: (144), (640) imply:
% 247.51/41.77  | | | | |   (642)  a_select3(q_ds1_filter, all_74_2, n0) = all_74_0
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | | REDUCE: (143), (640) imply:
% 247.51/41.77  | | | | |   (643)  a_select3(q_ds1_filter, n0, all_74_2) = all_74_1
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | | REDUCE: (146), (640) imply:
% 247.51/41.77  | | | | |   (644)  leq(n0, n5)
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | | REDUCE: (139), (640) imply:
% 247.51/41.77  | | | | |   (645)  leq(n0, n0)
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | | REDUCE: (640), (641) imply:
% 247.51/41.77  | | | | |   (646)   ~ gt(n0, n0)
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | | BETA: splitting (152) gives:
% 247.51/41.77  | | | | | 
% 247.51/41.77  | | | | | Case 1:
% 247.51/41.77  | | | | | | 
% 247.51/41.77  | | | | | |   (647)  gt(n5, all_74_2)
% 247.51/41.77  | | | | | | 
% 247.51/41.77  | | | | | | GROUND_INST: instantiating (1) with all_74_2, n5, n4, simplifying
% 247.51/41.77  | | | | | |              with (58), (122), (126), (647) gives:
% 247.51/41.77  | | | | | |   (648)  leq(all_74_2, n4)
% 247.51/41.77  | | | | | | 
% 247.51/41.77  | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n4, simplifying
% 247.51/41.77  | | | | | |              with (58), (119), (648) gives:
% 247.51/41.77  | | | | | |   (649)  all_74_2 = n4 | gt(n4, all_74_2)
% 247.51/41.77  | | | | | | 
% 247.51/41.77  | | | | | | BETA: splitting (151) gives:
% 247.51/41.77  | | | | | | 
% 247.51/41.77  | | | | | | Case 1:
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | |   (650)  all_74_2 = n0
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | REDUCE: (153), (650) imply:
% 247.51/41.77  | | | | | | |   (651)  gt(n0, n0)
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | PRED_UNIFY: (646), (651) imply:
% 247.51/41.77  | | | | | | |   (652)  $false
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | CLOSE: (652) is inconsistent.
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | Case 2:
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | |   (653)   ~ (all_74_2 = n0)
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | BETA: splitting (649) gives:
% 247.51/41.77  | | | | | | | 
% 247.51/41.77  | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | 
% 247.51/41.77  | | | | | | | |   (654)  gt(n4, all_74_2)
% 247.51/41.77  | | | | | | | | 
% 247.51/41.77  | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n4, n3,
% 247.51/41.77  | | | | | | | |              simplifying with (58), (119), (125), (654) gives:
% 247.51/41.77  | | | | | | | |   (655)  leq(all_74_2, n3)
% 247.51/41.77  | | | | | | | | 
% 247.51/41.77  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n3,
% 247.51/41.77  | | | | | | | |              simplifying with (58), (112), (655) gives:
% 247.51/41.77  | | | | | | | |   (656)  all_74_2 = n3 | gt(n3, all_74_2)
% 247.51/41.77  | | | | | | | | 
% 247.51/41.77  | | | | | | | | BETA: splitting (656) gives:
% 247.51/41.77  | | | | | | | | 
% 247.51/41.77  | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | |   (657)  gt(n3, all_74_2)
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n3, n2,
% 247.51/41.77  | | | | | | | | |              simplifying with (58), (112), (124), (657) gives:
% 247.51/41.77  | | | | | | | | |   (658)  leq(all_74_2, n2)
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_2, n2,
% 247.51/41.77  | | | | | | | | |              simplifying with (58), (101), (658) gives:
% 247.51/41.77  | | | | | | | | |   (659)  all_74_2 = n2 | gt(n2, all_74_2)
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | BETA: splitting (659) gives:
% 247.51/41.77  | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | |   (660)  gt(n2, all_74_2)
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_2, n2, n1,
% 247.51/41.77  | | | | | | | | | |              simplifying with (58), (101), (123), (660) gives:
% 247.51/41.77  | | | | | | | | | |   (661)  leq(all_74_2, n1)
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_2, simplifying with
% 247.51/41.77  | | | | | | | | | |              (58), (140), (661) gives:
% 247.51/41.77  | | | | | | | | | |   (662)  all_74_2 = n1 | all_74_2 = n0
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | BETA: splitting (662) gives:
% 247.51/41.77  | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | |   (663)  all_74_2 = n0
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REDUCE: (653), (663) imply:
% 247.51/41.77  | | | | | | | | | | |   (664)  $false
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | CLOSE: (664) is inconsistent.
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | |   (665)  all_74_2 = n1
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REDUCE: (642), (665) imply:
% 247.51/41.77  | | | | | | | | | | |   (666)  a_select3(q_ds1_filter, n1, n0) = all_74_0
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REDUCE: (643), (665) imply:
% 247.51/41.77  | | | | | | | | | | |   (667)  a_select3(q_ds1_filter, n0, n1) = all_74_1
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REDUCE: (145), (665) imply:
% 247.51/41.77  | | | | | | | | | | |   (668)  leq(n1, n5)
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | REDUCE: (140), (665) imply:
% 247.51/41.77  | | | | | | | | | | |   (669)  leq(n0, n1)
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n1, all_74_1,
% 247.51/41.77  | | | | | | | | | | |              simplifying with (12), (85), (645), (667), (669)
% 247.51/41.77  | | | | | | | | | | |              gives:
% 247.51/41.77  | | | | | | | | | | |   (670)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.77  | | | | | | | | | | |          (a_select3(q_ds1_filter, n1, n0) = all_74_1 &
% 247.51/41.77  | | | | | | | | | | |            $i(all_74_1))
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | BETA: splitting (670) gives:
% 247.51/41.77  | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | Case 1:
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | |   (671)   ~ leq(n0, all_74_21)
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | REDUCE: (135), (671) imply:
% 247.51/41.77  | | | | | | | | | | | |   (672)   ~ leq(n0, n5)
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | PRED_UNIFY: (644), (672) imply:
% 247.51/41.77  | | | | | | | | | | | |   (673)  $false
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | | CLOSE: (673) is inconsistent.
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.77  | | | | | | | | | | | Case 2:
% 247.51/41.77  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | |   (674)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.78  | | | | | | | | | | | |              n1, n0) = all_74_1 & $i(all_74_1))
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | BETA: splitting (674) gives:
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | |   (675)   ~ leq(n1, all_74_21)
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | | REDUCE: (135), (675) imply:
% 247.51/41.78  | | | | | | | | | | | | |   (676)   ~ leq(n1, n5)
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | | PRED_UNIFY: (668), (676) imply:
% 247.51/41.78  | | | | | | | | | | | | |   (677)  $false
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | | CLOSE: (677) is inconsistent.
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | |   (678)  a_select3(q_ds1_filter, n1, n0) = all_74_1 &
% 247.51/41.78  | | | | | | | | | | | | |          $i(all_74_1)
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | | ALPHA: (678) implies:
% 247.51/41.78  | | | | | | | | | | | | |   (679)  a_select3(q_ds1_filter, n1, n0) = all_74_1
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | | REF_CLOSE: (17), (138), (666), (679) are inconsistent by
% 247.51/41.78  | | | | | | | | | | | | |            sub-proof #52.
% 247.51/41.78  | | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | |   (680)  all_74_2 = n2
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | REDUCE: (642), (680) imply:
% 247.51/41.78  | | | | | | | | | |   (681)  a_select3(q_ds1_filter, n2, n0) = all_74_0
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | REDUCE: (643), (680) imply:
% 247.51/41.78  | | | | | | | | | |   (682)  a_select3(q_ds1_filter, n0, n2) = all_74_1
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | REDUCE: (145), (680) imply:
% 247.51/41.78  | | | | | | | | | |   (683)  leq(n2, n5)
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | REDUCE: (140), (680) imply:
% 247.51/41.78  | | | | | | | | | |   (684)  leq(n0, n2)
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n2, all_74_1,
% 247.51/41.78  | | | | | | | | | |              simplifying with (12), (101), (645), (682), (684)
% 247.51/41.78  | | | | | | | | | |              gives:
% 247.51/41.78  | | | | | | | | | |   (685)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.78  | | | | | | | | | |          (a_select3(q_ds1_filter, n2, n0) = all_74_1 &
% 247.51/41.78  | | | | | | | | | |            $i(all_74_1))
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | BETA: splitting (685) gives:
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | |   (686)   ~ leq(n0, all_74_21)
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | REDUCE: (135), (686) imply:
% 247.51/41.78  | | | | | | | | | | |   (687)   ~ leq(n0, n5)
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | PRED_UNIFY: (644), (687) imply:
% 247.51/41.78  | | | | | | | | | | |   (688)  $false
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | CLOSE: (688) is inconsistent.
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | |   (689)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.78  | | | | | | | | | | |              n2, n0) = all_74_1 & $i(all_74_1))
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | BETA: splitting (689) gives:
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | |   (690)   ~ leq(n2, all_74_21)
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | REDUCE: (135), (690) imply:
% 247.51/41.78  | | | | | | | | | | | |   (691)   ~ leq(n2, n5)
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | PRED_UNIFY: (683), (691) imply:
% 247.51/41.78  | | | | | | | | | | | |   (692)  $false
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | CLOSE: (692) is inconsistent.
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | |   (693)  a_select3(q_ds1_filter, n2, n0) = all_74_1 &
% 247.51/41.78  | | | | | | | | | | | |          $i(all_74_1)
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | ALPHA: (693) implies:
% 247.51/41.78  | | | | | | | | | | | |   (694)  a_select3(q_ds1_filter, n2, n0) = all_74_1
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n0,
% 247.51/41.78  | | | | | | | | | | | |              n2, q_ds1_filter, simplifying with (681), (694)
% 247.51/41.78  | | | | | | | | | | | |              gives:
% 247.51/41.78  | | | | | | | | | | | |   (695)  all_74_0 = all_74_1
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | REDUCE: (138), (695) imply:
% 247.51/41.78  | | | | | | | | | | | |   (696)  $false
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | | CLOSE: (696) is inconsistent.
% 247.51/41.78  | | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | |   (697)  all_74_2 = n3
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | REDUCE: (642), (697) imply:
% 247.51/41.78  | | | | | | | | |   (698)  a_select3(q_ds1_filter, n3, n0) = all_74_0
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | REDUCE: (643), (697) imply:
% 247.51/41.78  | | | | | | | | |   (699)  a_select3(q_ds1_filter, n0, n3) = all_74_1
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | REDUCE: (145), (697) imply:
% 247.51/41.78  | | | | | | | | |   (700)  leq(n3, n5)
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | REDUCE: (140), (697) imply:
% 247.51/41.78  | | | | | | | | |   (701)  leq(n0, n3)
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | GROUND_INST: instantiating (62) with n0, n3, all_74_1,
% 247.51/41.78  | | | | | | | | |              simplifying with (12), (112), (645), (699), (701)
% 247.51/41.78  | | | | | | | | |              gives:
% 247.51/41.78  | | | | | | | | |   (702)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.78  | | | | | | | | |          (a_select3(q_ds1_filter, n3, n0) = all_74_1 &
% 247.51/41.78  | | | | | | | | |            $i(all_74_1))
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | BETA: splitting (702) gives:
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | |   (703)   ~ leq(n0, all_74_21)
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | REDUCE: (135), (703) imply:
% 247.51/41.78  | | | | | | | | | |   (704)   ~ leq(n0, n5)
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | PRED_UNIFY: (644), (704) imply:
% 247.51/41.78  | | | | | | | | | |   (705)  $false
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | CLOSE: (705) is inconsistent.
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | |   (706)   ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.78  | | | | | | | | | |              n3, n0) = all_74_1 & $i(all_74_1))
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | BETA: splitting (706) gives:
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | |   (707)   ~ leq(n3, all_74_21)
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | REDUCE: (135), (707) imply:
% 247.51/41.78  | | | | | | | | | | |   (708)   ~ leq(n3, n5)
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | PRED_UNIFY: (700), (708) imply:
% 247.51/41.78  | | | | | | | | | | |   (709)  $false
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | CLOSE: (709) is inconsistent.
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | |   (710)  a_select3(q_ds1_filter, n3, n0) = all_74_1 &
% 247.51/41.78  | | | | | | | | | | |          $i(all_74_1)
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | ALPHA: (710) implies:
% 247.51/41.78  | | | | | | | | | | |   (711)  a_select3(q_ds1_filter, n3, n0) = all_74_1
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n0,
% 247.51/41.78  | | | | | | | | | | |              n3, q_ds1_filter, simplifying with (698), (711)
% 247.51/41.78  | | | | | | | | | | |              gives:
% 247.51/41.78  | | | | | | | | | | |   (712)  all_74_0 = all_74_1
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | REDUCE: (138), (712) imply:
% 247.51/41.78  | | | | | | | | | | |   (713)  $false
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | | CLOSE: (713) is inconsistent.
% 247.51/41.78  | | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | |   (714)  all_74_2 = n4
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | REDUCE: (642), (714) imply:
% 247.51/41.78  | | | | | | | |   (715)  a_select3(q_ds1_filter, n4, n0) = all_74_0
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | REDUCE: (643), (714) imply:
% 247.51/41.78  | | | | | | | |   (716)  a_select3(q_ds1_filter, n0, n4) = all_74_1
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | REDUCE: (145), (714) imply:
% 247.51/41.78  | | | | | | | |   (717)  leq(n4, n5)
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | REDUCE: (140), (714) imply:
% 247.51/41.78  | | | | | | | |   (718)  leq(n0, n4)
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | GROUND_INST: instantiating (62) with n0, n4, all_74_1,
% 247.51/41.78  | | | | | | | |              simplifying with (12), (119), (645), (716), (718)
% 247.51/41.78  | | | | | | | |              gives:
% 247.51/41.78  | | | | | | | |   (719)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.78  | | | | | | | |          (a_select3(q_ds1_filter, n4, n0) = all_74_1 &
% 247.51/41.78  | | | | | | | |            $i(all_74_1))
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | BETA: splitting (719) gives:
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | |   (720)   ~ leq(n0, all_74_21)
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | REDUCE: (135), (720) imply:
% 247.51/41.78  | | | | | | | | |   (721)   ~ leq(n0, n5)
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | PRED_UNIFY: (644), (721) imply:
% 247.51/41.78  | | | | | | | | |   (722)  $false
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | CLOSE: (722) is inconsistent.
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | |   (723)   ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter, n4,
% 247.51/41.78  | | | | | | | | |              n0) = all_74_1 & $i(all_74_1))
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | BETA: splitting (723) gives:
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | |   (724)   ~ leq(n4, all_74_21)
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | REDUCE: (135), (724) imply:
% 247.51/41.78  | | | | | | | | | |   (725)   ~ leq(n4, n5)
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | PRED_UNIFY: (717), (725) imply:
% 247.51/41.78  | | | | | | | | | |   (726)  $false
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | CLOSE: (726) is inconsistent.
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | |   (727)  a_select3(q_ds1_filter, n4, n0) = all_74_1 &
% 247.51/41.78  | | | | | | | | | |          $i(all_74_1)
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | ALPHA: (727) implies:
% 247.51/41.78  | | | | | | | | | |   (728)  a_select3(q_ds1_filter, n4, n0) = all_74_1
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | | REF_CLOSE: (17), (138), (715), (728) are inconsistent by
% 247.51/41.78  | | | | | | | | | |            sub-proof #51.
% 247.51/41.78  | | | | | | | | | | 
% 247.51/41.78  | | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | | 
% 247.51/41.78  | | | | | | | | End of split
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | End of split
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | End of split
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | Case 2:
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | |   (729)  all_74_2 = n5
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | | REDUCE: (642), (729) imply:
% 247.51/41.78  | | | | | |   (730)  a_select3(q_ds1_filter, n5, n0) = all_74_0
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | | REDUCE: (643), (729) imply:
% 247.51/41.78  | | | | | |   (731)  a_select3(q_ds1_filter, n0, n5) = all_74_1
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | | REDUCE: (145), (729) imply:
% 247.51/41.78  | | | | | |   (732)  leq(n5, n5)
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | | GROUND_INST: instantiating (62) with n0, n5, all_74_1, simplifying
% 247.51/41.78  | | | | | |              with (12), (122), (644), (645), (731) gives:
% 247.51/41.78  | | | | | |   (733)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.78  | | | | | |          (a_select3(q_ds1_filter, n5, n0) = all_74_1 & $i(all_74_1))
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | | BETA: splitting (733) gives:
% 247.51/41.78  | | | | | | 
% 247.51/41.78  | | | | | | Case 1:
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | |   (734)   ~ leq(n0, all_74_21)
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | | REDUCE: (135), (734) imply:
% 247.51/41.78  | | | | | | |   (735)   ~ leq(n0, n5)
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | | PRED_UNIFY: (644), (735) imply:
% 247.51/41.78  | | | | | | |   (736)  $false
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | | CLOSE: (736) is inconsistent.
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | Case 2:
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | |   (737)   ~ leq(n5, all_74_21) | (a_select3(q_ds1_filter, n5, n0)
% 247.51/41.78  | | | | | | |            = all_74_1 & $i(all_74_1))
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | | BETA: splitting (737) gives:
% 247.51/41.78  | | | | | | | 
% 247.51/41.78  | | | | | | | Case 1:
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | |   (738)   ~ leq(n5, all_74_21)
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | REDUCE: (135), (738) imply:
% 247.51/41.78  | | | | | | | |   (739)   ~ leq(n5, n5)
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | PRED_UNIFY: (732), (739) imply:
% 247.51/41.78  | | | | | | | |   (740)  $false
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | | CLOSE: (740) is inconsistent.
% 247.51/41.78  | | | | | | | | 
% 247.51/41.78  | | | | | | | Case 2:
% 247.51/41.78  | | | | | | | | 
% 247.51/41.79  | | | | | | | |   (741)  a_select3(q_ds1_filter, n5, n0) = all_74_1 &
% 247.51/41.79  | | | | | | | |          $i(all_74_1)
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | | ALPHA: (741) implies:
% 247.51/41.79  | | | | | | | |   (742)  a_select3(q_ds1_filter, n5, n0) = all_74_1
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | | REF_CLOSE: (17), (138), (730), (742) are inconsistent by
% 247.51/41.79  | | | | | | | |            sub-proof #50.
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | End of split
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | End of split
% 247.51/41.79  | | | | | | 
% 247.51/41.79  | | | | | End of split
% 247.51/41.79  | | | | | 
% 247.51/41.79  | | | | End of split
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | Case 2:
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | |   (743)  all_74_2 = n0
% 247.51/41.79  | | | |   (744)   ~ gt(all_74_2, n0)
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | | REDUCE: (144), (743) imply:
% 247.51/41.79  | | | |   (745)  a_select3(q_ds1_filter, n0, all_74_3) = all_74_0
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | | REDUCE: (143), (743) imply:
% 247.51/41.79  | | | |   (746)  a_select3(q_ds1_filter, all_74_3, n0) = all_74_1
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | | REDUCE: (145), (743) imply:
% 247.51/41.79  | | | |   (747)  leq(n0, n5)
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | | REDUCE: (140), (743) imply:
% 247.51/41.79  | | | |   (748)  leq(n0, n0)
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | | REDUCE: (743), (744) imply:
% 247.51/41.79  | | | |   (749)   ~ gt(n0, n0)
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | | BETA: splitting (147) gives:
% 247.51/41.79  | | | | 
% 247.51/41.79  | | | | Case 1:
% 247.51/41.79  | | | | | 
% 247.51/41.79  | | | | |   (750)  gt(all_74_3, n0)
% 247.51/41.79  | | | | | 
% 247.51/41.79  | | | | | BETA: splitting (150) gives:
% 247.51/41.79  | | | | | 
% 247.51/41.79  | | | | | Case 1:
% 247.51/41.79  | | | | | | 
% 247.51/41.79  | | | | | |   (751)  gt(n5, all_74_3)
% 247.51/41.79  | | | | | | 
% 247.51/41.79  | | | | | | GROUND_INST: instantiating (1) with all_74_3, n5, n4, simplifying
% 247.51/41.79  | | | | | |              with (57), (122), (126), (751) gives:
% 247.51/41.79  | | | | | |   (752)  leq(all_74_3, n4)
% 247.51/41.79  | | | | | | 
% 247.51/41.79  | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n4, simplifying
% 247.51/41.79  | | | | | |              with (57), (119), (752) gives:
% 247.51/41.79  | | | | | |   (753)  all_74_3 = n4 | gt(n4, all_74_3)
% 247.51/41.79  | | | | | | 
% 247.51/41.79  | | | | | | BETA: splitting (149) gives:
% 247.51/41.79  | | | | | | 
% 247.51/41.79  | | | | | | Case 1:
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | |   (754)  all_74_3 = n0
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | | REDUCE: (750), (754) imply:
% 247.51/41.79  | | | | | | |   (755)  gt(n0, n0)
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | | PRED_UNIFY: (749), (755) imply:
% 247.51/41.79  | | | | | | |   (756)  $false
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | | CLOSE: (756) is inconsistent.
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | Case 2:
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | |   (757)   ~ (all_74_3 = n0)
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | | BETA: splitting (753) gives:
% 247.51/41.79  | | | | | | | 
% 247.51/41.79  | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | |   (758)  gt(n4, all_74_3)
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n4, n3,
% 247.51/41.79  | | | | | | | |              simplifying with (57), (119), (125), (758) gives:
% 247.51/41.79  | | | | | | | |   (759)  leq(all_74_3, n3)
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n3,
% 247.51/41.79  | | | | | | | |              simplifying with (57), (112), (759) gives:
% 247.51/41.79  | | | | | | | |   (760)  all_74_3 = n3 | gt(n3, all_74_3)
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | | BETA: splitting (760) gives:
% 247.51/41.79  | | | | | | | | 
% 247.51/41.79  | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | |   (761)  gt(n3, all_74_3)
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n3, n2,
% 247.51/41.79  | | | | | | | | |              simplifying with (57), (112), (124), (761) gives:
% 247.51/41.79  | | | | | | | | |   (762)  leq(all_74_3, n2)
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_3, n2,
% 247.51/41.79  | | | | | | | | |              simplifying with (57), (101), (762) gives:
% 247.51/41.79  | | | | | | | | |   (763)  all_74_3 = n2 | gt(n2, all_74_3)
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | BETA: splitting (763) gives:
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | |   (764)  gt(n2, all_74_3)
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_3, n2, n1,
% 247.51/41.79  | | | | | | | | | |              simplifying with (57), (101), (123), (764) gives:
% 247.51/41.79  | | | | | | | | | |   (765)  leq(all_74_3, n1)
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_3, simplifying with
% 247.51/41.79  | | | | | | | | | |              (57), (139), (765) gives:
% 247.51/41.79  | | | | | | | | | |   (766)  all_74_3 = n1 | all_74_3 = n0
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | BETA: splitting (766) gives:
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | |   (767)  all_74_3 = n0
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | REDUCE: (757), (767) imply:
% 247.51/41.79  | | | | | | | | | | |   (768)  $false
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | CLOSE: (768) is inconsistent.
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | Case 2:
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | |   (769)  all_74_3 = n1
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | REDUCE: (746), (769) imply:
% 247.51/41.79  | | | | | | | | | | |   (770)  a_select3(q_ds1_filter, n1, n0) = all_74_1
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | REDUCE: (745), (769) imply:
% 247.51/41.79  | | | | | | | | | | |   (771)  a_select3(q_ds1_filter, n0, n1) = all_74_0
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | REDUCE: (146), (769) imply:
% 247.51/41.79  | | | | | | | | | | |   (772)  leq(n1, n5)
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | REDUCE: (139), (769) imply:
% 247.51/41.79  | | | | | | | | | | |   (773)  leq(n0, n1)
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n1, all_74_0,
% 247.51/41.79  | | | | | | | | | | |              simplifying with (12), (85), (748), (771), (773)
% 247.51/41.79  | | | | | | | | | | |              gives:
% 247.51/41.79  | | | | | | | | | | |   (774)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.79  | | | | | | | | | | |          (a_select3(q_ds1_filter, n1, n0) = all_74_0 &
% 247.51/41.79  | | | | | | | | | | |            $i(all_74_0))
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | BETA: splitting (774) gives:
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | |   (775)   ~ leq(n0, all_74_21)
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | REDUCE: (135), (775) imply:
% 247.51/41.79  | | | | | | | | | | | |   (776)   ~ leq(n0, n5)
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | PRED_UNIFY: (747), (776) imply:
% 247.51/41.79  | | | | | | | | | | | |   (777)  $false
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | CLOSE: (777) is inconsistent.
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | Case 2:
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | |   (778)   ~ leq(n1, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.79  | | | | | | | | | | | |              n1, n0) = all_74_0 & $i(all_74_0))
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | BETA: splitting (778) gives:
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | |   (779)   ~ leq(n1, all_74_21)
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | | REDUCE: (135), (779) imply:
% 247.51/41.79  | | | | | | | | | | | | |   (780)   ~ leq(n1, n5)
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | | PRED_UNIFY: (772), (780) imply:
% 247.51/41.79  | | | | | | | | | | | | |   (781)  $false
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | | CLOSE: (781) is inconsistent.
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | Case 2:
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | |   (782)  a_select3(q_ds1_filter, n1, n0) = all_74_0 &
% 247.51/41.79  | | | | | | | | | | | | |          $i(all_74_0)
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | | ALPHA: (782) implies:
% 247.51/41.79  | | | | | | | | | | | | |   (783)  a_select3(q_ds1_filter, n1, n0) = all_74_0
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | | REF_CLOSE: (17), (138), (770), (783) are inconsistent by
% 247.51/41.79  | | | | | | | | | | | | |            sub-proof #52.
% 247.51/41.79  | | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | End of split
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | End of split
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | End of split
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | Case 2:
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | |   (784)  all_74_3 = n2
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | REDUCE: (746), (784) imply:
% 247.51/41.79  | | | | | | | | | |   (785)  a_select3(q_ds1_filter, n2, n0) = all_74_1
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | REDUCE: (745), (784) imply:
% 247.51/41.79  | | | | | | | | | |   (786)  a_select3(q_ds1_filter, n0, n2) = all_74_0
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | REDUCE: (146), (784) imply:
% 247.51/41.79  | | | | | | | | | |   (787)  leq(n2, n5)
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | REDUCE: (139), (784) imply:
% 247.51/41.79  | | | | | | | | | |   (788)  leq(n0, n2)
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | GROUND_INST: instantiating (62) with n0, n2, all_74_0,
% 247.51/41.79  | | | | | | | | | |              simplifying with (12), (101), (748), (786), (788)
% 247.51/41.79  | | | | | | | | | |              gives:
% 247.51/41.79  | | | | | | | | | |   (789)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.79  | | | | | | | | | |          (a_select3(q_ds1_filter, n2, n0) = all_74_0 &
% 247.51/41.79  | | | | | | | | | |            $i(all_74_0))
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | BETA: splitting (789) gives:
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | |   (790)   ~ leq(n0, all_74_21)
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | REDUCE: (135), (790) imply:
% 247.51/41.79  | | | | | | | | | | |   (791)   ~ leq(n0, n5)
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | PRED_UNIFY: (747), (791) imply:
% 247.51/41.79  | | | | | | | | | | |   (792)  $false
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | CLOSE: (792) is inconsistent.
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | Case 2:
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | |   (793)   ~ leq(n2, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.79  | | | | | | | | | | |              n2, n0) = all_74_0 & $i(all_74_0))
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | BETA: splitting (793) gives:
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | |   (794)   ~ leq(n2, all_74_21)
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | REDUCE: (135), (794) imply:
% 247.51/41.79  | | | | | | | | | | | |   (795)   ~ leq(n2, n5)
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | PRED_UNIFY: (787), (795) imply:
% 247.51/41.79  | | | | | | | | | | | |   (796)  $false
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | CLOSE: (796) is inconsistent.
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | Case 2:
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | |   (797)  a_select3(q_ds1_filter, n2, n0) = all_74_0 &
% 247.51/41.79  | | | | | | | | | | | |          $i(all_74_0)
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | ALPHA: (797) implies:
% 247.51/41.79  | | | | | | | | | | | |   (798)  a_select3(q_ds1_filter, n2, n0) = all_74_0
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n0,
% 247.51/41.79  | | | | | | | | | | | |              n2, q_ds1_filter, simplifying with (785), (798)
% 247.51/41.79  | | | | | | | | | | | |              gives:
% 247.51/41.79  | | | | | | | | | | | |   (799)  all_74_0 = all_74_1
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | REDUCE: (138), (799) imply:
% 247.51/41.79  | | | | | | | | | | | |   (800)  $false
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | | CLOSE: (800) is inconsistent.
% 247.51/41.79  | | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | | End of split
% 247.51/41.79  | | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | End of split
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | End of split
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | Case 2:
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | |   (801)  all_74_3 = n3
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | REDUCE: (746), (801) imply:
% 247.51/41.79  | | | | | | | | |   (802)  a_select3(q_ds1_filter, n3, n0) = all_74_1
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | REDUCE: (745), (801) imply:
% 247.51/41.79  | | | | | | | | |   (803)  a_select3(q_ds1_filter, n0, n3) = all_74_0
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | REDUCE: (146), (801) imply:
% 247.51/41.79  | | | | | | | | |   (804)  leq(n3, n5)
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | REDUCE: (139), (801) imply:
% 247.51/41.79  | | | | | | | | |   (805)  leq(n0, n3)
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | GROUND_INST: instantiating (62) with n0, n3, all_74_0,
% 247.51/41.79  | | | | | | | | |              simplifying with (12), (112), (748), (803), (805)
% 247.51/41.79  | | | | | | | | |              gives:
% 247.51/41.79  | | | | | | | | |   (806)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.79  | | | | | | | | |          (a_select3(q_ds1_filter, n3, n0) = all_74_0 &
% 247.51/41.79  | | | | | | | | |            $i(all_74_0))
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | BETA: splitting (806) gives:
% 247.51/41.79  | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | Case 1:
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | |   (807)   ~ leq(n0, all_74_21)
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | REDUCE: (135), (807) imply:
% 247.51/41.79  | | | | | | | | | |   (808)   ~ leq(n0, n5)
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | PRED_UNIFY: (747), (808) imply:
% 247.51/41.79  | | | | | | | | | |   (809)  $false
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.79  | | | | | | | | | | CLOSE: (809) is inconsistent.
% 247.51/41.79  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | |   (810)   ~ leq(n3, all_74_21) | (a_select3(q_ds1_filter,
% 247.51/41.80  | | | | | | | | | |              n3, n0) = all_74_0 & $i(all_74_0))
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | BETA: splitting (810) gives:
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | |   (811)   ~ leq(n3, all_74_21)
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | | REDUCE: (135), (811) imply:
% 247.51/41.80  | | | | | | | | | | |   (812)   ~ leq(n3, n5)
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | | PRED_UNIFY: (804), (812) imply:
% 247.51/41.80  | | | | | | | | | | |   (813)  $false
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | | CLOSE: (813) is inconsistent.
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | |   (814)  a_select3(q_ds1_filter, n3, n0) = all_74_0 &
% 247.51/41.80  | | | | | | | | | | |          $i(all_74_0)
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | | ALPHA: (814) implies:
% 247.51/41.80  | | | | | | | | | | |   (815)  a_select3(q_ds1_filter, n3, n0) = all_74_0
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_0, all_74_1, n0,
% 247.51/41.80  | | | | | | | | | | |              n3, q_ds1_filter, simplifying with (802), (815)
% 247.51/41.80  | | | | | | | | | | |              gives:
% 247.51/41.80  | | | | | | | | | | |   (816)  all_74_0 = all_74_1
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | | REDUCE: (138), (816) imply:
% 247.51/41.80  | | | | | | | | | | |   (817)  $false
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | | CLOSE: (817) is inconsistent.
% 247.51/41.80  | | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | End of split
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | End of split
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | End of split
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (818)  all_74_3 = n4
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REDUCE: (746), (818) imply:
% 247.51/41.80  | | | | | | | |   (819)  a_select3(q_ds1_filter, n4, n0) = all_74_1
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REDUCE: (745), (818) imply:
% 247.51/41.80  | | | | | | | |   (820)  a_select3(q_ds1_filter, n0, n4) = all_74_0
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REDUCE: (146), (818) imply:
% 247.51/41.80  | | | | | | | |   (821)  leq(n4, n5)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REDUCE: (139), (818) imply:
% 247.51/41.80  | | | | | | | |   (822)  leq(n0, n4)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | GROUND_INST: instantiating (62) with n0, n4, all_74_0,
% 247.51/41.80  | | | | | | | |              simplifying with (12), (119), (748), (820), (822)
% 247.51/41.80  | | | | | | | |              gives:
% 247.51/41.80  | | | | | | | |   (823)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.80  | | | | | | | |          (a_select3(q_ds1_filter, n4, n0) = all_74_0 &
% 247.51/41.80  | | | | | | | |            $i(all_74_0))
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | BETA: splitting (823) gives:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | |   (824)   ~ leq(n0, all_74_21)
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | REDUCE: (135), (824) imply:
% 247.51/41.80  | | | | | | | | |   (825)   ~ leq(n0, n5)
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | PRED_UNIFY: (747), (825) imply:
% 247.51/41.80  | | | | | | | | |   (826)  $false
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | CLOSE: (826) is inconsistent.
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | |   (827)   ~ leq(n4, all_74_21) | (a_select3(q_ds1_filter, n4,
% 247.51/41.80  | | | | | | | | |              n0) = all_74_0 & $i(all_74_0))
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | BETA: splitting (827) gives:
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | |   (828)   ~ leq(n4, all_74_21)
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | REDUCE: (135), (828) imply:
% 247.51/41.80  | | | | | | | | | |   (829)   ~ leq(n4, n5)
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | PRED_UNIFY: (821), (829) imply:
% 247.51/41.80  | | | | | | | | | |   (830)  $false
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | CLOSE: (830) is inconsistent.
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | |   (831)  a_select3(q_ds1_filter, n4, n0) = all_74_0 &
% 247.51/41.80  | | | | | | | | | |          $i(all_74_0)
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | ALPHA: (831) implies:
% 247.51/41.80  | | | | | | | | | |   (832)  a_select3(q_ds1_filter, n4, n0) = all_74_0
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | | REF_CLOSE: (17), (138), (819), (832) are inconsistent by
% 247.51/41.80  | | | | | | | | | |            sub-proof #51.
% 247.51/41.80  | | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | End of split
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | End of split
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | End of split
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | End of split
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | Case 2:
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | |   (833)  all_74_3 = n5
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | REDUCE: (746), (833) imply:
% 247.51/41.80  | | | | | |   (834)  a_select3(q_ds1_filter, n5, n0) = all_74_1
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | REDUCE: (745), (833) imply:
% 247.51/41.80  | | | | | |   (835)  a_select3(q_ds1_filter, n0, n5) = all_74_0
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | REDUCE: (146), (833) imply:
% 247.51/41.80  | | | | | |   (836)  leq(n5, n5)
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | GROUND_INST: instantiating (62) with n0, n5, all_74_0, simplifying
% 247.51/41.80  | | | | | |              with (12), (122), (747), (748), (835) gives:
% 247.51/41.80  | | | | | |   (837)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.51/41.80  | | | | | |          (a_select3(q_ds1_filter, n5, n0) = all_74_0 & $i(all_74_0))
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | BETA: splitting (837) gives:
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | Case 1:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | |   (838)   ~ leq(n0, all_74_21)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | REDUCE: (135), (838) imply:
% 247.51/41.80  | | | | | | |   (839)   ~ leq(n0, n5)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | PRED_UNIFY: (747), (839) imply:
% 247.51/41.80  | | | | | | |   (840)  $false
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | CLOSE: (840) is inconsistent.
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | Case 2:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | |   (841)   ~ leq(n5, all_74_21) | (a_select3(q_ds1_filter, n5, n0)
% 247.51/41.80  | | | | | | |            = all_74_0 & $i(all_74_0))
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | BETA: splitting (841) gives:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (842)   ~ leq(n5, all_74_21)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REDUCE: (135), (842) imply:
% 247.51/41.80  | | | | | | | |   (843)   ~ leq(n5, n5)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | PRED_UNIFY: (836), (843) imply:
% 247.51/41.80  | | | | | | | |   (844)  $false
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | CLOSE: (844) is inconsistent.
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (845)  a_select3(q_ds1_filter, n5, n0) = all_74_0 &
% 247.51/41.80  | | | | | | | |          $i(all_74_0)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | ALPHA: (845) implies:
% 247.51/41.80  | | | | | | | |   (846)  a_select3(q_ds1_filter, n5, n0) = all_74_0
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REF_CLOSE: (17), (138), (834), (846) are inconsistent by
% 247.51/41.80  | | | | | | | |            sub-proof #50.
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | End of split
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | End of split
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | End of split
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | Case 2:
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | |   (847)  all_74_3 = n0
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | | REDUCE: (746), (847) imply:
% 247.51/41.80  | | | | |   (848)  a_select3(q_ds1_filter, n0, n0) = all_74_1
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | | REDUCE: (745), (847) imply:
% 247.51/41.80  | | | | |   (849)  a_select3(q_ds1_filter, n0, n0) = all_74_0
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | | GROUND_INST: instantiating (17) with all_74_1, all_74_0, n0, n0,
% 247.51/41.80  | | | | |              q_ds1_filter, simplifying with (848), (849) gives:
% 247.51/41.80  | | | | |   (850)  all_74_0 = all_74_1
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | | REDUCE: (138), (850) imply:
% 247.51/41.80  | | | | |   (851)  $false
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | | CLOSE: (851) is inconsistent.
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | End of split
% 247.51/41.80  | | | | 
% 247.51/41.80  | | | End of split
% 247.51/41.80  | | | 
% 247.51/41.80  | | Case 2:
% 247.51/41.80  | | | 
% 247.51/41.80  | | |   (852)   ~ (all_74_4 = all_74_5) & a_select3(r_ds1_filter, all_74_6,
% 247.51/41.80  | | |            all_74_7) = all_74_4 & a_select3(r_ds1_filter, all_74_7,
% 247.51/41.80  | | |            all_74_6) = all_74_5 & $i(all_74_4) & $i(all_74_5) &
% 247.51/41.80  | | |          leq(all_74_6, all_74_20) & leq(all_74_7, all_74_20) & leq(n0,
% 247.51/41.80  | | |            all_74_6) & leq(n0, all_74_7)
% 247.51/41.80  | | | 
% 247.51/41.80  | | | ALPHA: (852) implies:
% 247.51/41.80  | | |   (853)   ~ (all_74_4 = all_74_5)
% 247.51/41.80  | | |   (854)  leq(n0, all_74_7)
% 247.51/41.80  | | |   (855)  leq(n0, all_74_6)
% 247.51/41.80  | | |   (856)  leq(all_74_7, all_74_20)
% 247.51/41.80  | | |   (857)  leq(all_74_6, all_74_20)
% 247.51/41.80  | | |   (858)  a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5
% 247.51/41.80  | | |   (859)  a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4
% 247.51/41.80  | | | 
% 247.51/41.80  | | | REDUCE: (134), (857) imply:
% 247.51/41.80  | | |   (860)  leq(all_74_6, n2)
% 247.51/41.80  | | | 
% 247.51/41.80  | | | REDUCE: (134), (856) imply:
% 247.51/41.80  | | |   (861)  leq(all_74_7, n2)
% 247.51/41.80  | | | 
% 247.51/41.80  | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_7, simplifying with
% 247.51/41.80  | | |              (12), (55), (854) gives:
% 247.51/41.80  | | |   (862)  all_74_7 = n0 | gt(all_74_7, n0)
% 247.51/41.80  | | | 
% 247.51/41.80  | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_6, simplifying with
% 247.51/41.80  | | |              (12), (56), (855) gives:
% 247.51/41.80  | | |   (863)  all_74_6 = n0 | gt(all_74_6, n0)
% 247.51/41.80  | | | 
% 247.51/41.80  | | | GROUND_INST: instantiating (5) with all_74_7, simplifying with (55),
% 247.51/41.80  | | |              (854), (861) gives:
% 247.51/41.80  | | |   (864)  all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0
% 247.51/41.80  | | | 
% 247.51/41.80  | | | GROUND_INST: instantiating (leq_gt2) with all_74_7, n2, simplifying with
% 247.51/41.80  | | |              (55), (101), (861) gives:
% 247.51/41.80  | | |   (865)  all_74_7 = n2 | gt(n2, all_74_7)
% 247.51/41.80  | | | 
% 247.51/41.80  | | | GROUND_INST: instantiating (5) with all_74_6, simplifying with (56),
% 247.51/41.80  | | |              (855), (860) gives:
% 247.51/41.80  | | |   (866)  all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0
% 247.51/41.80  | | | 
% 247.51/41.80  | | | GROUND_INST: instantiating (leq_gt2) with all_74_6, n2, simplifying with
% 247.51/41.80  | | |              (56), (101), (860) gives:
% 247.51/41.80  | | |   (867)  all_74_6 = n2 | gt(n2, all_74_6)
% 247.51/41.80  | | | 
% 247.51/41.80  | | | BETA: splitting (863) gives:
% 247.51/41.80  | | | 
% 247.51/41.80  | | | Case 1:
% 247.51/41.80  | | | | 
% 247.51/41.80  | | | |   (868)  gt(all_74_6, n0)
% 247.51/41.80  | | | | 
% 247.51/41.80  | | | | BETA: splitting (862) gives:
% 247.51/41.80  | | | | 
% 247.51/41.80  | | | | Case 1:
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | |   (869)  gt(all_74_7, n0)
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | | BETA: splitting (865) gives:
% 247.51/41.80  | | | | | 
% 247.51/41.80  | | | | | Case 1:
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | |   (870)  gt(n2, all_74_7)
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying
% 247.51/41.80  | | | | | |              with (55), (101), (123), (870) gives:
% 247.51/41.80  | | | | | |   (871)  leq(all_74_7, n1)
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | BETA: splitting (867) gives:
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | Case 1:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | |   (872)  gt(n2, all_74_6)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying
% 247.51/41.80  | | | | | | |              with (56), (101), (123), (872) gives:
% 247.51/41.80  | | | | | | |   (873)  leq(all_74_6, n1)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | BETA: splitting (866) gives:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (874)  all_74_6 = n0
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REF_CLOSE: (56), (868), (874), (irreflexivity_gt) are
% 247.51/41.80  | | | | | | | |            inconsistent by sub-proof #49.
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (875)   ~ (all_74_6 = n0)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | BETA: splitting (864) gives:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | |   (876)  all_74_7 = n0
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | REF_CLOSE: (55), (869), (876), (irreflexivity_gt) are
% 247.51/41.80  | | | | | | | | |            inconsistent by sub-proof #48.
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | |   (877)   ~ (all_74_7 = n0)
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | | REF_CLOSE: (4), (17), (55), (56), (853), (854), (855), (858),
% 247.51/41.80  | | | | | | | | |            (859), (871), (873), (875), (877) are inconsistent
% 247.51/41.80  | | | | | | | | |            by sub-proof #47.
% 247.51/41.80  | | | | | | | | | 
% 247.51/41.80  | | | | | | | | End of split
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | End of split
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | Case 2:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | |   (878)  all_74_6 = n2
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | REDUCE: (859), (878) imply:
% 247.51/41.80  | | | | | | |   (879)  a_select3(r_ds1_filter, n2, all_74_7) = all_74_4
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | REDUCE: (858), (878) imply:
% 247.51/41.80  | | | | | | |   (880)  a_select3(r_ds1_filter, all_74_7, n2) = all_74_5
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | REDUCE: (860), (878) imply:
% 247.51/41.80  | | | | | | |   (881)  leq(n2, n2)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | REDUCE: (855), (878) imply:
% 247.51/41.80  | | | | | | |   (882)  leq(n0, n2)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | BETA: splitting (864) gives:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (883)  all_74_7 = n0
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REF_CLOSE: (55), (869), (883), (irreflexivity_gt) are
% 247.51/41.80  | | | | | | | |            inconsistent by sub-proof #48.
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (884)   ~ (all_74_7 = n0)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REF_CLOSE: (4), (17), (55), (63), (101), (134), (853), (854),
% 247.51/41.80  | | | | | | | |            (861), (871), (879), (880), (881), (882), (884) are
% 247.51/41.80  | | | | | | | |            inconsistent by sub-proof #46.
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | End of split
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | End of split
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | Case 2:
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | |   (885)  all_74_7 = n2
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | REDUCE: (859), (885) imply:
% 247.51/41.80  | | | | | |   (886)  a_select3(r_ds1_filter, all_74_6, n2) = all_74_4
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | REDUCE: (858), (885) imply:
% 247.51/41.80  | | | | | |   (887)  a_select3(r_ds1_filter, n2, all_74_6) = all_74_5
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | REDUCE: (861), (885) imply:
% 247.51/41.80  | | | | | |   (888)  leq(n2, n2)
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | REDUCE: (854), (885) imply:
% 247.51/41.80  | | | | | |   (889)  leq(n0, n2)
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | BETA: splitting (867) gives:
% 247.51/41.80  | | | | | | 
% 247.51/41.80  | | | | | | Case 1:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | |   (890)  gt(n2, all_74_6)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | GROUND_INST: instantiating (1) with all_74_6, n2, n1, simplifying
% 247.51/41.80  | | | | | | |              with (56), (101), (123), (890) gives:
% 247.51/41.80  | | | | | | |   (891)  leq(all_74_6, n1)
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | GROUND_INST: instantiating (4) with all_74_6, simplifying with
% 247.51/41.80  | | | | | | |              (56), (855), (891) gives:
% 247.51/41.80  | | | | | | |   (892)  all_74_6 = n1 | all_74_6 = n0
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | BETA: splitting (866) gives:
% 247.51/41.80  | | | | | | | 
% 247.51/41.80  | | | | | | | Case 1:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (893)  all_74_6 = n0
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | | REF_CLOSE: (56), (868), (893), (irreflexivity_gt) are
% 247.51/41.80  | | | | | | | |            inconsistent by sub-proof #49.
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | Case 2:
% 247.51/41.80  | | | | | | | | 
% 247.51/41.80  | | | | | | | |   (894)   ~ (all_74_6 = n0)
% 247.51/41.80  | | | | | | | | 
% 247.51/41.81  | | | | | | | | REF_CLOSE: (17), (56), (63), (101), (134), (853), (855), (860),
% 247.51/41.81  | | | | | | | |            (886), (887), (888), (889), (892), (894) are
% 247.51/41.81  | | | | | | | |            inconsistent by sub-proof #45.
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | End of split
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | Case 2:
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | |   (895)  all_74_6 = n2
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | REF_CLOSE: (17), (853), (886), (887), (895) are inconsistent by
% 247.51/41.81  | | | | | | |            sub-proof #44.
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | End of split
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | End of split
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | Case 2:
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | |   (896)  all_74_7 = n0
% 247.51/41.81  | | | | |   (897)   ~ gt(all_74_7, n0)
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | REDUCE: (896), (897) imply:
% 247.51/41.81  | | | | |   (898)   ~ gt(n0, n0)
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | REF_CLOSE: (1), (4), (17), (55), (56), (63), (101), (123), (134),
% 247.51/41.81  | | | | |            (853), (854), (855), (858), (859), (860), (861), (862),
% 247.51/41.81  | | | | |            (864), (865), (866), (867), (868), (898) are inconsistent
% 247.51/41.81  | | | | |            by sub-proof #41.
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | End of split
% 247.51/41.81  | | | | 
% 247.51/41.81  | | | Case 2:
% 247.51/41.81  | | | | 
% 247.51/41.81  | | | |   (899)  all_74_6 = n0
% 247.51/41.81  | | | |   (900)   ~ gt(all_74_6, n0)
% 247.51/41.81  | | | | 
% 247.51/41.81  | | | | REDUCE: (899), (900) imply:
% 247.51/41.81  | | | |   (901)   ~ gt(n0, n0)
% 247.51/41.81  | | | | 
% 247.51/41.81  | | | | BETA: splitting (863) gives:
% 247.51/41.81  | | | | 
% 247.51/41.81  | | | | Case 1:
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | |   (902)  gt(all_74_6, n0)
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | REF_CLOSE: (1), (4), (17), (55), (56), (63), (101), (123), (134),
% 247.51/41.81  | | | | |            (853), (854), (855), (858), (859), (860), (861), (862),
% 247.51/41.81  | | | | |            (864), (865), (866), (867), (901), (902) are inconsistent
% 247.51/41.81  | | | | |            by sub-proof #41.
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | Case 2:
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | REDUCE: (859), (899) imply:
% 247.51/41.81  | | | | |   (903)  a_select3(r_ds1_filter, n0, all_74_7) = all_74_4
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | REDUCE: (858), (899) imply:
% 247.51/41.81  | | | | |   (904)  a_select3(r_ds1_filter, all_74_7, n0) = all_74_5
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | REDUCE: (860), (899) imply:
% 247.51/41.81  | | | | |   (905)  leq(n0, n2)
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | REDUCE: (855), (899) imply:
% 247.51/41.81  | | | | |   (906)  leq(n0, n0)
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | BETA: splitting (862) gives:
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | | Case 1:
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | |   (907)  gt(all_74_7, n0)
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | | BETA: splitting (865) gives:
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | | Case 1:
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | |   (908)  gt(n2, all_74_7)
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | GROUND_INST: instantiating (1) with all_74_7, n2, n1, simplifying
% 247.51/41.81  | | | | | | |              with (55), (101), (123), (908) gives:
% 247.51/41.81  | | | | | | |   (909)  leq(all_74_7, n1)
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | GROUND_INST: instantiating (4) with all_74_7, simplifying with
% 247.51/41.81  | | | | | | |              (55), (854), (909) gives:
% 247.51/41.81  | | | | | | |   (910)  all_74_7 = n1 | all_74_7 = n0
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | BETA: splitting (864) gives:
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | Case 1:
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | |   (911)  all_74_7 = n0
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | REDUCE: (907), (911) imply:
% 247.51/41.81  | | | | | | | |   (912)  gt(n0, n0)
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | PRED_UNIFY: (901), (912) imply:
% 247.51/41.81  | | | | | | | |   (913)  $false
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | CLOSE: (913) is inconsistent.
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | Case 2:
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | |   (914)   ~ (all_74_7 = n0)
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | BETA: splitting (910) gives:
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | Case 1:
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | |   (915)  all_74_7 = n0
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | REDUCE: (914), (915) imply:
% 247.51/41.81  | | | | | | | | |   (916)  $false
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | CLOSE: (916) is inconsistent.
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | Case 2:
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | |   (917)  all_74_7 = n1
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | REDUCE: (904), (917) imply:
% 247.51/41.81  | | | | | | | | |   (918)  a_select3(r_ds1_filter, n1, n0) = all_74_5
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | REDUCE: (903), (917) imply:
% 247.51/41.81  | | | | | | | | |   (919)  a_select3(r_ds1_filter, n0, n1) = all_74_4
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | REDUCE: (861), (917) imply:
% 247.51/41.81  | | | | | | | | |   (920)  leq(n1, n2)
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | REDUCE: (854), (917) imply:
% 247.51/41.81  | | | | | | | | |   (921)  leq(n0, n1)
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | GROUND_INST: instantiating (63) with n0, n1, all_74_4,
% 247.51/41.81  | | | | | | | | |              simplifying with (12), (85), (906), (919), (921)
% 247.51/41.81  | | | | | | | | |              gives:
% 247.51/41.81  | | | | | | | | |   (922)   ~ leq(n1, all_74_20) |  ~ leq(n0, all_74_20) |
% 247.51/41.81  | | | | | | | | |          (a_select3(r_ds1_filter, n1, n0) = all_74_4 &
% 247.51/41.81  | | | | | | | | |            $i(all_74_4))
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | BETA: splitting (922) gives:
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | Case 1:
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | |   (923)   ~ leq(n0, all_74_20)
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | REDUCE: (134), (923) imply:
% 247.51/41.81  | | | | | | | | | |   (924)   ~ leq(n0, n2)
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | PRED_UNIFY: (905), (924) imply:
% 247.51/41.81  | | | | | | | | | |   (925)  $false
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | CLOSE: (925) is inconsistent.
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | Case 2:
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | |   (926)   ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter,
% 247.51/41.81  | | | | | | | | | |              n1, n0) = all_74_4 & $i(all_74_4))
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | BETA: splitting (926) gives:
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | Case 1:
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | |   (927)   ~ leq(n1, all_74_20)
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | | REDUCE: (134), (927) imply:
% 247.51/41.81  | | | | | | | | | | |   (928)   ~ leq(n1, n2)
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | | PRED_UNIFY: (920), (928) imply:
% 247.51/41.81  | | | | | | | | | | |   (929)  $false
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | | CLOSE: (929) is inconsistent.
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | Case 2:
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | |   (930)  a_select3(r_ds1_filter, n1, n0) = all_74_4 &
% 247.51/41.81  | | | | | | | | | | |          $i(all_74_4)
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | | ALPHA: (930) implies:
% 247.51/41.81  | | | | | | | | | | |   (931)  a_select3(r_ds1_filter, n1, n0) = all_74_4
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | | REF_CLOSE: (17), (853), (918), (931) are inconsistent by
% 247.51/41.81  | | | | | | | | | | |            sub-proof #43.
% 247.51/41.81  | | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | | End of split
% 247.51/41.81  | | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | End of split
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | End of split
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | End of split
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | Case 2:
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | |   (932)  all_74_7 = n2
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | REDUCE: (904), (932) imply:
% 247.51/41.81  | | | | | | |   (933)  a_select3(r_ds1_filter, n2, n0) = all_74_5
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | REDUCE: (903), (932) imply:
% 247.51/41.81  | | | | | | |   (934)  a_select3(r_ds1_filter, n0, n2) = all_74_4
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | REDUCE: (861), (932) imply:
% 247.51/41.81  | | | | | | |   (935)  leq(n2, n2)
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | GROUND_INST: instantiating (63) with n0, n2, all_74_4, simplifying
% 247.51/41.81  | | | | | | |              with (12), (101), (905), (906), (934) gives:
% 247.51/41.81  | | | | | | |   (936)   ~ leq(n2, all_74_20) |  ~ leq(n0, all_74_20) |
% 247.51/41.81  | | | | | | |          (a_select3(r_ds1_filter, n2, n0) = all_74_4 &
% 247.51/41.81  | | | | | | |            $i(all_74_4))
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | BETA: splitting (936) gives:
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | | Case 1:
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | |   (937)   ~ leq(n0, all_74_20)
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | REDUCE: (134), (937) imply:
% 247.51/41.81  | | | | | | | |   (938)   ~ leq(n0, n2)
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | PRED_UNIFY: (905), (938) imply:
% 247.51/41.81  | | | | | | | |   (939)  $false
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | CLOSE: (939) is inconsistent.
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | Case 2:
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | |   (940)   ~ leq(n2, all_74_20) | (a_select3(r_ds1_filter, n2,
% 247.51/41.81  | | | | | | | |              n0) = all_74_4 & $i(all_74_4))
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | BETA: splitting (940) gives:
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | | Case 1:
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | |   (941)   ~ leq(n2, all_74_20)
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | REDUCE: (134), (941) imply:
% 247.51/41.81  | | | | | | | | |   (942)   ~ leq(n2, n2)
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | PRED_UNIFY: (935), (942) imply:
% 247.51/41.81  | | | | | | | | |   (943)  $false
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | CLOSE: (943) is inconsistent.
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | Case 2:
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | |   (944)  a_select3(r_ds1_filter, n2, n0) = all_74_4 &
% 247.51/41.81  | | | | | | | | |          $i(all_74_4)
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | ALPHA: (944) implies:
% 247.51/41.81  | | | | | | | | |   (945)  a_select3(r_ds1_filter, n2, n0) = all_74_4
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | | REF_CLOSE: (17), (853), (933), (945) are inconsistent by
% 247.51/41.81  | | | | | | | | |            sub-proof #42.
% 247.51/41.81  | | | | | | | | | 
% 247.51/41.81  | | | | | | | | End of split
% 247.51/41.81  | | | | | | | | 
% 247.51/41.81  | | | | | | | End of split
% 247.51/41.81  | | | | | | | 
% 247.51/41.81  | | | | | | End of split
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | Case 2:
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | |   (946)  all_74_7 = n0
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | | REDUCE: (904), (946) imply:
% 247.51/41.81  | | | | | |   (947)  a_select3(r_ds1_filter, n0, n0) = all_74_5
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | | REDUCE: (903), (946) imply:
% 247.51/41.81  | | | | | |   (948)  a_select3(r_ds1_filter, n0, n0) = all_74_4
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | | GROUND_INST: instantiating (17) with all_74_5, all_74_4, n0, n0,
% 247.51/41.81  | | | | | |              r_ds1_filter, simplifying with (947), (948) gives:
% 247.51/41.81  | | | | | |   (949)  all_74_4 = all_74_5
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | | REDUCE: (853), (949) imply:
% 247.51/41.81  | | | | | |   (950)  $false
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | | CLOSE: (950) is inconsistent.
% 247.51/41.81  | | | | | | 
% 247.51/41.81  | | | | | End of split
% 247.51/41.81  | | | | | 
% 247.51/41.81  | | | | End of split
% 247.51/41.81  | | | | 
% 247.51/41.81  | | | End of split
% 247.51/41.81  | | | 
% 247.51/41.81  | | End of split
% 247.51/41.81  | | 
% 247.51/41.81  | Case 2:
% 247.51/41.81  | | 
% 247.51/41.82  | |   (951)  ( ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter, all_74_10,
% 247.51/41.82  | |              all_74_11) = all_74_8 & a_select3(pminus_ds1_filter, all_74_11,
% 247.51/41.82  | |              all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9) &
% 247.51/41.82  | |            leq(all_74_10, all_74_21) & leq(all_74_11, all_74_21) & leq(n0,
% 247.51/41.82  | |              all_74_10) & leq(n0, all_74_11)) | ( ~ (all_74_12 = all_74_13)
% 247.51/41.82  | |            & a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12
% 247.51/41.82  | |            & a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13
% 247.51/41.82  | |            & $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) &
% 247.51/41.82  | |            leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0,
% 247.51/41.82  | |              all_74_15)) | ( ~ (all_74_16 = all_74_17) &
% 247.51/41.82  | |            a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 &
% 247.51/41.82  | |            a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 &
% 247.51/41.82  | |            $i(all_74_16) & $i(all_74_17) & leq(all_74_18, all_74_21) &
% 247.51/41.82  | |            leq(all_74_19, all_74_21) & leq(n0, all_74_18) & leq(n0,
% 247.51/41.82  | |              all_74_19))
% 247.51/41.82  | | 
% 247.51/41.82  | | BETA: splitting (951) gives:
% 247.51/41.82  | | 
% 247.51/41.82  | | Case 1:
% 247.51/41.82  | | | 
% 247.51/41.82  | | |   (952)   ~ (all_74_8 = all_74_9) & a_select3(pminus_ds1_filter,
% 247.51/41.82  | | |            all_74_10, all_74_11) = all_74_8 & a_select3(pminus_ds1_filter,
% 247.51/41.82  | | |            all_74_11, all_74_10) = all_74_9 & $i(all_74_8) & $i(all_74_9)
% 247.51/41.82  | | |          & leq(all_74_10, all_74_21) & leq(all_74_11, all_74_21) & leq(n0,
% 247.51/41.82  | | |            all_74_10) & leq(n0, all_74_11)
% 247.51/41.82  | | | 
% 247.51/41.82  | | | ALPHA: (952) implies:
% 247.51/41.82  | | |   (953)   ~ (all_74_8 = all_74_9)
% 247.51/41.82  | | |   (954)  leq(n0, all_74_11)
% 247.51/41.82  | | |   (955)  leq(n0, all_74_10)
% 247.51/41.82  | | |   (956)  leq(all_74_11, all_74_21)
% 247.51/41.82  | | |   (957)  leq(all_74_10, all_74_21)
% 247.51/41.82  | | |   (958)  a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9
% 247.51/41.82  | | |   (959)  a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8
% 247.51/41.82  | | | 
% 247.51/41.82  | | | REDUCE: (135), (957) imply:
% 247.51/41.82  | | |   (960)  leq(all_74_10, n5)
% 247.51/41.82  | | | 
% 247.51/41.82  | | | REDUCE: (135), (956) imply:
% 247.51/41.82  | | |   (961)  leq(all_74_11, n5)
% 247.51/41.82  | | | 
% 247.51/41.82  | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_11, simplifying with
% 247.51/41.82  | | |              (12), (53), (954) gives:
% 247.51/41.82  | | |   (962)  all_74_11 = n0 | gt(all_74_11, n0)
% 247.51/41.82  | | | 
% 247.51/41.82  | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_10, simplifying with
% 247.51/41.82  | | |              (12), (54), (955) gives:
% 247.51/41.82  | | |   (963)  all_74_10 = n0 | gt(all_74_10, n0)
% 247.51/41.82  | | | 
% 247.51/41.82  | | | GROUND_INST: instantiating (3) with all_74_11, simplifying with (53),
% 247.51/41.82  | | |              (954), (961) gives:
% 247.51/41.82  | | |   (964)  all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2
% 247.51/41.82  | | |          | all_74_11 = n1 | all_74_11 = n0
% 247.51/41.82  | | | 
% 247.51/41.82  | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n5, simplifying with
% 247.51/41.82  | | |              (53), (122), (961) gives:
% 247.51/41.82  | | |   (965)  all_74_11 = n5 | gt(n5, all_74_11)
% 247.51/41.82  | | | 
% 247.51/41.82  | | | GROUND_INST: instantiating (3) with all_74_10, simplifying with (54),
% 247.51/41.82  | | |              (955), (960) gives:
% 247.51/41.82  | | |   (966)  all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2
% 247.51/41.82  | | |          | all_74_10 = n1 | all_74_10 = n0
% 247.51/41.82  | | | 
% 247.51/41.82  | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n5, simplifying with
% 247.51/41.82  | | |              (54), (122), (960) gives:
% 247.51/41.82  | | |   (967)  all_74_10 = n5 | gt(n5, all_74_10)
% 247.51/41.82  | | | 
% 247.51/41.82  | | | BETA: splitting (963) gives:
% 247.51/41.82  | | | 
% 247.51/41.82  | | | Case 1:
% 247.51/41.82  | | | | 
% 247.51/41.82  | | | |   (968)  gt(all_74_10, n0)
% 247.51/41.82  | | | | 
% 247.51/41.82  | | | | BETA: splitting (962) gives:
% 247.51/41.82  | | | | 
% 247.51/41.82  | | | | Case 1:
% 247.51/41.82  | | | | | 
% 247.51/41.82  | | | | |   (969)  gt(all_74_11, n0)
% 247.51/41.82  | | | | | 
% 247.51/41.82  | | | | | BETA: splitting (967) gives:
% 247.51/41.82  | | | | | 
% 247.51/41.82  | | | | | Case 1:
% 247.51/41.82  | | | | | | 
% 247.51/41.82  | | | | | |   (970)  gt(n5, all_74_10)
% 247.51/41.82  | | | | | | 
% 247.51/41.82  | | | | | | BETA: splitting (965) gives:
% 247.51/41.82  | | | | | | 
% 247.51/41.82  | | | | | | Case 1:
% 247.51/41.82  | | | | | | | 
% 247.51/41.82  | | | | | | |   (971)  gt(n5, all_74_11)
% 247.51/41.82  | | | | | | | 
% 247.51/41.82  | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying
% 247.51/41.82  | | | | | | |              with (53), (122), (126), (971) gives:
% 247.51/41.82  | | | | | | |   (972)  leq(all_74_11, n4)
% 247.51/41.82  | | | | | | | 
% 247.51/41.82  | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying
% 247.51/41.82  | | | | | | |              with (54), (122), (126), (970) gives:
% 247.51/41.82  | | | | | | |   (973)  leq(all_74_10, n4)
% 247.51/41.82  | | | | | | | 
% 247.51/41.82  | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4,
% 247.51/41.82  | | | | | | |              simplifying with (53), (119), (972) gives:
% 247.51/41.82  | | | | | | |   (974)  all_74_11 = n4 | gt(n4, all_74_11)
% 247.51/41.82  | | | | | | | 
% 247.51/41.82  | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4,
% 247.51/41.82  | | | | | | |              simplifying with (54), (119), (973) gives:
% 247.51/41.82  | | | | | | |   (975)  all_74_10 = n4 | gt(n4, all_74_10)
% 247.51/41.82  | | | | | | | 
% 247.51/41.82  | | | | | | | BETA: splitting (966) gives:
% 247.51/41.82  | | | | | | | 
% 247.51/41.82  | | | | | | | Case 1:
% 247.51/41.82  | | | | | | | | 
% 247.51/41.82  | | | | | | | |   (976)  all_74_10 = n0
% 247.51/41.82  | | | | | | | | 
% 247.51/41.82  | | | | | | | | REF_CLOSE: (54), (968), (976), (irreflexivity_gt) are
% 247.51/41.82  | | | | | | | |            inconsistent by sub-proof #40.
% 247.51/41.82  | | | | | | | | 
% 247.51/41.82  | | | | | | | Case 2:
% 247.51/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | |   (977)   ~ (all_74_10 = n0)
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | | BETA: splitting (964) gives:
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | | Case 1:
% 247.75/41.82  | | | | | | | | | 
% 247.75/41.82  | | | | | | | | |   (978)  all_74_11 = n0
% 247.75/41.82  | | | | | | | | | 
% 247.75/41.82  | | | | | | | | | REF_CLOSE: (53), (969), (978), (irreflexivity_gt) are
% 247.75/41.82  | | | | | | | | |            inconsistent by sub-proof #39.
% 247.75/41.82  | | | | | | | | | 
% 247.75/41.82  | | | | | | | | Case 2:
% 247.75/41.82  | | | | | | | | | 
% 247.75/41.82  | | | | | | | | |   (979)   ~ (all_74_11 = n0)
% 247.75/41.82  | | | | | | | | | 
% 247.75/41.82  | | | | | | | | | REF_CLOSE: (1), (4), (17), (53), (54), (64), (101), (112),
% 247.75/41.82  | | | | | | | | |            (119), (123), (124), (125), (135), (953), (954),
% 247.75/41.82  | | | | | | | | |            (955), (958), (959), (960), (961), (974), (975),
% 247.75/41.82  | | | | | | | | |            (977), (979), (leq_gt2) are inconsistent by
% 247.75/41.82  | | | | | | | | |            sub-proof #34.
% 247.75/41.82  | | | | | | | | | 
% 247.75/41.82  | | | | | | | | End of split
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | End of split
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | Case 2:
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | |   (980)  all_74_11 = n5
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | REDUCE: (959), (980) imply:
% 247.75/41.82  | | | | | | |   (981)  a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | REDUCE: (958), (980) imply:
% 247.75/41.82  | | | | | | |   (982)  a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | REDUCE: (961), (980) imply:
% 247.75/41.82  | | | | | | |   (983)  leq(n5, n5)
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | REDUCE: (954), (980) imply:
% 247.75/41.82  | | | | | | |   (984)  leq(n0, n5)
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | GROUND_INST: instantiating (1) with all_74_10, n5, n4, simplifying
% 247.75/41.82  | | | | | | |              with (54), (122), (126), (970) gives:
% 247.75/41.82  | | | | | | |   (985)  leq(all_74_10, n4)
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_10, n4,
% 247.75/41.82  | | | | | | |              simplifying with (54), (119), (985) gives:
% 247.75/41.82  | | | | | | |   (986)  all_74_10 = n4 | gt(n4, all_74_10)
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | BETA: splitting (966) gives:
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | | Case 1:
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | |   (987)  all_74_10 = n0
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | | REF_CLOSE: (54), (968), (987), (irreflexivity_gt) are
% 247.75/41.82  | | | | | | | |            inconsistent by sub-proof #40.
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | Case 2:
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | |   (988)   ~ (all_74_10 = n0)
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | | REF_CLOSE: (1), (4), (17), (54), (64), (101), (112), (119),
% 247.75/41.82  | | | | | | | |            (122), (123), (124), (125), (135), (953), (955),
% 247.75/41.82  | | | | | | | |            (960), (981), (982), (983), (984), (986), (988),
% 247.75/41.82  | | | | | | | |            (leq_gt2) are inconsistent by sub-proof #31.
% 247.75/41.82  | | | | | | | | 
% 247.75/41.82  | | | | | | | End of split
% 247.75/41.82  | | | | | | | 
% 247.75/41.82  | | | | | | End of split
% 247.75/41.82  | | | | | | 
% 247.75/41.82  | | | | | Case 2:
% 247.75/41.82  | | | | | | 
% 247.75/41.82  | | | | | |   (989)  all_74_10 = n5
% 247.75/41.82  | | | | | | 
% 247.75/41.82  | | | | | | REDUCE: (959), (989) imply:
% 247.75/41.82  | | | | | |   (990)  a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8
% 247.75/41.82  | | | | | | 
% 247.75/41.82  | | | | | | REDUCE: (958), (989) imply:
% 247.75/41.83  | | | | | |   (991)  a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | | REDUCE: (960), (989) imply:
% 247.75/41.83  | | | | | |   (992)  leq(n5, n5)
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | | REDUCE: (955), (989) imply:
% 247.75/41.83  | | | | | |   (993)  leq(n0, n5)
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | | BETA: splitting (965) gives:
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | | Case 1:
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | |   (994)  gt(n5, all_74_11)
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying
% 247.75/41.83  | | | | | | |              with (53), (122), (126), (994) gives:
% 247.75/41.83  | | | | | | |   (995)  leq(all_74_11, n4)
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4,
% 247.75/41.83  | | | | | | |              simplifying with (53), (119), (995) gives:
% 247.75/41.83  | | | | | | |   (996)  all_74_11 = n4 | gt(n4, all_74_11)
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | BETA: splitting (964) gives:
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | |   (997)  all_74_11 = n0
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | | REF_CLOSE: (53), (969), (997), (irreflexivity_gt) are
% 247.75/41.83  | | | | | | | |            inconsistent by sub-proof #39.
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | Case 2:
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | |   (998)   ~ (all_74_11 = n0)
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | | REF_CLOSE: (1), (4), (17), (53), (64), (101), (112), (119),
% 247.75/41.83  | | | | | | | |            (122), (123), (124), (125), (135), (953), (954),
% 247.75/41.83  | | | | | | | |            (961), (990), (991), (992), (993), (996), (998),
% 247.75/41.83  | | | | | | | |            (leq_gt2) are inconsistent by sub-proof #30.
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | End of split
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | Case 2:
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | |   (999)  all_74_11 = n5
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | REDUCE: (991), (999) imply:
% 247.75/41.83  | | | | | | |   (1000)  a_select3(pminus_ds1_filter, n5, n5) = all_74_9
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | REDUCE: (990), (999) imply:
% 247.75/41.83  | | | | | | |   (1001)  a_select3(pminus_ds1_filter, n5, n5) = all_74_8
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n5, n5,
% 247.75/41.83  | | | | | | |              pminus_ds1_filter, simplifying with (1000), (1001)
% 247.75/41.83  | | | | | | |              gives:
% 247.75/41.83  | | | | | | |   (1002)  all_74_8 = all_74_9
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | REDUCE: (953), (1002) imply:
% 247.75/41.83  | | | | | | |   (1003)  $false
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | CLOSE: (1003) is inconsistent.
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | End of split
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | End of split
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | Case 2:
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | |   (1004)  all_74_11 = n0
% 247.75/41.83  | | | | |   (1005)   ~ gt(all_74_11, n0)
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | REDUCE: (1004), (1005) imply:
% 247.75/41.83  | | | | |   (1006)   ~ gt(n0, n0)
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | REF_CLOSE: (1), (4), (17), (53), (54), (64), (101), (112), (119),
% 247.75/41.83  | | | | |            (122), (123), (124), (125), (126), (135), (953), (954),
% 247.75/41.83  | | | | |            (955), (958), (959), (960), (961), (962), (964), (965),
% 247.75/41.83  | | | | |            (966), (967), (968), (1006), (leq_gt2) are inconsistent by
% 247.75/41.83  | | | | |            sub-proof #26.
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | End of split
% 247.75/41.83  | | | | 
% 247.75/41.83  | | | Case 2:
% 247.75/41.83  | | | | 
% 247.75/41.83  | | | |   (1007)  all_74_10 = n0
% 247.75/41.83  | | | |   (1008)   ~ gt(all_74_10, n0)
% 247.75/41.83  | | | | 
% 247.75/41.83  | | | | REDUCE: (1007), (1008) imply:
% 247.75/41.83  | | | |   (1009)   ~ gt(n0, n0)
% 247.75/41.83  | | | | 
% 247.75/41.83  | | | | BETA: splitting (963) gives:
% 247.75/41.83  | | | | 
% 247.75/41.83  | | | | Case 1:
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | |   (1010)  gt(all_74_10, n0)
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | REF_CLOSE: (1), (4), (17), (53), (54), (64), (101), (112), (119),
% 247.75/41.83  | | | | |            (122), (123), (124), (125), (126), (135), (953), (954),
% 247.75/41.83  | | | | |            (955), (958), (959), (960), (961), (962), (964), (965),
% 247.75/41.83  | | | | |            (966), (967), (1009), (1010), (leq_gt2) are inconsistent by
% 247.75/41.83  | | | | |            sub-proof #26.
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | Case 2:
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | REDUCE: (959), (1007) imply:
% 247.75/41.83  | | | | |   (1011)  a_select3(pminus_ds1_filter, n0, all_74_11) = all_74_8
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | REDUCE: (958), (1007) imply:
% 247.75/41.83  | | | | |   (1012)  a_select3(pminus_ds1_filter, all_74_11, n0) = all_74_9
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | REDUCE: (960), (1007) imply:
% 247.75/41.83  | | | | |   (1013)  leq(n0, n5)
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | REDUCE: (955), (1007) imply:
% 247.75/41.83  | | | | |   (1014)  leq(n0, n0)
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | BETA: splitting (962) gives:
% 247.75/41.83  | | | | | 
% 247.75/41.83  | | | | | Case 1:
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | |   (1015)  gt(all_74_11, n0)
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | | BETA: splitting (965) gives:
% 247.75/41.83  | | | | | | 
% 247.75/41.83  | | | | | | Case 1:
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | |   (1016)  gt(n5, all_74_11)
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n5, n4, simplifying
% 247.75/41.83  | | | | | | |              with (53), (122), (126), (1016) gives:
% 247.75/41.83  | | | | | | |   (1017)  leq(all_74_11, n4)
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n4,
% 247.75/41.83  | | | | | | |              simplifying with (53), (119), (1017) gives:
% 247.75/41.83  | | | | | | |   (1018)  all_74_11 = n4 | gt(n4, all_74_11)
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | BETA: splitting (964) gives:
% 247.75/41.83  | | | | | | | 
% 247.75/41.83  | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | |   (1019)  all_74_11 = n0
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | | REDUCE: (1015), (1019) imply:
% 247.75/41.83  | | | | | | | |   (1020)  gt(n0, n0)
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | | PRED_UNIFY: (1009), (1020) imply:
% 247.75/41.83  | | | | | | | |   (1021)  $false
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | | CLOSE: (1021) is inconsistent.
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | Case 2:
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | |   (1022)   ~ (all_74_11 = n0)
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | | BETA: splitting (1018) gives:
% 247.75/41.83  | | | | | | | | 
% 247.75/41.83  | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | 
% 247.75/41.83  | | | | | | | | |   (1023)  gt(n4, all_74_11)
% 247.75/41.83  | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n4, n3,
% 247.75/41.83  | | | | | | | | |              simplifying with (53), (119), (125), (1023) gives:
% 247.75/41.83  | | | | | | | | |   (1024)  leq(all_74_11, n3)
% 247.75/41.83  | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n3,
% 247.75/41.83  | | | | | | | | |              simplifying with (53), (112), (1024) gives:
% 247.75/41.83  | | | | | | | | |   (1025)  all_74_11 = n3 | gt(n3, all_74_11)
% 247.75/41.83  | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | BETA: splitting (1025) gives:
% 247.75/41.83  | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | |   (1026)  gt(n3, all_74_11)
% 247.75/41.83  | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n3, n2,
% 247.75/41.83  | | | | | | | | | |              simplifying with (53), (112), (124), (1026) gives:
% 247.75/41.83  | | | | | | | | | |   (1027)  leq(all_74_11, n2)
% 247.75/41.83  | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_11, n2,
% 247.75/41.83  | | | | | | | | | |              simplifying with (53), (101), (1027) gives:
% 247.75/41.83  | | | | | | | | | |   (1028)  all_74_11 = n2 | gt(n2, all_74_11)
% 247.75/41.83  | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | BETA: splitting (1028) gives:
% 247.75/41.83  | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | |   (1029)  gt(n2, all_74_11)
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_11, n2, n1,
% 247.75/41.83  | | | | | | | | | | |              simplifying with (53), (101), (123), (1029) gives:
% 247.75/41.83  | | | | | | | | | | |   (1030)  leq(all_74_11, n1)
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_11, simplifying with
% 247.75/41.83  | | | | | | | | | | |              (53), (954), (1030) gives:
% 247.75/41.83  | | | | | | | | | | |   (1031)  all_74_11 = n1 | all_74_11 = n0
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | BETA: splitting (1031) gives:
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | |   (1032)  all_74_11 = n0
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | REDUCE: (1022), (1032) imply:
% 247.75/41.83  | | | | | | | | | | | |   (1033)  $false
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | CLOSE: (1033) is inconsistent.
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | Case 2:
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | |   (1034)  all_74_11 = n1
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | REDUCE: (1012), (1034) imply:
% 247.75/41.83  | | | | | | | | | | | |   (1035)  a_select3(pminus_ds1_filter, n1, n0) = all_74_9
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | REDUCE: (1011), (1034) imply:
% 247.75/41.83  | | | | | | | | | | | |   (1036)  a_select3(pminus_ds1_filter, n0, n1) = all_74_8
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | REDUCE: (961), (1034) imply:
% 247.75/41.83  | | | | | | | | | | | |   (1037)  leq(n1, n5)
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | REDUCE: (954), (1034) imply:
% 247.75/41.83  | | | | | | | | | | | |   (1038)  leq(n0, n1)
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n1, all_74_8,
% 247.75/41.83  | | | | | | | | | | | |              simplifying with (12), (85), (1014), (1036),
% 247.75/41.83  | | | | | | | | | | | |              (1038) gives:
% 247.75/41.83  | | | | | | | | | | | |   (1039)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.75/41.83  | | | | | | | | | | | |           (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 &
% 247.75/41.83  | | | | | | | | | | | |             $i(all_74_8))
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | BETA: splitting (1039) gives:
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | |   (1040)   ~ leq(n0, all_74_21)
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | REDUCE: (135), (1040) imply:
% 247.75/41.83  | | | | | | | | | | | | |   (1041)   ~ leq(n0, n5)
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | PRED_UNIFY: (1013), (1041) imply:
% 247.75/41.83  | | | | | | | | | | | | |   (1042)  $false
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | CLOSE: (1042) is inconsistent.
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | Case 2:
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | |   (1043)   ~ leq(n1, all_74_21) |
% 247.75/41.83  | | | | | | | | | | | | |           (a_select3(pminus_ds1_filter, n1, n0) = all_74_8 &
% 247.75/41.83  | | | | | | | | | | | | |             $i(all_74_8))
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | BETA: splitting (1043) gives:
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | |   (1044)   ~ leq(n1, all_74_21)
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | | REDUCE: (135), (1044) imply:
% 247.75/41.83  | | | | | | | | | | | | | |   (1045)   ~ leq(n1, n5)
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | | PRED_UNIFY: (1037), (1045) imply:
% 247.75/41.83  | | | | | | | | | | | | | |   (1046)  $false
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | | CLOSE: (1046) is inconsistent.
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | Case 2:
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | |   (1047)  a_select3(pminus_ds1_filter, n1, n0) = all_74_8 &
% 247.75/41.83  | | | | | | | | | | | | | |           $i(all_74_8)
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | | ALPHA: (1047) implies:
% 247.75/41.83  | | | | | | | | | | | | | |   (1048)  a_select3(pminus_ds1_filter, n1, n0) = all_74_8
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n0,
% 247.75/41.83  | | | | | | | | | | | | | |              n1, pminus_ds1_filter, simplifying with (1035),
% 247.75/41.83  | | | | | | | | | | | | | |              (1048) gives:
% 247.75/41.83  | | | | | | | | | | | | | |   (1049)  all_74_8 = all_74_9
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | | REDUCE: (953), (1049) imply:
% 247.75/41.83  | | | | | | | | | | | | | |   (1050)  $false
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | | CLOSE: (1050) is inconsistent.
% 247.75/41.83  | | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | | End of split
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | End of split
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | End of split
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | Case 2:
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | |   (1051)  all_74_11 = n2
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | REDUCE: (1012), (1051) imply:
% 247.75/41.83  | | | | | | | | | | |   (1052)  a_select3(pminus_ds1_filter, n2, n0) = all_74_9
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | REDUCE: (1011), (1051) imply:
% 247.75/41.83  | | | | | | | | | | |   (1053)  a_select3(pminus_ds1_filter, n0, n2) = all_74_8
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | REDUCE: (961), (1051) imply:
% 247.75/41.83  | | | | | | | | | | |   (1054)  leq(n2, n5)
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | REDUCE: (954), (1051) imply:
% 247.75/41.83  | | | | | | | | | | |   (1055)  leq(n0, n2)
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n2, all_74_8,
% 247.75/41.83  | | | | | | | | | | |              simplifying with (12), (101), (1014), (1053),
% 247.75/41.83  | | | | | | | | | | |              (1055) gives:
% 247.75/41.83  | | | | | | | | | | |   (1056)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.75/41.83  | | | | | | | | | | |           (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 &
% 247.75/41.83  | | | | | | | | | | |             $i(all_74_8))
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | BETA: splitting (1056) gives:
% 247.75/41.83  | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | |   (1057)   ~ leq(n0, all_74_21)
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | REDUCE: (135), (1057) imply:
% 247.75/41.83  | | | | | | | | | | | |   (1058)   ~ leq(n0, n5)
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | PRED_UNIFY: (1013), (1058) imply:
% 247.75/41.83  | | | | | | | | | | | |   (1059)  $false
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | CLOSE: (1059) is inconsistent.
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | Case 2:
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | |   (1060)   ~ leq(n2, all_74_21) |
% 247.75/41.83  | | | | | | | | | | | |           (a_select3(pminus_ds1_filter, n2, n0) = all_74_8 &
% 247.75/41.83  | | | | | | | | | | | |             $i(all_74_8))
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | BETA: splitting (1060) gives:
% 247.75/41.83  | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | Case 1:
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.83  | | | | | | | | | | | | |   (1061)   ~ leq(n2, all_74_21)
% 247.75/41.83  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | | REDUCE: (135), (1061) imply:
% 247.75/41.84  | | | | | | | | | | | | |   (1062)   ~ leq(n2, n5)
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | | PRED_UNIFY: (1054), (1062) imply:
% 247.75/41.84  | | | | | | | | | | | | |   (1063)  $false
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | | CLOSE: (1063) is inconsistent.
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | |   (1064)  a_select3(pminus_ds1_filter, n2, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | | | | | |           $i(all_74_8)
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | | ALPHA: (1064) implies:
% 247.75/41.84  | | | | | | | | | | | | |   (1065)  a_select3(pminus_ds1_filter, n2, n0) = all_74_8
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n0,
% 247.75/41.84  | | | | | | | | | | | | |              n2, pminus_ds1_filter, simplifying with (1052),
% 247.75/41.84  | | | | | | | | | | | | |              (1065) gives:
% 247.75/41.84  | | | | | | | | | | | | |   (1066)  all_74_8 = all_74_9
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | | REDUCE: (953), (1066) imply:
% 247.75/41.84  | | | | | | | | | | | | |   (1067)  $false
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | | CLOSE: (1067) is inconsistent.
% 247.75/41.84  | | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | |   (1068)  all_74_11 = n3
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | REDUCE: (1012), (1068) imply:
% 247.75/41.84  | | | | | | | | | |   (1069)  a_select3(pminus_ds1_filter, n3, n0) = all_74_9
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | REDUCE: (1011), (1068) imply:
% 247.75/41.84  | | | | | | | | | |   (1070)  a_select3(pminus_ds1_filter, n0, n3) = all_74_8
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | REDUCE: (961), (1068) imply:
% 247.75/41.84  | | | | | | | | | |   (1071)  leq(n3, n5)
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | REDUCE: (954), (1068) imply:
% 247.75/41.84  | | | | | | | | | |   (1072)  leq(n0, n3)
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | GROUND_INST: instantiating (64) with n0, n3, all_74_8,
% 247.75/41.84  | | | | | | | | | |              simplifying with (12), (112), (1014), (1070),
% 247.75/41.84  | | | | | | | | | |              (1072) gives:
% 247.75/41.84  | | | | | | | | | |   (1073)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.75/41.84  | | | | | | | | | |           (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | | |             $i(all_74_8))
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | BETA: splitting (1073) gives:
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | |   (1074)   ~ leq(n0, all_74_21)
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | REDUCE: (135), (1074) imply:
% 247.75/41.84  | | | | | | | | | | |   (1075)   ~ leq(n0, n5)
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | PRED_UNIFY: (1013), (1075) imply:
% 247.75/41.84  | | | | | | | | | | |   (1076)  $false
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | CLOSE: (1076) is inconsistent.
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | |   (1077)   ~ leq(n3, all_74_21) |
% 247.75/41.84  | | | | | | | | | | |           (a_select3(pminus_ds1_filter, n3, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | | | |             $i(all_74_8))
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | BETA: splitting (1077) gives:
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | |   (1078)   ~ leq(n3, all_74_21)
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | REDUCE: (135), (1078) imply:
% 247.75/41.84  | | | | | | | | | | | |   (1079)   ~ leq(n3, n5)
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | PRED_UNIFY: (1071), (1079) imply:
% 247.75/41.84  | | | | | | | | | | | |   (1080)  $false
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | CLOSE: (1080) is inconsistent.
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | |   (1081)  a_select3(pminus_ds1_filter, n3, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | | | | |           $i(all_74_8)
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | ALPHA: (1081) implies:
% 247.75/41.84  | | | | | | | | | | | |   (1082)  a_select3(pminus_ds1_filter, n3, n0) = all_74_8
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | | REF_CLOSE: (17), (953), (1069), (1082) are inconsistent by
% 247.75/41.84  | | | | | | | | | | | |            sub-proof #29.
% 247.75/41.84  | | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | |   (1083)  all_74_11 = n4
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (1012), (1083) imply:
% 247.75/41.84  | | | | | | | | |   (1084)  a_select3(pminus_ds1_filter, n4, n0) = all_74_9
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (1011), (1083) imply:
% 247.75/41.84  | | | | | | | | |   (1085)  a_select3(pminus_ds1_filter, n0, n4) = all_74_8
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (961), (1083) imply:
% 247.75/41.84  | | | | | | | | |   (1086)  leq(n4, n5)
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (954), (1083) imply:
% 247.75/41.84  | | | | | | | | |   (1087)  leq(n0, n4)
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | GROUND_INST: instantiating (64) with n0, n4, all_74_8,
% 247.75/41.84  | | | | | | | | |              simplifying with (12), (119), (1014), (1085),
% 247.75/41.84  | | | | | | | | |              (1087) gives:
% 247.75/41.84  | | | | | | | | |   (1088)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.75/41.84  | | | | | | | | |           (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | |             $i(all_74_8))
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | BETA: splitting (1088) gives:
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | |   (1089)   ~ leq(n0, all_74_21)
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | REDUCE: (135), (1089) imply:
% 247.75/41.84  | | | | | | | | | |   (1090)   ~ leq(n0, n5)
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | PRED_UNIFY: (1013), (1090) imply:
% 247.75/41.84  | | | | | | | | | |   (1091)  $false
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | CLOSE: (1091) is inconsistent.
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | |   (1092)   ~ leq(n4, all_74_21) |
% 247.75/41.84  | | | | | | | | | |           (a_select3(pminus_ds1_filter, n4, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | | |             $i(all_74_8))
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | BETA: splitting (1092) gives:
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | |   (1093)   ~ leq(n4, all_74_21)
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | REDUCE: (135), (1093) imply:
% 247.75/41.84  | | | | | | | | | | |   (1094)   ~ leq(n4, n5)
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | PRED_UNIFY: (1086), (1094) imply:
% 247.75/41.84  | | | | | | | | | | |   (1095)  $false
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | CLOSE: (1095) is inconsistent.
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | |   (1096)  a_select3(pminus_ds1_filter, n4, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | | | |           $i(all_74_8)
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | ALPHA: (1096) implies:
% 247.75/41.84  | | | | | | | | | | |   (1097)  a_select3(pminus_ds1_filter, n4, n0) = all_74_8
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | | REF_CLOSE: (17), (953), (1084), (1097) are inconsistent by
% 247.75/41.84  | | | | | | | | | | |            sub-proof #28.
% 247.75/41.84  | | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | End of split
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | Case 2:
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | |   (1098)  all_74_11 = n5
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | REDUCE: (1012), (1098) imply:
% 247.75/41.84  | | | | | | |   (1099)  a_select3(pminus_ds1_filter, n5, n0) = all_74_9
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | REDUCE: (1011), (1098) imply:
% 247.75/41.84  | | | | | | |   (1100)  a_select3(pminus_ds1_filter, n0, n5) = all_74_8
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | REDUCE: (961), (1098) imply:
% 247.75/41.84  | | | | | | |   (1101)  leq(n5, n5)
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | GROUND_INST: instantiating (64) with n0, n5, all_74_8, simplifying
% 247.75/41.84  | | | | | | |              with (12), (122), (1013), (1014), (1100) gives:
% 247.75/41.84  | | | | | | |   (1102)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.75/41.84  | | | | | | |           (a_select3(pminus_ds1_filter, n5, n0) = all_74_8 &
% 247.75/41.84  | | | | | | |             $i(all_74_8))
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | BETA: splitting (1102) gives:
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | |   (1103)   ~ leq(n0, all_74_21)
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | REDUCE: (135), (1103) imply:
% 247.75/41.84  | | | | | | | |   (1104)   ~ leq(n0, n5)
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | PRED_UNIFY: (1013), (1104) imply:
% 247.75/41.84  | | | | | | | |   (1105)  $false
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | CLOSE: (1105) is inconsistent.
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | |   (1106)   ~ leq(n5, all_74_21) | (a_select3(pminus_ds1_filter,
% 247.75/41.84  | | | | | | | |               n5, n0) = all_74_8 & $i(all_74_8))
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | BETA: splitting (1106) gives:
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | |   (1107)   ~ leq(n5, all_74_21)
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (135), (1107) imply:
% 247.75/41.84  | | | | | | | | |   (1108)   ~ leq(n5, n5)
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | PRED_UNIFY: (1101), (1108) imply:
% 247.75/41.84  | | | | | | | | |   (1109)  $false
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | CLOSE: (1109) is inconsistent.
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | Case 2:
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | |   (1110)  a_select3(pminus_ds1_filter, n5, n0) = all_74_8 &
% 247.75/41.84  | | | | | | | | |           $i(all_74_8)
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | ALPHA: (1110) implies:
% 247.75/41.84  | | | | | | | | |   (1111)  a_select3(pminus_ds1_filter, n5, n0) = all_74_8
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REF_CLOSE: (17), (953), (1099), (1111) are inconsistent by
% 247.75/41.84  | | | | | | | | |            sub-proof #27.
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | End of split
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | End of split
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | End of split
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | Case 2:
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | |   (1112)  all_74_11 = n0
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | | REDUCE: (1012), (1112) imply:
% 247.75/41.84  | | | | | |   (1113)  a_select3(pminus_ds1_filter, n0, n0) = all_74_9
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | | REDUCE: (1011), (1112) imply:
% 247.75/41.84  | | | | | |   (1114)  a_select3(pminus_ds1_filter, n0, n0) = all_74_8
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | | GROUND_INST: instantiating (17) with all_74_9, all_74_8, n0, n0,
% 247.75/41.84  | | | | | |              pminus_ds1_filter, simplifying with (1113), (1114)
% 247.75/41.84  | | | | | |              gives:
% 247.75/41.84  | | | | | |   (1115)  all_74_8 = all_74_9
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | | REDUCE: (953), (1115) imply:
% 247.75/41.84  | | | | | |   (1116)  $false
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | | CLOSE: (1116) is inconsistent.
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | End of split
% 247.75/41.84  | | | | | 
% 247.75/41.84  | | | | End of split
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | End of split
% 247.75/41.84  | | | 
% 247.75/41.84  | | Case 2:
% 247.75/41.84  | | | 
% 247.75/41.84  | | |   (1117)  ( ~ (all_74_12 = all_74_13) & a_select3(pminus_ds1_filter,
% 247.75/41.84  | | |               all_74_14, all_74_15) = all_74_12 &
% 247.75/41.84  | | |             a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13
% 247.75/41.84  | | |             & $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) &
% 247.75/41.84  | | |             leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0,
% 247.75/41.84  | | |               all_74_15)) | ( ~ (all_74_16 = all_74_17) &
% 247.75/41.84  | | |             a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16 &
% 247.75/41.84  | | |             a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17 &
% 247.75/41.84  | | |             $i(all_74_16) & $i(all_74_17) & leq(all_74_18, all_74_21) &
% 247.75/41.84  | | |             leq(all_74_19, all_74_21) & leq(n0, all_74_18) & leq(n0,
% 247.75/41.84  | | |               all_74_19))
% 247.75/41.84  | | | 
% 247.75/41.84  | | | BETA: splitting (1117) gives:
% 247.75/41.84  | | | 
% 247.75/41.84  | | | Case 1:
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | |   (1118)   ~ (all_74_12 = all_74_13) & a_select3(pminus_ds1_filter,
% 247.75/41.84  | | | |             all_74_14, all_74_15) = all_74_12 &
% 247.75/41.84  | | | |           a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13
% 247.75/41.84  | | | |           & $i(all_74_12) & $i(all_74_13) & leq(all_74_14, all_74_21) &
% 247.75/41.84  | | | |           leq(all_74_15, all_74_21) & leq(n0, all_74_14) & leq(n0,
% 247.75/41.84  | | | |             all_74_15)
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | ALPHA: (1118) implies:
% 247.75/41.84  | | | |   (1119)   ~ (all_74_12 = all_74_13)
% 247.75/41.84  | | | |   (1120)  leq(n0, all_74_15)
% 247.75/41.84  | | | |   (1121)  leq(n0, all_74_14)
% 247.75/41.84  | | | |   (1122)  leq(all_74_15, all_74_21)
% 247.75/41.84  | | | |   (1123)  leq(all_74_14, all_74_21)
% 247.75/41.84  | | | |   (1124)  a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13
% 247.75/41.84  | | | |   (1125)  a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | REDUCE: (135), (1123) imply:
% 247.75/41.84  | | | |   (1126)  leq(all_74_14, n5)
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | REDUCE: (135), (1122) imply:
% 247.75/41.84  | | | |   (1127)  leq(all_74_15, n5)
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_15, simplifying
% 247.75/41.84  | | | |              with (12), (51), (1120) gives:
% 247.75/41.84  | | | |   (1128)  all_74_15 = n0 | gt(all_74_15, n0)
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_14, simplifying
% 247.75/41.84  | | | |              with (12), (52), (1121) gives:
% 247.75/41.84  | | | |   (1129)  all_74_14 = n0 | gt(all_74_14, n0)
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | GROUND_INST: instantiating (3) with all_74_15, simplifying with (51),
% 247.75/41.84  | | | |              (1120), (1127) gives:
% 247.75/41.84  | | | |   (1130)  all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | all_74_15 =
% 247.75/41.84  | | | |           n2 | all_74_15 = n1 | all_74_15 = n0
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n5, simplifying
% 247.75/41.84  | | | |              with (51), (122), (1127) gives:
% 247.75/41.84  | | | |   (1131)  all_74_15 = n5 | gt(n5, all_74_15)
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | GROUND_INST: instantiating (3) with all_74_14, simplifying with (52),
% 247.75/41.84  | | | |              (1121), (1126) gives:
% 247.75/41.84  | | | |   (1132)  all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 =
% 247.75/41.84  | | | |           n2 | all_74_14 = n1 | all_74_14 = n0
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n5, simplifying
% 247.75/41.84  | | | |              with (52), (122), (1126) gives:
% 247.75/41.84  | | | |   (1133)  all_74_14 = n5 | gt(n5, all_74_14)
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | BETA: splitting (1129) gives:
% 247.75/41.84  | | | | 
% 247.75/41.84  | | | | Case 1:
% 247.75/41.84  | | | | | 
% 247.75/41.84  | | | | |   (1134)  gt(all_74_14, n0)
% 247.75/41.84  | | | | | 
% 247.75/41.84  | | | | | BETA: splitting (1128) gives:
% 247.75/41.84  | | | | | 
% 247.75/41.84  | | | | | Case 1:
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | |   (1135)  gt(all_74_15, n0)
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | | BETA: splitting (1133) gives:
% 247.75/41.84  | | | | | | 
% 247.75/41.84  | | | | | | Case 1:
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | |   (1136)  gt(n5, all_74_14)
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | GROUND_INST: instantiating (1) with all_74_14, n5, n4, simplifying
% 247.75/41.84  | | | | | | |              with (52), (122), (126), (1136) gives:
% 247.75/41.84  | | | | | | |   (1137)  leq(all_74_14, n4)
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | BETA: splitting (1131) gives:
% 247.75/41.84  | | | | | | | 
% 247.75/41.84  | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | |   (1138)  gt(n5, all_74_15)
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4,
% 247.75/41.84  | | | | | | | |              simplifying with (51), (122), (126), (1138) gives:
% 247.75/41.84  | | | | | | | |   (1139)  leq(all_74_15, n4)
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4,
% 247.75/41.84  | | | | | | | |              simplifying with (52), (119), (1137) gives:
% 247.75/41.84  | | | | | | | |   (1140)  all_74_14 = n4 | gt(n4, all_74_14)
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | BETA: splitting (1132) gives:
% 247.75/41.84  | | | | | | | | 
% 247.75/41.84  | | | | | | | | Case 1:
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | |   (1141)  all_74_14 = n0
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (1125), (1141) imply:
% 247.75/41.84  | | | | | | | | |   (1142)  a_select3(pminus_ds1_filter, n0, all_74_15) =
% 247.75/41.84  | | | | | | | | |           all_74_12
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (1124), (1141) imply:
% 247.75/41.84  | | | | | | | | |   (1143)  a_select3(pminus_ds1_filter, all_74_15, n0) =
% 247.75/41.84  | | | | | | | | |           all_74_13
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (1126), (1141) imply:
% 247.75/41.84  | | | | | | | | |   (1144)  leq(n0, n5)
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.84  | | | | | | | | | REDUCE: (1121), (1141) imply:
% 247.75/41.84  | | | | | | | | |   (1145)  leq(n0, n0)
% 247.75/41.84  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | BETA: splitting (1130) gives:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | Case 1:
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | |   (1146)  all_74_15 = n0
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REDUCE: (1143), (1146) imply:
% 247.75/41.85  | | | | | | | | | |   (1147)  a_select3(pminus_ds1_filter, n0, n0) = all_74_13
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REDUCE: (1142), (1146) imply:
% 247.75/41.85  | | | | | | | | | |   (1148)  a_select3(pminus_ds1_filter, n0, n0) = all_74_12
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_13, all_74_12, n0,
% 247.75/41.85  | | | | | | | | | |              n0, pminus_ds1_filter, simplifying with (1147),
% 247.75/41.85  | | | | | | | | | |              (1148) gives:
% 247.75/41.85  | | | | | | | | | |   (1149)  all_74_12 = all_74_13
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REDUCE: (1119), (1149) imply:
% 247.75/41.85  | | | | | | | | | |   (1150)  $false
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | CLOSE: (1150) is inconsistent.
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | |   (1151)   ~ (all_74_15 = n0)
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4,
% 247.75/41.85  | | | | | | | | | |              simplifying with (51), (119), (1139) gives:
% 247.75/41.85  | | | | | | | | | |   (1152)  all_74_15 = n4 | gt(n4, all_74_15)
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REF_CLOSE: (1), (4), (12), (17), (51), (64), (101), (112),
% 247.75/41.85  | | | | | | | | | |            (119), (123), (124), (125), (135), (1119), (1120),
% 247.75/41.85  | | | | | | | | | |            (1127), (1142), (1143), (1144), (1145), (1151),
% 247.75/41.85  | | | | | | | | | |            (1152), (leq_gt2) are inconsistent by sub-proof
% 247.75/41.85  | | | | | | | | | |            #22.
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | End of split
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | |   (1153)   ~ (all_74_14 = n0)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | BETA: splitting (1130) gives:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | Case 1:
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | |   (1154)  all_74_15 = n0
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REDUCE: (1125), (1154) imply:
% 247.75/41.85  | | | | | | | | | |   (1155)  a_select3(pminus_ds1_filter, all_74_14, n0) =
% 247.75/41.85  | | | | | | | | | |           all_74_12
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REDUCE: (1124), (1154) imply:
% 247.75/41.85  | | | | | | | | | |   (1156)  a_select3(pminus_ds1_filter, n0, all_74_14) =
% 247.75/41.85  | | | | | | | | | |           all_74_13
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REDUCE: (1127), (1154) imply:
% 247.75/41.85  | | | | | | | | | |   (1157)  leq(n0, n5)
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REDUCE: (1120), (1154) imply:
% 247.75/41.85  | | | | | | | | | |   (1158)  leq(n0, n0)
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REF_CLOSE: (1), (4), (12), (17), (52), (64), (101), (112),
% 247.75/41.85  | | | | | | | | | |            (119), (123), (124), (125), (135), (1119), (1121),
% 247.75/41.85  | | | | | | | | | |            (1126), (1140), (1153), (1155), (1156), (1157),
% 247.75/41.85  | | | | | | | | | |            (1158), (leq_gt2) are inconsistent by sub-proof
% 247.75/41.85  | | | | | | | | | |            #21.
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | |   (1159)   ~ (all_74_15 = n0)
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4,
% 247.75/41.85  | | | | | | | | | |              simplifying with (51), (119), (1139) gives:
% 247.75/41.85  | | | | | | | | | |   (1160)  all_74_15 = n4 | gt(n4, all_74_15)
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (64), (101), (112),
% 247.75/41.85  | | | | | | | | | |            (119), (123), (124), (125), (135), (1119), (1120),
% 247.75/41.85  | | | | | | | | | |            (1121), (1124), (1125), (1126), (1127), (1140),
% 247.75/41.85  | | | | | | | | | |            (1153), (1159), (1160), (leq_gt2) are inconsistent
% 247.75/41.85  | | | | | | | | | |            by sub-proof #16.
% 247.75/41.85  | | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | End of split
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | End of split
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | |   (1161)  all_74_15 = n5
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1125), (1161) imply:
% 247.75/41.85  | | | | | | | |   (1162)  a_select3(pminus_ds1_filter, all_74_14, n5) =
% 247.75/41.85  | | | | | | | |           all_74_12
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1124), (1161) imply:
% 247.75/41.85  | | | | | | | |   (1163)  a_select3(pminus_ds1_filter, n5, all_74_14) =
% 247.75/41.85  | | | | | | | |           all_74_13
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1127), (1161) imply:
% 247.75/41.85  | | | | | | | |   (1164)  leq(n5, n5)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1120), (1161) imply:
% 247.75/41.85  | | | | | | | |   (1165)  leq(n0, n5)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_14, n4,
% 247.75/41.85  | | | | | | | |              simplifying with (52), (119), (1137) gives:
% 247.75/41.85  | | | | | | | |   (1166)  all_74_14 = n4 | gt(n4, all_74_14)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | BETA: splitting (1132) gives:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | Case 1:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | |   (1167)  all_74_14 = n0
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | REDUCE: (1134), (1167) imply:
% 247.75/41.85  | | | | | | | | |   (1168)  gt(n0, n0)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0,
% 247.75/41.85  | | | | | | | | |              simplifying with (12), (1168) gives:
% 247.75/41.85  | | | | | | | | |   (1169)  $false
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | CLOSE: (1169) is inconsistent.
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | |   (1170)   ~ (all_74_14 = n0)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | REF_CLOSE: (1), (4), (17), (52), (64), (101), (112), (119),
% 247.75/41.85  | | | | | | | | |            (122), (123), (124), (125), (135), (1119), (1121),
% 247.75/41.85  | | | | | | | | |            (1126), (1162), (1163), (1164), (1165), (1166),
% 247.75/41.85  | | | | | | | | |            (1170), (leq_gt2) are inconsistent by sub-proof
% 247.75/41.85  | | | | | | | | |            #14.
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | End of split
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | End of split
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | Case 2:
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | |   (1171)  all_74_14 = n5
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | REDUCE: (1125), (1171) imply:
% 247.75/41.85  | | | | | | |   (1172)  a_select3(pminus_ds1_filter, n5, all_74_15) = all_74_12
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | REDUCE: (1124), (1171) imply:
% 247.75/41.85  | | | | | | |   (1173)  a_select3(pminus_ds1_filter, all_74_15, n5) = all_74_13
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | REDUCE: (1126), (1171) imply:
% 247.75/41.85  | | | | | | |   (1174)  leq(n5, n5)
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | REDUCE: (1121), (1171) imply:
% 247.75/41.85  | | | | | | |   (1175)  leq(n0, n5)
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | BETA: splitting (1131) gives:
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | Case 1:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | |   (1176)  gt(n5, all_74_15)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4,
% 247.75/41.85  | | | | | | | |              simplifying with (51), (122), (126), (1176) gives:
% 247.75/41.85  | | | | | | | |   (1177)  leq(all_74_15, n4)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | BETA: splitting (1130) gives:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | Case 1:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | |   (1178)  all_74_15 = n0
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | REDUCE: (1135), (1178) imply:
% 247.75/41.85  | | | | | | | | |   (1179)  gt(n0, n0)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | GROUND_INST: instantiating (irreflexivity_gt) with n0,
% 247.75/41.85  | | | | | | | | |              simplifying with (12), (1179) gives:
% 247.75/41.85  | | | | | | | | |   (1180)  $false
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | CLOSE: (1180) is inconsistent.
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | |   (1181)   ~ (all_74_15 = n0)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4,
% 247.75/41.85  | | | | | | | | |              simplifying with (51), (119), (1177) gives:
% 247.75/41.85  | | | | | | | | |   (1182)  all_74_15 = n4 | gt(n4, all_74_15)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | REF_CLOSE: (1), (4), (17), (51), (64), (101), (112), (119),
% 247.75/41.85  | | | | | | | | |            (122), (123), (124), (125), (135), (1119), (1120),
% 247.75/41.85  | | | | | | | | |            (1127), (1172), (1173), (1174), (1175), (1181),
% 247.75/41.85  | | | | | | | | |            (1182), (leq_gt2) are inconsistent by sub-proof
% 247.75/41.85  | | | | | | | | |            #13.
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | End of split
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | |   (1183)  all_74_15 = n5
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1173), (1183) imply:
% 247.75/41.85  | | | | | | | |   (1184)  a_select3(pminus_ds1_filter, n5, n5) = all_74_13
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1172), (1183) imply:
% 247.75/41.85  | | | | | | | |   (1185)  a_select3(pminus_ds1_filter, n5, n5) = all_74_12
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | GROUND_INST: instantiating (17) with all_74_13, all_74_12, n5,
% 247.75/41.85  | | | | | | | |              n5, pminus_ds1_filter, simplifying with (1184),
% 247.75/41.85  | | | | | | | |              (1185) gives:
% 247.75/41.85  | | | | | | | |   (1186)  all_74_12 = all_74_13
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1119), (1186) imply:
% 247.75/41.85  | | | | | | | |   (1187)  $false
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | CLOSE: (1187) is inconsistent.
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | End of split
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | End of split
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | Case 2:
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | |   (1188)  all_74_15 = n0
% 247.75/41.85  | | | | | |   (1189)   ~ gt(all_74_15, n0)
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | REDUCE: (1188), (1189) imply:
% 247.75/41.85  | | | | | |   (1190)   ~ gt(n0, n0)
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (64), (101), (112), (119),
% 247.75/41.85  | | | | | |            (122), (123), (124), (125), (126), (135), (1119), (1120),
% 247.75/41.85  | | | | | |            (1121), (1124), (1125), (1126), (1127), (1128), (1130),
% 247.75/41.85  | | | | | |            (1131), (1132), (1133), (1134), (1190), (leq_gt2) are
% 247.75/41.85  | | | | | |            inconsistent by sub-proof #12.
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | End of split
% 247.75/41.85  | | | | | 
% 247.75/41.85  | | | | Case 2:
% 247.75/41.85  | | | | | 
% 247.75/41.85  | | | | |   (1191)  all_74_14 = n0
% 247.75/41.85  | | | | |   (1192)   ~ gt(all_74_14, n0)
% 247.75/41.85  | | | | | 
% 247.75/41.85  | | | | | REDUCE: (1191), (1192) imply:
% 247.75/41.85  | | | | |   (1193)   ~ gt(n0, n0)
% 247.75/41.85  | | | | | 
% 247.75/41.85  | | | | | BETA: splitting (1129) gives:
% 247.75/41.85  | | | | | 
% 247.75/41.85  | | | | | Case 1:
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | |   (1194)  gt(all_74_14, n0)
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | REF_CLOSE: (1), (4), (17), (51), (52), (64), (101), (112), (119),
% 247.75/41.85  | | | | | |            (122), (123), (124), (125), (126), (135), (1119), (1120),
% 247.75/41.85  | | | | | |            (1121), (1124), (1125), (1126), (1127), (1128), (1130),
% 247.75/41.85  | | | | | |            (1131), (1132), (1133), (1193), (1194), (leq_gt2) are
% 247.75/41.85  | | | | | |            inconsistent by sub-proof #12.
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | Case 2:
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | REDUCE: (1125), (1191) imply:
% 247.75/41.85  | | | | | |   (1195)  a_select3(pminus_ds1_filter, n0, all_74_15) = all_74_12
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | REDUCE: (1124), (1191) imply:
% 247.75/41.85  | | | | | |   (1196)  a_select3(pminus_ds1_filter, all_74_15, n0) = all_74_13
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | REDUCE: (1126), (1191) imply:
% 247.75/41.85  | | | | | |   (1197)  leq(n0, n5)
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | REDUCE: (1121), (1191) imply:
% 247.75/41.85  | | | | | |   (1198)  leq(n0, n0)
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | BETA: splitting (1128) gives:
% 247.75/41.85  | | | | | | 
% 247.75/41.85  | | | | | | Case 1:
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | |   (1199)  gt(all_74_15, n0)
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | BETA: splitting (1131) gives:
% 247.75/41.85  | | | | | | | 
% 247.75/41.85  | | | | | | | Case 1:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | |   (1200)  gt(n5, all_74_15)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | GROUND_INST: instantiating (1) with all_74_15, n5, n4,
% 247.75/41.85  | | | | | | | |              simplifying with (51), (122), (126), (1200) gives:
% 247.75/41.85  | | | | | | | |   (1201)  leq(all_74_15, n4)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_15, n4,
% 247.75/41.85  | | | | | | | |              simplifying with (51), (119), (1201) gives:
% 247.75/41.85  | | | | | | | |   (1202)  all_74_15 = n4 | gt(n4, all_74_15)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | BETA: splitting (1130) gives:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | Case 1:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | |   (1203)  all_74_15 = n0
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | REDUCE: (1199), (1203) imply:
% 247.75/41.85  | | | | | | | | |   (1204)  gt(n0, n0)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | PRED_UNIFY: (1193), (1204) imply:
% 247.75/41.85  | | | | | | | | |   (1205)  $false
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | CLOSE: (1205) is inconsistent.
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | |   (1206)   ~ (all_74_15 = n0)
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | | REF_CLOSE: (1), (4), (12), (17), (51), (64), (101), (112),
% 247.75/41.85  | | | | | | | | |            (119), (123), (124), (125), (135), (1119), (1120),
% 247.75/41.85  | | | | | | | | |            (1127), (1195), (1196), (1197), (1198), (1202),
% 247.75/41.85  | | | | | | | | |            (1206), (leq_gt2) are inconsistent by sub-proof
% 247.75/41.85  | | | | | | | | |            #22.
% 247.75/41.85  | | | | | | | | | 
% 247.75/41.85  | | | | | | | | End of split
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | Case 2:
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | |   (1207)  all_74_15 = n5
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1196), (1207) imply:
% 247.75/41.85  | | | | | | | |   (1208)  a_select3(pminus_ds1_filter, n5, n0) = all_74_13
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1195), (1207) imply:
% 247.75/41.85  | | | | | | | |   (1209)  a_select3(pminus_ds1_filter, n0, n5) = all_74_12
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | REDUCE: (1127), (1207) imply:
% 247.75/41.85  | | | | | | | |   (1210)  leq(n5, n5)
% 247.75/41.85  | | | | | | | | 
% 247.75/41.85  | | | | | | | | GROUND_INST: instantiating (64) with n0, n5, all_74_12,
% 247.75/41.85  | | | | | | | |              simplifying with (12), (122), (1197), (1198),
% 247.75/41.85  | | | | | | | |              (1209) gives:
% 247.75/41.85  | | | | | | | |   (1211)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.75/41.85  | | | | | | | |           (a_select3(pminus_ds1_filter, n5, n0) = all_74_12 &
% 247.75/41.85  | | | | | | | |             $i(all_74_12))
% 247.75/41.85  | | | | | | | | 
% 247.75/41.86  | | | | | | | | BETA: splitting (1211) gives:
% 247.75/41.86  | | | | | | | | 
% 247.75/41.86  | | | | | | | | Case 1:
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | |   (1212)   ~ leq(n0, all_74_21)
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | REDUCE: (135), (1212) imply:
% 247.75/41.86  | | | | | | | | |   (1213)   ~ leq(n0, n5)
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | PRED_UNIFY: (1197), (1213) imply:
% 247.75/41.86  | | | | | | | | |   (1214)  $false
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | CLOSE: (1214) is inconsistent.
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | Case 2:
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | |   (1215)   ~ leq(n5, all_74_21) |
% 247.75/41.86  | | | | | | | | |           (a_select3(pminus_ds1_filter, n5, n0) = all_74_12 &
% 247.75/41.86  | | | | | | | | |             $i(all_74_12))
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | BETA: splitting (1215) gives:
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | Case 1:
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | |   (1216)   ~ leq(n5, all_74_21)
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | | REDUCE: (135), (1216) imply:
% 247.75/41.86  | | | | | | | | | |   (1217)   ~ leq(n5, n5)
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | | PRED_UNIFY: (1210), (1217) imply:
% 247.75/41.86  | | | | | | | | | |   (1218)  $false
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | | CLOSE: (1218) is inconsistent.
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | Case 2:
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | |   (1219)  a_select3(pminus_ds1_filter, n5, n0) = all_74_12 &
% 247.75/41.86  | | | | | | | | | |           $i(all_74_12)
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | | ALPHA: (1219) implies:
% 247.75/41.86  | | | | | | | | | |   (1220)  a_select3(pminus_ds1_filter, n5, n0) = all_74_12
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_12, all_74_13, n0,
% 247.75/41.86  | | | | | | | | | |              n5, pminus_ds1_filter, simplifying with (1208),
% 247.75/41.86  | | | | | | | | | |              (1220) gives:
% 247.75/41.86  | | | | | | | | | |   (1221)  all_74_12 = all_74_13
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | | REDUCE: (1119), (1221) imply:
% 247.75/41.86  | | | | | | | | | |   (1222)  $false
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | | CLOSE: (1222) is inconsistent.
% 247.75/41.86  | | | | | | | | | | 
% 247.75/41.86  | | | | | | | | | End of split
% 247.75/41.86  | | | | | | | | | 
% 247.75/41.86  | | | | | | | | End of split
% 247.75/41.86  | | | | | | | | 
% 247.75/41.86  | | | | | | | End of split
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | Case 2:
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | |   (1223)  all_74_15 = n0
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | | REDUCE: (1196), (1223) imply:
% 247.75/41.86  | | | | | | |   (1224)  a_select3(pminus_ds1_filter, n0, n0) = all_74_13
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | | REDUCE: (1195), (1223) imply:
% 247.75/41.86  | | | | | | |   (1225)  a_select3(pminus_ds1_filter, n0, n0) = all_74_12
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | | GROUND_INST: instantiating (17) with all_74_13, all_74_12, n0, n0,
% 247.75/41.86  | | | | | | |              pminus_ds1_filter, simplifying with (1224), (1225)
% 247.75/41.86  | | | | | | |              gives:
% 247.75/41.86  | | | | | | |   (1226)  all_74_12 = all_74_13
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | | REDUCE: (1119), (1226) imply:
% 247.75/41.86  | | | | | | |   (1227)  $false
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | | CLOSE: (1227) is inconsistent.
% 247.75/41.86  | | | | | | | 
% 247.75/41.86  | | | | | | End of split
% 247.75/41.86  | | | | | | 
% 247.75/41.86  | | | | | End of split
% 247.75/41.86  | | | | | 
% 247.75/41.86  | | | | End of split
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | Case 2:
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | |   (1228)   ~ (all_74_16 = all_74_17) & a_select3(id_ds1_filter,
% 247.75/41.86  | | | |             all_74_18, all_74_19) = all_74_16 & a_select3(id_ds1_filter,
% 247.75/41.86  | | | |             all_74_19, all_74_18) = all_74_17 & $i(all_74_16) &
% 247.75/41.86  | | | |           $i(all_74_17) & leq(all_74_18, all_74_21) & leq(all_74_19,
% 247.75/41.86  | | | |             all_74_21) & leq(n0, all_74_18) & leq(n0, all_74_19)
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | | ALPHA: (1228) implies:
% 247.75/41.86  | | | |   (1229)   ~ (all_74_16 = all_74_17)
% 247.75/41.86  | | | |   (1230)  leq(n0, all_74_19)
% 247.75/41.86  | | | |   (1231)  leq(n0, all_74_18)
% 247.75/41.86  | | | |   (1232)  leq(all_74_19, all_74_21)
% 247.75/41.86  | | | |   (1233)  leq(all_74_18, all_74_21)
% 247.75/41.86  | | | |   (1234)  a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17
% 247.75/41.86  | | | |   (1235)  a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | | REDUCE: (135), (1233) imply:
% 247.75/41.86  | | | |   (1236)  leq(all_74_18, n5)
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | | REDUCE: (135), (1232) imply:
% 247.75/41.86  | | | |   (1237)  leq(all_74_19, n5)
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_19, simplifying
% 247.75/41.86  | | | |              with (12), (49), (1230) gives:
% 247.75/41.86  | | | |   (1238)  all_74_19 = n0 | gt(all_74_19, n0)
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | | GROUND_INST: instantiating (leq_gt2) with n0, all_74_18, simplifying
% 247.75/41.86  | | | |              with (12), (50), (1231) gives:
% 247.75/41.86  | | | |   (1239)  all_74_18 = n0 | gt(all_74_18, n0)
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | | GROUND_INST: instantiating (3) with all_74_19, simplifying with (49),
% 247.75/41.86  | | | |              (1230), (1237) gives:
% 247.75/41.86  | | | |   (1240)  all_74_19 = n5 | all_74_19 = n4 | all_74_19 = n3 | all_74_19 =
% 247.75/41.86  | | | |           n2 | all_74_19 = n1 | all_74_19 = n0
% 247.75/41.86  | | | | 
% 247.75/41.86  | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n5, simplifying
% 247.75/41.86  | | | |              with (49), (122), (1237) gives:
% 247.75/41.86  | | | |   (1241)  all_74_19 = n5 | gt(n5, all_74_19)
% 247.91/41.86  | | | | 
% 247.91/41.86  | | | | GROUND_INST: instantiating (3) with all_74_18, simplifying with (50),
% 247.91/41.86  | | | |              (1231), (1236) gives:
% 247.91/41.86  | | | |   (1242)  all_74_18 = n5 | all_74_18 = n4 | all_74_18 = n3 | all_74_18 =
% 247.91/41.86  | | | |           n2 | all_74_18 = n1 | all_74_18 = n0
% 247.91/41.86  | | | | 
% 247.91/41.86  | | | | GROUND_INST: instantiating (leq_gt2) with all_74_18, n5, simplifying
% 247.91/41.86  | | | |              with (50), (122), (1236) gives:
% 247.91/41.86  | | | |   (1243)  all_74_18 = n5 | gt(n5, all_74_18)
% 247.91/41.86  | | | | 
% 247.91/41.86  | | | | BETA: splitting (1239) gives:
% 247.91/41.86  | | | | 
% 247.91/41.86  | | | | Case 1:
% 247.91/41.86  | | | | | 
% 247.91/41.86  | | | | |   (1244)  gt(all_74_18, n0)
% 247.91/41.86  | | | | | 
% 247.91/41.86  | | | | | BETA: splitting (1238) gives:
% 247.91/41.86  | | | | | 
% 247.91/41.86  | | | | | Case 1:
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | |   (1245)  gt(all_74_19, n0)
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | | BETA: splitting (1243) gives:
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | | Case 1:
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | |   (1246)  gt(n5, all_74_18)
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | BETA: splitting (1241) gives:
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | Case 1:
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | |   (1247)  gt(n5, all_74_19)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n5, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (49), (122), (126), (1247) gives:
% 247.91/41.86  | | | | | | | |   (1248)  leq(all_74_19, n4)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (1) with all_74_18, n5, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (50), (122), (126), (1246) gives:
% 247.91/41.86  | | | | | | | |   (1249)  leq(all_74_18, n4)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (49), (119), (1248) gives:
% 247.91/41.86  | | | | | | | |   (1250)  all_74_19 = n4 | gt(n4, all_74_19)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_18, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (50), (119), (1249) gives:
% 247.91/41.86  | | | | | | | |   (1251)  all_74_18 = n4 | gt(n4, all_74_18)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | BETA: splitting (1240) gives:
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | Case 1:
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | |   (1252)  all_74_19 = n0
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | REF_CLOSE: (49), (1245), (1252), (irreflexivity_gt) are
% 247.91/41.86  | | | | | | | | |            inconsistent by sub-proof #11.
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | Case 2:
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | |   (1253)   ~ (all_74_19 = n0)
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | BETA: splitting (1242) gives:
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | Case 1:
% 247.91/41.86  | | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | |   (1254)  all_74_18 = n0
% 247.91/41.86  | | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | | REF_CLOSE: (50), (1244), (1254), (irreflexivity_gt) are
% 247.91/41.86  | | | | | | | | | |            inconsistent by sub-proof #10.
% 247.91/41.86  | | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | Case 2:
% 247.91/41.86  | | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | |   (1255)   ~ (all_74_18 = n0)
% 247.91/41.86  | | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (65), (101), (112),
% 247.91/41.86  | | | | | | | | | |            (119), (123), (124), (125), (135), (1229), (1230),
% 247.91/41.86  | | | | | | | | | |            (1231), (1234), (1235), (1236), (1237), (1250),
% 247.91/41.86  | | | | | | | | | |            (1251), (1253), (1255), (leq_gt2) are inconsistent
% 247.91/41.86  | | | | | | | | | |            by sub-proof #6.
% 247.91/41.86  | | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | End of split
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | End of split
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | Case 2:
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | |   (1256)  all_74_19 = n5
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | REDUCE: (1235), (1256) imply:
% 247.91/41.86  | | | | | | | |   (1257)  a_select3(id_ds1_filter, all_74_18, n5) = all_74_16
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | REDUCE: (1234), (1256) imply:
% 247.91/41.86  | | | | | | | |   (1258)  a_select3(id_ds1_filter, n5, all_74_18) = all_74_17
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | REDUCE: (1237), (1256) imply:
% 247.91/41.86  | | | | | | | |   (1259)  leq(n5, n5)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | REDUCE: (1230), (1256) imply:
% 247.91/41.86  | | | | | | | |   (1260)  leq(n0, n5)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (1) with all_74_18, n5, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (50), (122), (126), (1246) gives:
% 247.91/41.86  | | | | | | | |   (1261)  leq(all_74_18, n4)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_18, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (50), (119), (1261) gives:
% 247.91/41.86  | | | | | | | |   (1262)  all_74_18 = n4 | gt(n4, all_74_18)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | BETA: splitting (1242) gives:
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | Case 1:
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | |   (1263)  all_74_18 = n0
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | REF_CLOSE: (50), (1244), (1263), (irreflexivity_gt) are
% 247.91/41.86  | | | | | | | | |            inconsistent by sub-proof #10.
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | Case 2:
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | |   (1264)   ~ (all_74_18 = n0)
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | REF_CLOSE: (1), (4), (17), (50), (65), (101), (112), (119),
% 247.91/41.86  | | | | | | | | |            (122), (123), (124), (125), (135), (1229), (1231),
% 247.91/41.86  | | | | | | | | |            (1236), (1257), (1258), (1259), (1260), (1262),
% 247.91/41.86  | | | | | | | | |            (1264), (leq_gt2) are inconsistent by sub-proof #4.
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | End of split
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | End of split
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | Case 2:
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | |   (1265)  all_74_18 = n5
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | REDUCE: (1235), (1265) imply:
% 247.91/41.86  | | | | | | |   (1266)  a_select3(id_ds1_filter, n5, all_74_19) = all_74_16
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | REDUCE: (1234), (1265) imply:
% 247.91/41.86  | | | | | | |   (1267)  a_select3(id_ds1_filter, all_74_19, n5) = all_74_17
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | REDUCE: (1236), (1265) imply:
% 247.91/41.86  | | | | | | |   (1268)  leq(n5, n5)
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | REDUCE: (1231), (1265) imply:
% 247.91/41.86  | | | | | | |   (1269)  leq(n0, n5)
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | BETA: splitting (1241) gives:
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | | Case 1:
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | |   (1270)  gt(n5, all_74_19)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n5, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (49), (122), (126), (1270) gives:
% 247.91/41.86  | | | | | | | |   (1271)  leq(all_74_19, n4)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n4,
% 247.91/41.86  | | | | | | | |              simplifying with (49), (119), (1271) gives:
% 247.91/41.86  | | | | | | | |   (1272)  all_74_19 = n4 | gt(n4, all_74_19)
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | BETA: splitting (1240) gives:
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | Case 1:
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | |   (1273)  all_74_19 = n0
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | REF_CLOSE: (49), (1245), (1273), (irreflexivity_gt) are
% 247.91/41.86  | | | | | | | | |            inconsistent by sub-proof #11.
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | Case 2:
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | |   (1274)   ~ (all_74_19 = n0)
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | | REF_CLOSE: (1), (4), (17), (49), (65), (101), (112), (119),
% 247.91/41.86  | | | | | | | | |            (122), (123), (124), (125), (135), (1229), (1230),
% 247.91/41.86  | | | | | | | | |            (1237), (1266), (1267), (1268), (1269), (1272),
% 247.91/41.86  | | | | | | | | |            (1274), (leq_gt2) are inconsistent by sub-proof #3.
% 247.91/41.86  | | | | | | | | | 
% 247.91/41.86  | | | | | | | | End of split
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | Case 2:
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | |   (1275)  all_74_19 = n5
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | REDUCE: (1267), (1275) imply:
% 247.91/41.86  | | | | | | | |   (1276)  a_select3(id_ds1_filter, n5, n5) = all_74_17
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | REDUCE: (1266), (1275) imply:
% 247.91/41.86  | | | | | | | |   (1277)  a_select3(id_ds1_filter, n5, n5) = all_74_16
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n5,
% 247.91/41.86  | | | | | | | |              n5, id_ds1_filter, simplifying with (1276), (1277)
% 247.91/41.86  | | | | | | | |              gives:
% 247.91/41.86  | | | | | | | |   (1278)  all_74_16 = all_74_17
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | REDUCE: (1229), (1278) imply:
% 247.91/41.86  | | | | | | | |   (1279)  $false
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | | CLOSE: (1279) is inconsistent.
% 247.91/41.86  | | | | | | | | 
% 247.91/41.86  | | | | | | | End of split
% 247.91/41.86  | | | | | | | 
% 247.91/41.86  | | | | | | End of split
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | Case 2:
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | |   (1280)  all_74_19 = n0
% 247.91/41.86  | | | | | |   (1281)   ~ gt(all_74_19, n0)
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | | REDUCE: (1280), (1281) imply:
% 247.91/41.86  | | | | | |   (1282)   ~ gt(n0, n0)
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (65), (101), (112), (119),
% 247.91/41.86  | | | | | |            (122), (123), (124), (125), (126), (135), (1229), (1230),
% 247.91/41.86  | | | | | |            (1231), (1234), (1235), (1236), (1237), (1238), (1240),
% 247.91/41.86  | | | | | |            (1241), (1242), (1243), (1244), (1282), (leq_gt2) are
% 247.91/41.86  | | | | | |            inconsistent by sub-proof #1.
% 247.91/41.86  | | | | | | 
% 247.91/41.86  | | | | | End of split
% 247.91/41.86  | | | | | 
% 247.91/41.86  | | | | Case 2:
% 247.91/41.86  | | | | | 
% 247.91/41.86  | | | | |   (1283)  all_74_18 = n0
% 247.91/41.86  | | | | |   (1284)   ~ gt(all_74_18, n0)
% 247.91/41.86  | | | | | 
% 247.91/41.86  | | | | | REDUCE: (1283), (1284) imply:
% 247.91/41.86  | | | | |   (1285)   ~ gt(n0, n0)
% 247.91/41.86  | | | | | 
% 247.91/41.87  | | | | | BETA: splitting (1239) gives:
% 247.91/41.87  | | | | | 
% 247.91/41.87  | | | | | Case 1:
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | |   (1286)  gt(all_74_18, n0)
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | REF_CLOSE: (1), (4), (17), (49), (50), (65), (101), (112), (119),
% 247.91/41.87  | | | | | |            (122), (123), (124), (125), (126), (135), (1229), (1230),
% 247.91/41.87  | | | | | |            (1231), (1234), (1235), (1236), (1237), (1238), (1240),
% 247.91/41.87  | | | | | |            (1241), (1242), (1243), (1285), (1286), (leq_gt2) are
% 247.91/41.87  | | | | | |            inconsistent by sub-proof #1.
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | Case 2:
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | REDUCE: (1235), (1283) imply:
% 247.91/41.87  | | | | | |   (1287)  a_select3(id_ds1_filter, n0, all_74_19) = all_74_16
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | REDUCE: (1234), (1283) imply:
% 247.91/41.87  | | | | | |   (1288)  a_select3(id_ds1_filter, all_74_19, n0) = all_74_17
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | REDUCE: (1236), (1283) imply:
% 247.91/41.87  | | | | | |   (1289)  leq(n0, n5)
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | REDUCE: (1231), (1283) imply:
% 247.91/41.87  | | | | | |   (1290)  leq(n0, n0)
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | BETA: splitting (1238) gives:
% 247.91/41.87  | | | | | | 
% 247.91/41.87  | | | | | | Case 1:
% 247.91/41.87  | | | | | | | 
% 247.91/41.87  | | | | | | |   (1291)  gt(all_74_19, n0)
% 247.91/41.87  | | | | | | | 
% 247.91/41.87  | | | | | | | BETA: splitting (1241) gives:
% 247.91/41.87  | | | | | | | 
% 247.91/41.87  | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | 
% 247.91/41.87  | | | | | | | |   (1292)  gt(n5, all_74_19)
% 247.91/41.87  | | | | | | | | 
% 247.91/41.87  | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n5, n4,
% 247.91/41.87  | | | | | | | |              simplifying with (49), (122), (126), (1292) gives:
% 247.91/41.87  | | | | | | | |   (1293)  leq(all_74_19, n4)
% 247.91/41.87  | | | | | | | | 
% 247.91/41.87  | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n4,
% 247.91/41.87  | | | | | | | |              simplifying with (49), (119), (1293) gives:
% 247.91/41.87  | | | | | | | |   (1294)  all_74_19 = n4 | gt(n4, all_74_19)
% 247.91/41.87  | | | | | | | | 
% 247.91/41.87  | | | | | | | | BETA: splitting (1240) gives:
% 247.91/41.87  | | | | | | | | 
% 247.91/41.87  | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | |   (1295)  all_74_19 = n0
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | REDUCE: (1291), (1295) imply:
% 247.91/41.87  | | | | | | | | |   (1296)  gt(n0, n0)
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | PRED_UNIFY: (1285), (1296) imply:
% 247.91/41.87  | | | | | | | | |   (1297)  $false
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | CLOSE: (1297) is inconsistent.
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | |   (1298)   ~ (all_74_19 = n0)
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | BETA: splitting (1294) gives:
% 247.91/41.87  | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | |   (1299)  gt(n4, all_74_19)
% 247.91/41.87  | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n4, n3,
% 247.91/41.87  | | | | | | | | | |              simplifying with (49), (119), (125), (1299) gives:
% 247.91/41.87  | | | | | | | | | |   (1300)  leq(all_74_19, n3)
% 247.91/41.87  | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n3,
% 247.91/41.87  | | | | | | | | | |              simplifying with (49), (112), (1300) gives:
% 247.91/41.87  | | | | | | | | | |   (1301)  all_74_19 = n3 | gt(n3, all_74_19)
% 247.91/41.87  | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | BETA: splitting (1301) gives:
% 247.91/41.87  | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | |   (1302)  gt(n3, all_74_19)
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n3, n2,
% 247.91/41.87  | | | | | | | | | | |              simplifying with (49), (112), (124), (1302) gives:
% 247.91/41.87  | | | | | | | | | | |   (1303)  leq(all_74_19, n2)
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | GROUND_INST: instantiating (leq_gt2) with all_74_19, n2,
% 247.91/41.87  | | | | | | | | | | |              simplifying with (49), (101), (1303) gives:
% 247.91/41.87  | | | | | | | | | | |   (1304)  all_74_19 = n2 | gt(n2, all_74_19)
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | BETA: splitting (1304) gives:
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | |   (1305)  gt(n2, all_74_19)
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_74_19, n2, n1,
% 247.91/41.87  | | | | | | | | | | | |              simplifying with (49), (101), (123), (1305) gives:
% 247.91/41.87  | | | | | | | | | | | |   (1306)  leq(all_74_19, n1)
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_74_19, simplifying with
% 247.91/41.87  | | | | | | | | | | | |              (49), (1230), (1306) gives:
% 247.91/41.87  | | | | | | | | | | | |   (1307)  all_74_19 = n1 | all_74_19 = n0
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | BETA: splitting (1307) gives:
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | |   (1308)  all_74_19 = n0
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (1298), (1308) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1309)  $false
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | CLOSE: (1309) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | |   (1310)  all_74_19 = n1
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (1288), (1310) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1311)  a_select3(id_ds1_filter, n1, n0) = all_74_17
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (1287), (1310) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1312)  a_select3(id_ds1_filter, n0, n1) = all_74_16
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (1237), (1310) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1313)  leq(n1, n5)
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (1230), (1310) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1314)  leq(n0, n1)
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n1, all_74_16,
% 247.91/41.87  | | | | | | | | | | | | |              simplifying with (12), (85), (1290), (1312),
% 247.91/41.87  | | | | | | | | | | | | |              (1314) gives:
% 247.91/41.87  | | | | | | | | | | | | |   (1315)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.87  | | | | | | | | | | | | |           (a_select3(id_ds1_filter, n1, n0) = all_74_16 &
% 247.91/41.87  | | | | | | | | | | | | |             $i(all_74_16))
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | BETA: splitting (1315) gives:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | |   (1316)   ~ leq(n0, all_74_21)
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | REDUCE: (135), (1316) imply:
% 247.91/41.87  | | | | | | | | | | | | | |   (1317)   ~ leq(n0, n5)
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | PRED_UNIFY: (1289), (1317) imply:
% 247.91/41.87  | | | | | | | | | | | | | |   (1318)  $false
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | CLOSE: (1318) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | |   (1319)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter,
% 247.91/41.87  | | | | | | | | | | | | | |               n1, n0) = all_74_16 & $i(all_74_16))
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | BETA: splitting (1319) gives:
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | |   (1320)   ~ leq(n1, all_74_21)
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | | REDUCE: (135), (1320) imply:
% 247.91/41.87  | | | | | | | | | | | | | | |   (1321)   ~ leq(n1, n5)
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | | PRED_UNIFY: (1313), (1321) imply:
% 247.91/41.87  | | | | | | | | | | | | | | |   (1322)  $false
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | | CLOSE: (1322) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | |   (1323)  a_select3(id_ds1_filter, n1, n0) = all_74_16 &
% 247.91/41.87  | | | | | | | | | | | | | | |           $i(all_74_16)
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | | ALPHA: (1323) implies:
% 247.91/41.87  | | | | | | | | | | | | | | |   (1324)  a_select3(id_ds1_filter, n1, n0) = all_74_16
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n0,
% 247.91/41.87  | | | | | | | | | | | | | | |              n1, id_ds1_filter, simplifying with (1311), (1324)
% 247.91/41.87  | | | | | | | | | | | | | | |              gives:
% 247.91/41.87  | | | | | | | | | | | | | | |   (1325)  all_74_16 = all_74_17
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | | REDUCE: (1229), (1325) imply:
% 247.91/41.87  | | | | | | | | | | | | | | |   (1326)  $false
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | | CLOSE: (1326) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | End of split
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | End of split
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | End of split
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | |   (1327)  all_74_19 = n2
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | REDUCE: (1288), (1327) imply:
% 247.91/41.87  | | | | | | | | | | | |   (1328)  a_select3(id_ds1_filter, n2, n0) = all_74_17
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | REDUCE: (1287), (1327) imply:
% 247.91/41.87  | | | | | | | | | | | |   (1329)  a_select3(id_ds1_filter, n0, n2) = all_74_16
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | REDUCE: (1237), (1327) imply:
% 247.91/41.87  | | | | | | | | | | | |   (1330)  leq(n2, n5)
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | REDUCE: (1230), (1327) imply:
% 247.91/41.87  | | | | | | | | | | | |   (1331)  leq(n0, n2)
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n2, all_74_16,
% 247.91/41.87  | | | | | | | | | | | |              simplifying with (12), (101), (1290), (1329),
% 247.91/41.87  | | | | | | | | | | | |              (1331) gives:
% 247.91/41.87  | | | | | | | | | | | |   (1332)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.87  | | | | | | | | | | | |           (a_select3(id_ds1_filter, n2, n0) = all_74_16 &
% 247.91/41.87  | | | | | | | | | | | |             $i(all_74_16))
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | BETA: splitting (1332) gives:
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | |   (1333)   ~ leq(n0, all_74_21)
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (135), (1333) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1334)   ~ leq(n0, n5)
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | PRED_UNIFY: (1289), (1334) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1335)  $false
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | CLOSE: (1335) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | |   (1336)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter,
% 247.91/41.87  | | | | | | | | | | | | |               n2, n0) = all_74_16 & $i(all_74_16))
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | BETA: splitting (1336) gives:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | |   (1337)   ~ leq(n2, all_74_21)
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | REDUCE: (135), (1337) imply:
% 247.91/41.87  | | | | | | | | | | | | | |   (1338)   ~ leq(n2, n5)
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | PRED_UNIFY: (1330), (1338) imply:
% 247.91/41.87  | | | | | | | | | | | | | |   (1339)  $false
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | CLOSE: (1339) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | |   (1340)  a_select3(id_ds1_filter, n2, n0) = all_74_16 &
% 247.91/41.87  | | | | | | | | | | | | | |           $i(all_74_16)
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | ALPHA: (1340) implies:
% 247.91/41.87  | | | | | | | | | | | | | |   (1341)  a_select3(id_ds1_filter, n2, n0) = all_74_16
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n0,
% 247.91/41.87  | | | | | | | | | | | | | |              n2, id_ds1_filter, simplifying with (1328), (1341)
% 247.91/41.87  | | | | | | | | | | | | | |              gives:
% 247.91/41.87  | | | | | | | | | | | | | |   (1342)  all_74_16 = all_74_17
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | REDUCE: (1229), (1342) imply:
% 247.91/41.87  | | | | | | | | | | | | | |   (1343)  $false
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | | CLOSE: (1343) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | End of split
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | End of split
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | End of split
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | |   (1344)  all_74_19 = n3
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | REDUCE: (1288), (1344) imply:
% 247.91/41.87  | | | | | | | | | | |   (1345)  a_select3(id_ds1_filter, n3, n0) = all_74_17
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | REDUCE: (1287), (1344) imply:
% 247.91/41.87  | | | | | | | | | | |   (1346)  a_select3(id_ds1_filter, n0, n3) = all_74_16
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | REDUCE: (1237), (1344) imply:
% 247.91/41.87  | | | | | | | | | | |   (1347)  leq(n3, n5)
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | REDUCE: (1230), (1344) imply:
% 247.91/41.87  | | | | | | | | | | |   (1348)  leq(n0, n3)
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n3, all_74_16,
% 247.91/41.87  | | | | | | | | | | |              simplifying with (12), (112), (1290), (1346),
% 247.91/41.87  | | | | | | | | | | |              (1348) gives:
% 247.91/41.87  | | | | | | | | | | |   (1349)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.87  | | | | | | | | | | |           (a_select3(id_ds1_filter, n3, n0) = all_74_16 &
% 247.91/41.87  | | | | | | | | | | |             $i(all_74_16))
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | BETA: splitting (1349) gives:
% 247.91/41.87  | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | |   (1350)   ~ leq(n0, all_74_21)
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | REDUCE: (135), (1350) imply:
% 247.91/41.87  | | | | | | | | | | | |   (1351)   ~ leq(n0, n5)
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | PRED_UNIFY: (1289), (1351) imply:
% 247.91/41.87  | | | | | | | | | | | |   (1352)  $false
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | CLOSE: (1352) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | |   (1353)   ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter,
% 247.91/41.87  | | | | | | | | | | | |               n3, n0) = all_74_16 & $i(all_74_16))
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | BETA: splitting (1353) gives:
% 247.91/41.87  | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | Case 1:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | |   (1354)   ~ leq(n3, all_74_21)
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (135), (1354) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1355)   ~ leq(n3, n5)
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | PRED_UNIFY: (1347), (1355) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1356)  $false
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | CLOSE: (1356) is inconsistent.
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | Case 2:
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | |   (1357)  a_select3(id_ds1_filter, n3, n0) = all_74_16 &
% 247.91/41.87  | | | | | | | | | | | | |           $i(all_74_16)
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | ALPHA: (1357) implies:
% 247.91/41.87  | | | | | | | | | | | | |   (1358)  a_select3(id_ds1_filter, n3, n0) = all_74_16
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n0,
% 247.91/41.87  | | | | | | | | | | | | |              n3, id_ds1_filter, simplifying with (1345), (1358)
% 247.91/41.87  | | | | | | | | | | | | |              gives:
% 247.91/41.87  | | | | | | | | | | | | |   (1359)  all_74_16 = all_74_17
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.87  | | | | | | | | | | | | | REDUCE: (1229), (1359) imply:
% 247.91/41.87  | | | | | | | | | | | | |   (1360)  $false
% 247.91/41.87  | | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | | CLOSE: (1360) is inconsistent.
% 247.91/41.88  | | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | Case 2:
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | |   (1361)  all_74_19 = n4
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | REDUCE: (1288), (1361) imply:
% 247.91/41.88  | | | | | | | | | |   (1362)  a_select3(id_ds1_filter, n4, n0) = all_74_17
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | REDUCE: (1287), (1361) imply:
% 247.91/41.88  | | | | | | | | | |   (1363)  a_select3(id_ds1_filter, n0, n4) = all_74_16
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | REDUCE: (1237), (1361) imply:
% 247.91/41.88  | | | | | | | | | |   (1364)  leq(n4, n5)
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | REDUCE: (1230), (1361) imply:
% 247.91/41.88  | | | | | | | | | |   (1365)  leq(n0, n4)
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | GROUND_INST: instantiating (65) with n0, n4, all_74_16,
% 247.91/41.88  | | | | | | | | | |              simplifying with (12), (119), (1290), (1363),
% 247.91/41.88  | | | | | | | | | |              (1365) gives:
% 247.91/41.88  | | | | | | | | | |   (1366)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.88  | | | | | | | | | |           (a_select3(id_ds1_filter, n4, n0) = all_74_16 &
% 247.91/41.88  | | | | | | | | | |             $i(all_74_16))
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | BETA: splitting (1366) gives:
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | Case 1:
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | |   (1367)   ~ leq(n0, all_74_21)
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | REDUCE: (135), (1367) imply:
% 247.91/41.88  | | | | | | | | | | |   (1368)   ~ leq(n0, n5)
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | PRED_UNIFY: (1289), (1368) imply:
% 247.91/41.88  | | | | | | | | | | |   (1369)  $false
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | CLOSE: (1369) is inconsistent.
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | Case 2:
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | |   (1370)   ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter,
% 247.91/41.88  | | | | | | | | | | |               n4, n0) = all_74_16 & $i(all_74_16))
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | BETA: splitting (1370) gives:
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | Case 1:
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | |   (1371)   ~ leq(n4, all_74_21)
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | REDUCE: (135), (1371) imply:
% 247.91/41.88  | | | | | | | | | | | |   (1372)   ~ leq(n4, n5)
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | PRED_UNIFY: (1364), (1372) imply:
% 247.91/41.88  | | | | | | | | | | | |   (1373)  $false
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | CLOSE: (1373) is inconsistent.
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | Case 2:
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | |   (1374)  a_select3(id_ds1_filter, n4, n0) = all_74_16 &
% 247.91/41.88  | | | | | | | | | | | |           $i(all_74_16)
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | ALPHA: (1374) implies:
% 247.91/41.88  | | | | | | | | | | | |   (1375)  a_select3(id_ds1_filter, n4, n0) = all_74_16
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n0,
% 247.91/41.88  | | | | | | | | | | | |              n4, id_ds1_filter, simplifying with (1362), (1375)
% 247.91/41.88  | | | | | | | | | | | |              gives:
% 247.91/41.88  | | | | | | | | | | | |   (1376)  all_74_16 = all_74_17
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | REDUCE: (1229), (1376) imply:
% 247.91/41.88  | | | | | | | | | | | |   (1377)  $false
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | | CLOSE: (1377) is inconsistent.
% 247.91/41.88  | | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | Case 2:
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | |   (1378)  all_74_19 = n5
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | | REDUCE: (1288), (1378) imply:
% 247.91/41.88  | | | | | | | |   (1379)  a_select3(id_ds1_filter, n5, n0) = all_74_17
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | | REDUCE: (1287), (1378) imply:
% 247.91/41.88  | | | | | | | |   (1380)  a_select3(id_ds1_filter, n0, n5) = all_74_16
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | | REDUCE: (1237), (1378) imply:
% 247.91/41.88  | | | | | | | |   (1381)  leq(n5, n5)
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | | GROUND_INST: instantiating (65) with n0, n5, all_74_16,
% 247.91/41.88  | | | | | | | |              simplifying with (12), (122), (1289), (1290),
% 247.91/41.88  | | | | | | | |              (1380) gives:
% 247.91/41.88  | | | | | | | |   (1382)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.88  | | | | | | | |           (a_select3(id_ds1_filter, n5, n0) = all_74_16 &
% 247.91/41.88  | | | | | | | |             $i(all_74_16))
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | | BETA: splitting (1382) gives:
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | | Case 1:
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | |   (1383)   ~ leq(n0, all_74_21)
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | REDUCE: (135), (1383) imply:
% 247.91/41.88  | | | | | | | | |   (1384)   ~ leq(n0, n5)
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | PRED_UNIFY: (1289), (1384) imply:
% 247.91/41.88  | | | | | | | | |   (1385)  $false
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | CLOSE: (1385) is inconsistent.
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | Case 2:
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | |   (1386)   ~ leq(n5, all_74_21) | (a_select3(id_ds1_filter,
% 247.91/41.88  | | | | | | | | |               n5, n0) = all_74_16 & $i(all_74_16))
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | BETA: splitting (1386) gives:
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | Case 1:
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | |   (1387)   ~ leq(n5, all_74_21)
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | REDUCE: (135), (1387) imply:
% 247.91/41.88  | | | | | | | | | |   (1388)   ~ leq(n5, n5)
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | PRED_UNIFY: (1381), (1388) imply:
% 247.91/41.88  | | | | | | | | | |   (1389)  $false
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | CLOSE: (1389) is inconsistent.
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | Case 2:
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | |   (1390)  a_select3(id_ds1_filter, n5, n0) = all_74_16 &
% 247.91/41.88  | | | | | | | | | |           $i(all_74_16)
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | ALPHA: (1390) implies:
% 247.91/41.88  | | | | | | | | | |   (1391)  a_select3(id_ds1_filter, n5, n0) = all_74_16
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | | REF_CLOSE: (17), (1229), (1379), (1391) are inconsistent by
% 247.91/41.88  | | | | | | | | | |            sub-proof #2.
% 247.91/41.88  | | | | | | | | | | 
% 247.91/41.88  | | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | | 
% 247.91/41.88  | | | | | | | | End of split
% 247.91/41.88  | | | | | | | | 
% 247.91/41.88  | | | | | | | End of split
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | Case 2:
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | |   (1392)  all_74_19 = n0
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | | REDUCE: (1288), (1392) imply:
% 247.91/41.88  | | | | | | |   (1393)  a_select3(id_ds1_filter, n0, n0) = all_74_17
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | | REDUCE: (1287), (1392) imply:
% 247.91/41.88  | | | | | | |   (1394)  a_select3(id_ds1_filter, n0, n0) = all_74_16
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | | GROUND_INST: instantiating (17) with all_74_17, all_74_16, n0, n0,
% 247.91/41.88  | | | | | | |              id_ds1_filter, simplifying with (1393), (1394) gives:
% 247.91/41.88  | | | | | | |   (1395)  all_74_16 = all_74_17
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | | REDUCE: (1229), (1395) imply:
% 247.91/41.88  | | | | | | |   (1396)  $false
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | | CLOSE: (1396) is inconsistent.
% 247.91/41.88  | | | | | | | 
% 247.91/41.88  | | | | | | End of split
% 247.91/41.88  | | | | | | 
% 247.91/41.88  | | | | | End of split
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | End of split
% 247.91/41.88  | | | | 
% 247.91/41.88  | | | End of split
% 247.91/41.88  | | | 
% 247.91/41.88  | | End of split
% 247.91/41.88  | | 
% 247.91/41.88  | End of split
% 247.91/41.88  | 
% 247.91/41.88  End of proof
% 247.91/41.88  
% 247.91/41.88  Sub-proof #1 shows that the following formulas are inconsistent:
% 247.91/41.88  ----------------------------------------------------------------
% 247.91/41.88    (1)  gt(all_74_18, n0)
% 247.91/41.88    (2)  all_74_19 = n0 | gt(all_74_19, n0)
% 247.91/41.88    (3)  leq(n0, all_74_18)
% 247.91/41.88    (4)   ~ gt(n0, n0)
% 247.91/41.88    (5)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 247.91/41.88           leq(n0, v0))
% 247.91/41.88    (6)  leq(all_74_19, n5)
% 247.91/41.88    (7)  all_74_21 = n5
% 247.91/41.88    (8)  a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17
% 247.91/41.88    (9)  pred(n5) = n4
% 247.91/41.88    (10)  $i(n3)
% 247.91/41.88    (11)  $i(all_74_18)
% 247.91/41.88    (12)  pred(n2) = n1
% 247.91/41.88    (13)  pred(n4) = n3
% 247.91/41.88    (14)  pred(n3) = n2
% 247.91/41.88    (15)  leq(all_74_18, n5)
% 247.91/41.88    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 247.91/41.88            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 247.91/41.88    (17)  $i(all_74_19)
% 247.91/41.88    (18)  $i(n4)
% 247.91/41.88    (19)  all_74_18 = n5 | all_74_18 = n4 | all_74_18 = n3 | all_74_18 = n2 |
% 247.91/41.88          all_74_18 = n1 | all_74_18 = n0
% 247.91/41.88    (20)  a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16
% 247.91/41.88    (21)  all_74_19 = n5 | gt(n5, all_74_19)
% 247.91/41.88    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 247.91/41.88                v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_21) |  ~
% 247.91/41.88            leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 247.91/41.88            (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 247.91/41.88    (23)  $i(n2)
% 247.91/41.88    (24)  $i(n5)
% 247.91/41.88    (25)  leq(n0, all_74_19)
% 247.91/41.88    (26)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 247.91/41.88            leq(v0, v1) | gt(v1, v0))
% 247.91/41.88    (27)  all_74_19 = n5 | all_74_19 = n4 | all_74_19 = n3 | all_74_19 = n2 |
% 247.91/41.88          all_74_19 = n1 | all_74_19 = n0
% 247.91/41.88    (28)  all_74_18 = n5 | gt(n5, all_74_18)
% 247.91/41.88    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 247.91/41.88          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 247.91/41.88              v0))
% 247.91/41.88    (30)   ~ (all_74_16 = all_74_17)
% 247.91/41.88  
% 247.91/41.88  Begin of proof
% 247.91/41.88  | 
% 247.91/41.88  | BETA: splitting (2) gives:
% 247.91/41.88  | 
% 247.91/41.88  | Case 1:
% 247.91/41.88  | | 
% 247.91/41.88  | |   (31)  gt(all_74_19, n0)
% 247.91/41.88  | | 
% 247.91/41.88  | | BETA: splitting (28) gives:
% 247.91/41.88  | | 
% 247.91/41.88  | | Case 1:
% 247.91/41.88  | | | 
% 247.91/41.88  | | |   (32)  gt(n5, all_74_18)
% 247.91/41.88  | | | 
% 247.91/41.88  | | | GROUND_INST: instantiating (16) with all_74_18, n5, n4, simplifying with
% 247.91/41.88  | | |              (9), (11), (24), (32) gives:
% 247.91/41.88  | | |   (33)  leq(all_74_18, n4)
% 247.91/41.88  | | | 
% 247.91/41.88  | | | GROUND_INST: instantiating (26) with all_74_18, n4, simplifying with (11),
% 247.91/41.88  | | |              (18), (33) gives:
% 247.91/41.88  | | |   (34)  all_74_18 = n4 | gt(n4, all_74_18)
% 247.91/41.88  | | | 
% 247.91/41.88  | | | BETA: splitting (21) gives:
% 247.91/41.88  | | | 
% 247.91/41.88  | | | Case 1:
% 247.91/41.88  | | | | 
% 247.91/41.88  | | | |   (35)  gt(n5, all_74_19)
% 247.91/41.88  | | | | 
% 247.91/41.88  | | | | GROUND_INST: instantiating (16) with all_74_19, n5, n4, simplifying with
% 247.91/41.88  | | | |              (9), (17), (24), (35) gives:
% 247.91/41.88  | | | |   (36)  leq(all_74_19, n4)
% 247.91/41.88  | | | | 
% 247.91/41.88  | | | | GROUND_INST: instantiating (26) with all_74_19, n4, simplifying with
% 247.91/41.88  | | | |              (17), (18), (36) gives:
% 247.91/41.88  | | | |   (37)  all_74_19 = n4 | gt(n4, all_74_19)
% 247.91/41.88  | | | | 
% 247.91/41.88  | | | | BETA: splitting (27) gives:
% 247.91/41.88  | | | | 
% 247.91/41.88  | | | | Case 1:
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | |   (38)  all_74_19 = n0
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | | REDUCE: (31), (38) imply:
% 247.91/41.88  | | | | |   (39)  gt(n0, n0)
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | | PRED_UNIFY: (4), (39) imply:
% 247.91/41.88  | | | | |   (40)  $false
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | | CLOSE: (40) is inconsistent.
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | Case 2:
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | |   (41)   ~ (all_74_19 = n0)
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | | BETA: splitting (19) gives:
% 247.91/41.88  | | | | | 
% 247.91/41.88  | | | | | Case 1:
% 247.91/41.88  | | | | | | 
% 247.91/41.88  | | | | | |   (42)  all_74_18 = n0
% 247.91/41.88  | | | | | | 
% 247.91/41.88  | | | | | | REDUCE: (1), (42) imply:
% 247.91/41.89  | | | | | |   (43)  gt(n0, n0)
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | PRED_UNIFY: (4), (43) imply:
% 247.91/41.89  | | | | | |   (44)  $false
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | CLOSE: (44) is inconsistent.
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | Case 2:
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | |   (45)   ~ (all_74_18 = n0)
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 247.91/41.89  | | | | | |            (15), (16), (17), (18), (20), (22), (23), (25), (26),
% 247.91/41.89  | | | | | |            (29), (30), (34), (37), (41), (45) are inconsistent by
% 247.91/41.89  | | | | | |            sub-proof #6.
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | End of split
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | End of split
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | Case 2:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | |   (46)  all_74_19 = n5
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (20), (46) imply:
% 247.91/41.89  | | | |   (47)  a_select3(id_ds1_filter, all_74_18, n5) = all_74_16
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (8), (46) imply:
% 247.91/41.89  | | | |   (48)  a_select3(id_ds1_filter, n5, all_74_18) = all_74_17
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (6), (46) imply:
% 247.91/41.89  | | | |   (49)  leq(n5, n5)
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (25), (46) imply:
% 247.91/41.89  | | | |   (50)  leq(n0, n5)
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | BETA: splitting (19) gives:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | Case 1:
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | |   (51)  all_74_18 = n0
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | REDUCE: (1), (51) imply:
% 247.91/41.89  | | | | |   (52)  gt(n0, n0)
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | PRED_UNIFY: (4), (52) imply:
% 247.91/41.89  | | | | |   (53)  $false
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | CLOSE: (53) is inconsistent.
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | Case 2:
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | |   (54)   ~ (all_74_18 = n0)
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | REF_CLOSE: (3), (5), (7), (10), (11), (12), (13), (14), (15), (16),
% 247.91/41.89  | | | | |            (18), (22), (23), (24), (26), (29), (30), (34), (47), (48),
% 247.91/41.89  | | | | |            (49), (50), (54) are inconsistent by sub-proof #4.
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | End of split
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | End of split
% 247.91/41.89  | | | 
% 247.91/41.89  | | Case 2:
% 247.91/41.89  | | | 
% 247.91/41.89  | | |   (55)  all_74_18 = n5
% 247.91/41.89  | | | 
% 247.91/41.89  | | | REDUCE: (20), (55) imply:
% 247.91/41.89  | | |   (56)  a_select3(id_ds1_filter, n5, all_74_19) = all_74_16
% 247.91/41.89  | | | 
% 247.91/41.89  | | | REDUCE: (8), (55) imply:
% 247.91/41.89  | | |   (57)  a_select3(id_ds1_filter, all_74_19, n5) = all_74_17
% 247.91/41.89  | | | 
% 247.91/41.89  | | | REDUCE: (15), (55) imply:
% 247.91/41.89  | | |   (58)  leq(n5, n5)
% 247.91/41.89  | | | 
% 247.91/41.89  | | | REDUCE: (3), (55) imply:
% 247.91/41.89  | | |   (59)  leq(n0, n5)
% 247.91/41.89  | | | 
% 247.91/41.89  | | | BETA: splitting (21) gives:
% 247.91/41.89  | | | 
% 247.91/41.89  | | | Case 1:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | |   (60)  gt(n5, all_74_19)
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | GROUND_INST: instantiating (16) with all_74_19, n5, n4, simplifying with
% 247.91/41.89  | | | |              (9), (17), (24), (60) gives:
% 247.91/41.89  | | | |   (61)  leq(all_74_19, n4)
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | GROUND_INST: instantiating (26) with all_74_19, n4, simplifying with
% 247.91/41.89  | | | |              (17), (18), (61) gives:
% 247.91/41.89  | | | |   (62)  all_74_19 = n4 | gt(n4, all_74_19)
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | BETA: splitting (27) gives:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | Case 1:
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | |   (63)  all_74_19 = n0
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | REDUCE: (31), (63) imply:
% 247.91/41.89  | | | | |   (64)  gt(n0, n0)
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | PRED_UNIFY: (4), (64) imply:
% 247.91/41.89  | | | | |   (65)  $false
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | CLOSE: (65) is inconsistent.
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | Case 2:
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | |   (66)   ~ (all_74_19 = n0)
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | REF_CLOSE: (5), (6), (7), (10), (12), (13), (14), (16), (17), (18),
% 247.91/41.89  | | | | |            (22), (23), (24), (25), (26), (29), (30), (56), (57), (58),
% 247.91/41.89  | | | | |            (59), (62), (66) are inconsistent by sub-proof #3.
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | End of split
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | Case 2:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | |   (67)  all_74_19 = n5
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (57), (67) imply:
% 247.91/41.89  | | | |   (68)  a_select3(id_ds1_filter, n5, n5) = all_74_17
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (56), (67) imply:
% 247.91/41.89  | | | |   (69)  a_select3(id_ds1_filter, n5, n5) = all_74_16
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | GROUND_INST: instantiating (29) with all_74_17, all_74_16, n5, n5,
% 247.91/41.89  | | | |              id_ds1_filter, simplifying with (68), (69) gives:
% 247.91/41.89  | | | |   (70)  all_74_16 = all_74_17
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (30), (70) imply:
% 247.91/41.89  | | | |   (71)  $false
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | CLOSE: (71) is inconsistent.
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | End of split
% 247.91/41.89  | | | 
% 247.91/41.89  | | End of split
% 247.91/41.89  | | 
% 247.91/41.89  | Case 2:
% 247.91/41.89  | | 
% 247.91/41.89  | |   (72)  all_74_19 = n0
% 247.91/41.89  | |   (73)   ~ gt(all_74_19, n0)
% 247.91/41.89  | | 
% 247.91/41.89  | | REDUCE: (20), (72) imply:
% 247.91/41.89  | |   (74)  a_select3(id_ds1_filter, all_74_18, n0) = all_74_16
% 247.91/41.89  | | 
% 247.91/41.89  | | REDUCE: (8), (72) imply:
% 247.91/41.89  | |   (75)  a_select3(id_ds1_filter, n0, all_74_18) = all_74_17
% 247.91/41.89  | | 
% 247.91/41.89  | | REDUCE: (17), (72) imply:
% 247.91/41.89  | |   (76)  $i(n0)
% 247.91/41.89  | | 
% 247.91/41.89  | | REDUCE: (6), (72) imply:
% 247.91/41.89  | |   (77)  leq(n0, n5)
% 247.91/41.89  | | 
% 247.91/41.89  | | REDUCE: (25), (72) imply:
% 247.91/41.89  | |   (78)  leq(n0, n0)
% 247.91/41.89  | | 
% 247.91/41.89  | | BETA: splitting (28) gives:
% 247.91/41.89  | | 
% 247.91/41.89  | | Case 1:
% 247.91/41.89  | | | 
% 247.91/41.89  | | |   (79)  gt(n5, all_74_18)
% 247.91/41.89  | | | 
% 247.91/41.89  | | | GROUND_INST: instantiating (16) with all_74_18, n5, n4, simplifying with
% 247.91/41.89  | | |              (9), (11), (24), (79) gives:
% 247.91/41.89  | | |   (80)  leq(all_74_18, n4)
% 247.91/41.89  | | | 
% 247.91/41.89  | | | GROUND_INST: instantiating (26) with all_74_18, n4, simplifying with (11),
% 247.91/41.89  | | |              (18), (80) gives:
% 247.91/41.89  | | |   (81)  all_74_18 = n4 | gt(n4, all_74_18)
% 247.91/41.89  | | | 
% 247.91/41.89  | | | BETA: splitting (19) gives:
% 247.91/41.89  | | | 
% 247.91/41.89  | | | Case 1:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | |   (82)  all_74_18 = n0
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | REDUCE: (1), (82) imply:
% 247.91/41.89  | | | |   (83)  gt(n0, n0)
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | PRED_UNIFY: (4), (83) imply:
% 247.91/41.89  | | | |   (84)  $false
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | CLOSE: (84) is inconsistent.
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | Case 2:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | |   (85)   ~ (all_74_18 = n0)
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | BETA: splitting (81) gives:
% 247.91/41.89  | | | | 
% 247.91/41.89  | | | | Case 1:
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | |   (86)  gt(n4, all_74_18)
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | GROUND_INST: instantiating (16) with all_74_18, n4, n3, simplifying
% 247.91/41.89  | | | | |              with (11), (13), (18), (86) gives:
% 247.91/41.89  | | | | |   (87)  leq(all_74_18, n3)
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | GROUND_INST: instantiating (26) with all_74_18, n3, simplifying with
% 247.91/41.89  | | | | |              (10), (11), (87) gives:
% 247.91/41.89  | | | | |   (88)  all_74_18 = n3 | gt(n3, all_74_18)
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | BETA: splitting (88) gives:
% 247.91/41.89  | | | | | 
% 247.91/41.89  | | | | | Case 1:
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | |   (89)  gt(n3, all_74_18)
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | GROUND_INST: instantiating (16) with all_74_18, n3, n2, simplifying
% 247.91/41.89  | | | | | |              with (10), (11), (14), (89) gives:
% 247.91/41.89  | | | | | |   (90)  leq(all_74_18, n2)
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | GROUND_INST: instantiating (26) with all_74_18, n2, simplifying with
% 247.91/41.89  | | | | | |              (11), (23), (90) gives:
% 247.91/41.89  | | | | | |   (91)  all_74_18 = n2 | gt(n2, all_74_18)
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | BETA: splitting (91) gives:
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | Case 1:
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | |   (92)  gt(n2, all_74_18)
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | GROUND_INST: instantiating (16) with all_74_18, n2, n1,
% 247.91/41.89  | | | | | | |              simplifying with (11), (12), (23), (92) gives:
% 247.91/41.89  | | | | | | |   (93)  leq(all_74_18, n1)
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | GROUND_INST: instantiating (5) with all_74_18, simplifying with
% 247.91/41.89  | | | | | | |              (3), (11), (93) gives:
% 247.91/41.89  | | | | | | |   (94)  all_74_18 = n1 | all_74_18 = n0
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | BETA: splitting (94) gives:
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | Case 1:
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | |   (95)  all_74_18 = n0
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | REDUCE: (85), (95) imply:
% 247.91/41.89  | | | | | | | |   (96)  $false
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | CLOSE: (96) is inconsistent.
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | Case 2:
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | |   (97)  all_74_18 = n1
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | REDUCE: (74), (97) imply:
% 247.91/41.89  | | | | | | | |   (98)  a_select3(id_ds1_filter, n1, n0) = all_74_16
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | REDUCE: (75), (97) imply:
% 247.91/41.89  | | | | | | | |   (99)  a_select3(id_ds1_filter, n0, n1) = all_74_17
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | REDUCE: (11), (97) imply:
% 247.91/41.89  | | | | | | | |   (100)  $i(n1)
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | REDUCE: (15), (97) imply:
% 247.91/41.89  | | | | | | | |   (101)  leq(n1, n5)
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | REDUCE: (3), (97) imply:
% 247.91/41.89  | | | | | | | |   (102)  leq(n0, n1)
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | GROUND_INST: instantiating (22) with n0, n1, all_74_17,
% 247.91/41.89  | | | | | | | |              simplifying with (76), (78), (99), (100), (102)
% 247.91/41.89  | | | | | | | |              gives:
% 247.91/41.89  | | | | | | | |   (103)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.89  | | | | | | | |          (a_select3(id_ds1_filter, n1, n0) = all_74_17 &
% 247.91/41.89  | | | | | | | |            $i(all_74_17))
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | BETA: splitting (103) gives:
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | Case 1:
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | |   (104)   ~ leq(n0, all_74_21)
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | REDUCE: (7), (104) imply:
% 247.91/41.89  | | | | | | | | |   (105)   ~ leq(n0, n5)
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | PRED_UNIFY: (77), (105) imply:
% 247.91/41.89  | | | | | | | | |   (106)  $false
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | CLOSE: (106) is inconsistent.
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | Case 2:
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | |   (107)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n1,
% 247.91/41.89  | | | | | | | | |              n0) = all_74_17 & $i(all_74_17))
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | BETA: splitting (107) gives:
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | Case 1:
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | |   (108)   ~ leq(n1, all_74_21)
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | | REDUCE: (7), (108) imply:
% 247.91/41.89  | | | | | | | | | |   (109)   ~ leq(n1, n5)
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | | PRED_UNIFY: (101), (109) imply:
% 247.91/41.89  | | | | | | | | | |   (110)  $false
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | | CLOSE: (110) is inconsistent.
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | Case 2:
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | |   (111)  a_select3(id_ds1_filter, n1, n0) = all_74_17 &
% 247.91/41.89  | | | | | | | | | |          $i(all_74_17)
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | | ALPHA: (111) implies:
% 247.91/41.89  | | | | | | | | | |   (112)  a_select3(id_ds1_filter, n1, n0) = all_74_17
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | | GROUND_INST: instantiating (29) with all_74_17, all_74_16, n0,
% 247.91/41.89  | | | | | | | | | |              n1, id_ds1_filter, simplifying with (98), (112)
% 247.91/41.89  | | | | | | | | | |              gives:
% 247.91/41.89  | | | | | | | | | |   (113)  all_74_16 = all_74_17
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | | REDUCE: (30), (113) imply:
% 247.91/41.89  | | | | | | | | | |   (114)  $false
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | | CLOSE: (114) is inconsistent.
% 247.91/41.89  | | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | End of split
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | End of split
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | End of split
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | Case 2:
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | |   (115)  all_74_18 = n2
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | REDUCE: (74), (115) imply:
% 247.91/41.89  | | | | | | |   (116)  a_select3(id_ds1_filter, n2, n0) = all_74_16
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | REDUCE: (75), (115) imply:
% 247.91/41.89  | | | | | | |   (117)  a_select3(id_ds1_filter, n0, n2) = all_74_17
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | REDUCE: (15), (115) imply:
% 247.91/41.89  | | | | | | |   (118)  leq(n2, n5)
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | REDUCE: (3), (115) imply:
% 247.91/41.89  | | | | | | |   (119)  leq(n0, n2)
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | GROUND_INST: instantiating (22) with n0, n2, all_74_17,
% 247.91/41.89  | | | | | | |              simplifying with (23), (76), (78), (117), (119)
% 247.91/41.89  | | | | | | |              gives:
% 247.91/41.89  | | | | | | |   (120)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.89  | | | | | | |          (a_select3(id_ds1_filter, n2, n0) = all_74_17 &
% 247.91/41.89  | | | | | | |            $i(all_74_17))
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | BETA: splitting (120) gives:
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | | Case 1:
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | |   (121)   ~ leq(n0, all_74_21)
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | REDUCE: (7), (121) imply:
% 247.91/41.89  | | | | | | | |   (122)   ~ leq(n0, n5)
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | PRED_UNIFY: (77), (122) imply:
% 247.91/41.89  | | | | | | | |   (123)  $false
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | CLOSE: (123) is inconsistent.
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | Case 2:
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | |   (124)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n2,
% 247.91/41.89  | | | | | | | |              n0) = all_74_17 & $i(all_74_17))
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | BETA: splitting (124) gives:
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | | Case 1:
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | |   (125)   ~ leq(n2, all_74_21)
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | REDUCE: (7), (125) imply:
% 247.91/41.89  | | | | | | | | |   (126)   ~ leq(n2, n5)
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | PRED_UNIFY: (118), (126) imply:
% 247.91/41.89  | | | | | | | | |   (127)  $false
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | CLOSE: (127) is inconsistent.
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | Case 2:
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | |   (128)  a_select3(id_ds1_filter, n2, n0) = all_74_17 &
% 247.91/41.89  | | | | | | | | |          $i(all_74_17)
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | ALPHA: (128) implies:
% 247.91/41.89  | | | | | | | | |   (129)  a_select3(id_ds1_filter, n2, n0) = all_74_17
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | GROUND_INST: instantiating (29) with all_74_17, all_74_16, n0,
% 247.91/41.89  | | | | | | | | |              n2, id_ds1_filter, simplifying with (116), (129)
% 247.91/41.89  | | | | | | | | |              gives:
% 247.91/41.89  | | | | | | | | |   (130)  all_74_16 = all_74_17
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | REDUCE: (30), (130) imply:
% 247.91/41.89  | | | | | | | | |   (131)  $false
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | | CLOSE: (131) is inconsistent.
% 247.91/41.89  | | | | | | | | | 
% 247.91/41.89  | | | | | | | | End of split
% 247.91/41.89  | | | | | | | | 
% 247.91/41.89  | | | | | | | End of split
% 247.91/41.89  | | | | | | | 
% 247.91/41.89  | | | | | | End of split
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | Case 2:
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | |   (132)  all_74_18 = n3
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | REDUCE: (74), (132) imply:
% 247.91/41.89  | | | | | |   (133)  a_select3(id_ds1_filter, n3, n0) = all_74_16
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | REDUCE: (75), (132) imply:
% 247.91/41.89  | | | | | |   (134)  a_select3(id_ds1_filter, n0, n3) = all_74_17
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | REDUCE: (15), (132) imply:
% 247.91/41.89  | | | | | |   (135)  leq(n3, n5)
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | REDUCE: (3), (132) imply:
% 247.91/41.89  | | | | | |   (136)  leq(n0, n3)
% 247.91/41.89  | | | | | | 
% 247.91/41.89  | | | | | | GROUND_INST: instantiating (22) with n0, n3, all_74_17, simplifying
% 247.91/41.89  | | | | | |              with (10), (76), (78), (134), (136) gives:
% 247.91/41.90  | | | | | |   (137)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.90  | | | | | |          (a_select3(id_ds1_filter, n3, n0) = all_74_17 &
% 247.91/41.90  | | | | | |            $i(all_74_17))
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | BETA: splitting (137) gives:
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | Case 1:
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | |   (138)   ~ leq(n0, all_74_21)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | REDUCE: (7), (138) imply:
% 247.91/41.90  | | | | | | |   (139)   ~ leq(n0, n5)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | PRED_UNIFY: (77), (139) imply:
% 247.91/41.90  | | | | | | |   (140)  $false
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | CLOSE: (140) is inconsistent.
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | Case 2:
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | |   (141)   ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n3, n0)
% 247.91/41.90  | | | | | | |            = all_74_17 & $i(all_74_17))
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | BETA: splitting (141) gives:
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | Case 1:
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | |   (142)   ~ leq(n3, all_74_21)
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | | REDUCE: (7), (142) imply:
% 247.91/41.90  | | | | | | | |   (143)   ~ leq(n3, n5)
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | | PRED_UNIFY: (135), (143) imply:
% 247.91/41.90  | | | | | | | |   (144)  $false
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | | CLOSE: (144) is inconsistent.
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | Case 2:
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | |   (145)  a_select3(id_ds1_filter, n3, n0) = all_74_17 &
% 247.91/41.90  | | | | | | | |          $i(all_74_17)
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | | ALPHA: (145) implies:
% 247.91/41.90  | | | | | | | |   (146)  a_select3(id_ds1_filter, n3, n0) = all_74_17
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | | GROUND_INST: instantiating (29) with all_74_17, all_74_16, n0,
% 247.91/41.90  | | | | | | | |              n3, id_ds1_filter, simplifying with (133), (146)
% 247.91/41.90  | | | | | | | |              gives:
% 247.91/41.90  | | | | | | | |   (147)  all_74_16 = all_74_17
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | | REDUCE: (30), (147) imply:
% 247.91/41.90  | | | | | | | |   (148)  $false
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | | CLOSE: (148) is inconsistent.
% 247.91/41.90  | | | | | | | | 
% 247.91/41.90  | | | | | | | End of split
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | End of split
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | End of split
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | Case 2:
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | |   (149)  all_74_18 = n4
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (74), (149) imply:
% 247.91/41.90  | | | | |   (150)  a_select3(id_ds1_filter, n4, n0) = all_74_16
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (75), (149) imply:
% 247.91/41.90  | | | | |   (151)  a_select3(id_ds1_filter, n0, n4) = all_74_17
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (15), (149) imply:
% 247.91/41.90  | | | | |   (152)  leq(n4, n5)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (3), (149) imply:
% 247.91/41.90  | | | | |   (153)  leq(n0, n4)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | GROUND_INST: instantiating (22) with n0, n4, all_74_17, simplifying
% 247.91/41.90  | | | | |              with (18), (76), (78), (151), (153) gives:
% 247.91/41.90  | | | | |   (154)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.90  | | | | |          (a_select3(id_ds1_filter, n4, n0) = all_74_17 &
% 247.91/41.90  | | | | |            $i(all_74_17))
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | BETA: splitting (154) gives:
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | Case 1:
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | |   (155)   ~ leq(n0, all_74_21)
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | REDUCE: (7), (155) imply:
% 247.91/41.90  | | | | | |   (156)   ~ leq(n0, n5)
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | PRED_UNIFY: (77), (156) imply:
% 247.91/41.90  | | | | | |   (157)  $false
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | CLOSE: (157) is inconsistent.
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | Case 2:
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | |   (158)   ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter, n4, n0) =
% 247.91/41.90  | | | | | |            all_74_17 & $i(all_74_17))
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | BETA: splitting (158) gives:
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | Case 1:
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | |   (159)   ~ leq(n4, all_74_21)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | REDUCE: (7), (159) imply:
% 247.91/41.90  | | | | | | |   (160)   ~ leq(n4, n5)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | PRED_UNIFY: (152), (160) imply:
% 247.91/41.90  | | | | | | |   (161)  $false
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | CLOSE: (161) is inconsistent.
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | Case 2:
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | |   (162)  a_select3(id_ds1_filter, n4, n0) = all_74_17 &
% 247.91/41.90  | | | | | | |          $i(all_74_17)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | ALPHA: (162) implies:
% 247.91/41.90  | | | | | | |   (163)  a_select3(id_ds1_filter, n4, n0) = all_74_17
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | GROUND_INST: instantiating (29) with all_74_17, all_74_16, n0, n4,
% 247.91/41.90  | | | | | | |              id_ds1_filter, simplifying with (150), (163) gives:
% 247.91/41.90  | | | | | | |   (164)  all_74_16 = all_74_17
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | REDUCE: (30), (164) imply:
% 247.91/41.90  | | | | | | |   (165)  $false
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | CLOSE: (165) is inconsistent.
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | End of split
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | End of split
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | End of split
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | End of split
% 247.91/41.90  | | | 
% 247.91/41.90  | | Case 2:
% 247.91/41.90  | | | 
% 247.91/41.90  | | |   (166)  all_74_18 = n5
% 247.91/41.90  | | | 
% 247.91/41.90  | | | REDUCE: (74), (166) imply:
% 247.91/41.90  | | |   (167)  a_select3(id_ds1_filter, n5, n0) = all_74_16
% 247.91/41.90  | | | 
% 247.91/41.90  | | | REDUCE: (75), (166) imply:
% 247.91/41.90  | | |   (168)  a_select3(id_ds1_filter, n0, n5) = all_74_17
% 247.91/41.90  | | | 
% 247.91/41.90  | | | REDUCE: (15), (166) imply:
% 247.91/41.90  | | |   (169)  leq(n5, n5)
% 247.91/41.90  | | | 
% 247.91/41.90  | | | GROUND_INST: instantiating (22) with n0, n5, all_74_17, simplifying with
% 247.91/41.90  | | |              (24), (76), (77), (78), (168) gives:
% 247.91/41.90  | | |   (170)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 247.91/41.90  | | |          (a_select3(id_ds1_filter, n5, n0) = all_74_17 & $i(all_74_17))
% 247.91/41.90  | | | 
% 247.91/41.90  | | | BETA: splitting (170) gives:
% 247.91/41.90  | | | 
% 247.91/41.90  | | | Case 1:
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | |   (171)   ~ leq(n0, all_74_21)
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | REDUCE: (7), (171) imply:
% 247.91/41.90  | | | |   (172)   ~ leq(n0, n5)
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | PRED_UNIFY: (77), (172) imply:
% 247.91/41.90  | | | |   (173)  $false
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | CLOSE: (173) is inconsistent.
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | Case 2:
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | |   (174)   ~ leq(n5, all_74_21) | (a_select3(id_ds1_filter, n5, n0) =
% 247.91/41.90  | | | |            all_74_17 & $i(all_74_17))
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | BETA: splitting (174) gives:
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | Case 1:
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | |   (175)   ~ leq(n5, all_74_21)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (7), (175) imply:
% 247.91/41.90  | | | | |   (176)   ~ leq(n5, n5)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | PRED_UNIFY: (169), (176) imply:
% 247.91/41.90  | | | | |   (177)  $false
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | CLOSE: (177) is inconsistent.
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | Case 2:
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | |   (178)  a_select3(id_ds1_filter, n5, n0) = all_74_17 & $i(all_74_17)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | ALPHA: (178) implies:
% 247.91/41.90  | | | | |   (179)  a_select3(id_ds1_filter, n5, n0) = all_74_17
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REF_CLOSE: (29), (30), (167), (179) are inconsistent by sub-proof #2.
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | End of split
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | End of split
% 247.91/41.90  | | | 
% 247.91/41.90  | | End of split
% 247.91/41.90  | | 
% 247.91/41.90  | End of split
% 247.91/41.90  | 
% 247.91/41.90  End of proof
% 247.91/41.90  
% 247.91/41.90  Sub-proof #2 shows that the following formulas are inconsistent:
% 247.91/41.90  ----------------------------------------------------------------
% 247.91/41.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 247.91/41.90           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 247.91/41.90             v0))
% 247.91/41.90    (2)  a_select3(id_ds1_filter, n5, n0) = all_74_16
% 247.91/41.90    (3)  a_select3(id_ds1_filter, n5, n0) = all_74_17
% 247.91/41.90    (4)   ~ (all_74_16 = all_74_17)
% 247.91/41.90  
% 247.91/41.90  Begin of proof
% 247.91/41.90  | 
% 247.91/41.90  | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n0, n5,
% 247.91/41.90  |              id_ds1_filter, simplifying with (2), (3) gives:
% 247.91/41.90  |   (5)  all_74_16 = all_74_17
% 247.91/41.90  | 
% 247.91/41.90  | REDUCE: (4), (5) imply:
% 247.91/41.90  |   (6)  $false
% 247.91/41.90  | 
% 247.91/41.90  | CLOSE: (6) is inconsistent.
% 247.91/41.90  | 
% 247.91/41.90  End of proof
% 247.91/41.90  
% 247.91/41.90  Sub-proof #3 shows that the following formulas are inconsistent:
% 247.91/41.90  ----------------------------------------------------------------
% 247.91/41.90    (1)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 247.91/41.90           leq(n0, v0))
% 247.91/41.90    (2)  a_select3(id_ds1_filter, n5, all_74_19) = all_74_16
% 247.91/41.90    (3)  leq(n0, n5)
% 247.91/41.90    (4)  leq(all_74_19, n5)
% 247.91/41.90    (5)  all_74_21 = n5
% 247.91/41.90    (6)  $i(n3)
% 247.91/41.90    (7)  a_select3(id_ds1_filter, all_74_19, n5) = all_74_17
% 247.91/41.90    (8)  all_74_19 = n4 | gt(n4, all_74_19)
% 247.91/41.90    (9)  pred(n2) = n1
% 247.91/41.90    (10)  pred(n4) = n3
% 247.91/41.90    (11)  pred(n3) = n2
% 247.91/41.90    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 247.91/41.90            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 247.91/41.90    (13)  $i(all_74_19)
% 247.91/41.90    (14)  $i(n4)
% 247.91/41.90    (15)  leq(n5, n5)
% 247.91/41.90    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 247.91/41.90                v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_21) |  ~
% 247.91/41.90            leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 247.91/41.90            (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 247.91/41.90    (17)  $i(n2)
% 247.91/41.90    (18)  $i(n5)
% 247.91/41.90    (19)   ~ (all_74_19 = n0)
% 247.91/41.90    (20)  leq(n0, all_74_19)
% 247.91/41.90    (21)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 247.91/41.90            leq(v0, v1) | gt(v1, v0))
% 247.91/41.90    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 247.91/41.90          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 247.91/41.90              v0))
% 247.91/41.90    (23)   ~ (all_74_16 = all_74_17)
% 247.91/41.90  
% 247.91/41.90  Begin of proof
% 247.91/41.90  | 
% 247.91/41.90  | BETA: splitting (8) gives:
% 247.91/41.90  | 
% 247.91/41.90  | Case 1:
% 247.91/41.90  | | 
% 247.91/41.90  | |   (24)  gt(n4, all_74_19)
% 247.91/41.90  | | 
% 247.91/41.90  | | GROUND_INST: instantiating (12) with all_74_19, n4, n3, simplifying with
% 247.91/41.90  | |              (10), (13), (14), (24) gives:
% 247.91/41.90  | |   (25)  leq(all_74_19, n3)
% 247.91/41.90  | | 
% 247.91/41.90  | | GROUND_INST: instantiating (21) with all_74_19, n3, simplifying with (6),
% 247.91/41.90  | |              (13), (25) gives:
% 247.91/41.90  | |   (26)  all_74_19 = n3 | gt(n3, all_74_19)
% 247.91/41.90  | | 
% 247.91/41.90  | | BETA: splitting (26) gives:
% 247.91/41.90  | | 
% 247.91/41.90  | | Case 1:
% 247.91/41.90  | | | 
% 247.91/41.90  | | |   (27)  gt(n3, all_74_19)
% 247.91/41.90  | | | 
% 247.91/41.90  | | | GROUND_INST: instantiating (12) with all_74_19, n3, n2, simplifying with
% 247.91/41.90  | | |              (6), (11), (13), (27) gives:
% 247.91/41.90  | | |   (28)  leq(all_74_19, n2)
% 247.91/41.90  | | | 
% 247.91/41.90  | | | GROUND_INST: instantiating (21) with all_74_19, n2, simplifying with (13),
% 247.91/41.90  | | |              (17), (28) gives:
% 247.91/41.90  | | |   (29)  all_74_19 = n2 | gt(n2, all_74_19)
% 247.91/41.90  | | | 
% 247.91/41.90  | | | BETA: splitting (29) gives:
% 247.91/41.90  | | | 
% 247.91/41.90  | | | Case 1:
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | |   (30)  gt(n2, all_74_19)
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | GROUND_INST: instantiating (12) with all_74_19, n2, n1, simplifying with
% 247.91/41.90  | | | |              (9), (13), (17), (30) gives:
% 247.91/41.90  | | | |   (31)  leq(all_74_19, n1)
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | GROUND_INST: instantiating (1) with all_74_19, simplifying with (13),
% 247.91/41.90  | | | |              (20), (31) gives:
% 247.91/41.90  | | | |   (32)  all_74_19 = n1 | all_74_19 = n0
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | BETA: splitting (32) gives:
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | | Case 1:
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | |   (33)  all_74_19 = n0
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (19), (33) imply:
% 247.91/41.90  | | | | |   (34)  $false
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | CLOSE: (34) is inconsistent.
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | Case 2:
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | |   (35)  all_74_19 = n1
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (7), (35) imply:
% 247.91/41.90  | | | | |   (36)  a_select3(id_ds1_filter, n1, n5) = all_74_17
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (2), (35) imply:
% 247.91/41.90  | | | | |   (37)  a_select3(id_ds1_filter, n5, n1) = all_74_16
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (13), (35) imply:
% 247.91/41.90  | | | | |   (38)  $i(n1)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (4), (35) imply:
% 247.91/41.90  | | | | |   (39)  leq(n1, n5)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | REDUCE: (20), (35) imply:
% 247.91/41.90  | | | | |   (40)  leq(n0, n1)
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | GROUND_INST: instantiating (16) with n1, n5, all_74_17, simplifying
% 247.91/41.90  | | | | |              with (3), (18), (36), (38), (40) gives:
% 247.91/41.90  | | | | |   (41)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.91/41.90  | | | | |         (a_select3(id_ds1_filter, n5, n1) = all_74_17 & $i(all_74_17))
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | BETA: splitting (41) gives:
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | | Case 1:
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | |   (42)   ~ leq(n5, all_74_21)
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | REDUCE: (5), (42) imply:
% 247.91/41.90  | | | | | |   (43)   ~ leq(n5, n5)
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | PRED_UNIFY: (15), (43) imply:
% 247.91/41.90  | | | | | |   (44)  $false
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | CLOSE: (44) is inconsistent.
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | Case 2:
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n5, n1) =
% 247.91/41.90  | | | | | |           all_74_17 & $i(all_74_17))
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | BETA: splitting (45) gives:
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | | Case 1:
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | REDUCE: (5), (46) imply:
% 247.91/41.90  | | | | | | |   (47)   ~ leq(n1, n5)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 247.91/41.90  | | | | | | |   (48)  $false
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | CLOSE: (48) is inconsistent.
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | Case 2:
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | |   (49)  a_select3(id_ds1_filter, n5, n1) = all_74_17 &
% 247.91/41.90  | | | | | | |         $i(all_74_17)
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | ALPHA: (49) implies:
% 247.91/41.90  | | | | | | |   (50)  a_select3(id_ds1_filter, n5, n1) = all_74_17
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | GROUND_INST: instantiating (22) with all_74_17, all_74_16, n1, n5,
% 247.91/41.90  | | | | | | |              id_ds1_filter, simplifying with (37), (50) gives:
% 247.91/41.90  | | | | | | |   (51)  all_74_16 = all_74_17
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | REDUCE: (23), (51) imply:
% 247.91/41.90  | | | | | | |   (52)  $false
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | | CLOSE: (52) is inconsistent.
% 247.91/41.90  | | | | | | | 
% 247.91/41.90  | | | | | | End of split
% 247.91/41.90  | | | | | | 
% 247.91/41.90  | | | | | End of split
% 247.91/41.90  | | | | | 
% 247.91/41.90  | | | | End of split
% 247.91/41.90  | | | | 
% 247.91/41.90  | | | Case 2:
% 247.91/41.90  | | | | 
% 247.91/41.91  | | | |   (53)  all_74_19 = n2
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REDUCE: (7), (53) imply:
% 247.91/41.91  | | | |   (54)  a_select3(id_ds1_filter, n2, n5) = all_74_17
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REDUCE: (2), (53) imply:
% 247.91/41.91  | | | |   (55)  a_select3(id_ds1_filter, n5, n2) = all_74_16
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REDUCE: (4), (53) imply:
% 247.91/41.91  | | | |   (56)  leq(n2, n5)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REDUCE: (20), (53) imply:
% 247.91/41.91  | | | |   (57)  leq(n0, n2)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | GROUND_INST: instantiating (16) with n2, n5, all_74_17, simplifying with
% 247.91/41.91  | | | |              (3), (17), (18), (54), (57) gives:
% 247.91/41.91  | | | |   (58)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.91/41.91  | | | |         (a_select3(id_ds1_filter, n5, n2) = all_74_17 & $i(all_74_17))
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | BETA: splitting (58) gives:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | Case 1:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | |   (59)   ~ leq(n5, all_74_21)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (5), (59) imply:
% 247.91/41.91  | | | | |   (60)   ~ leq(n5, n5)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | PRED_UNIFY: (15), (60) imply:
% 247.91/41.91  | | | | |   (61)  $false
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | CLOSE: (61) is inconsistent.
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | Case 2:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | |   (62)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n5, n2) =
% 247.91/41.91  | | | | |           all_74_17 & $i(all_74_17))
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | BETA: splitting (62) gives:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | Case 1:
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | |   (63)   ~ leq(n2, all_74_21)
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | REDUCE: (5), (63) imply:
% 247.91/41.91  | | | | | |   (64)   ~ leq(n2, n5)
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | PRED_UNIFY: (56), (64) imply:
% 247.91/41.91  | | | | | |   (65)  $false
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | CLOSE: (65) is inconsistent.
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | Case 2:
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | |   (66)  a_select3(id_ds1_filter, n5, n2) = all_74_17 & $i(all_74_17)
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | ALPHA: (66) implies:
% 247.91/41.91  | | | | | |   (67)  a_select3(id_ds1_filter, n5, n2) = all_74_17
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | GROUND_INST: instantiating (22) with all_74_17, all_74_16, n2, n5,
% 247.91/41.91  | | | | | |              id_ds1_filter, simplifying with (55), (67) gives:
% 247.91/41.91  | | | | | |   (68)  all_74_16 = all_74_17
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | REDUCE: (23), (68) imply:
% 247.91/41.91  | | | | | |   (69)  $false
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | CLOSE: (69) is inconsistent.
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | End of split
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | End of split
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | End of split
% 247.91/41.91  | | | 
% 247.91/41.91  | | Case 2:
% 247.91/41.91  | | | 
% 247.91/41.91  | | |   (70)  all_74_19 = n3
% 247.91/41.91  | | | 
% 247.91/41.91  | | | REDUCE: (7), (70) imply:
% 247.91/41.91  | | |   (71)  a_select3(id_ds1_filter, n3, n5) = all_74_17
% 247.91/41.91  | | | 
% 247.91/41.91  | | | REDUCE: (2), (70) imply:
% 247.91/41.91  | | |   (72)  a_select3(id_ds1_filter, n5, n3) = all_74_16
% 247.91/41.91  | | | 
% 247.91/41.91  | | | REDUCE: (4), (70) imply:
% 247.91/41.91  | | |   (73)  leq(n3, n5)
% 247.91/41.91  | | | 
% 247.91/41.91  | | | REDUCE: (20), (70) imply:
% 247.91/41.91  | | |   (74)  leq(n0, n3)
% 247.91/41.91  | | | 
% 247.91/41.91  | | | GROUND_INST: instantiating (16) with n3, n5, all_74_17, simplifying with
% 247.91/41.91  | | |              (3), (6), (18), (71), (74) gives:
% 247.91/41.91  | | |   (75)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 247.91/41.91  | | |         (a_select3(id_ds1_filter, n5, n3) = all_74_17 & $i(all_74_17))
% 247.91/41.91  | | | 
% 247.91/41.91  | | | BETA: splitting (75) gives:
% 247.91/41.91  | | | 
% 247.91/41.91  | | | Case 1:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | |   (76)   ~ leq(n5, all_74_21)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REDUCE: (5), (76) imply:
% 247.91/41.91  | | | |   (77)   ~ leq(n5, n5)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | PRED_UNIFY: (15), (77) imply:
% 247.91/41.91  | | | |   (78)  $false
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | CLOSE: (78) is inconsistent.
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | Case 2:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | |   (79)   ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n5, n3) =
% 247.91/41.91  | | | |           all_74_17 & $i(all_74_17))
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | BETA: splitting (79) gives:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | Case 1:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | |   (80)   ~ leq(n3, all_74_21)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (5), (80) imply:
% 247.91/41.91  | | | | |   (81)   ~ leq(n3, n5)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | PRED_UNIFY: (73), (81) imply:
% 247.91/41.91  | | | | |   (82)  $false
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | CLOSE: (82) is inconsistent.
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | Case 2:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | |   (83)  a_select3(id_ds1_filter, n5, n3) = all_74_17 & $i(all_74_17)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | ALPHA: (83) implies:
% 247.91/41.91  | | | | |   (84)  a_select3(id_ds1_filter, n5, n3) = all_74_17
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | GROUND_INST: instantiating (22) with all_74_17, all_74_16, n3, n5,
% 247.91/41.91  | | | | |              id_ds1_filter, simplifying with (72), (84) gives:
% 247.91/41.91  | | | | |   (85)  all_74_16 = all_74_17
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (23), (85) imply:
% 247.91/41.91  | | | | |   (86)  $false
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | CLOSE: (86) is inconsistent.
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | End of split
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | End of split
% 247.91/41.91  | | | 
% 247.91/41.91  | | End of split
% 247.91/41.91  | | 
% 247.91/41.91  | Case 2:
% 247.91/41.91  | | 
% 247.91/41.91  | |   (87)  all_74_19 = n4
% 247.91/41.91  | | 
% 247.91/41.91  | | REDUCE: (7), (87) imply:
% 247.91/41.91  | |   (88)  a_select3(id_ds1_filter, n4, n5) = all_74_17
% 247.91/41.91  | | 
% 247.91/41.91  | | REDUCE: (2), (87) imply:
% 247.91/41.91  | |   (89)  a_select3(id_ds1_filter, n5, n4) = all_74_16
% 247.91/41.91  | | 
% 247.91/41.91  | | REDUCE: (4), (87) imply:
% 247.91/41.91  | |   (90)  leq(n4, n5)
% 247.91/41.91  | | 
% 247.91/41.91  | | REDUCE: (20), (87) imply:
% 247.91/41.91  | |   (91)  leq(n0, n4)
% 247.91/41.91  | | 
% 247.91/41.91  | | GROUND_INST: instantiating (16) with n4, n5, all_74_17, simplifying with
% 247.91/41.91  | |              (3), (14), (18), (88), (91) gives:
% 247.91/41.91  | |   (92)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 247.91/41.91  | |         (a_select3(id_ds1_filter, n5, n4) = all_74_17 & $i(all_74_17))
% 247.91/41.91  | | 
% 247.91/41.91  | | BETA: splitting (92) gives:
% 247.91/41.91  | | 
% 247.91/41.91  | | Case 1:
% 247.91/41.91  | | | 
% 247.91/41.91  | | |   (93)   ~ leq(n5, all_74_21)
% 247.91/41.91  | | | 
% 247.91/41.91  | | | REDUCE: (5), (93) imply:
% 247.91/41.91  | | |   (94)   ~ leq(n5, n5)
% 247.91/41.91  | | | 
% 247.91/41.91  | | | PRED_UNIFY: (15), (94) imply:
% 247.91/41.91  | | |   (95)  $false
% 247.91/41.91  | | | 
% 247.91/41.91  | | | CLOSE: (95) is inconsistent.
% 247.91/41.91  | | | 
% 247.91/41.91  | | Case 2:
% 247.91/41.91  | | | 
% 247.91/41.91  | | |   (96)   ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter, n5, n4) =
% 247.91/41.91  | | |           all_74_17 & $i(all_74_17))
% 247.91/41.91  | | | 
% 247.91/41.91  | | | BETA: splitting (96) gives:
% 247.91/41.91  | | | 
% 247.91/41.91  | | | Case 1:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | |   (97)   ~ leq(n4, all_74_21)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REDUCE: (5), (97) imply:
% 247.91/41.91  | | | |   (98)   ~ leq(n4, n5)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | PRED_UNIFY: (90), (98) imply:
% 247.91/41.91  | | | |   (99)  $false
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | CLOSE: (99) is inconsistent.
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | Case 2:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | |   (100)  a_select3(id_ds1_filter, n5, n4) = all_74_17 & $i(all_74_17)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | ALPHA: (100) implies:
% 247.91/41.91  | | | |   (101)  a_select3(id_ds1_filter, n5, n4) = all_74_17
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REF_CLOSE: (22), (23), (89), (101) are inconsistent by sub-proof #5.
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | End of split
% 247.91/41.91  | | | 
% 247.91/41.91  | | End of split
% 247.91/41.91  | | 
% 247.91/41.91  | End of split
% 247.91/41.91  | 
% 247.91/41.91  End of proof
% 247.91/41.91  
% 247.91/41.91  Sub-proof #4 shows that the following formulas are inconsistent:
% 247.91/41.91  ----------------------------------------------------------------
% 247.91/41.91    (1)  leq(n0, all_74_18)
% 247.91/41.91    (2)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 247.91/41.91           leq(n0, v0))
% 247.91/41.91    (3)  leq(n0, n5)
% 247.91/41.91    (4)  all_74_21 = n5
% 247.91/41.91    (5)  a_select3(id_ds1_filter, n5, all_74_18) = all_74_17
% 247.91/41.91    (6)  $i(n3)
% 247.91/41.91    (7)  $i(all_74_18)
% 247.91/41.91    (8)   ~ (all_74_18 = n0)
% 247.91/41.91    (9)  pred(n2) = n1
% 247.91/41.91    (10)  pred(n4) = n3
% 247.91/41.91    (11)  pred(n3) = n2
% 247.91/41.91    (12)  leq(all_74_18, n5)
% 247.91/41.91    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 247.91/41.91            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 247.91/41.91    (14)  $i(n4)
% 247.91/41.91    (15)  leq(n5, n5)
% 247.91/41.91    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 247.91/41.91                v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_21) |  ~
% 247.91/41.91            leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 247.91/41.91            (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 247.91/41.91    (17)  $i(n2)
% 247.91/41.91    (18)  $i(n5)
% 247.91/41.91    (19)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 247.91/41.91            leq(v0, v1) | gt(v1, v0))
% 247.91/41.91    (20)  a_select3(id_ds1_filter, all_74_18, n5) = all_74_16
% 247.91/41.91    (21)  all_74_18 = n4 | gt(n4, all_74_18)
% 247.91/41.91    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 247.91/41.91          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 247.91/41.91              v0))
% 247.91/41.91    (23)   ~ (all_74_16 = all_74_17)
% 247.91/41.91  
% 247.91/41.91  Begin of proof
% 247.91/41.91  | 
% 247.91/41.91  | BETA: splitting (21) gives:
% 247.91/41.91  | 
% 247.91/41.91  | Case 1:
% 247.91/41.91  | | 
% 247.91/41.91  | |   (24)  gt(n4, all_74_18)
% 247.91/41.91  | | 
% 247.91/41.91  | | GROUND_INST: instantiating (13) with all_74_18, n4, n3, simplifying with
% 247.91/41.91  | |              (7), (10), (14), (24) gives:
% 247.91/41.91  | |   (25)  leq(all_74_18, n3)
% 247.91/41.91  | | 
% 247.91/41.91  | | GROUND_INST: instantiating (19) with all_74_18, n3, simplifying with (6),
% 247.91/41.91  | |              (7), (25) gives:
% 247.91/41.91  | |   (26)  all_74_18 = n3 | gt(n3, all_74_18)
% 247.91/41.91  | | 
% 247.91/41.91  | | BETA: splitting (26) gives:
% 247.91/41.91  | | 
% 247.91/41.91  | | Case 1:
% 247.91/41.91  | | | 
% 247.91/41.91  | | |   (27)  gt(n3, all_74_18)
% 247.91/41.91  | | | 
% 247.91/41.91  | | | GROUND_INST: instantiating (13) with all_74_18, n3, n2, simplifying with
% 247.91/41.91  | | |              (6), (7), (11), (27) gives:
% 247.91/41.91  | | |   (28)  leq(all_74_18, n2)
% 247.91/41.91  | | | 
% 247.91/41.91  | | | GROUND_INST: instantiating (19) with all_74_18, n2, simplifying with (7),
% 247.91/41.91  | | |              (17), (28) gives:
% 247.91/41.91  | | |   (29)  all_74_18 = n2 | gt(n2, all_74_18)
% 247.91/41.91  | | | 
% 247.91/41.91  | | | BETA: splitting (29) gives:
% 247.91/41.91  | | | 
% 247.91/41.91  | | | Case 1:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | |   (30)  gt(n2, all_74_18)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | GROUND_INST: instantiating (13) with all_74_18, n2, n1, simplifying with
% 247.91/41.91  | | | |              (7), (9), (17), (30) gives:
% 247.91/41.91  | | | |   (31)  leq(all_74_18, n1)
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | GROUND_INST: instantiating (2) with all_74_18, simplifying with (1),
% 247.91/41.91  | | | |              (7), (31) gives:
% 247.91/41.91  | | | |   (32)  all_74_18 = n1 | all_74_18 = n0
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | BETA: splitting (32) gives:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | Case 1:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | |   (33)  all_74_18 = n0
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (8), (33) imply:
% 247.91/41.91  | | | | |   (34)  $false
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | CLOSE: (34) is inconsistent.
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | Case 2:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | |   (35)  all_74_18 = n1
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (20), (35) imply:
% 247.91/41.91  | | | | |   (36)  a_select3(id_ds1_filter, n1, n5) = all_74_16
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (5), (35) imply:
% 247.91/41.91  | | | | |   (37)  a_select3(id_ds1_filter, n5, n1) = all_74_17
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (7), (35) imply:
% 247.91/41.91  | | | | |   (38)  $i(n1)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (12), (35) imply:
% 247.91/41.91  | | | | |   (39)  leq(n1, n5)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | REDUCE: (1), (35) imply:
% 247.91/41.91  | | | | |   (40)  leq(n0, n1)
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | GROUND_INST: instantiating (16) with n1, n5, all_74_16, simplifying
% 247.91/41.91  | | | | |              with (3), (18), (36), (38), (40) gives:
% 247.91/41.91  | | | | |   (41)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.91/41.91  | | | | |         (a_select3(id_ds1_filter, n5, n1) = all_74_16 & $i(all_74_16))
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | BETA: splitting (41) gives:
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | | Case 1:
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | |   (42)   ~ leq(n5, all_74_21)
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | REDUCE: (4), (42) imply:
% 247.91/41.91  | | | | | |   (43)   ~ leq(n5, n5)
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | PRED_UNIFY: (15), (43) imply:
% 247.91/41.91  | | | | | |   (44)  $false
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | CLOSE: (44) is inconsistent.
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | Case 2:
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n5, n1) =
% 247.91/41.91  | | | | | |           all_74_16 & $i(all_74_16))
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | BETA: splitting (45) gives:
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | | Case 1:
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | | REDUCE: (4), (46) imply:
% 247.91/41.91  | | | | | | |   (47)   ~ leq(n1, n5)
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 247.91/41.91  | | | | | | |   (48)  $false
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | | CLOSE: (48) is inconsistent.
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | Case 2:
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | |   (49)  a_select3(id_ds1_filter, n5, n1) = all_74_16 &
% 247.91/41.91  | | | | | | |         $i(all_74_16)
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | | ALPHA: (49) implies:
% 247.91/41.91  | | | | | | |   (50)  a_select3(id_ds1_filter, n5, n1) = all_74_16
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | | GROUND_INST: instantiating (22) with all_74_17, all_74_16, n1, n5,
% 247.91/41.91  | | | | | | |              id_ds1_filter, simplifying with (37), (50) gives:
% 247.91/41.91  | | | | | | |   (51)  all_74_16 = all_74_17
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | | REDUCE: (23), (51) imply:
% 247.91/41.91  | | | | | | |   (52)  $false
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | | CLOSE: (52) is inconsistent.
% 247.91/41.91  | | | | | | | 
% 247.91/41.91  | | | | | | End of split
% 247.91/41.91  | | | | | | 
% 247.91/41.91  | | | | | End of split
% 247.91/41.91  | | | | | 
% 247.91/41.91  | | | | End of split
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | Case 2:
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | |   (53)  all_74_18 = n2
% 247.91/41.91  | | | | 
% 247.91/41.91  | | | | REDUCE: (20), (53) imply:
% 247.91/41.91  | | | |   (54)  a_select3(id_ds1_filter, n2, n5) = all_74_16
% 247.91/41.91  | | | | 
% 247.91/41.92  | | | | REDUCE: (5), (53) imply:
% 247.91/41.92  | | | |   (55)  a_select3(id_ds1_filter, n5, n2) = all_74_17
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | REDUCE: (12), (53) imply:
% 247.91/41.92  | | | |   (56)  leq(n2, n5)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | REDUCE: (1), (53) imply:
% 247.91/41.92  | | | |   (57)  leq(n0, n2)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | GROUND_INST: instantiating (16) with n2, n5, all_74_16, simplifying with
% 247.91/41.92  | | | |              (3), (17), (18), (54), (57) gives:
% 247.91/41.92  | | | |   (58)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.91/41.92  | | | |         (a_select3(id_ds1_filter, n5, n2) = all_74_16 & $i(all_74_16))
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | BETA: splitting (58) gives:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | Case 1:
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | |   (59)   ~ leq(n5, all_74_21)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | REDUCE: (4), (59) imply:
% 247.91/41.92  | | | | |   (60)   ~ leq(n5, n5)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | PRED_UNIFY: (15), (60) imply:
% 247.91/41.92  | | | | |   (61)  $false
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | CLOSE: (61) is inconsistent.
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | Case 2:
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | |   (62)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n5, n2) =
% 247.91/41.92  | | | | |           all_74_16 & $i(all_74_16))
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | BETA: splitting (62) gives:
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | Case 1:
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | |   (63)   ~ leq(n2, all_74_21)
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | REDUCE: (4), (63) imply:
% 247.91/41.92  | | | | | |   (64)   ~ leq(n2, n5)
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | PRED_UNIFY: (56), (64) imply:
% 247.91/41.92  | | | | | |   (65)  $false
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | CLOSE: (65) is inconsistent.
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | Case 2:
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | |   (66)  a_select3(id_ds1_filter, n5, n2) = all_74_16 & $i(all_74_16)
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | ALPHA: (66) implies:
% 247.91/41.92  | | | | | |   (67)  a_select3(id_ds1_filter, n5, n2) = all_74_16
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | GROUND_INST: instantiating (22) with all_74_17, all_74_16, n2, n5,
% 247.91/41.92  | | | | | |              id_ds1_filter, simplifying with (55), (67) gives:
% 247.91/41.92  | | | | | |   (68)  all_74_16 = all_74_17
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | REDUCE: (23), (68) imply:
% 247.91/41.92  | | | | | |   (69)  $false
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | CLOSE: (69) is inconsistent.
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | End of split
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | End of split
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | End of split
% 247.91/41.92  | | | 
% 247.91/41.92  | | Case 2:
% 247.91/41.92  | | | 
% 247.91/41.92  | | |   (70)  all_74_18 = n3
% 247.91/41.92  | | | 
% 247.91/41.92  | | | REDUCE: (20), (70) imply:
% 247.91/41.92  | | |   (71)  a_select3(id_ds1_filter, n3, n5) = all_74_16
% 247.91/41.92  | | | 
% 247.91/41.92  | | | REDUCE: (5), (70) imply:
% 247.91/41.92  | | |   (72)  a_select3(id_ds1_filter, n5, n3) = all_74_17
% 247.91/41.92  | | | 
% 247.91/41.92  | | | REDUCE: (12), (70) imply:
% 247.91/41.92  | | |   (73)  leq(n3, n5)
% 247.91/41.92  | | | 
% 247.91/41.92  | | | REDUCE: (1), (70) imply:
% 247.91/41.92  | | |   (74)  leq(n0, n3)
% 247.91/41.92  | | | 
% 247.91/41.92  | | | GROUND_INST: instantiating (16) with n3, n5, all_74_16, simplifying with
% 247.91/41.92  | | |              (3), (6), (18), (71), (74) gives:
% 247.91/41.92  | | |   (75)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 247.91/41.92  | | |         (a_select3(id_ds1_filter, n5, n3) = all_74_16 & $i(all_74_16))
% 247.91/41.92  | | | 
% 247.91/41.92  | | | BETA: splitting (75) gives:
% 247.91/41.92  | | | 
% 247.91/41.92  | | | Case 1:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | |   (76)   ~ leq(n5, all_74_21)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | REDUCE: (4), (76) imply:
% 247.91/41.92  | | | |   (77)   ~ leq(n5, n5)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | PRED_UNIFY: (15), (77) imply:
% 247.91/41.92  | | | |   (78)  $false
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | CLOSE: (78) is inconsistent.
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | Case 2:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | |   (79)   ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n5, n3) =
% 247.91/41.92  | | | |           all_74_16 & $i(all_74_16))
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | BETA: splitting (79) gives:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | Case 1:
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | |   (80)   ~ leq(n3, all_74_21)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | REDUCE: (4), (80) imply:
% 247.91/41.92  | | | | |   (81)   ~ leq(n3, n5)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | PRED_UNIFY: (73), (81) imply:
% 247.91/41.92  | | | | |   (82)  $false
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | CLOSE: (82) is inconsistent.
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | Case 2:
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | |   (83)  a_select3(id_ds1_filter, n5, n3) = all_74_16 & $i(all_74_16)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | ALPHA: (83) implies:
% 247.91/41.92  | | | | |   (84)  a_select3(id_ds1_filter, n5, n3) = all_74_16
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | GROUND_INST: instantiating (22) with all_74_17, all_74_16, n3, n5,
% 247.91/41.92  | | | | |              id_ds1_filter, simplifying with (72), (84) gives:
% 247.91/41.92  | | | | |   (85)  all_74_16 = all_74_17
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | REDUCE: (23), (85) imply:
% 247.91/41.92  | | | | |   (86)  $false
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | CLOSE: (86) is inconsistent.
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | End of split
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | End of split
% 247.91/41.92  | | | 
% 247.91/41.92  | | End of split
% 247.91/41.92  | | 
% 247.91/41.92  | Case 2:
% 247.91/41.92  | | 
% 247.91/41.92  | |   (87)  all_74_18 = n4
% 247.91/41.92  | | 
% 247.91/41.92  | | REDUCE: (20), (87) imply:
% 247.91/41.92  | |   (88)  a_select3(id_ds1_filter, n4, n5) = all_74_16
% 247.91/41.92  | | 
% 247.91/41.92  | | REDUCE: (5), (87) imply:
% 247.91/41.92  | |   (89)  a_select3(id_ds1_filter, n5, n4) = all_74_17
% 247.91/41.92  | | 
% 247.91/41.92  | | REDUCE: (12), (87) imply:
% 247.91/41.92  | |   (90)  leq(n4, n5)
% 247.91/41.92  | | 
% 247.91/41.92  | | REDUCE: (1), (87) imply:
% 247.91/41.92  | |   (91)  leq(n0, n4)
% 247.91/41.92  | | 
% 247.91/41.92  | | GROUND_INST: instantiating (16) with n4, n5, all_74_16, simplifying with
% 247.91/41.92  | |              (3), (14), (18), (88), (91) gives:
% 247.91/41.92  | |   (92)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 247.91/41.92  | |         (a_select3(id_ds1_filter, n5, n4) = all_74_16 & $i(all_74_16))
% 247.91/41.92  | | 
% 247.91/41.92  | | BETA: splitting (92) gives:
% 247.91/41.92  | | 
% 247.91/41.92  | | Case 1:
% 247.91/41.92  | | | 
% 247.91/41.92  | | |   (93)   ~ leq(n5, all_74_21)
% 247.91/41.92  | | | 
% 247.91/41.92  | | | REDUCE: (4), (93) imply:
% 247.91/41.92  | | |   (94)   ~ leq(n5, n5)
% 247.91/41.92  | | | 
% 247.91/41.92  | | | PRED_UNIFY: (15), (94) imply:
% 247.91/41.92  | | |   (95)  $false
% 247.91/41.92  | | | 
% 247.91/41.92  | | | CLOSE: (95) is inconsistent.
% 247.91/41.92  | | | 
% 247.91/41.92  | | Case 2:
% 247.91/41.92  | | | 
% 247.91/41.92  | | |   (96)   ~ leq(n4, all_74_21) | (a_select3(id_ds1_filter, n5, n4) =
% 247.91/41.92  | | |           all_74_16 & $i(all_74_16))
% 247.91/41.92  | | | 
% 247.91/41.92  | | | BETA: splitting (96) gives:
% 247.91/41.92  | | | 
% 247.91/41.92  | | | Case 1:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | |   (97)   ~ leq(n4, all_74_21)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | REDUCE: (4), (97) imply:
% 247.91/41.92  | | | |   (98)   ~ leq(n4, n5)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | PRED_UNIFY: (90), (98) imply:
% 247.91/41.92  | | | |   (99)  $false
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | CLOSE: (99) is inconsistent.
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | Case 2:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | |   (100)  a_select3(id_ds1_filter, n5, n4) = all_74_16 & $i(all_74_16)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | ALPHA: (100) implies:
% 247.91/41.92  | | | |   (101)  a_select3(id_ds1_filter, n5, n4) = all_74_16
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | REF_CLOSE: (22), (23), (89), (101) are inconsistent by sub-proof #5.
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | End of split
% 247.91/41.92  | | | 
% 247.91/41.92  | | End of split
% 247.91/41.92  | | 
% 247.91/41.92  | End of split
% 247.91/41.92  | 
% 247.91/41.92  End of proof
% 247.91/41.92  
% 247.91/41.92  Sub-proof #5 shows that the following formulas are inconsistent:
% 247.91/41.92  ----------------------------------------------------------------
% 247.91/41.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 247.91/41.92           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 247.91/41.92             v0))
% 247.91/41.92    (2)  a_select3(id_ds1_filter, n5, n4) = all_74_16
% 247.91/41.92    (3)  a_select3(id_ds1_filter, n5, n4) = all_74_17
% 247.91/41.92    (4)   ~ (all_74_16 = all_74_17)
% 247.91/41.92  
% 247.91/41.92  Begin of proof
% 247.91/41.92  | 
% 247.91/41.92  | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n4, n5,
% 247.91/41.92  |              id_ds1_filter, simplifying with (2), (3) gives:
% 247.91/41.92  |   (5)  all_74_16 = all_74_17
% 247.91/41.92  | 
% 247.91/41.92  | REDUCE: (4), (5) imply:
% 247.91/41.92  |   (6)  $false
% 247.91/41.92  | 
% 247.91/41.92  | CLOSE: (6) is inconsistent.
% 247.91/41.92  | 
% 247.91/41.92  End of proof
% 247.91/41.92  
% 247.91/41.92  Sub-proof #6 shows that the following formulas are inconsistent:
% 247.91/41.92  ----------------------------------------------------------------
% 247.91/41.92    (1)  leq(n0, all_74_18)
% 247.91/41.92    (2)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 247.91/41.92           leq(n0, v0))
% 247.91/41.92    (3)  leq(all_74_19, n5)
% 247.91/41.92    (4)  all_74_21 = n5
% 247.91/41.92    (5)  a_select3(id_ds1_filter, all_74_19, all_74_18) = all_74_17
% 247.91/41.92    (6)  $i(n3)
% 247.91/41.92    (7)  $i(all_74_18)
% 247.91/41.92    (8)   ~ (all_74_18 = n0)
% 247.91/41.92    (9)  all_74_19 = n4 | gt(n4, all_74_19)
% 247.91/41.92    (10)  pred(n2) = n1
% 247.91/41.92    (11)  pred(n4) = n3
% 247.91/41.92    (12)  pred(n3) = n2
% 247.91/41.92    (13)  leq(all_74_18, n5)
% 247.91/41.92    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 247.91/41.92            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 247.91/41.92    (15)  $i(all_74_19)
% 247.91/41.92    (16)  $i(n4)
% 247.91/41.92    (17)  a_select3(id_ds1_filter, all_74_18, all_74_19) = all_74_16
% 247.91/41.92    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(id_ds1_filter,
% 247.91/41.92                v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_21) |  ~
% 247.91/41.92            leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 247.91/41.92            (a_select3(id_ds1_filter, v1, v0) = v2 & $i(v2)))
% 247.91/41.92    (19)  $i(n2)
% 247.91/41.92    (20)   ~ (all_74_19 = n0)
% 247.91/41.92    (21)  leq(n0, all_74_19)
% 247.91/41.92    (22)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 247.91/41.92            leq(v0, v1) | gt(v1, v0))
% 247.91/41.92    (23)  all_74_18 = n4 | gt(n4, all_74_18)
% 247.91/41.92    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 247.91/41.92          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 247.91/41.92              v0))
% 247.91/41.92    (25)   ~ (all_74_16 = all_74_17)
% 247.91/41.92  
% 247.91/41.92  Begin of proof
% 247.91/41.92  | 
% 247.91/41.92  | BETA: splitting (23) gives:
% 247.91/41.92  | 
% 247.91/41.92  | Case 1:
% 247.91/41.92  | | 
% 247.91/41.92  | |   (26)  gt(n4, all_74_18)
% 247.91/41.92  | | 
% 247.91/41.92  | | GROUND_INST: instantiating (14) with all_74_18, n4, n3, simplifying with
% 247.91/41.92  | |              (7), (11), (16), (26) gives:
% 247.91/41.92  | |   (27)  leq(all_74_18, n3)
% 247.91/41.92  | | 
% 247.91/41.92  | | GROUND_INST: instantiating (22) with all_74_18, n3, simplifying with (6),
% 247.91/41.92  | |              (7), (27) gives:
% 247.91/41.92  | |   (28)  all_74_18 = n3 | gt(n3, all_74_18)
% 247.91/41.92  | | 
% 247.91/41.92  | | BETA: splitting (9) gives:
% 247.91/41.92  | | 
% 247.91/41.92  | | Case 1:
% 247.91/41.92  | | | 
% 247.91/41.92  | | |   (29)  gt(n4, all_74_19)
% 247.91/41.92  | | | 
% 247.91/41.92  | | | GROUND_INST: instantiating (14) with all_74_19, n4, n3, simplifying with
% 247.91/41.92  | | |              (11), (15), (16), (29) gives:
% 247.91/41.92  | | |   (30)  leq(all_74_19, n3)
% 247.91/41.92  | | | 
% 247.91/41.92  | | | GROUND_INST: instantiating (22) with all_74_19, n3, simplifying with (6),
% 247.91/41.92  | | |              (15), (30) gives:
% 247.91/41.92  | | |   (31)  all_74_19 = n3 | gt(n3, all_74_19)
% 247.91/41.92  | | | 
% 247.91/41.92  | | | BETA: splitting (28) gives:
% 247.91/41.92  | | | 
% 247.91/41.92  | | | Case 1:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | |   (32)  gt(n3, all_74_18)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | GROUND_INST: instantiating (14) with all_74_18, n3, n2, simplifying with
% 247.91/41.92  | | | |              (6), (7), (12), (32) gives:
% 247.91/41.92  | | | |   (33)  leq(all_74_18, n2)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | GROUND_INST: instantiating (22) with all_74_18, n2, simplifying with
% 247.91/41.92  | | | |              (7), (19), (33) gives:
% 247.91/41.92  | | | |   (34)  all_74_18 = n2 | gt(n2, all_74_18)
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | BETA: splitting (31) gives:
% 247.91/41.92  | | | | 
% 247.91/41.92  | | | | Case 1:
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | |   (35)  gt(n3, all_74_19)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | GROUND_INST: instantiating (14) with all_74_19, n3, n2, simplifying
% 247.91/41.92  | | | | |              with (6), (12), (15), (35) gives:
% 247.91/41.92  | | | | |   (36)  leq(all_74_19, n2)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | GROUND_INST: instantiating (22) with all_74_19, n2, simplifying with
% 247.91/41.92  | | | | |              (15), (19), (36) gives:
% 247.91/41.92  | | | | |   (37)  all_74_19 = n2 | gt(n2, all_74_19)
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | BETA: splitting (34) gives:
% 247.91/41.92  | | | | | 
% 247.91/41.92  | | | | | Case 1:
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | |   (38)  gt(n2, all_74_18)
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | GROUND_INST: instantiating (14) with all_74_18, n2, n1, simplifying
% 247.91/41.92  | | | | | |              with (7), (10), (19), (38) gives:
% 247.91/41.92  | | | | | |   (39)  leq(all_74_18, n1)
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | GROUND_INST: instantiating (2) with all_74_18, simplifying with (1),
% 247.91/41.92  | | | | | |              (7), (39) gives:
% 247.91/41.92  | | | | | |   (40)  all_74_18 = n1 | all_74_18 = n0
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | BETA: splitting (40) gives:
% 247.91/41.92  | | | | | | 
% 247.91/41.92  | | | | | | Case 1:
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | |   (41)  all_74_18 = n0
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | REDUCE: (8), (41) imply:
% 247.91/41.92  | | | | | | |   (42)  $false
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | CLOSE: (42) is inconsistent.
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | Case 2:
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | |   (43)  all_74_18 = n1
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | REDUCE: (17), (43) imply:
% 247.91/41.92  | | | | | | |   (44)  a_select3(id_ds1_filter, n1, all_74_19) = all_74_16
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | REDUCE: (5), (43) imply:
% 247.91/41.92  | | | | | | |   (45)  a_select3(id_ds1_filter, all_74_19, n1) = all_74_17
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | REDUCE: (7), (43) imply:
% 247.91/41.92  | | | | | | |   (46)  $i(n1)
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | REDUCE: (13), (43) imply:
% 247.91/41.92  | | | | | | |   (47)  leq(n1, n5)
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | REDUCE: (1), (43) imply:
% 247.91/41.92  | | | | | | |   (48)  leq(n0, n1)
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | BETA: splitting (37) gives:
% 247.91/41.92  | | | | | | | 
% 247.91/41.92  | | | | | | | Case 1:
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | |   (49)  gt(n2, all_74_19)
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | | GROUND_INST: instantiating (14) with all_74_19, n2, n1,
% 247.91/41.92  | | | | | | | |              simplifying with (10), (15), (19), (49) gives:
% 247.91/41.92  | | | | | | | |   (50)  leq(all_74_19, n1)
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | | GROUND_INST: instantiating (2) with all_74_19, simplifying with
% 247.91/41.92  | | | | | | | |              (15), (21), (50) gives:
% 247.91/41.92  | | | | | | | |   (51)  all_74_19 = n1 | all_74_19 = n0
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | | BETA: splitting (51) gives:
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | | Case 1:
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | |   (52)  all_74_19 = n0
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | | REDUCE: (20), (52) imply:
% 247.91/41.92  | | | | | | | | |   (53)  $false
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | | CLOSE: (53) is inconsistent.
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | Case 2:
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | |   (54)  all_74_19 = n1
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | | REDUCE: (45), (54) imply:
% 247.91/41.92  | | | | | | | | |   (55)  a_select3(id_ds1_filter, n1, n1) = all_74_17
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | | REDUCE: (44), (54) imply:
% 247.91/41.92  | | | | | | | | |   (56)  a_select3(id_ds1_filter, n1, n1) = all_74_16
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n1,
% 247.91/41.92  | | | | | | | | |              n1, id_ds1_filter, simplifying with (55), (56)
% 247.91/41.92  | | | | | | | | |              gives:
% 247.91/41.92  | | | | | | | | |   (57)  all_74_16 = all_74_17
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | | REDUCE: (25), (57) imply:
% 247.91/41.92  | | | | | | | | |   (58)  $false
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | | CLOSE: (58) is inconsistent.
% 247.91/41.92  | | | | | | | | | 
% 247.91/41.92  | | | | | | | | End of split
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | Case 2:
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | |   (59)  all_74_19 = n2
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | | REDUCE: (45), (59) imply:
% 247.91/41.92  | | | | | | | |   (60)  a_select3(id_ds1_filter, n2, n1) = all_74_17
% 247.91/41.92  | | | | | | | | 
% 247.91/41.92  | | | | | | | | REDUCE: (44), (59) imply:
% 247.91/41.92  | | | | | | | |   (61)  a_select3(id_ds1_filter, n1, n2) = all_74_16
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (3), (59) imply:
% 247.91/41.93  | | | | | | | |   (62)  leq(n2, n5)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (21), (59) imply:
% 247.91/41.93  | | | | | | | |   (63)  leq(n0, n2)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | GROUND_INST: instantiating (18) with n1, n2, all_74_16,
% 247.91/41.93  | | | | | | | |              simplifying with (19), (46), (48), (61), (63)
% 247.91/41.93  | | | | | | | |              gives:
% 247.91/41.93  | | | | | | | |   (64)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.91/41.93  | | | | | | | |         (a_select3(id_ds1_filter, n2, n1) = all_74_16 &
% 247.91/41.93  | | | | | | | |           $i(all_74_16))
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | BETA: splitting (64) gives:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | |   (65)   ~ leq(n2, all_74_21)
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | REDUCE: (4), (65) imply:
% 247.91/41.93  | | | | | | | | |   (66)   ~ leq(n2, n5)
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | PRED_UNIFY: (62), (66) imply:
% 247.91/41.93  | | | | | | | | |   (67)  $false
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | CLOSE: (67) is inconsistent.
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | |   (68)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n2,
% 247.91/41.93  | | | | | | | | |             n1) = all_74_16 & $i(all_74_16))
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | BETA: splitting (68) gives:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | |   (69)   ~ leq(n1, all_74_21)
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | REDUCE: (4), (69) imply:
% 247.91/41.93  | | | | | | | | | |   (70)   ~ leq(n1, n5)
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | PRED_UNIFY: (47), (70) imply:
% 247.91/41.93  | | | | | | | | | |   (71)  $false
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | CLOSE: (71) is inconsistent.
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | |   (72)  a_select3(id_ds1_filter, n2, n1) = all_74_16 &
% 247.91/41.93  | | | | | | | | | |         $i(all_74_16)
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | ALPHA: (72) implies:
% 247.91/41.93  | | | | | | | | | |   (73)  a_select3(id_ds1_filter, n2, n1) = all_74_16
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | REF_CLOSE: (24), (25), (60), (73) are inconsistent by
% 247.91/41.93  | | | | | | | | | |            sub-proof #9.
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | End of split
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | End of split
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | End of split
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | End of split
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | Case 2:
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | |   (74)  all_74_18 = n2
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (17), (74) imply:
% 247.91/41.93  | | | | | |   (75)  a_select3(id_ds1_filter, n2, all_74_19) = all_74_16
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (5), (74) imply:
% 247.91/41.93  | | | | | |   (76)  a_select3(id_ds1_filter, all_74_19, n2) = all_74_17
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (13), (74) imply:
% 247.91/41.93  | | | | | |   (77)  leq(n2, n5)
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (1), (74) imply:
% 247.91/41.93  | | | | | |   (78)  leq(n0, n2)
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | BETA: splitting (37) gives:
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | Case 1:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | |   (79)  gt(n2, all_74_19)
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | GROUND_INST: instantiating (14) with all_74_19, n2, n1,
% 247.91/41.93  | | | | | | |              simplifying with (10), (15), (19), (79) gives:
% 247.91/41.93  | | | | | | |   (80)  leq(all_74_19, n1)
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | GROUND_INST: instantiating (2) with all_74_19, simplifying with
% 247.91/41.93  | | | | | | |              (15), (21), (80) gives:
% 247.91/41.93  | | | | | | |   (81)  all_74_19 = n1 | all_74_19 = n0
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | BETA: splitting (81) gives:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | |   (82)  all_74_19 = n0
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (20), (82) imply:
% 247.91/41.93  | | | | | | | |   (83)  $false
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | CLOSE: (83) is inconsistent.
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | |   (84)  all_74_19 = n1
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (76), (84) imply:
% 247.91/41.93  | | | | | | | |   (85)  a_select3(id_ds1_filter, n1, n2) = all_74_17
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (75), (84) imply:
% 247.91/41.93  | | | | | | | |   (86)  a_select3(id_ds1_filter, n2, n1) = all_74_16
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (15), (84) imply:
% 247.91/41.93  | | | | | | | |   (87)  $i(n1)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (3), (84) imply:
% 247.91/41.93  | | | | | | | |   (88)  leq(n1, n5)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (21), (84) imply:
% 247.91/41.93  | | | | | | | |   (89)  leq(n0, n1)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | GROUND_INST: instantiating (18) with n1, n2, all_74_17,
% 247.91/41.93  | | | | | | | |              simplifying with (19), (78), (85), (87), (89)
% 247.91/41.93  | | | | | | | |              gives:
% 247.91/41.93  | | | | | | | |   (90)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.91/41.93  | | | | | | | |         (a_select3(id_ds1_filter, n2, n1) = all_74_17 &
% 247.91/41.93  | | | | | | | |           $i(all_74_17))
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | BETA: splitting (90) gives:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | |   (91)   ~ leq(n2, all_74_21)
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | REDUCE: (4), (91) imply:
% 247.91/41.93  | | | | | | | | |   (92)   ~ leq(n2, n5)
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | PRED_UNIFY: (77), (92) imply:
% 247.91/41.93  | | | | | | | | |   (93)  $false
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | CLOSE: (93) is inconsistent.
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | |   (94)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n2,
% 247.91/41.93  | | | | | | | | |             n1) = all_74_17 & $i(all_74_17))
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | BETA: splitting (94) gives:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | |   (95)   ~ leq(n1, all_74_21)
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | REDUCE: (4), (95) imply:
% 247.91/41.93  | | | | | | | | | |   (96)   ~ leq(n1, n5)
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | PRED_UNIFY: (88), (96) imply:
% 247.91/41.93  | | | | | | | | | |   (97)  $false
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | CLOSE: (97) is inconsistent.
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | |   (98)  a_select3(id_ds1_filter, n2, n1) = all_74_17 &
% 247.91/41.93  | | | | | | | | | |         $i(all_74_17)
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | ALPHA: (98) implies:
% 247.91/41.93  | | | | | | | | | |   (99)  a_select3(id_ds1_filter, n2, n1) = all_74_17
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | | REF_CLOSE: (24), (25), (86), (99) are inconsistent by
% 247.91/41.93  | | | | | | | | | |            sub-proof #9.
% 247.91/41.93  | | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | End of split
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | End of split
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | End of split
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | Case 2:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | |   (100)  all_74_19 = n2
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (76), (100) imply:
% 247.91/41.93  | | | | | | |   (101)  a_select3(id_ds1_filter, n2, n2) = all_74_17
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (75), (100) imply:
% 247.91/41.93  | | | | | | |   (102)  a_select3(id_ds1_filter, n2, n2) = all_74_16
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n2, n2,
% 247.91/41.93  | | | | | | |              id_ds1_filter, simplifying with (101), (102) gives:
% 247.91/41.93  | | | | | | |   (103)  all_74_16 = all_74_17
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (25), (103) imply:
% 247.91/41.93  | | | | | | |   (104)  $false
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | CLOSE: (104) is inconsistent.
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | End of split
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | End of split
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | Case 2:
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | |   (105)  all_74_19 = n3
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | | REDUCE: (17), (105) imply:
% 247.91/41.93  | | | | |   (106)  a_select3(id_ds1_filter, all_74_18, n3) = all_74_16
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | | REDUCE: (5), (105) imply:
% 247.91/41.93  | | | | |   (107)  a_select3(id_ds1_filter, n3, all_74_18) = all_74_17
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | | REDUCE: (3), (105) imply:
% 247.91/41.93  | | | | |   (108)  leq(n3, n5)
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | | REDUCE: (21), (105) imply:
% 247.91/41.93  | | | | |   (109)  leq(n0, n3)
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | | BETA: splitting (34) gives:
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | | Case 1:
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | |   (110)  gt(n2, all_74_18)
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | GROUND_INST: instantiating (14) with all_74_18, n2, n1, simplifying
% 247.91/41.93  | | | | | |              with (7), (10), (19), (110) gives:
% 247.91/41.93  | | | | | |   (111)  leq(all_74_18, n1)
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | GROUND_INST: instantiating (2) with all_74_18, simplifying with (1),
% 247.91/41.93  | | | | | |              (7), (111) gives:
% 247.91/41.93  | | | | | |   (112)  all_74_18 = n1 | all_74_18 = n0
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | BETA: splitting (112) gives:
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | Case 1:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | |   (113)  all_74_18 = n0
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (8), (113) imply:
% 247.91/41.93  | | | | | | |   (114)  $false
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | CLOSE: (114) is inconsistent.
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | Case 2:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | |   (115)  all_74_18 = n1
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (106), (115) imply:
% 247.91/41.93  | | | | | | |   (116)  a_select3(id_ds1_filter, n1, n3) = all_74_16
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (107), (115) imply:
% 247.91/41.93  | | | | | | |   (117)  a_select3(id_ds1_filter, n3, n1) = all_74_17
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (7), (115) imply:
% 247.91/41.93  | | | | | | |   (118)  $i(n1)
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (13), (115) imply:
% 247.91/41.93  | | | | | | |   (119)  leq(n1, n5)
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (1), (115) imply:
% 247.91/41.93  | | | | | | |   (120)  leq(n0, n1)
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | GROUND_INST: instantiating (18) with n1, n3, all_74_16,
% 247.91/41.93  | | | | | | |              simplifying with (6), (109), (116), (118), (120)
% 247.91/41.93  | | | | | | |              gives:
% 247.91/41.93  | | | | | | |   (121)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 247.91/41.93  | | | | | | |          (a_select3(id_ds1_filter, n3, n1) = all_74_16 &
% 247.91/41.93  | | | | | | |            $i(all_74_16))
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | BETA: splitting (121) gives:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | |   (122)   ~ leq(n3, all_74_21)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (4), (122) imply:
% 247.91/41.93  | | | | | | | |   (123)   ~ leq(n3, n5)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | PRED_UNIFY: (108), (123) imply:
% 247.91/41.93  | | | | | | | |   (124)  $false
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | CLOSE: (124) is inconsistent.
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | |   (125)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n3,
% 247.91/41.93  | | | | | | | |              n1) = all_74_16 & $i(all_74_16))
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | BETA: splitting (125) gives:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | |   (126)   ~ leq(n1, all_74_21)
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | REDUCE: (4), (126) imply:
% 247.91/41.93  | | | | | | | | |   (127)   ~ leq(n1, n5)
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | PRED_UNIFY: (119), (127) imply:
% 247.91/41.93  | | | | | | | | |   (128)  $false
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | CLOSE: (128) is inconsistent.
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | |   (129)  a_select3(id_ds1_filter, n3, n1) = all_74_16 &
% 247.91/41.93  | | | | | | | | |          $i(all_74_16)
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | ALPHA: (129) implies:
% 247.91/41.93  | | | | | | | | |   (130)  a_select3(id_ds1_filter, n3, n1) = all_74_16
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n1,
% 247.91/41.93  | | | | | | | | |              n3, id_ds1_filter, simplifying with (117), (130)
% 247.91/41.93  | | | | | | | | |              gives:
% 247.91/41.93  | | | | | | | | |   (131)  all_74_16 = all_74_17
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | REDUCE: (25), (131) imply:
% 247.91/41.93  | | | | | | | | |   (132)  $false
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | | CLOSE: (132) is inconsistent.
% 247.91/41.93  | | | | | | | | | 
% 247.91/41.93  | | | | | | | | End of split
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | End of split
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | End of split
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | Case 2:
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | |   (133)  all_74_18 = n2
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (106), (133) imply:
% 247.91/41.93  | | | | | |   (134)  a_select3(id_ds1_filter, n2, n3) = all_74_16
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (107), (133) imply:
% 247.91/41.93  | | | | | |   (135)  a_select3(id_ds1_filter, n3, n2) = all_74_17
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (13), (133) imply:
% 247.91/41.93  | | | | | |   (136)  leq(n2, n5)
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | REDUCE: (1), (133) imply:
% 247.91/41.93  | | | | | |   (137)  leq(n0, n2)
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | GROUND_INST: instantiating (18) with n2, n3, all_74_16, simplifying
% 247.91/41.93  | | | | | |              with (6), (19), (109), (134), (137) gives:
% 247.91/41.93  | | | | | |   (138)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 247.91/41.93  | | | | | |          (a_select3(id_ds1_filter, n3, n2) = all_74_16 &
% 247.91/41.93  | | | | | |            $i(all_74_16))
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | BETA: splitting (138) gives:
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | | Case 1:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | |   (139)   ~ leq(n3, all_74_21)
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | REDUCE: (4), (139) imply:
% 247.91/41.93  | | | | | | |   (140)   ~ leq(n3, n5)
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | PRED_UNIFY: (108), (140) imply:
% 247.91/41.93  | | | | | | |   (141)  $false
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | CLOSE: (141) is inconsistent.
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | Case 2:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | |   (142)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n3, n2)
% 247.91/41.93  | | | | | | |            = all_74_16 & $i(all_74_16))
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | BETA: splitting (142) gives:
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | | Case 1:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | |   (143)   ~ leq(n2, all_74_21)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REDUCE: (4), (143) imply:
% 247.91/41.93  | | | | | | | |   (144)   ~ leq(n2, n5)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | PRED_UNIFY: (136), (144) imply:
% 247.91/41.93  | | | | | | | |   (145)  $false
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | CLOSE: (145) is inconsistent.
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | Case 2:
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | |   (146)  a_select3(id_ds1_filter, n3, n2) = all_74_16 &
% 247.91/41.93  | | | | | | | |          $i(all_74_16)
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | ALPHA: (146) implies:
% 247.91/41.93  | | | | | | | |   (147)  a_select3(id_ds1_filter, n3, n2) = all_74_16
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | | REF_CLOSE: (24), (25), (135), (147) are inconsistent by
% 247.91/41.93  | | | | | | | |            sub-proof #8.
% 247.91/41.93  | | | | | | | | 
% 247.91/41.93  | | | | | | | End of split
% 247.91/41.93  | | | | | | | 
% 247.91/41.93  | | | | | | End of split
% 247.91/41.93  | | | | | | 
% 247.91/41.93  | | | | | End of split
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | End of split
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | Case 2:
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | |   (148)  all_74_18 = n3
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | | REDUCE: (17), (148) imply:
% 247.91/41.93  | | | |   (149)  a_select3(id_ds1_filter, n3, all_74_19) = all_74_16
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | | REDUCE: (5), (148) imply:
% 247.91/41.93  | | | |   (150)  a_select3(id_ds1_filter, all_74_19, n3) = all_74_17
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | | REDUCE: (13), (148) imply:
% 247.91/41.93  | | | |   (151)  leq(n3, n5)
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | | REDUCE: (1), (148) imply:
% 247.91/41.93  | | | |   (152)  leq(n0, n3)
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | | BETA: splitting (31) gives:
% 247.91/41.93  | | | | 
% 247.91/41.93  | | | | Case 1:
% 247.91/41.93  | | | | | 
% 247.91/41.93  | | | | |   (153)  gt(n3, all_74_19)
% 247.91/41.93  | | | | | 
% 248.24/41.94  | | | | | GROUND_INST: instantiating (14) with all_74_19, n3, n2, simplifying
% 248.24/41.94  | | | | |              with (6), (12), (15), (153) gives:
% 248.24/41.94  | | | | |   (154)  leq(all_74_19, n2)
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | GROUND_INST: instantiating (22) with all_74_19, n2, simplifying with
% 248.24/41.94  | | | | |              (15), (19), (154) gives:
% 248.24/41.94  | | | | |   (155)  all_74_19 = n2 | gt(n2, all_74_19)
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | BETA: splitting (155) gives:
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | Case 1:
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | |   (156)  gt(n2, all_74_19)
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | GROUND_INST: instantiating (14) with all_74_19, n2, n1, simplifying
% 248.24/41.94  | | | | | |              with (10), (15), (19), (156) gives:
% 248.24/41.94  | | | | | |   (157)  leq(all_74_19, n1)
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | GROUND_INST: instantiating (2) with all_74_19, simplifying with
% 248.24/41.94  | | | | | |              (15), (21), (157) gives:
% 248.24/41.94  | | | | | |   (158)  all_74_19 = n1 | all_74_19 = n0
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | BETA: splitting (158) gives:
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | Case 1:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | |   (159)  all_74_19 = n0
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (20), (159) imply:
% 248.24/41.94  | | | | | | |   (160)  $false
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | CLOSE: (160) is inconsistent.
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | Case 2:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | |   (161)  all_74_19 = n1
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (150), (161) imply:
% 248.24/41.94  | | | | | | |   (162)  a_select3(id_ds1_filter, n1, n3) = all_74_17
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (149), (161) imply:
% 248.24/41.94  | | | | | | |   (163)  a_select3(id_ds1_filter, n3, n1) = all_74_16
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (15), (161) imply:
% 248.24/41.94  | | | | | | |   (164)  $i(n1)
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (3), (161) imply:
% 248.24/41.94  | | | | | | |   (165)  leq(n1, n5)
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (21), (161) imply:
% 248.24/41.94  | | | | | | |   (166)  leq(n0, n1)
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | GROUND_INST: instantiating (18) with n1, n3, all_74_17,
% 248.24/41.94  | | | | | | |              simplifying with (6), (152), (162), (164), (166)
% 248.24/41.94  | | | | | | |              gives:
% 248.24/41.94  | | | | | | |   (167)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.24/41.94  | | | | | | |          (a_select3(id_ds1_filter, n3, n1) = all_74_17 &
% 248.24/41.94  | | | | | | |            $i(all_74_17))
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | BETA: splitting (167) gives:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | Case 1:
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | |   (168)   ~ leq(n3, all_74_21)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | REDUCE: (4), (168) imply:
% 248.24/41.94  | | | | | | | |   (169)   ~ leq(n3, n5)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | PRED_UNIFY: (151), (169) imply:
% 248.24/41.94  | | | | | | | |   (170)  $false
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | CLOSE: (170) is inconsistent.
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | Case 2:
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | |   (171)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n3,
% 248.24/41.94  | | | | | | | |              n1) = all_74_17 & $i(all_74_17))
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | BETA: splitting (171) gives:
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | Case 1:
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | |   (172)   ~ leq(n1, all_74_21)
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | | REDUCE: (4), (172) imply:
% 248.24/41.94  | | | | | | | | |   (173)   ~ leq(n1, n5)
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | | PRED_UNIFY: (165), (173) imply:
% 248.24/41.94  | | | | | | | | |   (174)  $false
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | | CLOSE: (174) is inconsistent.
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | Case 2:
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | |   (175)  a_select3(id_ds1_filter, n3, n1) = all_74_17 &
% 248.24/41.94  | | | | | | | | |          $i(all_74_17)
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | | ALPHA: (175) implies:
% 248.24/41.94  | | | | | | | | |   (176)  a_select3(id_ds1_filter, n3, n1) = all_74_17
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n1,
% 248.24/41.94  | | | | | | | | |              n3, id_ds1_filter, simplifying with (163), (176)
% 248.24/41.94  | | | | | | | | |              gives:
% 248.24/41.94  | | | | | | | | |   (177)  all_74_16 = all_74_17
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | | REDUCE: (25), (177) imply:
% 248.24/41.94  | | | | | | | | |   (178)  $false
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | | CLOSE: (178) is inconsistent.
% 248.24/41.94  | | | | | | | | | 
% 248.24/41.94  | | | | | | | | End of split
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | End of split
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | End of split
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | Case 2:
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | |   (179)  all_74_19 = n2
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (150), (179) imply:
% 248.24/41.94  | | | | | |   (180)  a_select3(id_ds1_filter, n2, n3) = all_74_17
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (149), (179) imply:
% 248.24/41.94  | | | | | |   (181)  a_select3(id_ds1_filter, n3, n2) = all_74_16
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (3), (179) imply:
% 248.24/41.94  | | | | | |   (182)  leq(n2, n5)
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (21), (179) imply:
% 248.24/41.94  | | | | | |   (183)  leq(n0, n2)
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | GROUND_INST: instantiating (18) with n2, n3, all_74_17, simplifying
% 248.24/41.94  | | | | | |              with (6), (19), (152), (180), (183) gives:
% 248.24/41.94  | | | | | |   (184)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.24/41.94  | | | | | |          (a_select3(id_ds1_filter, n3, n2) = all_74_17 &
% 248.24/41.94  | | | | | |            $i(all_74_17))
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | BETA: splitting (184) gives:
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | Case 1:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | |   (185)   ~ leq(n3, all_74_21)
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (4), (185) imply:
% 248.24/41.94  | | | | | | |   (186)   ~ leq(n3, n5)
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | PRED_UNIFY: (151), (186) imply:
% 248.24/41.94  | | | | | | |   (187)  $false
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | CLOSE: (187) is inconsistent.
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | Case 2:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | |   (188)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n3, n2)
% 248.24/41.94  | | | | | | |            = all_74_17 & $i(all_74_17))
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | BETA: splitting (188) gives:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | Case 1:
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | |   (189)   ~ leq(n2, all_74_21)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | REDUCE: (4), (189) imply:
% 248.24/41.94  | | | | | | | |   (190)   ~ leq(n2, n5)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | PRED_UNIFY: (182), (190) imply:
% 248.24/41.94  | | | | | | | |   (191)  $false
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | CLOSE: (191) is inconsistent.
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | Case 2:
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | |   (192)  a_select3(id_ds1_filter, n3, n2) = all_74_17 &
% 248.24/41.94  | | | | | | | |          $i(all_74_17)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | ALPHA: (192) implies:
% 248.24/41.94  | | | | | | | |   (193)  a_select3(id_ds1_filter, n3, n2) = all_74_17
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | REF_CLOSE: (24), (25), (181), (193) are inconsistent by
% 248.24/41.94  | | | | | | | |            sub-proof #8.
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | End of split
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | End of split
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | End of split
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | Case 2:
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | |   (194)  all_74_19 = n3
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | REDUCE: (150), (194) imply:
% 248.24/41.94  | | | | |   (195)  a_select3(id_ds1_filter, n3, n3) = all_74_17
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | REDUCE: (149), (194) imply:
% 248.24/41.94  | | | | |   (196)  a_select3(id_ds1_filter, n3, n3) = all_74_16
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n3, n3,
% 248.24/41.94  | | | | |              id_ds1_filter, simplifying with (195), (196) gives:
% 248.24/41.94  | | | | |   (197)  all_74_16 = all_74_17
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | REDUCE: (25), (197) imply:
% 248.24/41.94  | | | | |   (198)  $false
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | CLOSE: (198) is inconsistent.
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | End of split
% 248.24/41.94  | | | | 
% 248.24/41.94  | | | End of split
% 248.24/41.94  | | | 
% 248.24/41.94  | | Case 2:
% 248.24/41.94  | | | 
% 248.24/41.94  | | |   (199)  all_74_19 = n4
% 248.24/41.94  | | | 
% 248.24/41.94  | | | REDUCE: (17), (199) imply:
% 248.24/41.94  | | |   (200)  a_select3(id_ds1_filter, all_74_18, n4) = all_74_16
% 248.24/41.94  | | | 
% 248.24/41.94  | | | REDUCE: (5), (199) imply:
% 248.24/41.94  | | |   (201)  a_select3(id_ds1_filter, n4, all_74_18) = all_74_17
% 248.24/41.94  | | | 
% 248.24/41.94  | | | REDUCE: (3), (199) imply:
% 248.24/41.94  | | |   (202)  leq(n4, n5)
% 248.24/41.94  | | | 
% 248.24/41.94  | | | REDUCE: (21), (199) imply:
% 248.24/41.94  | | |   (203)  leq(n0, n4)
% 248.24/41.94  | | | 
% 248.24/41.94  | | | BETA: splitting (28) gives:
% 248.24/41.94  | | | 
% 248.24/41.94  | | | Case 1:
% 248.24/41.94  | | | | 
% 248.24/41.94  | | | |   (204)  gt(n3, all_74_18)
% 248.24/41.94  | | | | 
% 248.24/41.94  | | | | GROUND_INST: instantiating (14) with all_74_18, n3, n2, simplifying with
% 248.24/41.94  | | | |              (6), (7), (12), (204) gives:
% 248.24/41.94  | | | |   (205)  leq(all_74_18, n2)
% 248.24/41.94  | | | | 
% 248.24/41.94  | | | | GROUND_INST: instantiating (22) with all_74_18, n2, simplifying with
% 248.24/41.94  | | | |              (7), (19), (205) gives:
% 248.24/41.94  | | | |   (206)  all_74_18 = n2 | gt(n2, all_74_18)
% 248.24/41.94  | | | | 
% 248.24/41.94  | | | | BETA: splitting (206) gives:
% 248.24/41.94  | | | | 
% 248.24/41.94  | | | | Case 1:
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | |   (207)  gt(n2, all_74_18)
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | GROUND_INST: instantiating (14) with all_74_18, n2, n1, simplifying
% 248.24/41.94  | | | | |              with (7), (10), (19), (207) gives:
% 248.24/41.94  | | | | |   (208)  leq(all_74_18, n1)
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | GROUND_INST: instantiating (2) with all_74_18, simplifying with (1),
% 248.24/41.94  | | | | |              (7), (208) gives:
% 248.24/41.94  | | | | |   (209)  all_74_18 = n1 | all_74_18 = n0
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | BETA: splitting (209) gives:
% 248.24/41.94  | | | | | 
% 248.24/41.94  | | | | | Case 1:
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | |   (210)  all_74_18 = n0
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (8), (210) imply:
% 248.24/41.94  | | | | | |   (211)  $false
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | CLOSE: (211) is inconsistent.
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | Case 2:
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | |   (212)  all_74_18 = n1
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (200), (212) imply:
% 248.24/41.94  | | | | | |   (213)  a_select3(id_ds1_filter, n1, n4) = all_74_16
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (201), (212) imply:
% 248.24/41.94  | | | | | |   (214)  a_select3(id_ds1_filter, n4, n1) = all_74_17
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (7), (212) imply:
% 248.24/41.94  | | | | | |   (215)  $i(n1)
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (13), (212) imply:
% 248.24/41.94  | | | | | |   (216)  leq(n1, n5)
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | REDUCE: (1), (212) imply:
% 248.24/41.94  | | | | | |   (217)  leq(n0, n1)
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | GROUND_INST: instantiating (18) with n1, n4, all_74_16, simplifying
% 248.24/41.94  | | | | | |              with (16), (203), (213), (215), (217) gives:
% 248.24/41.94  | | | | | |   (218)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.24/41.94  | | | | | |          (a_select3(id_ds1_filter, n4, n1) = all_74_16 &
% 248.24/41.94  | | | | | |            $i(all_74_16))
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | BETA: splitting (218) gives:
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | | Case 1:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | |   (219)   ~ leq(n4, all_74_21)
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | REDUCE: (4), (219) imply:
% 248.24/41.94  | | | | | | |   (220)   ~ leq(n4, n5)
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | PRED_UNIFY: (202), (220) imply:
% 248.24/41.94  | | | | | | |   (221)  $false
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | CLOSE: (221) is inconsistent.
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | Case 2:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | |   (222)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n4, n1)
% 248.24/41.94  | | | | | | |            = all_74_16 & $i(all_74_16))
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | BETA: splitting (222) gives:
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | | Case 1:
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | |   (223)   ~ leq(n1, all_74_21)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | REDUCE: (4), (223) imply:
% 248.24/41.94  | | | | | | | |   (224)   ~ leq(n1, n5)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | PRED_UNIFY: (216), (224) imply:
% 248.24/41.94  | | | | | | | |   (225)  $false
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | CLOSE: (225) is inconsistent.
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | Case 2:
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | |   (226)  a_select3(id_ds1_filter, n4, n1) = all_74_16 &
% 248.24/41.94  | | | | | | | |          $i(all_74_16)
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | ALPHA: (226) implies:
% 248.24/41.94  | | | | | | | |   (227)  a_select3(id_ds1_filter, n4, n1) = all_74_16
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n1,
% 248.24/41.94  | | | | | | | |              n4, id_ds1_filter, simplifying with (214), (227)
% 248.24/41.94  | | | | | | | |              gives:
% 248.24/41.94  | | | | | | | |   (228)  all_74_16 = all_74_17
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | REDUCE: (25), (228) imply:
% 248.24/41.94  | | | | | | | |   (229)  $false
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | | CLOSE: (229) is inconsistent.
% 248.24/41.94  | | | | | | | | 
% 248.24/41.94  | | | | | | | End of split
% 248.24/41.94  | | | | | | | 
% 248.24/41.94  | | | | | | End of split
% 248.24/41.94  | | | | | | 
% 248.24/41.94  | | | | | End of split
% 248.24/41.94  | | | | | 
% 248.24/41.95  | | | | Case 2:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | |   (230)  all_74_18 = n2
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (200), (230) imply:
% 248.24/41.95  | | | | |   (231)  a_select3(id_ds1_filter, n2, n4) = all_74_16
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (201), (230) imply:
% 248.24/41.95  | | | | |   (232)  a_select3(id_ds1_filter, n4, n2) = all_74_17
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (13), (230) imply:
% 248.24/41.95  | | | | |   (233)  leq(n2, n5)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (1), (230) imply:
% 248.24/41.95  | | | | |   (234)  leq(n0, n2)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | GROUND_INST: instantiating (18) with n2, n4, all_74_16, simplifying
% 248.24/41.95  | | | | |              with (16), (19), (203), (231), (234) gives:
% 248.24/41.95  | | | | |   (235)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.24/41.95  | | | | |          (a_select3(id_ds1_filter, n4, n2) = all_74_16 &
% 248.24/41.95  | | | | |            $i(all_74_16))
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | BETA: splitting (235) gives:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | Case 1:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (236)   ~ leq(n4, all_74_21)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (4), (236) imply:
% 248.24/41.95  | | | | | |   (237)   ~ leq(n4, n5)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | PRED_UNIFY: (202), (237) imply:
% 248.24/41.95  | | | | | |   (238)  $false
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | CLOSE: (238) is inconsistent.
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | Case 2:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (239)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n4, n2) =
% 248.24/41.95  | | | | | |            all_74_16 & $i(all_74_16))
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | BETA: splitting (239) gives:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | Case 1:
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | |   (240)   ~ leq(n2, all_74_21)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | REDUCE: (4), (240) imply:
% 248.24/41.95  | | | | | | |   (241)   ~ leq(n2, n5)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | PRED_UNIFY: (233), (241) imply:
% 248.24/41.95  | | | | | | |   (242)  $false
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | CLOSE: (242) is inconsistent.
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | Case 2:
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | |   (243)  a_select3(id_ds1_filter, n4, n2) = all_74_16 &
% 248.24/41.95  | | | | | | |          $i(all_74_16)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | ALPHA: (243) implies:
% 248.24/41.95  | | | | | | |   (244)  a_select3(id_ds1_filter, n4, n2) = all_74_16
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n2, n4,
% 248.24/41.95  | | | | | | |              id_ds1_filter, simplifying with (232), (244) gives:
% 248.24/41.95  | | | | | | |   (245)  all_74_16 = all_74_17
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | REDUCE: (25), (245) imply:
% 248.24/41.95  | | | | | | |   (246)  $false
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | CLOSE: (246) is inconsistent.
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | End of split
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | End of split
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | End of split
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | Case 2:
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | |   (247)  all_74_18 = n3
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (200), (247) imply:
% 248.24/41.95  | | | |   (248)  a_select3(id_ds1_filter, n3, n4) = all_74_16
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (201), (247) imply:
% 248.24/41.95  | | | |   (249)  a_select3(id_ds1_filter, n4, n3) = all_74_17
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (13), (247) imply:
% 248.24/41.95  | | | |   (250)  leq(n3, n5)
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (1), (247) imply:
% 248.24/41.95  | | | |   (251)  leq(n0, n3)
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | GROUND_INST: instantiating (18) with n3, n4, all_74_16, simplifying with
% 248.24/41.95  | | | |              (6), (16), (203), (248), (251) gives:
% 248.24/41.95  | | | |   (252)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.24/41.95  | | | |          (a_select3(id_ds1_filter, n4, n3) = all_74_16 & $i(all_74_16))
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | BETA: splitting (252) gives:
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | Case 1:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | |   (253)   ~ leq(n4, all_74_21)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (4), (253) imply:
% 248.24/41.95  | | | | |   (254)   ~ leq(n4, n5)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | PRED_UNIFY: (202), (254) imply:
% 248.24/41.95  | | | | |   (255)  $false
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | CLOSE: (255) is inconsistent.
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | Case 2:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | |   (256)   ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n4, n3) =
% 248.24/41.95  | | | | |            all_74_16 & $i(all_74_16))
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | BETA: splitting (256) gives:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | Case 1:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (257)   ~ leq(n3, all_74_21)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (4), (257) imply:
% 248.24/41.95  | | | | | |   (258)   ~ leq(n3, n5)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | PRED_UNIFY: (250), (258) imply:
% 248.24/41.95  | | | | | |   (259)  $false
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | CLOSE: (259) is inconsistent.
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | Case 2:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (260)  a_select3(id_ds1_filter, n4, n3) = all_74_16 &
% 248.24/41.95  | | | | | |          $i(all_74_16)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | ALPHA: (260) implies:
% 248.24/41.95  | | | | | |   (261)  a_select3(id_ds1_filter, n4, n3) = all_74_16
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REF_CLOSE: (24), (25), (249), (261) are inconsistent by sub-proof
% 248.24/41.95  | | | | | |            #7.
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | End of split
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | End of split
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | End of split
% 248.24/41.95  | | | 
% 248.24/41.95  | | End of split
% 248.24/41.95  | | 
% 248.24/41.95  | Case 2:
% 248.24/41.95  | | 
% 248.24/41.95  | |   (262)  all_74_18 = n4
% 248.24/41.95  | | 
% 248.24/41.95  | | REDUCE: (17), (262) imply:
% 248.24/41.95  | |   (263)  a_select3(id_ds1_filter, n4, all_74_19) = all_74_16
% 248.24/41.95  | | 
% 248.24/41.95  | | REDUCE: (5), (262) imply:
% 248.24/41.95  | |   (264)  a_select3(id_ds1_filter, all_74_19, n4) = all_74_17
% 248.24/41.95  | | 
% 248.24/41.95  | | REDUCE: (13), (262) imply:
% 248.24/41.95  | |   (265)  leq(n4, n5)
% 248.24/41.95  | | 
% 248.24/41.95  | | REDUCE: (1), (262) imply:
% 248.24/41.95  | |   (266)  leq(n0, n4)
% 248.24/41.95  | | 
% 248.24/41.95  | | BETA: splitting (9) gives:
% 248.24/41.95  | | 
% 248.24/41.95  | | Case 1:
% 248.24/41.95  | | | 
% 248.24/41.95  | | |   (267)  gt(n4, all_74_19)
% 248.24/41.95  | | | 
% 248.24/41.95  | | | GROUND_INST: instantiating (14) with all_74_19, n4, n3, simplifying with
% 248.24/41.95  | | |              (11), (15), (16), (267) gives:
% 248.24/41.95  | | |   (268)  leq(all_74_19, n3)
% 248.24/41.95  | | | 
% 248.24/41.95  | | | GROUND_INST: instantiating (22) with all_74_19, n3, simplifying with (6),
% 248.24/41.95  | | |              (15), (268) gives:
% 248.24/41.95  | | |   (269)  all_74_19 = n3 | gt(n3, all_74_19)
% 248.24/41.95  | | | 
% 248.24/41.95  | | | BETA: splitting (269) gives:
% 248.24/41.95  | | | 
% 248.24/41.95  | | | Case 1:
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | |   (270)  gt(n3, all_74_19)
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | GROUND_INST: instantiating (14) with all_74_19, n3, n2, simplifying with
% 248.24/41.95  | | | |              (6), (12), (15), (270) gives:
% 248.24/41.95  | | | |   (271)  leq(all_74_19, n2)
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | GROUND_INST: instantiating (22) with all_74_19, n2, simplifying with
% 248.24/41.95  | | | |              (15), (19), (271) gives:
% 248.24/41.95  | | | |   (272)  all_74_19 = n2 | gt(n2, all_74_19)
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | BETA: splitting (272) gives:
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | Case 1:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | |   (273)  gt(n2, all_74_19)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | GROUND_INST: instantiating (14) with all_74_19, n2, n1, simplifying
% 248.24/41.95  | | | | |              with (10), (15), (19), (273) gives:
% 248.24/41.95  | | | | |   (274)  leq(all_74_19, n1)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | GROUND_INST: instantiating (2) with all_74_19, simplifying with (15),
% 248.24/41.95  | | | | |              (21), (274) gives:
% 248.24/41.95  | | | | |   (275)  all_74_19 = n1 | all_74_19 = n0
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | BETA: splitting (275) gives:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | Case 1:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (276)  all_74_19 = n0
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (20), (276) imply:
% 248.24/41.95  | | | | | |   (277)  $false
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | CLOSE: (277) is inconsistent.
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | Case 2:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (278)  all_74_19 = n1
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (264), (278) imply:
% 248.24/41.95  | | | | | |   (279)  a_select3(id_ds1_filter, n1, n4) = all_74_17
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (263), (278) imply:
% 248.24/41.95  | | | | | |   (280)  a_select3(id_ds1_filter, n4, n1) = all_74_16
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (15), (278) imply:
% 248.24/41.95  | | | | | |   (281)  $i(n1)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (3), (278) imply:
% 248.24/41.95  | | | | | |   (282)  leq(n1, n5)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (21), (278) imply:
% 248.24/41.95  | | | | | |   (283)  leq(n0, n1)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | GROUND_INST: instantiating (18) with n1, n4, all_74_17, simplifying
% 248.24/41.95  | | | | | |              with (16), (266), (279), (281), (283) gives:
% 248.24/41.95  | | | | | |   (284)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.24/41.95  | | | | | |          (a_select3(id_ds1_filter, n4, n1) = all_74_17 &
% 248.24/41.95  | | | | | |            $i(all_74_17))
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | BETA: splitting (284) gives:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | Case 1:
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | |   (285)   ~ leq(n4, all_74_21)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | REDUCE: (4), (285) imply:
% 248.24/41.95  | | | | | | |   (286)   ~ leq(n4, n5)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | PRED_UNIFY: (265), (286) imply:
% 248.24/41.95  | | | | | | |   (287)  $false
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | CLOSE: (287) is inconsistent.
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | Case 2:
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | |   (288)   ~ leq(n1, all_74_21) | (a_select3(id_ds1_filter, n4, n1)
% 248.24/41.95  | | | | | | |            = all_74_17 & $i(all_74_17))
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | BETA: splitting (288) gives:
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | Case 1:
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | |   (289)   ~ leq(n1, all_74_21)
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | | REDUCE: (4), (289) imply:
% 248.24/41.95  | | | | | | | |   (290)   ~ leq(n1, n5)
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | | PRED_UNIFY: (282), (290) imply:
% 248.24/41.95  | | | | | | | |   (291)  $false
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | | CLOSE: (291) is inconsistent.
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | Case 2:
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | |   (292)  a_select3(id_ds1_filter, n4, n1) = all_74_17 &
% 248.24/41.95  | | | | | | | |          $i(all_74_17)
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | | ALPHA: (292) implies:
% 248.24/41.95  | | | | | | | |   (293)  a_select3(id_ds1_filter, n4, n1) = all_74_17
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n1,
% 248.24/41.95  | | | | | | | |              n4, id_ds1_filter, simplifying with (280), (293)
% 248.24/41.95  | | | | | | | |              gives:
% 248.24/41.95  | | | | | | | |   (294)  all_74_16 = all_74_17
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | | REDUCE: (25), (294) imply:
% 248.24/41.95  | | | | | | | |   (295)  $false
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | | CLOSE: (295) is inconsistent.
% 248.24/41.95  | | | | | | | | 
% 248.24/41.95  | | | | | | | End of split
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | End of split
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | End of split
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | Case 2:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | |   (296)  all_74_19 = n2
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (264), (296) imply:
% 248.24/41.95  | | | | |   (297)  a_select3(id_ds1_filter, n2, n4) = all_74_17
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (263), (296) imply:
% 248.24/41.95  | | | | |   (298)  a_select3(id_ds1_filter, n4, n2) = all_74_16
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (3), (296) imply:
% 248.24/41.95  | | | | |   (299)  leq(n2, n5)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (21), (296) imply:
% 248.24/41.95  | | | | |   (300)  leq(n0, n2)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | GROUND_INST: instantiating (18) with n2, n4, all_74_17, simplifying
% 248.24/41.95  | | | | |              with (16), (19), (266), (297), (300) gives:
% 248.24/41.95  | | | | |   (301)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.24/41.95  | | | | |          (a_select3(id_ds1_filter, n4, n2) = all_74_17 &
% 248.24/41.95  | | | | |            $i(all_74_17))
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | BETA: splitting (301) gives:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | Case 1:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (302)   ~ leq(n4, all_74_21)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (4), (302) imply:
% 248.24/41.95  | | | | | |   (303)   ~ leq(n4, n5)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | PRED_UNIFY: (265), (303) imply:
% 248.24/41.95  | | | | | |   (304)  $false
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | CLOSE: (304) is inconsistent.
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | Case 2:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (305)   ~ leq(n2, all_74_21) | (a_select3(id_ds1_filter, n4, n2) =
% 248.24/41.95  | | | | | |            all_74_17 & $i(all_74_17))
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | BETA: splitting (305) gives:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | Case 1:
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | |   (306)   ~ leq(n2, all_74_21)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | REDUCE: (4), (306) imply:
% 248.24/41.95  | | | | | | |   (307)   ~ leq(n2, n5)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | PRED_UNIFY: (299), (307) imply:
% 248.24/41.95  | | | | | | |   (308)  $false
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | CLOSE: (308) is inconsistent.
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | Case 2:
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | |   (309)  a_select3(id_ds1_filter, n4, n2) = all_74_17 &
% 248.24/41.95  | | | | | | |          $i(all_74_17)
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | ALPHA: (309) implies:
% 248.24/41.95  | | | | | | |   (310)  a_select3(id_ds1_filter, n4, n2) = all_74_17
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n2, n4,
% 248.24/41.95  | | | | | | |              id_ds1_filter, simplifying with (298), (310) gives:
% 248.24/41.95  | | | | | | |   (311)  all_74_16 = all_74_17
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | REDUCE: (25), (311) imply:
% 248.24/41.95  | | | | | | |   (312)  $false
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | | CLOSE: (312) is inconsistent.
% 248.24/41.95  | | | | | | | 
% 248.24/41.95  | | | | | | End of split
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | End of split
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | End of split
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | Case 2:
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | |   (313)  all_74_19 = n3
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (264), (313) imply:
% 248.24/41.95  | | | |   (314)  a_select3(id_ds1_filter, n3, n4) = all_74_17
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (263), (313) imply:
% 248.24/41.95  | | | |   (315)  a_select3(id_ds1_filter, n4, n3) = all_74_16
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (3), (313) imply:
% 248.24/41.95  | | | |   (316)  leq(n3, n5)
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | REDUCE: (21), (313) imply:
% 248.24/41.95  | | | |   (317)  leq(n0, n3)
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | GROUND_INST: instantiating (18) with n3, n4, all_74_17, simplifying with
% 248.24/41.95  | | | |              (6), (16), (266), (314), (317) gives:
% 248.24/41.95  | | | |   (318)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.24/41.95  | | | |          (a_select3(id_ds1_filter, n4, n3) = all_74_17 & $i(all_74_17))
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | BETA: splitting (318) gives:
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | | Case 1:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | |   (319)   ~ leq(n4, all_74_21)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | REDUCE: (4), (319) imply:
% 248.24/41.95  | | | | |   (320)   ~ leq(n4, n5)
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | PRED_UNIFY: (265), (320) imply:
% 248.24/41.95  | | | | |   (321)  $false
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | CLOSE: (321) is inconsistent.
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | Case 2:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | |   (322)   ~ leq(n3, all_74_21) | (a_select3(id_ds1_filter, n4, n3) =
% 248.24/41.95  | | | | |            all_74_17 & $i(all_74_17))
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | BETA: splitting (322) gives:
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | | Case 1:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (323)   ~ leq(n3, all_74_21)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REDUCE: (4), (323) imply:
% 248.24/41.95  | | | | | |   (324)   ~ leq(n3, n5)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | PRED_UNIFY: (316), (324) imply:
% 248.24/41.95  | | | | | |   (325)  $false
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | CLOSE: (325) is inconsistent.
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | Case 2:
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | |   (326)  a_select3(id_ds1_filter, n4, n3) = all_74_17 &
% 248.24/41.95  | | | | | |          $i(all_74_17)
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | ALPHA: (326) implies:
% 248.24/41.95  | | | | | |   (327)  a_select3(id_ds1_filter, n4, n3) = all_74_17
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | | REF_CLOSE: (24), (25), (315), (327) are inconsistent by sub-proof
% 248.24/41.95  | | | | | |            #7.
% 248.24/41.95  | | | | | | 
% 248.24/41.95  | | | | | End of split
% 248.24/41.95  | | | | | 
% 248.24/41.95  | | | | End of split
% 248.24/41.95  | | | | 
% 248.24/41.95  | | | End of split
% 248.24/41.95  | | | 
% 248.24/41.95  | | Case 2:
% 248.24/41.95  | | | 
% 248.24/41.95  | | |   (328)  all_74_19 = n4
% 248.24/41.95  | | | 
% 248.24/41.95  | | | REDUCE: (264), (328) imply:
% 248.24/41.95  | | |   (329)  a_select3(id_ds1_filter, n4, n4) = all_74_17
% 248.24/41.95  | | | 
% 248.24/41.95  | | | REDUCE: (263), (328) imply:
% 248.24/41.95  | | |   (330)  a_select3(id_ds1_filter, n4, n4) = all_74_16
% 248.24/41.95  | | | 
% 248.24/41.95  | | | GROUND_INST: instantiating (24) with all_74_17, all_74_16, n4, n4,
% 248.24/41.95  | | |              id_ds1_filter, simplifying with (329), (330) gives:
% 248.24/41.95  | | |   (331)  all_74_16 = all_74_17
% 248.24/41.95  | | | 
% 248.24/41.95  | | | REDUCE: (25), (331) imply:
% 248.24/41.95  | | |   (332)  $false
% 248.24/41.95  | | | 
% 248.24/41.95  | | | CLOSE: (332) is inconsistent.
% 248.24/41.95  | | | 
% 248.24/41.95  | | End of split
% 248.24/41.95  | | 
% 248.24/41.95  | End of split
% 248.24/41.95  | 
% 248.24/41.95  End of proof
% 248.24/41.95  
% 248.24/41.95  Sub-proof #7 shows that the following formulas are inconsistent:
% 248.24/41.95  ----------------------------------------------------------------
% 248.24/41.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.24/41.95           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.24/41.95             v0))
% 248.24/41.95    (2)  a_select3(id_ds1_filter, n4, n3) = all_74_16
% 248.24/41.95    (3)  a_select3(id_ds1_filter, n4, n3) = all_74_17
% 248.24/41.95    (4)   ~ (all_74_16 = all_74_17)
% 248.24/41.95  
% 248.24/41.95  Begin of proof
% 248.24/41.95  | 
% 248.24/41.95  | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n3, n4,
% 248.24/41.95  |              id_ds1_filter, simplifying with (2), (3) gives:
% 248.24/41.95  |   (5)  all_74_16 = all_74_17
% 248.24/41.95  | 
% 248.24/41.95  | REDUCE: (4), (5) imply:
% 248.24/41.95  |   (6)  $false
% 248.24/41.95  | 
% 248.24/41.95  | CLOSE: (6) is inconsistent.
% 248.24/41.95  | 
% 248.24/41.95  End of proof
% 248.24/41.95  
% 248.24/41.95  Sub-proof #8 shows that the following formulas are inconsistent:
% 248.24/41.95  ----------------------------------------------------------------
% 248.24/41.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.24/41.95           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.24/41.95             v0))
% 248.24/41.95    (2)  a_select3(id_ds1_filter, n3, n2) = all_74_16
% 248.24/41.95    (3)  a_select3(id_ds1_filter, n3, n2) = all_74_17
% 248.24/41.95    (4)   ~ (all_74_16 = all_74_17)
% 248.24/41.95  
% 248.24/41.95  Begin of proof
% 248.24/41.95  | 
% 248.24/41.95  | GROUND_INST: instantiating (1) with all_74_17, all_74_16, n2, n3,
% 248.24/41.95  |              id_ds1_filter, simplifying with (2), (3) gives:
% 248.24/41.95  |   (5)  all_74_16 = all_74_17
% 248.24/41.95  | 
% 248.24/41.95  | REDUCE: (4), (5) imply:
% 248.24/41.95  |   (6)  $false
% 248.24/41.95  | 
% 248.24/41.95  | CLOSE: (6) is inconsistent.
% 248.24/41.95  | 
% 248.24/41.95  End of proof
% 248.24/41.95  
% 248.24/41.95  Sub-proof #9 shows that the following formulas are inconsistent:
% 248.24/41.95  ----------------------------------------------------------------
% 248.24/41.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.24/41.95           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.24/41.95             v0))
% 248.24/41.95    (2)  a_select3(id_ds1_filter, n2, n1) = all_74_16
% 248.24/41.95    (3)  a_select3(id_ds1_filter, n2, n1) = all_74_17
% 248.24/41.96    (4)   ~ (all_74_16 = all_74_17)
% 248.24/41.96  
% 248.24/41.96  Begin of proof
% 248.24/41.96  | 
% 248.24/41.96  | GROUND_INST: instantiating (1) with all_74_16, all_74_17, n1, n2,
% 248.24/41.96  |              id_ds1_filter, simplifying with (2), (3) gives:
% 248.24/41.96  |   (5)  all_74_16 = all_74_17
% 248.24/41.96  | 
% 248.24/41.96  | REDUCE: (4), (5) imply:
% 248.24/41.96  |   (6)  $false
% 248.24/41.96  | 
% 248.24/41.96  | CLOSE: (6) is inconsistent.
% 248.24/41.96  | 
% 248.24/41.96  End of proof
% 248.24/41.96  
% 248.24/41.96  Sub-proof #10 shows that the following formulas are inconsistent:
% 248.24/41.96  ----------------------------------------------------------------
% 248.24/41.96    (1)  $i(all_74_18)
% 248.24/41.96    (2)  all_74_18 = n0
% 248.24/41.96    (3)  gt(all_74_18, n0)
% 248.24/41.96    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.24/41.96  
% 248.24/41.96  Begin of proof
% 248.24/41.96  | 
% 248.24/41.96  | REDUCE: (1), (2) imply:
% 248.24/41.96  |   (5)  $i(n0)
% 248.24/41.96  | 
% 248.24/41.96  | REDUCE: (2), (3) imply:
% 248.24/41.96  |   (6)  gt(n0, n0)
% 248.24/41.96  | 
% 248.24/41.96  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.24/41.96  |   (7)  $false
% 248.24/41.96  | 
% 248.24/41.96  | CLOSE: (7) is inconsistent.
% 248.24/41.96  | 
% 248.24/41.96  End of proof
% 248.24/41.96  
% 248.24/41.96  Sub-proof #11 shows that the following formulas are inconsistent:
% 248.24/41.96  ----------------------------------------------------------------
% 248.24/41.96    (1)  $i(all_74_19)
% 248.24/41.96    (2)  all_74_19 = n0
% 248.24/41.96    (3)  gt(all_74_19, n0)
% 248.24/41.96    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.24/41.96  
% 248.24/41.96  Begin of proof
% 248.24/41.96  | 
% 248.24/41.96  | REDUCE: (1), (2) imply:
% 248.24/41.96  |   (5)  $i(n0)
% 248.24/41.96  | 
% 248.24/41.96  | REDUCE: (2), (3) imply:
% 248.24/41.96  |   (6)  gt(n0, n0)
% 248.24/41.96  | 
% 248.24/41.96  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.24/41.96  |   (7)  $false
% 248.24/41.96  | 
% 248.24/41.96  | CLOSE: (7) is inconsistent.
% 248.24/41.96  | 
% 248.24/41.96  End of proof
% 248.24/41.96  
% 248.24/41.96  Sub-proof #12 shows that the following formulas are inconsistent:
% 248.24/41.96  ----------------------------------------------------------------
% 248.24/41.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.24/41.96           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.24/41.96           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.24/41.96           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.24/41.96    (2)   ~ gt(n0, n0)
% 248.24/41.96    (3)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.24/41.96           leq(n0, v0))
% 248.24/41.96    (4)  all_74_21 = n5
% 248.24/41.96    (5)  pred(n5) = n4
% 248.24/41.96    (6)  leq(n0, all_74_14)
% 248.24/41.96    (7)  leq(all_74_15, n5)
% 248.24/41.96    (8)  $i(n3)
% 248.24/41.96    (9)  all_74_15 = n0 | gt(all_74_15, n0)
% 248.24/41.96    (10)  all_74_15 = n5 | all_74_15 = n4 | all_74_15 = n3 | all_74_15 = n2 |
% 248.24/41.96          all_74_15 = n1 | all_74_15 = n0
% 248.24/41.96    (11)  $i(all_74_14)
% 248.24/41.96    (12)  a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13
% 248.24/41.96    (13)  gt(all_74_14, n0)
% 248.24/41.96    (14)  pred(n2) = n1
% 248.24/41.96    (15)  pred(n4) = n3
% 248.24/41.96    (16)  pred(n3) = n2
% 248.24/41.96    (17)  all_74_14 = n5 | all_74_14 = n4 | all_74_14 = n3 | all_74_14 = n2 |
% 248.24/41.96          all_74_14 = n1 | all_74_14 = n0
% 248.24/41.96    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.24/41.96            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.24/41.96    (19)  $i(n4)
% 248.24/41.96    (20)  leq(n0, all_74_15)
% 248.24/41.96    (21)  all_74_15 = n5 | gt(n5, all_74_15)
% 248.24/41.96    (22)  $i(all_74_15)
% 248.24/41.96    (23)  a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12
% 248.24/41.96    (24)   ~ (all_74_12 = all_74_13)
% 248.24/41.96    (25)  $i(n2)
% 248.24/41.96    (26)  $i(n5)
% 248.24/41.96    (27)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.24/41.96            leq(v0, v1) | gt(v1, v0))
% 248.24/41.96    (28)  leq(all_74_14, n5)
% 248.24/41.96    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.24/41.96          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.24/41.96              v0))
% 248.24/41.96    (30)  all_74_14 = n5 | gt(n5, all_74_14)
% 248.24/41.96  
% 248.24/41.96  Begin of proof
% 248.24/41.96  | 
% 248.24/41.96  | BETA: splitting (9) gives:
% 248.24/41.96  | 
% 248.24/41.96  | Case 1:
% 248.24/41.96  | | 
% 248.24/41.96  | |   (31)  gt(all_74_15, n0)
% 248.24/41.96  | | 
% 248.24/41.96  | | BETA: splitting (30) gives:
% 248.24/41.96  | | 
% 248.24/41.96  | | Case 1:
% 248.24/41.96  | | | 
% 248.24/41.96  | | |   (32)  gt(n5, all_74_14)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | GROUND_INST: instantiating (18) with all_74_14, n5, n4, simplifying with
% 248.24/41.96  | | |              (5), (11), (26), (32) gives:
% 248.24/41.96  | | |   (33)  leq(all_74_14, n4)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | GROUND_INST: instantiating (27) with all_74_14, n4, simplifying with (11),
% 248.24/41.96  | | |              (19), (33) gives:
% 248.24/41.96  | | |   (34)  all_74_14 = n4 | gt(n4, all_74_14)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | BETA: splitting (21) gives:
% 248.24/41.96  | | | 
% 248.24/41.96  | | | Case 1:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (35)  gt(n5, all_74_15)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | GROUND_INST: instantiating (18) with all_74_15, n5, n4, simplifying with
% 248.24/41.96  | | | |              (5), (22), (26), (35) gives:
% 248.24/41.96  | | | |   (36)  leq(all_74_15, n4)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | GROUND_INST: instantiating (27) with all_74_15, n4, simplifying with
% 248.24/41.96  | | | |              (19), (22), (36) gives:
% 248.24/41.96  | | | |   (37)  all_74_15 = n4 | gt(n4, all_74_15)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | BETA: splitting (10) gives:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | Case 1:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (38)  all_74_15 = n0
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | REDUCE: (31), (38) imply:
% 248.24/41.96  | | | | |   (39)  gt(n0, n0)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | PRED_UNIFY: (2), (39) imply:
% 248.24/41.96  | | | | |   (40)  $false
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | CLOSE: (40) is inconsistent.
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | Case 2:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (41)   ~ (all_74_15 = n0)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | BETA: splitting (17) gives:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | Case 1:
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | |   (42)  all_74_14 = n0
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | | REDUCE: (13), (42) imply:
% 248.24/41.96  | | | | | |   (43)  gt(n0, n0)
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | | PRED_UNIFY: (2), (43) imply:
% 248.24/41.96  | | | | | |   (44)  $false
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | | CLOSE: (44) is inconsistent.
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | Case 2:
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | |   (45)   ~ (all_74_14 = n0)
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (11), (12), (14), (15),
% 248.24/41.96  | | | | | |            (16), (18), (19), (20), (22), (23), (24), (25), (27),
% 248.24/41.96  | | | | | |            (28), (29), (34), (37), (41), (45) are inconsistent by
% 248.24/41.96  | | | | | |            sub-proof #16.
% 248.24/41.96  | | | | | | 
% 248.24/41.96  | | | | | End of split
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | End of split
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | Case 2:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (46)  all_74_15 = n5
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (23), (46) imply:
% 248.24/41.96  | | | |   (47)  a_select3(pminus_ds1_filter, all_74_14, n5) = all_74_12
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (12), (46) imply:
% 248.24/41.96  | | | |   (48)  a_select3(pminus_ds1_filter, n5, all_74_14) = all_74_13
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (7), (46) imply:
% 248.24/41.96  | | | |   (49)  leq(n5, n5)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (20), (46) imply:
% 248.24/41.96  | | | |   (50)  leq(n0, n5)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | BETA: splitting (17) gives:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | Case 1:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (51)  all_74_14 = n0
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | REDUCE: (13), (51) imply:
% 248.24/41.96  | | | | |   (52)  gt(n0, n0)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | PRED_UNIFY: (2), (52) imply:
% 248.24/41.96  | | | | |   (53)  $false
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | CLOSE: (53) is inconsistent.
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | Case 2:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (54)   ~ (all_74_14 = n0)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | REF_CLOSE: (1), (3), (4), (6), (8), (11), (14), (15), (16), (18),
% 248.24/41.96  | | | | |            (19), (24), (25), (26), (27), (28), (29), (34), (47), (48),
% 248.24/41.96  | | | | |            (49), (50), (54) are inconsistent by sub-proof #14.
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | End of split
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | End of split
% 248.24/41.96  | | | 
% 248.24/41.96  | | Case 2:
% 248.24/41.96  | | | 
% 248.24/41.96  | | |   (55)  all_74_14 = n5
% 248.24/41.96  | | | 
% 248.24/41.96  | | | REDUCE: (23), (55) imply:
% 248.24/41.96  | | |   (56)  a_select3(pminus_ds1_filter, n5, all_74_15) = all_74_12
% 248.24/41.96  | | | 
% 248.24/41.96  | | | REDUCE: (12), (55) imply:
% 248.24/41.96  | | |   (57)  a_select3(pminus_ds1_filter, all_74_15, n5) = all_74_13
% 248.24/41.96  | | | 
% 248.24/41.96  | | | REDUCE: (28), (55) imply:
% 248.24/41.96  | | |   (58)  leq(n5, n5)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | REDUCE: (6), (55) imply:
% 248.24/41.96  | | |   (59)  leq(n0, n5)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | BETA: splitting (21) gives:
% 248.24/41.96  | | | 
% 248.24/41.96  | | | Case 1:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (60)  gt(n5, all_74_15)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | GROUND_INST: instantiating (18) with all_74_15, n5, n4, simplifying with
% 248.24/41.96  | | | |              (5), (22), (26), (60) gives:
% 248.24/41.96  | | | |   (61)  leq(all_74_15, n4)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | GROUND_INST: instantiating (27) with all_74_15, n4, simplifying with
% 248.24/41.96  | | | |              (19), (22), (61) gives:
% 248.24/41.96  | | | |   (62)  all_74_15 = n4 | gt(n4, all_74_15)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | BETA: splitting (10) gives:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | Case 1:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (63)  all_74_15 = n0
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | REDUCE: (31), (63) imply:
% 248.24/41.96  | | | | |   (64)  gt(n0, n0)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | PRED_UNIFY: (2), (64) imply:
% 248.24/41.96  | | | | |   (65)  $false
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | CLOSE: (65) is inconsistent.
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | Case 2:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (66)   ~ (all_74_15 = n0)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (14), (15), (16), (18), (19),
% 248.24/41.96  | | | | |            (20), (22), (24), (25), (26), (27), (29), (56), (57), (58),
% 248.24/41.96  | | | | |            (59), (62), (66) are inconsistent by sub-proof #13.
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | End of split
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | Case 2:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (67)  all_74_15 = n5
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (57), (67) imply:
% 248.24/41.96  | | | |   (68)  a_select3(pminus_ds1_filter, n5, n5) = all_74_13
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (56), (67) imply:
% 248.24/41.96  | | | |   (69)  a_select3(pminus_ds1_filter, n5, n5) = all_74_12
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | GROUND_INST: instantiating (29) with all_74_13, all_74_12, n5, n5,
% 248.24/41.96  | | | |              pminus_ds1_filter, simplifying with (68), (69) gives:
% 248.24/41.96  | | | |   (70)  all_74_12 = all_74_13
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (24), (70) imply:
% 248.24/41.96  | | | |   (71)  $false
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | CLOSE: (71) is inconsistent.
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | End of split
% 248.24/41.96  | | | 
% 248.24/41.96  | | End of split
% 248.24/41.96  | | 
% 248.24/41.96  | Case 2:
% 248.24/41.96  | | 
% 248.24/41.96  | |   (72)  all_74_15 = n0
% 248.24/41.96  | |   (73)   ~ gt(all_74_15, n0)
% 248.24/41.96  | | 
% 248.24/41.96  | | REDUCE: (23), (72) imply:
% 248.24/41.96  | |   (74)  a_select3(pminus_ds1_filter, all_74_14, n0) = all_74_12
% 248.24/41.96  | | 
% 248.24/41.96  | | REDUCE: (12), (72) imply:
% 248.24/41.96  | |   (75)  a_select3(pminus_ds1_filter, n0, all_74_14) = all_74_13
% 248.24/41.96  | | 
% 248.24/41.96  | | REDUCE: (22), (72) imply:
% 248.24/41.96  | |   (76)  $i(n0)
% 248.24/41.96  | | 
% 248.24/41.96  | | REDUCE: (7), (72) imply:
% 248.24/41.96  | |   (77)  leq(n0, n5)
% 248.24/41.96  | | 
% 248.24/41.96  | | REDUCE: (20), (72) imply:
% 248.24/41.96  | |   (78)  leq(n0, n0)
% 248.24/41.96  | | 
% 248.24/41.96  | | BETA: splitting (30) gives:
% 248.24/41.96  | | 
% 248.24/41.96  | | Case 1:
% 248.24/41.96  | | | 
% 248.24/41.96  | | |   (79)  gt(n5, all_74_14)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | GROUND_INST: instantiating (18) with all_74_14, n5, n4, simplifying with
% 248.24/41.96  | | |              (5), (11), (26), (79) gives:
% 248.24/41.96  | | |   (80)  leq(all_74_14, n4)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | GROUND_INST: instantiating (27) with all_74_14, n4, simplifying with (11),
% 248.24/41.96  | | |              (19), (80) gives:
% 248.24/41.96  | | |   (81)  all_74_14 = n4 | gt(n4, all_74_14)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | BETA: splitting (17) gives:
% 248.24/41.96  | | | 
% 248.24/41.96  | | | Case 1:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (82)  all_74_14 = n0
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (13), (82) imply:
% 248.24/41.96  | | | |   (83)  gt(n0, n0)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | PRED_UNIFY: (2), (83) imply:
% 248.24/41.96  | | | |   (84)  $false
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | CLOSE: (84) is inconsistent.
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | Case 2:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (85)   ~ (all_74_14 = n0)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REF_CLOSE: (1), (3), (4), (6), (8), (11), (14), (15), (16), (18), (19),
% 248.24/41.96  | | | |            (24), (25), (27), (28), (29), (74), (75), (76), (77), (78),
% 248.24/41.96  | | | |            (81), (85) are inconsistent by sub-proof #21.
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | End of split
% 248.24/41.96  | | | 
% 248.24/41.96  | | Case 2:
% 248.24/41.96  | | | 
% 248.24/41.96  | | |   (86)  all_74_14 = n5
% 248.24/41.96  | | | 
% 248.24/41.96  | | | REDUCE: (74), (86) imply:
% 248.24/41.96  | | |   (87)  a_select3(pminus_ds1_filter, n5, n0) = all_74_12
% 248.24/41.96  | | | 
% 248.24/41.96  | | | REDUCE: (75), (86) imply:
% 248.24/41.96  | | |   (88)  a_select3(pminus_ds1_filter, n0, n5) = all_74_13
% 248.24/41.96  | | | 
% 248.24/41.96  | | | REDUCE: (28), (86) imply:
% 248.24/41.96  | | |   (89)  leq(n5, n5)
% 248.24/41.96  | | | 
% 248.24/41.96  | | | GROUND_INST: instantiating (1) with n0, n5, all_74_13, simplifying with
% 248.24/41.96  | | |              (26), (76), (77), (78), (88) gives:
% 248.24/41.96  | | |   (90)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.24/41.96  | | |         (a_select3(pminus_ds1_filter, n5, n0) = all_74_13 & $i(all_74_13))
% 248.24/41.96  | | | 
% 248.24/41.96  | | | BETA: splitting (90) gives:
% 248.24/41.96  | | | 
% 248.24/41.96  | | | Case 1:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (91)   ~ leq(n0, all_74_21)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | REDUCE: (4), (91) imply:
% 248.24/41.96  | | | |   (92)   ~ leq(n0, n5)
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | PRED_UNIFY: (77), (92) imply:
% 248.24/41.96  | | | |   (93)  $false
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | CLOSE: (93) is inconsistent.
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | Case 2:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | |   (94)   ~ leq(n5, all_74_21) | (a_select3(pminus_ds1_filter, n5, n0) =
% 248.24/41.96  | | | |           all_74_13 & $i(all_74_13))
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | BETA: splitting (94) gives:
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | | Case 1:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (95)   ~ leq(n5, all_74_21)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | REDUCE: (4), (95) imply:
% 248.24/41.96  | | | | |   (96)   ~ leq(n5, n5)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | PRED_UNIFY: (89), (96) imply:
% 248.24/41.96  | | | | |   (97)  $false
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | CLOSE: (97) is inconsistent.
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | Case 2:
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | |   (98)  a_select3(pminus_ds1_filter, n5, n0) = all_74_13 &
% 248.24/41.96  | | | | |         $i(all_74_13)
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | ALPHA: (98) implies:
% 248.24/41.96  | | | | |   (99)  a_select3(pminus_ds1_filter, n5, n0) = all_74_13
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | GROUND_INST: instantiating (29) with all_74_12, all_74_13, n0, n5,
% 248.24/41.96  | | | | |              pminus_ds1_filter, simplifying with (87), (99) gives:
% 248.24/41.96  | | | | |   (100)  all_74_12 = all_74_13
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | REDUCE: (24), (100) imply:
% 248.24/41.96  | | | | |   (101)  $false
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | | CLOSE: (101) is inconsistent.
% 248.24/41.96  | | | | | 
% 248.24/41.96  | | | | End of split
% 248.24/41.96  | | | | 
% 248.24/41.96  | | | End of split
% 248.24/41.96  | | | 
% 248.24/41.96  | | End of split
% 248.24/41.96  | | 
% 248.24/41.96  | End of split
% 248.24/41.96  | 
% 248.24/41.96  End of proof
% 248.24/41.96  
% 248.24/41.96  Sub-proof #13 shows that the following formulas are inconsistent:
% 248.24/41.96  ----------------------------------------------------------------
% 248.24/41.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.24/41.96           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.24/41.96           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.24/41.96           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.24/41.96    (2)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.24/41.96           leq(n0, v0))
% 248.24/41.96    (3)  leq(n0, n5)
% 248.24/41.96    (4)  all_74_21 = n5
% 248.24/41.96    (5)   ~ (all_74_15 = n0)
% 248.24/41.96    (6)  leq(all_74_15, n5)
% 248.24/41.96    (7)  $i(n3)
% 248.24/41.96    (8)  pred(n2) = n1
% 248.24/41.96    (9)  pred(n4) = n3
% 248.24/41.96    (10)  pred(n3) = n2
% 248.24/41.96    (11)  all_74_15 = n4 | gt(n4, all_74_15)
% 248.24/41.97    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.24/41.97            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.24/41.97    (13)  $i(n4)
% 248.24/41.97    (14)  leq(n0, all_74_15)
% 248.24/41.97    (15)  $i(all_74_15)
% 248.24/41.97    (16)  leq(n5, n5)
% 248.24/41.97    (17)   ~ (all_74_12 = all_74_13)
% 248.24/41.97    (18)  $i(n2)
% 248.24/41.97    (19)  $i(n5)
% 248.24/41.97    (20)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.24/41.97            leq(v0, v1) | gt(v1, v0))
% 248.24/41.97    (21)  a_select3(pminus_ds1_filter, n5, all_74_15) = all_74_12
% 248.24/41.97    (22)  a_select3(pminus_ds1_filter, all_74_15, n5) = all_74_13
% 248.24/41.97    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.24/41.97          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.24/41.97              v0))
% 248.24/41.97  
% 248.24/41.97  Begin of proof
% 248.24/41.97  | 
% 248.24/41.97  | BETA: splitting (11) gives:
% 248.24/41.97  | 
% 248.24/41.97  | Case 1:
% 248.24/41.97  | | 
% 248.24/41.97  | |   (24)  gt(n4, all_74_15)
% 248.24/41.97  | | 
% 248.24/41.97  | | GROUND_INST: instantiating (12) with all_74_15, n4, n3, simplifying with
% 248.24/41.97  | |              (9), (13), (15), (24) gives:
% 248.24/41.97  | |   (25)  leq(all_74_15, n3)
% 248.24/41.97  | | 
% 248.24/41.97  | | GROUND_INST: instantiating (20) with all_74_15, n3, simplifying with (7),
% 248.24/41.97  | |              (15), (25) gives:
% 248.24/41.97  | |   (26)  all_74_15 = n3 | gt(n3, all_74_15)
% 248.24/41.97  | | 
% 248.24/41.97  | | BETA: splitting (26) gives:
% 248.24/41.97  | | 
% 248.24/41.97  | | Case 1:
% 248.24/41.97  | | | 
% 248.24/41.97  | | |   (27)  gt(n3, all_74_15)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | GROUND_INST: instantiating (12) with all_74_15, n3, n2, simplifying with
% 248.24/41.97  | | |              (7), (10), (15), (27) gives:
% 248.24/41.97  | | |   (28)  leq(all_74_15, n2)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | GROUND_INST: instantiating (20) with all_74_15, n2, simplifying with (15),
% 248.24/41.97  | | |              (18), (28) gives:
% 248.24/41.97  | | |   (29)  all_74_15 = n2 | gt(n2, all_74_15)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | BETA: splitting (29) gives:
% 248.24/41.97  | | | 
% 248.24/41.97  | | | Case 1:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | |   (30)  gt(n2, all_74_15)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | GROUND_INST: instantiating (12) with all_74_15, n2, n1, simplifying with
% 248.24/41.97  | | | |              (8), (15), (18), (30) gives:
% 248.24/41.97  | | | |   (31)  leq(all_74_15, n1)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | GROUND_INST: instantiating (2) with all_74_15, simplifying with (14),
% 248.24/41.97  | | | |              (15), (31) gives:
% 248.24/41.97  | | | |   (32)  all_74_15 = n1 | all_74_15 = n0
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | BETA: splitting (32) gives:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | Case 1:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (33)  all_74_15 = n0
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (5), (33) imply:
% 248.24/41.97  | | | | |   (34)  $false
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | CLOSE: (34) is inconsistent.
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | Case 2:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (35)  all_74_15 = n1
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (22), (35) imply:
% 248.24/41.97  | | | | |   (36)  a_select3(pminus_ds1_filter, n1, n5) = all_74_13
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (21), (35) imply:
% 248.24/41.97  | | | | |   (37)  a_select3(pminus_ds1_filter, n5, n1) = all_74_12
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (15), (35) imply:
% 248.24/41.97  | | | | |   (38)  $i(n1)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (6), (35) imply:
% 248.24/41.97  | | | | |   (39)  leq(n1, n5)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (14), (35) imply:
% 248.24/41.97  | | | | |   (40)  leq(n0, n1)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | GROUND_INST: instantiating (1) with n1, n5, all_74_13, simplifying
% 248.24/41.97  | | | | |              with (3), (19), (36), (38), (40) gives:
% 248.24/41.97  | | | | |   (41)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.24/41.97  | | | | |         (a_select3(pminus_ds1_filter, n5, n1) = all_74_13 &
% 248.24/41.97  | | | | |           $i(all_74_13))
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | BETA: splitting (41) gives:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | Case 1:
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | |   (42)   ~ leq(n5, all_74_21)
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | REDUCE: (4), (42) imply:
% 248.24/41.97  | | | | | |   (43)   ~ leq(n5, n5)
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | PRED_UNIFY: (16), (43) imply:
% 248.24/41.97  | | | | | |   (44)  $false
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | CLOSE: (44) is inconsistent.
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | Case 2:
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n5,
% 248.24/41.97  | | | | | |             n1) = all_74_13 & $i(all_74_13))
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | BETA: splitting (45) gives:
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | Case 1:
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | | REDUCE: (4), (46) imply:
% 248.24/41.97  | | | | | | |   (47)   ~ leq(n1, n5)
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 248.24/41.97  | | | | | | |   (48)  $false
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | | CLOSE: (48) is inconsistent.
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | Case 2:
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | |   (49)  a_select3(pminus_ds1_filter, n5, n1) = all_74_13 &
% 248.24/41.97  | | | | | | |         $i(all_74_13)
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | | ALPHA: (49) implies:
% 248.24/41.97  | | | | | | |   (50)  a_select3(pminus_ds1_filter, n5, n1) = all_74_13
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | | GROUND_INST: instantiating (23) with all_74_13, all_74_12, n1, n5,
% 248.24/41.97  | | | | | | |              pminus_ds1_filter, simplifying with (37), (50) gives:
% 248.24/41.97  | | | | | | |   (51)  all_74_12 = all_74_13
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | | REDUCE: (17), (51) imply:
% 248.24/41.97  | | | | | | |   (52)  $false
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | | CLOSE: (52) is inconsistent.
% 248.24/41.97  | | | | | | | 
% 248.24/41.97  | | | | | | End of split
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | End of split
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | End of split
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | Case 2:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | |   (53)  all_74_15 = n2
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | REDUCE: (22), (53) imply:
% 248.24/41.97  | | | |   (54)  a_select3(pminus_ds1_filter, n2, n5) = all_74_13
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | REDUCE: (21), (53) imply:
% 248.24/41.97  | | | |   (55)  a_select3(pminus_ds1_filter, n5, n2) = all_74_12
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | REDUCE: (6), (53) imply:
% 248.24/41.97  | | | |   (56)  leq(n2, n5)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | REDUCE: (14), (53) imply:
% 248.24/41.97  | | | |   (57)  leq(n0, n2)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | GROUND_INST: instantiating (1) with n2, n5, all_74_13, simplifying with
% 248.24/41.97  | | | |              (3), (18), (19), (54), (57) gives:
% 248.24/41.97  | | | |   (58)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.24/41.97  | | | |         (a_select3(pminus_ds1_filter, n5, n2) = all_74_13 &
% 248.24/41.97  | | | |           $i(all_74_13))
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | BETA: splitting (58) gives:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | Case 1:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (59)   ~ leq(n5, all_74_21)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (4), (59) imply:
% 248.24/41.97  | | | | |   (60)   ~ leq(n5, n5)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | PRED_UNIFY: (16), (60) imply:
% 248.24/41.97  | | | | |   (61)  $false
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | CLOSE: (61) is inconsistent.
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | Case 2:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (62)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n5, n2)
% 248.24/41.97  | | | | |           = all_74_13 & $i(all_74_13))
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | BETA: splitting (62) gives:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | Case 1:
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | |   (63)   ~ leq(n2, all_74_21)
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | REDUCE: (4), (63) imply:
% 248.24/41.97  | | | | | |   (64)   ~ leq(n2, n5)
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | PRED_UNIFY: (56), (64) imply:
% 248.24/41.97  | | | | | |   (65)  $false
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | CLOSE: (65) is inconsistent.
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | Case 2:
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | |   (66)  a_select3(pminus_ds1_filter, n5, n2) = all_74_13 &
% 248.24/41.97  | | | | | |         $i(all_74_13)
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | ALPHA: (66) implies:
% 248.24/41.97  | | | | | |   (67)  a_select3(pminus_ds1_filter, n5, n2) = all_74_13
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | GROUND_INST: instantiating (23) with all_74_13, all_74_12, n2, n5,
% 248.24/41.97  | | | | | |              pminus_ds1_filter, simplifying with (55), (67) gives:
% 248.24/41.97  | | | | | |   (68)  all_74_12 = all_74_13
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | REDUCE: (17), (68) imply:
% 248.24/41.97  | | | | | |   (69)  $false
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | | CLOSE: (69) is inconsistent.
% 248.24/41.97  | | | | | | 
% 248.24/41.97  | | | | | End of split
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | End of split
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | End of split
% 248.24/41.97  | | | 
% 248.24/41.97  | | Case 2:
% 248.24/41.97  | | | 
% 248.24/41.97  | | |   (70)  all_74_15 = n3
% 248.24/41.97  | | | 
% 248.24/41.97  | | | REDUCE: (22), (70) imply:
% 248.24/41.97  | | |   (71)  a_select3(pminus_ds1_filter, n3, n5) = all_74_13
% 248.24/41.97  | | | 
% 248.24/41.97  | | | REDUCE: (21), (70) imply:
% 248.24/41.97  | | |   (72)  a_select3(pminus_ds1_filter, n5, n3) = all_74_12
% 248.24/41.97  | | | 
% 248.24/41.97  | | | REDUCE: (6), (70) imply:
% 248.24/41.97  | | |   (73)  leq(n3, n5)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | REDUCE: (14), (70) imply:
% 248.24/41.97  | | |   (74)  leq(n0, n3)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | GROUND_INST: instantiating (1) with n3, n5, all_74_13, simplifying with
% 248.24/41.97  | | |              (3), (7), (19), (71), (74) gives:
% 248.24/41.97  | | |   (75)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.24/41.97  | | |         (a_select3(pminus_ds1_filter, n5, n3) = all_74_13 & $i(all_74_13))
% 248.24/41.97  | | | 
% 248.24/41.97  | | | BETA: splitting (75) gives:
% 248.24/41.97  | | | 
% 248.24/41.97  | | | Case 1:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | |   (76)   ~ leq(n5, all_74_21)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | REDUCE: (4), (76) imply:
% 248.24/41.97  | | | |   (77)   ~ leq(n5, n5)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | PRED_UNIFY: (16), (77) imply:
% 248.24/41.97  | | | |   (78)  $false
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | CLOSE: (78) is inconsistent.
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | Case 2:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | |   (79)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n5, n3) =
% 248.24/41.97  | | | |           all_74_13 & $i(all_74_13))
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | BETA: splitting (79) gives:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | Case 1:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (80)   ~ leq(n3, all_74_21)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (4), (80) imply:
% 248.24/41.97  | | | | |   (81)   ~ leq(n3, n5)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | PRED_UNIFY: (73), (81) imply:
% 248.24/41.97  | | | | |   (82)  $false
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | CLOSE: (82) is inconsistent.
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | Case 2:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (83)  a_select3(pminus_ds1_filter, n5, n3) = all_74_13 &
% 248.24/41.97  | | | | |         $i(all_74_13)
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | ALPHA: (83) implies:
% 248.24/41.97  | | | | |   (84)  a_select3(pminus_ds1_filter, n5, n3) = all_74_13
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REF_CLOSE: (17), (23), (72), (84) are inconsistent by sub-proof #15.
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | End of split
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | End of split
% 248.24/41.97  | | | 
% 248.24/41.97  | | End of split
% 248.24/41.97  | | 
% 248.24/41.97  | Case 2:
% 248.24/41.97  | | 
% 248.24/41.97  | |   (85)  all_74_15 = n4
% 248.24/41.97  | | 
% 248.24/41.97  | | REDUCE: (22), (85) imply:
% 248.24/41.97  | |   (86)  a_select3(pminus_ds1_filter, n4, n5) = all_74_13
% 248.24/41.97  | | 
% 248.24/41.97  | | REDUCE: (21), (85) imply:
% 248.24/41.97  | |   (87)  a_select3(pminus_ds1_filter, n5, n4) = all_74_12
% 248.24/41.97  | | 
% 248.24/41.97  | | REDUCE: (6), (85) imply:
% 248.24/41.97  | |   (88)  leq(n4, n5)
% 248.24/41.97  | | 
% 248.24/41.97  | | REDUCE: (14), (85) imply:
% 248.24/41.97  | |   (89)  leq(n0, n4)
% 248.24/41.97  | | 
% 248.24/41.97  | | GROUND_INST: instantiating (1) with n4, n5, all_74_13, simplifying with (3),
% 248.24/41.97  | |              (13), (19), (86), (89) gives:
% 248.24/41.97  | |   (90)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 248.24/41.97  | |         (a_select3(pminus_ds1_filter, n5, n4) = all_74_13 & $i(all_74_13))
% 248.24/41.97  | | 
% 248.24/41.97  | | BETA: splitting (90) gives:
% 248.24/41.97  | | 
% 248.24/41.97  | | Case 1:
% 248.24/41.97  | | | 
% 248.24/41.97  | | |   (91)   ~ leq(n5, all_74_21)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | REDUCE: (4), (91) imply:
% 248.24/41.97  | | |   (92)   ~ leq(n5, n5)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | PRED_UNIFY: (16), (92) imply:
% 248.24/41.97  | | |   (93)  $false
% 248.24/41.97  | | | 
% 248.24/41.97  | | | CLOSE: (93) is inconsistent.
% 248.24/41.97  | | | 
% 248.24/41.97  | | Case 2:
% 248.24/41.97  | | | 
% 248.24/41.97  | | |   (94)   ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n5, n4) =
% 248.24/41.97  | | |           all_74_13 & $i(all_74_13))
% 248.24/41.97  | | | 
% 248.24/41.97  | | | BETA: splitting (94) gives:
% 248.24/41.97  | | | 
% 248.24/41.97  | | | Case 1:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | |   (95)   ~ leq(n4, all_74_21)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | REDUCE: (4), (95) imply:
% 248.24/41.97  | | | |   (96)   ~ leq(n4, n5)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | PRED_UNIFY: (88), (96) imply:
% 248.24/41.97  | | | |   (97)  $false
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | CLOSE: (97) is inconsistent.
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | Case 2:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | |   (98)  a_select3(pminus_ds1_filter, n5, n4) = all_74_13 & $i(all_74_13)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | ALPHA: (98) implies:
% 248.24/41.97  | | | |   (99)  a_select3(pminus_ds1_filter, n5, n4) = all_74_13
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | GROUND_INST: instantiating (23) with all_74_13, all_74_12, n4, n5,
% 248.24/41.97  | | | |              pminus_ds1_filter, simplifying with (87), (99) gives:
% 248.24/41.97  | | | |   (100)  all_74_12 = all_74_13
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | REDUCE: (17), (100) imply:
% 248.24/41.97  | | | |   (101)  $false
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | CLOSE: (101) is inconsistent.
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | End of split
% 248.24/41.97  | | | 
% 248.24/41.97  | | End of split
% 248.24/41.97  | | 
% 248.24/41.97  | End of split
% 248.24/41.97  | 
% 248.24/41.97  End of proof
% 248.24/41.97  
% 248.24/41.97  Sub-proof #14 shows that the following formulas are inconsistent:
% 248.24/41.97  ----------------------------------------------------------------
% 248.24/41.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.24/41.97           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.24/41.97           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.24/41.97           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.24/41.97    (2)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.24/41.97           leq(n0, v0))
% 248.24/41.97    (3)  leq(n0, n5)
% 248.24/41.97    (4)  all_74_21 = n5
% 248.24/41.97    (5)  a_select3(pminus_ds1_filter, n5, all_74_14) = all_74_13
% 248.24/41.97    (6)  leq(n0, all_74_14)
% 248.24/41.97    (7)  $i(n3)
% 248.24/41.97    (8)  a_select3(pminus_ds1_filter, all_74_14, n5) = all_74_12
% 248.24/41.97    (9)  all_74_14 = n4 | gt(n4, all_74_14)
% 248.24/41.97    (10)  $i(all_74_14)
% 248.24/41.97    (11)  pred(n2) = n1
% 248.24/41.97    (12)  pred(n4) = n3
% 248.24/41.97    (13)  pred(n3) = n2
% 248.24/41.97    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.24/41.97            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.24/41.97    (15)  $i(n4)
% 248.24/41.97    (16)  leq(n5, n5)
% 248.24/41.97    (17)   ~ (all_74_14 = n0)
% 248.24/41.97    (18)   ~ (all_74_12 = all_74_13)
% 248.24/41.97    (19)  $i(n2)
% 248.24/41.97    (20)  $i(n5)
% 248.24/41.97    (21)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.24/41.97            leq(v0, v1) | gt(v1, v0))
% 248.24/41.97    (22)  leq(all_74_14, n5)
% 248.24/41.97    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.24/41.97          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.24/41.97              v0))
% 248.24/41.97  
% 248.24/41.97  Begin of proof
% 248.24/41.97  | 
% 248.24/41.97  | BETA: splitting (9) gives:
% 248.24/41.97  | 
% 248.24/41.97  | Case 1:
% 248.24/41.97  | | 
% 248.24/41.97  | |   (24)  gt(n4, all_74_14)
% 248.24/41.97  | | 
% 248.24/41.97  | | GROUND_INST: instantiating (14) with all_74_14, n4, n3, simplifying with
% 248.24/41.97  | |              (10), (12), (15), (24) gives:
% 248.24/41.97  | |   (25)  leq(all_74_14, n3)
% 248.24/41.97  | | 
% 248.24/41.97  | | GROUND_INST: instantiating (21) with all_74_14, n3, simplifying with (7),
% 248.24/41.97  | |              (10), (25) gives:
% 248.24/41.97  | |   (26)  all_74_14 = n3 | gt(n3, all_74_14)
% 248.24/41.97  | | 
% 248.24/41.97  | | BETA: splitting (26) gives:
% 248.24/41.97  | | 
% 248.24/41.97  | | Case 1:
% 248.24/41.97  | | | 
% 248.24/41.97  | | |   (27)  gt(n3, all_74_14)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | GROUND_INST: instantiating (14) with all_74_14, n3, n2, simplifying with
% 248.24/41.97  | | |              (7), (10), (13), (27) gives:
% 248.24/41.97  | | |   (28)  leq(all_74_14, n2)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | GROUND_INST: instantiating (21) with all_74_14, n2, simplifying with (10),
% 248.24/41.97  | | |              (19), (28) gives:
% 248.24/41.97  | | |   (29)  all_74_14 = n2 | gt(n2, all_74_14)
% 248.24/41.97  | | | 
% 248.24/41.97  | | | BETA: splitting (29) gives:
% 248.24/41.97  | | | 
% 248.24/41.97  | | | Case 1:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | |   (30)  gt(n2, all_74_14)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | GROUND_INST: instantiating (14) with all_74_14, n2, n1, simplifying with
% 248.24/41.97  | | | |              (10), (11), (19), (30) gives:
% 248.24/41.97  | | | |   (31)  leq(all_74_14, n1)
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | GROUND_INST: instantiating (2) with all_74_14, simplifying with (6),
% 248.24/41.97  | | | |              (10), (31) gives:
% 248.24/41.97  | | | |   (32)  all_74_14 = n1 | all_74_14 = n0
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | BETA: splitting (32) gives:
% 248.24/41.97  | | | | 
% 248.24/41.97  | | | | Case 1:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (33)  all_74_14 = n0
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (17), (33) imply:
% 248.24/41.97  | | | | |   (34)  $false
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | CLOSE: (34) is inconsistent.
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | Case 2:
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | |   (35)  all_74_14 = n1
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (8), (35) imply:
% 248.24/41.97  | | | | |   (36)  a_select3(pminus_ds1_filter, n1, n5) = all_74_12
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (5), (35) imply:
% 248.24/41.97  | | | | |   (37)  a_select3(pminus_ds1_filter, n5, n1) = all_74_13
% 248.24/41.97  | | | | | 
% 248.24/41.97  | | | | | REDUCE: (10), (35) imply:
% 248.40/41.98  | | | | |   (38)  $i(n1)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | REDUCE: (22), (35) imply:
% 248.40/41.98  | | | | |   (39)  leq(n1, n5)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | REDUCE: (6), (35) imply:
% 248.40/41.98  | | | | |   (40)  leq(n0, n1)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | GROUND_INST: instantiating (1) with n1, n5, all_74_12, simplifying
% 248.40/41.98  | | | | |              with (3), (20), (36), (38), (40) gives:
% 248.40/41.98  | | | | |   (41)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/41.98  | | | | |         (a_select3(pminus_ds1_filter, n5, n1) = all_74_12 &
% 248.40/41.98  | | | | |           $i(all_74_12))
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | BETA: splitting (41) gives:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | Case 1:
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | |   (42)   ~ leq(n5, all_74_21)
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | REDUCE: (4), (42) imply:
% 248.40/41.98  | | | | | |   (43)   ~ leq(n5, n5)
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | PRED_UNIFY: (16), (43) imply:
% 248.40/41.98  | | | | | |   (44)  $false
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | CLOSE: (44) is inconsistent.
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | Case 2:
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n5,
% 248.40/41.98  | | | | | |             n1) = all_74_12 & $i(all_74_12))
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | BETA: splitting (45) gives:
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | Case 1:
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (4), (46) imply:
% 248.40/41.98  | | | | | | |   (47)   ~ leq(n1, n5)
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 248.40/41.98  | | | | | | |   (48)  $false
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | CLOSE: (48) is inconsistent.
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | Case 2:
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | |   (49)  a_select3(pminus_ds1_filter, n5, n1) = all_74_12 &
% 248.40/41.98  | | | | | | |         $i(all_74_12)
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | ALPHA: (49) implies:
% 248.40/41.98  | | | | | | |   (50)  a_select3(pminus_ds1_filter, n5, n1) = all_74_12
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | GROUND_INST: instantiating (23) with all_74_13, all_74_12, n1, n5,
% 248.40/41.98  | | | | | | |              pminus_ds1_filter, simplifying with (37), (50) gives:
% 248.40/41.98  | | | | | | |   (51)  all_74_12 = all_74_13
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (18), (51) imply:
% 248.40/41.98  | | | | | | |   (52)  $false
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | CLOSE: (52) is inconsistent.
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | End of split
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | End of split
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | End of split
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | Case 2:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | |   (53)  all_74_14 = n2
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | REDUCE: (8), (53) imply:
% 248.40/41.98  | | | |   (54)  a_select3(pminus_ds1_filter, n2, n5) = all_74_12
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | REDUCE: (5), (53) imply:
% 248.40/41.98  | | | |   (55)  a_select3(pminus_ds1_filter, n5, n2) = all_74_13
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | REDUCE: (22), (53) imply:
% 248.40/41.98  | | | |   (56)  leq(n2, n5)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | REDUCE: (6), (53) imply:
% 248.40/41.98  | | | |   (57)  leq(n0, n2)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | GROUND_INST: instantiating (1) with n2, n5, all_74_12, simplifying with
% 248.40/41.98  | | | |              (3), (19), (20), (54), (57) gives:
% 248.40/41.98  | | | |   (58)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/41.98  | | | |         (a_select3(pminus_ds1_filter, n5, n2) = all_74_12 &
% 248.40/41.98  | | | |           $i(all_74_12))
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | BETA: splitting (58) gives:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | Case 1:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | |   (59)   ~ leq(n5, all_74_21)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | REDUCE: (4), (59) imply:
% 248.40/41.98  | | | | |   (60)   ~ leq(n5, n5)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | PRED_UNIFY: (16), (60) imply:
% 248.40/41.98  | | | | |   (61)  $false
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | CLOSE: (61) is inconsistent.
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | Case 2:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | |   (62)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n5, n2)
% 248.40/41.98  | | | | |           = all_74_12 & $i(all_74_12))
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | BETA: splitting (62) gives:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | Case 1:
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | |   (63)   ~ leq(n2, all_74_21)
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | REDUCE: (4), (63) imply:
% 248.40/41.98  | | | | | |   (64)   ~ leq(n2, n5)
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | PRED_UNIFY: (56), (64) imply:
% 248.40/41.98  | | | | | |   (65)  $false
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | CLOSE: (65) is inconsistent.
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | Case 2:
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | |   (66)  a_select3(pminus_ds1_filter, n5, n2) = all_74_12 &
% 248.40/41.98  | | | | | |         $i(all_74_12)
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | ALPHA: (66) implies:
% 248.40/41.98  | | | | | |   (67)  a_select3(pminus_ds1_filter, n5, n2) = all_74_12
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | GROUND_INST: instantiating (23) with all_74_13, all_74_12, n2, n5,
% 248.40/41.98  | | | | | |              pminus_ds1_filter, simplifying with (55), (67) gives:
% 248.40/41.98  | | | | | |   (68)  all_74_12 = all_74_13
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | REDUCE: (18), (68) imply:
% 248.40/41.98  | | | | | |   (69)  $false
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | CLOSE: (69) is inconsistent.
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | End of split
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | End of split
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | End of split
% 248.40/41.98  | | | 
% 248.40/41.98  | | Case 2:
% 248.40/41.98  | | | 
% 248.40/41.98  | | |   (70)  all_74_14 = n3
% 248.40/41.98  | | | 
% 248.40/41.98  | | | REDUCE: (8), (70) imply:
% 248.40/41.98  | | |   (71)  a_select3(pminus_ds1_filter, n3, n5) = all_74_12
% 248.40/41.98  | | | 
% 248.40/41.98  | | | REDUCE: (5), (70) imply:
% 248.40/41.98  | | |   (72)  a_select3(pminus_ds1_filter, n5, n3) = all_74_13
% 248.40/41.98  | | | 
% 248.40/41.98  | | | REDUCE: (22), (70) imply:
% 248.40/41.98  | | |   (73)  leq(n3, n5)
% 248.40/41.98  | | | 
% 248.40/41.98  | | | REDUCE: (6), (70) imply:
% 248.40/41.98  | | |   (74)  leq(n0, n3)
% 248.40/41.98  | | | 
% 248.40/41.98  | | | GROUND_INST: instantiating (1) with n3, n5, all_74_12, simplifying with
% 248.40/41.98  | | |              (3), (7), (20), (71), (74) gives:
% 248.40/41.98  | | |   (75)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.40/41.98  | | |         (a_select3(pminus_ds1_filter, n5, n3) = all_74_12 & $i(all_74_12))
% 248.40/41.98  | | | 
% 248.40/41.98  | | | BETA: splitting (75) gives:
% 248.40/41.98  | | | 
% 248.40/41.98  | | | Case 1:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | |   (76)   ~ leq(n5, all_74_21)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | REDUCE: (4), (76) imply:
% 248.40/41.98  | | | |   (77)   ~ leq(n5, n5)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | PRED_UNIFY: (16), (77) imply:
% 248.40/41.98  | | | |   (78)  $false
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | CLOSE: (78) is inconsistent.
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | Case 2:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | |   (79)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n5, n3) =
% 248.40/41.98  | | | |           all_74_12 & $i(all_74_12))
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | BETA: splitting (79) gives:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | Case 1:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | |   (80)   ~ leq(n3, all_74_21)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | REDUCE: (4), (80) imply:
% 248.40/41.98  | | | | |   (81)   ~ leq(n3, n5)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | PRED_UNIFY: (73), (81) imply:
% 248.40/41.98  | | | | |   (82)  $false
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | CLOSE: (82) is inconsistent.
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | Case 2:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | |   (83)  a_select3(pminus_ds1_filter, n5, n3) = all_74_12 &
% 248.40/41.98  | | | | |         $i(all_74_12)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | ALPHA: (83) implies:
% 248.40/41.98  | | | | |   (84)  a_select3(pminus_ds1_filter, n5, n3) = all_74_12
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | REF_CLOSE: (18), (23), (72), (84) are inconsistent by sub-proof #15.
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | End of split
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | End of split
% 248.40/41.98  | | | 
% 248.40/41.98  | | End of split
% 248.40/41.98  | | 
% 248.40/41.98  | Case 2:
% 248.40/41.98  | | 
% 248.40/41.98  | |   (85)  all_74_14 = n4
% 248.40/41.98  | | 
% 248.40/41.98  | | REDUCE: (8), (85) imply:
% 248.40/41.98  | |   (86)  a_select3(pminus_ds1_filter, n4, n5) = all_74_12
% 248.40/41.98  | | 
% 248.40/41.98  | | REDUCE: (5), (85) imply:
% 248.40/41.98  | |   (87)  a_select3(pminus_ds1_filter, n5, n4) = all_74_13
% 248.40/41.98  | | 
% 248.40/41.98  | | REDUCE: (22), (85) imply:
% 248.40/41.98  | |   (88)  leq(n4, n5)
% 248.40/41.98  | | 
% 248.40/41.98  | | REDUCE: (6), (85) imply:
% 248.40/41.98  | |   (89)  leq(n0, n4)
% 248.40/41.98  | | 
% 248.40/41.98  | | GROUND_INST: instantiating (1) with n4, n5, all_74_12, simplifying with (3),
% 248.40/41.98  | |              (15), (20), (86), (89) gives:
% 248.40/41.98  | |   (90)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 248.40/41.98  | |         (a_select3(pminus_ds1_filter, n5, n4) = all_74_12 & $i(all_74_12))
% 248.40/41.98  | | 
% 248.40/41.98  | | BETA: splitting (90) gives:
% 248.40/41.98  | | 
% 248.40/41.98  | | Case 1:
% 248.40/41.98  | | | 
% 248.40/41.98  | | |   (91)   ~ leq(n5, all_74_21)
% 248.40/41.98  | | | 
% 248.40/41.98  | | | REDUCE: (4), (91) imply:
% 248.40/41.98  | | |   (92)   ~ leq(n5, n5)
% 248.40/41.98  | | | 
% 248.40/41.98  | | | PRED_UNIFY: (16), (92) imply:
% 248.40/41.98  | | |   (93)  $false
% 248.40/41.98  | | | 
% 248.40/41.98  | | | CLOSE: (93) is inconsistent.
% 248.40/41.98  | | | 
% 248.40/41.98  | | Case 2:
% 248.40/41.98  | | | 
% 248.40/41.98  | | |   (94)   ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n5, n4) =
% 248.40/41.98  | | |           all_74_12 & $i(all_74_12))
% 248.40/41.98  | | | 
% 248.40/41.98  | | | BETA: splitting (94) gives:
% 248.40/41.98  | | | 
% 248.40/41.98  | | | Case 1:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | |   (95)   ~ leq(n4, all_74_21)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | REDUCE: (4), (95) imply:
% 248.40/41.98  | | | |   (96)   ~ leq(n4, n5)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | PRED_UNIFY: (88), (96) imply:
% 248.40/41.98  | | | |   (97)  $false
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | CLOSE: (97) is inconsistent.
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | Case 2:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | |   (98)  a_select3(pminus_ds1_filter, n5, n4) = all_74_12 & $i(all_74_12)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | ALPHA: (98) implies:
% 248.40/41.98  | | | |   (99)  a_select3(pminus_ds1_filter, n5, n4) = all_74_12
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | GROUND_INST: instantiating (23) with all_74_13, all_74_12, n4, n5,
% 248.40/41.98  | | | |              pminus_ds1_filter, simplifying with (87), (99) gives:
% 248.40/41.98  | | | |   (100)  all_74_12 = all_74_13
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | REDUCE: (18), (100) imply:
% 248.40/41.98  | | | |   (101)  $false
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | CLOSE: (101) is inconsistent.
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | End of split
% 248.40/41.98  | | | 
% 248.40/41.98  | | End of split
% 248.40/41.98  | | 
% 248.40/41.98  | End of split
% 248.40/41.98  | 
% 248.40/41.98  End of proof
% 248.40/41.98  
% 248.40/41.98  Sub-proof #15 shows that the following formulas are inconsistent:
% 248.40/41.98  ----------------------------------------------------------------
% 248.40/41.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/41.98           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/41.98             v0))
% 248.40/41.98    (2)  a_select3(pminus_ds1_filter, n5, n3) = all_74_12
% 248.40/41.98    (3)  a_select3(pminus_ds1_filter, n5, n3) = all_74_13
% 248.40/41.98    (4)   ~ (all_74_12 = all_74_13)
% 248.40/41.98  
% 248.40/41.98  Begin of proof
% 248.40/41.98  | 
% 248.40/41.98  | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n3, n5,
% 248.40/41.98  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/41.98  |   (5)  all_74_12 = all_74_13
% 248.40/41.98  | 
% 248.40/41.98  | REDUCE: (4), (5) imply:
% 248.40/41.98  |   (6)  $false
% 248.40/41.98  | 
% 248.40/41.98  | CLOSE: (6) is inconsistent.
% 248.40/41.98  | 
% 248.40/41.98  End of proof
% 248.40/41.98  
% 248.40/41.98  Sub-proof #16 shows that the following formulas are inconsistent:
% 248.40/41.98  ----------------------------------------------------------------
% 248.40/41.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.40/41.98           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.40/41.98           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.40/41.98           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/41.98    (2)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/41.98           leq(n0, v0))
% 248.40/41.98    (3)  all_74_21 = n5
% 248.40/41.98    (4)   ~ (all_74_15 = n0)
% 248.40/41.98    (5)  leq(n0, all_74_14)
% 248.40/41.98    (6)  leq(all_74_15, n5)
% 248.40/41.98    (7)  $i(n3)
% 248.40/41.98    (8)  all_74_14 = n4 | gt(n4, all_74_14)
% 248.40/41.98    (9)  $i(all_74_14)
% 248.40/41.98    (10)  a_select3(pminus_ds1_filter, all_74_15, all_74_14) = all_74_13
% 248.40/41.98    (11)  pred(n2) = n1
% 248.40/41.98    (12)  pred(n4) = n3
% 248.40/41.98    (13)  pred(n3) = n2
% 248.40/41.98    (14)  all_74_15 = n4 | gt(n4, all_74_15)
% 248.40/41.98    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/41.98            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/41.98    (16)  $i(n4)
% 248.40/41.98    (17)  leq(n0, all_74_15)
% 248.40/41.98    (18)  $i(all_74_15)
% 248.40/41.98    (19)  a_select3(pminus_ds1_filter, all_74_14, all_74_15) = all_74_12
% 248.40/41.98    (20)   ~ (all_74_14 = n0)
% 248.40/41.98    (21)   ~ (all_74_12 = all_74_13)
% 248.40/41.98    (22)  $i(n2)
% 248.40/41.98    (23)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.40/41.98            leq(v0, v1) | gt(v1, v0))
% 248.40/41.98    (24)  leq(all_74_14, n5)
% 248.40/41.98    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/41.98          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/41.98              v0))
% 248.40/41.98  
% 248.40/41.98  Begin of proof
% 248.40/41.98  | 
% 248.40/41.98  | BETA: splitting (8) gives:
% 248.40/41.98  | 
% 248.40/41.98  | Case 1:
% 248.40/41.98  | | 
% 248.40/41.98  | |   (26)  gt(n4, all_74_14)
% 248.40/41.98  | | 
% 248.40/41.98  | | GROUND_INST: instantiating (15) with all_74_14, n4, n3, simplifying with
% 248.40/41.98  | |              (9), (12), (16), (26) gives:
% 248.40/41.98  | |   (27)  leq(all_74_14, n3)
% 248.40/41.98  | | 
% 248.40/41.98  | | GROUND_INST: instantiating (23) with all_74_14, n3, simplifying with (7),
% 248.40/41.98  | |              (9), (27) gives:
% 248.40/41.98  | |   (28)  all_74_14 = n3 | gt(n3, all_74_14)
% 248.40/41.98  | | 
% 248.40/41.98  | | BETA: splitting (14) gives:
% 248.40/41.98  | | 
% 248.40/41.98  | | Case 1:
% 248.40/41.98  | | | 
% 248.40/41.98  | | |   (29)  gt(n4, all_74_15)
% 248.40/41.98  | | | 
% 248.40/41.98  | | | GROUND_INST: instantiating (15) with all_74_15, n4, n3, simplifying with
% 248.40/41.98  | | |              (12), (16), (18), (29) gives:
% 248.40/41.98  | | |   (30)  leq(all_74_15, n3)
% 248.40/41.98  | | | 
% 248.40/41.98  | | | GROUND_INST: instantiating (23) with all_74_15, n3, simplifying with (7),
% 248.40/41.98  | | |              (18), (30) gives:
% 248.40/41.98  | | |   (31)  all_74_15 = n3 | gt(n3, all_74_15)
% 248.40/41.98  | | | 
% 248.40/41.98  | | | BETA: splitting (28) gives:
% 248.40/41.98  | | | 
% 248.40/41.98  | | | Case 1:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | |   (32)  gt(n3, all_74_14)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | GROUND_INST: instantiating (15) with all_74_14, n3, n2, simplifying with
% 248.40/41.98  | | | |              (7), (9), (13), (32) gives:
% 248.40/41.98  | | | |   (33)  leq(all_74_14, n2)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | GROUND_INST: instantiating (23) with all_74_14, n2, simplifying with
% 248.40/41.98  | | | |              (9), (22), (33) gives:
% 248.40/41.98  | | | |   (34)  all_74_14 = n2 | gt(n2, all_74_14)
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | BETA: splitting (31) gives:
% 248.40/41.98  | | | | 
% 248.40/41.98  | | | | Case 1:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | |   (35)  gt(n3, all_74_15)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | GROUND_INST: instantiating (15) with all_74_15, n3, n2, simplifying
% 248.40/41.98  | | | | |              with (7), (13), (18), (35) gives:
% 248.40/41.98  | | | | |   (36)  leq(all_74_15, n2)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | GROUND_INST: instantiating (23) with all_74_15, n2, simplifying with
% 248.40/41.98  | | | | |              (18), (22), (36) gives:
% 248.40/41.98  | | | | |   (37)  all_74_15 = n2 | gt(n2, all_74_15)
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | BETA: splitting (34) gives:
% 248.40/41.98  | | | | | 
% 248.40/41.98  | | | | | Case 1:
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | |   (38)  gt(n2, all_74_14)
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | GROUND_INST: instantiating (15) with all_74_14, n2, n1, simplifying
% 248.40/41.98  | | | | | |              with (9), (11), (22), (38) gives:
% 248.40/41.98  | | | | | |   (39)  leq(all_74_14, n1)
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | GROUND_INST: instantiating (2) with all_74_14, simplifying with (5),
% 248.40/41.98  | | | | | |              (9), (39) gives:
% 248.40/41.98  | | | | | |   (40)  all_74_14 = n1 | all_74_14 = n0
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | BETA: splitting (40) gives:
% 248.40/41.98  | | | | | | 
% 248.40/41.98  | | | | | | Case 1:
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | |   (41)  all_74_14 = n0
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (20), (41) imply:
% 248.40/41.98  | | | | | | |   (42)  $false
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | CLOSE: (42) is inconsistent.
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | Case 2:
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | |   (43)  all_74_14 = n1
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (19), (43) imply:
% 248.40/41.98  | | | | | | |   (44)  a_select3(pminus_ds1_filter, n1, all_74_15) = all_74_12
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (10), (43) imply:
% 248.40/41.98  | | | | | | |   (45)  a_select3(pminus_ds1_filter, all_74_15, n1) = all_74_13
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (9), (43) imply:
% 248.40/41.98  | | | | | | |   (46)  $i(n1)
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (24), (43) imply:
% 248.40/41.98  | | | | | | |   (47)  leq(n1, n5)
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | REDUCE: (5), (43) imply:
% 248.40/41.98  | | | | | | |   (48)  leq(n0, n1)
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | BETA: splitting (37) gives:
% 248.40/41.98  | | | | | | | 
% 248.40/41.98  | | | | | | | Case 1:
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | |   (49)  gt(n2, all_74_15)
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | GROUND_INST: instantiating (15) with all_74_15, n2, n1,
% 248.40/41.98  | | | | | | | |              simplifying with (11), (18), (22), (49) gives:
% 248.40/41.98  | | | | | | | |   (50)  leq(all_74_15, n1)
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | GROUND_INST: instantiating (2) with all_74_15, simplifying with
% 248.40/41.98  | | | | | | | |              (17), (18), (50) gives:
% 248.40/41.98  | | | | | | | |   (51)  all_74_15 = n1 | all_74_15 = n0
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | BETA: splitting (51) gives:
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | Case 1:
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | |   (52)  all_74_15 = n0
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | | REDUCE: (4), (52) imply:
% 248.40/41.98  | | | | | | | | |   (53)  $false
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | | CLOSE: (53) is inconsistent.
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | Case 2:
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | |   (54)  all_74_15 = n1
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | | REDUCE: (45), (54) imply:
% 248.40/41.98  | | | | | | | | |   (55)  a_select3(pminus_ds1_filter, n1, n1) = all_74_13
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | | REDUCE: (44), (54) imply:
% 248.40/41.98  | | | | | | | | |   (56)  a_select3(pminus_ds1_filter, n1, n1) = all_74_12
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | | GROUND_INST: instantiating (25) with all_74_13, all_74_12, n1,
% 248.40/41.98  | | | | | | | | |              n1, pminus_ds1_filter, simplifying with (55), (56)
% 248.40/41.98  | | | | | | | | |              gives:
% 248.40/41.98  | | | | | | | | |   (57)  all_74_12 = all_74_13
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | | REDUCE: (21), (57) imply:
% 248.40/41.98  | | | | | | | | |   (58)  $false
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | | CLOSE: (58) is inconsistent.
% 248.40/41.98  | | | | | | | | | 
% 248.40/41.98  | | | | | | | | End of split
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | Case 2:
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | |   (59)  all_74_15 = n2
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | REDUCE: (45), (59) imply:
% 248.40/41.98  | | | | | | | |   (60)  a_select3(pminus_ds1_filter, n2, n1) = all_74_13
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | REDUCE: (44), (59) imply:
% 248.40/41.98  | | | | | | | |   (61)  a_select3(pminus_ds1_filter, n1, n2) = all_74_12
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | REDUCE: (6), (59) imply:
% 248.40/41.98  | | | | | | | |   (62)  leq(n2, n5)
% 248.40/41.98  | | | | | | | | 
% 248.40/41.98  | | | | | | | | REDUCE: (17), (59) imply:
% 248.40/41.98  | | | | | | | |   (63)  leq(n0, n2)
% 248.40/41.98  | | | | | | | | 
% 248.40/41.99  | | | | | | | | GROUND_INST: instantiating (1) with n1, n2, all_74_12,
% 248.40/41.99  | | | | | | | |              simplifying with (22), (46), (48), (61), (63)
% 248.40/41.99  | | | | | | | |              gives:
% 248.40/41.99  | | | | | | | |   (64)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/41.99  | | | | | | | |         (a_select3(pminus_ds1_filter, n2, n1) = all_74_12 &
% 248.40/41.99  | | | | | | | |           $i(all_74_12))
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | BETA: splitting (64) gives:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (65)   ~ leq(n2, all_74_21)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | REDUCE: (3), (65) imply:
% 248.40/41.99  | | | | | | | | |   (66)   ~ leq(n2, n5)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | PRED_UNIFY: (62), (66) imply:
% 248.40/41.99  | | | | | | | | |   (67)  $false
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | CLOSE: (67) is inconsistent.
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (68)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/41.99  | | | | | | | | |             n2, n1) = all_74_12 & $i(all_74_12))
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | BETA: splitting (68) gives:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | |   (69)   ~ leq(n1, all_74_21)
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | REDUCE: (3), (69) imply:
% 248.40/41.99  | | | | | | | | | |   (70)   ~ leq(n1, n5)
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | PRED_UNIFY: (47), (70) imply:
% 248.40/41.99  | | | | | | | | | |   (71)  $false
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | CLOSE: (71) is inconsistent.
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | |   (72)  a_select3(pminus_ds1_filter, n2, n1) = all_74_12 &
% 248.40/41.99  | | | | | | | | | |         $i(all_74_12)
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | ALPHA: (72) implies:
% 248.40/41.99  | | | | | | | | | |   (73)  a_select3(pminus_ds1_filter, n2, n1) = all_74_12
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | REF_CLOSE: (21), (25), (60), (73) are inconsistent by
% 248.40/41.99  | | | | | | | | | |            sub-proof #20.
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | End of split
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | End of split
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | End of split
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | End of split
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | Case 2:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | |   (74)  all_74_14 = n2
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (19), (74) imply:
% 248.40/41.99  | | | | | |   (75)  a_select3(pminus_ds1_filter, n2, all_74_15) = all_74_12
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (10), (74) imply:
% 248.40/41.99  | | | | | |   (76)  a_select3(pminus_ds1_filter, all_74_15, n2) = all_74_13
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (24), (74) imply:
% 248.40/41.99  | | | | | |   (77)  leq(n2, n5)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (5), (74) imply:
% 248.40/41.99  | | | | | |   (78)  leq(n0, n2)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | BETA: splitting (37) gives:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | Case 1:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (79)  gt(n2, all_74_15)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | GROUND_INST: instantiating (15) with all_74_15, n2, n1,
% 248.40/41.99  | | | | | | |              simplifying with (11), (18), (22), (79) gives:
% 248.40/41.99  | | | | | | |   (80)  leq(all_74_15, n1)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | GROUND_INST: instantiating (2) with all_74_15, simplifying with
% 248.40/41.99  | | | | | | |              (17), (18), (80) gives:
% 248.40/41.99  | | | | | | |   (81)  all_74_15 = n1 | all_74_15 = n0
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | BETA: splitting (81) gives:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (82)  all_74_15 = n0
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (4), (82) imply:
% 248.40/41.99  | | | | | | | |   (83)  $false
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | CLOSE: (83) is inconsistent.
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (84)  all_74_15 = n1
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (76), (84) imply:
% 248.40/41.99  | | | | | | | |   (85)  a_select3(pminus_ds1_filter, n1, n2) = all_74_13
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (75), (84) imply:
% 248.40/41.99  | | | | | | | |   (86)  a_select3(pminus_ds1_filter, n2, n1) = all_74_12
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (18), (84) imply:
% 248.40/41.99  | | | | | | | |   (87)  $i(n1)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (6), (84) imply:
% 248.40/41.99  | | | | | | | |   (88)  leq(n1, n5)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (17), (84) imply:
% 248.40/41.99  | | | | | | | |   (89)  leq(n0, n1)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | GROUND_INST: instantiating (1) with n1, n2, all_74_13,
% 248.40/41.99  | | | | | | | |              simplifying with (22), (78), (85), (87), (89)
% 248.40/41.99  | | | | | | | |              gives:
% 248.40/41.99  | | | | | | | |   (90)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/41.99  | | | | | | | |         (a_select3(pminus_ds1_filter, n2, n1) = all_74_13 &
% 248.40/41.99  | | | | | | | |           $i(all_74_13))
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | BETA: splitting (90) gives:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (91)   ~ leq(n2, all_74_21)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | REDUCE: (3), (91) imply:
% 248.40/41.99  | | | | | | | | |   (92)   ~ leq(n2, n5)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | PRED_UNIFY: (77), (92) imply:
% 248.40/41.99  | | | | | | | | |   (93)  $false
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | CLOSE: (93) is inconsistent.
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (94)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/41.99  | | | | | | | | |             n2, n1) = all_74_13 & $i(all_74_13))
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | BETA: splitting (94) gives:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | |   (95)   ~ leq(n1, all_74_21)
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | REDUCE: (3), (95) imply:
% 248.40/41.99  | | | | | | | | | |   (96)   ~ leq(n1, n5)
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | PRED_UNIFY: (88), (96) imply:
% 248.40/41.99  | | | | | | | | | |   (97)  $false
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | CLOSE: (97) is inconsistent.
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | |   (98)  a_select3(pminus_ds1_filter, n2, n1) = all_74_13 &
% 248.40/41.99  | | | | | | | | | |         $i(all_74_13)
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | ALPHA: (98) implies:
% 248.40/41.99  | | | | | | | | | |   (99)  a_select3(pminus_ds1_filter, n2, n1) = all_74_13
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | | REF_CLOSE: (21), (25), (86), (99) are inconsistent by
% 248.40/41.99  | | | | | | | | | |            sub-proof #20.
% 248.40/41.99  | | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | End of split
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | End of split
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | End of split
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | Case 2:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (100)  all_74_15 = n2
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (76), (100) imply:
% 248.40/41.99  | | | | | | |   (101)  a_select3(pminus_ds1_filter, n2, n2) = all_74_13
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (75), (100) imply:
% 248.40/41.99  | | | | | | |   (102)  a_select3(pminus_ds1_filter, n2, n2) = all_74_12
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | GROUND_INST: instantiating (25) with all_74_13, all_74_12, n2, n2,
% 248.40/41.99  | | | | | | |              pminus_ds1_filter, simplifying with (101), (102)
% 248.40/41.99  | | | | | | |              gives:
% 248.40/41.99  | | | | | | |   (103)  all_74_12 = all_74_13
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (21), (103) imply:
% 248.40/41.99  | | | | | | |   (104)  $false
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | CLOSE: (104) is inconsistent.
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | End of split
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | End of split
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | Case 2:
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | |   (105)  all_74_15 = n3
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | REDUCE: (19), (105) imply:
% 248.40/41.99  | | | | |   (106)  a_select3(pminus_ds1_filter, all_74_14, n3) = all_74_12
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | REDUCE: (10), (105) imply:
% 248.40/41.99  | | | | |   (107)  a_select3(pminus_ds1_filter, n3, all_74_14) = all_74_13
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | REDUCE: (6), (105) imply:
% 248.40/41.99  | | | | |   (108)  leq(n3, n5)
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | REDUCE: (17), (105) imply:
% 248.40/41.99  | | | | |   (109)  leq(n0, n3)
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | BETA: splitting (34) gives:
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | Case 1:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | |   (110)  gt(n2, all_74_14)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | GROUND_INST: instantiating (15) with all_74_14, n2, n1, simplifying
% 248.40/41.99  | | | | | |              with (9), (11), (22), (110) gives:
% 248.40/41.99  | | | | | |   (111)  leq(all_74_14, n1)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | GROUND_INST: instantiating (2) with all_74_14, simplifying with (5),
% 248.40/41.99  | | | | | |              (9), (111) gives:
% 248.40/41.99  | | | | | |   (112)  all_74_14 = n1 | all_74_14 = n0
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | BETA: splitting (112) gives:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | Case 1:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (113)  all_74_14 = n0
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (20), (113) imply:
% 248.40/41.99  | | | | | | |   (114)  $false
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | CLOSE: (114) is inconsistent.
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | Case 2:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (115)  all_74_14 = n1
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (106), (115) imply:
% 248.40/41.99  | | | | | | |   (116)  a_select3(pminus_ds1_filter, n1, n3) = all_74_12
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (107), (115) imply:
% 248.40/41.99  | | | | | | |   (117)  a_select3(pminus_ds1_filter, n3, n1) = all_74_13
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (9), (115) imply:
% 248.40/41.99  | | | | | | |   (118)  $i(n1)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (24), (115) imply:
% 248.40/41.99  | | | | | | |   (119)  leq(n1, n5)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (5), (115) imply:
% 248.40/41.99  | | | | | | |   (120)  leq(n0, n1)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | GROUND_INST: instantiating (1) with n1, n3, all_74_12, simplifying
% 248.40/41.99  | | | | | | |              with (7), (109), (116), (118), (120) gives:
% 248.40/41.99  | | | | | | |   (121)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/41.99  | | | | | | |          (a_select3(pminus_ds1_filter, n3, n1) = all_74_12 &
% 248.40/41.99  | | | | | | |            $i(all_74_12))
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | BETA: splitting (121) gives:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (122)   ~ leq(n3, all_74_21)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (3), (122) imply:
% 248.40/41.99  | | | | | | | |   (123)   ~ leq(n3, n5)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | PRED_UNIFY: (108), (123) imply:
% 248.40/41.99  | | | | | | | |   (124)  $false
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | CLOSE: (124) is inconsistent.
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (125)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/41.99  | | | | | | | |              n3, n1) = all_74_12 & $i(all_74_12))
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | BETA: splitting (125) gives:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (126)   ~ leq(n1, all_74_21)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | REDUCE: (3), (126) imply:
% 248.40/41.99  | | | | | | | | |   (127)   ~ leq(n1, n5)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | PRED_UNIFY: (119), (127) imply:
% 248.40/41.99  | | | | | | | | |   (128)  $false
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | CLOSE: (128) is inconsistent.
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (129)  a_select3(pminus_ds1_filter, n3, n1) = all_74_12 &
% 248.40/41.99  | | | | | | | | |          $i(all_74_12)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | ALPHA: (129) implies:
% 248.40/41.99  | | | | | | | | |   (130)  a_select3(pminus_ds1_filter, n3, n1) = all_74_12
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | REF_CLOSE: (21), (25), (117), (130) are inconsistent by
% 248.40/41.99  | | | | | | | | |            sub-proof #19.
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | End of split
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | End of split
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | End of split
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | Case 2:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | |   (131)  all_74_14 = n2
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (106), (131) imply:
% 248.40/41.99  | | | | | |   (132)  a_select3(pminus_ds1_filter, n2, n3) = all_74_12
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (107), (131) imply:
% 248.40/41.99  | | | | | |   (133)  a_select3(pminus_ds1_filter, n3, n2) = all_74_13
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (24), (131) imply:
% 248.40/41.99  | | | | | |   (134)  leq(n2, n5)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (5), (131) imply:
% 248.40/41.99  | | | | | |   (135)  leq(n0, n2)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | GROUND_INST: instantiating (1) with n2, n3, all_74_12, simplifying
% 248.40/41.99  | | | | | |              with (7), (22), (109), (132), (135) gives:
% 248.40/41.99  | | | | | |   (136)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/41.99  | | | | | |          (a_select3(pminus_ds1_filter, n3, n2) = all_74_12 &
% 248.40/41.99  | | | | | |            $i(all_74_12))
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | BETA: splitting (136) gives:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | Case 1:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (137)   ~ leq(n3, all_74_21)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (3), (137) imply:
% 248.40/41.99  | | | | | | |   (138)   ~ leq(n3, n5)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | PRED_UNIFY: (108), (138) imply:
% 248.40/41.99  | | | | | | |   (139)  $false
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | CLOSE: (139) is inconsistent.
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | Case 2:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (140)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n3,
% 248.40/41.99  | | | | | | |              n2) = all_74_12 & $i(all_74_12))
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | BETA: splitting (140) gives:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (141)   ~ leq(n2, all_74_21)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (3), (141) imply:
% 248.40/41.99  | | | | | | | |   (142)   ~ leq(n2, n5)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | PRED_UNIFY: (134), (142) imply:
% 248.40/41.99  | | | | | | | |   (143)  $false
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | CLOSE: (143) is inconsistent.
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (144)  a_select3(pminus_ds1_filter, n3, n2) = all_74_12 &
% 248.40/41.99  | | | | | | | |          $i(all_74_12)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | ALPHA: (144) implies:
% 248.40/41.99  | | | | | | | |   (145)  a_select3(pminus_ds1_filter, n3, n2) = all_74_12
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | GROUND_INST: instantiating (25) with all_74_13, all_74_12, n2,
% 248.40/41.99  | | | | | | | |              n3, pminus_ds1_filter, simplifying with (133),
% 248.40/41.99  | | | | | | | |              (145) gives:
% 248.40/41.99  | | | | | | | |   (146)  all_74_12 = all_74_13
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (21), (146) imply:
% 248.40/41.99  | | | | | | | |   (147)  $false
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | CLOSE: (147) is inconsistent.
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | End of split
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | End of split
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | End of split
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | End of split
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | Case 2:
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | |   (148)  all_74_14 = n3
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | | REDUCE: (19), (148) imply:
% 248.40/41.99  | | | |   (149)  a_select3(pminus_ds1_filter, n3, all_74_15) = all_74_12
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | | REDUCE: (10), (148) imply:
% 248.40/41.99  | | | |   (150)  a_select3(pminus_ds1_filter, all_74_15, n3) = all_74_13
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | | REDUCE: (24), (148) imply:
% 248.40/41.99  | | | |   (151)  leq(n3, n5)
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | | REDUCE: (5), (148) imply:
% 248.40/41.99  | | | |   (152)  leq(n0, n3)
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | | BETA: splitting (31) gives:
% 248.40/41.99  | | | | 
% 248.40/41.99  | | | | Case 1:
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | |   (153)  gt(n3, all_74_15)
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | GROUND_INST: instantiating (15) with all_74_15, n3, n2, simplifying
% 248.40/41.99  | | | | |              with (7), (13), (18), (153) gives:
% 248.40/41.99  | | | | |   (154)  leq(all_74_15, n2)
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | GROUND_INST: instantiating (23) with all_74_15, n2, simplifying with
% 248.40/41.99  | | | | |              (18), (22), (154) gives:
% 248.40/41.99  | | | | |   (155)  all_74_15 = n2 | gt(n2, all_74_15)
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | BETA: splitting (155) gives:
% 248.40/41.99  | | | | | 
% 248.40/41.99  | | | | | Case 1:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | |   (156)  gt(n2, all_74_15)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | GROUND_INST: instantiating (15) with all_74_15, n2, n1, simplifying
% 248.40/41.99  | | | | | |              with (11), (18), (22), (156) gives:
% 248.40/41.99  | | | | | |   (157)  leq(all_74_15, n1)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | GROUND_INST: instantiating (2) with all_74_15, simplifying with
% 248.40/41.99  | | | | | |              (17), (18), (157) gives:
% 248.40/41.99  | | | | | |   (158)  all_74_15 = n1 | all_74_15 = n0
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | BETA: splitting (158) gives:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | Case 1:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (159)  all_74_15 = n0
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (4), (159) imply:
% 248.40/41.99  | | | | | | |   (160)  $false
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | CLOSE: (160) is inconsistent.
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | Case 2:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | |   (161)  all_74_15 = n1
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (150), (161) imply:
% 248.40/41.99  | | | | | | |   (162)  a_select3(pminus_ds1_filter, n1, n3) = all_74_13
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (149), (161) imply:
% 248.40/41.99  | | | | | | |   (163)  a_select3(pminus_ds1_filter, n3, n1) = all_74_12
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (18), (161) imply:
% 248.40/41.99  | | | | | | |   (164)  $i(n1)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (6), (161) imply:
% 248.40/41.99  | | | | | | |   (165)  leq(n1, n5)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | REDUCE: (17), (161) imply:
% 248.40/41.99  | | | | | | |   (166)  leq(n0, n1)
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | GROUND_INST: instantiating (1) with n1, n3, all_74_13, simplifying
% 248.40/41.99  | | | | | | |              with (7), (152), (162), (164), (166) gives:
% 248.40/41.99  | | | | | | |   (167)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/41.99  | | | | | | |          (a_select3(pminus_ds1_filter, n3, n1) = all_74_13 &
% 248.40/41.99  | | | | | | |            $i(all_74_13))
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | BETA: splitting (167) gives:
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (168)   ~ leq(n3, all_74_21)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | REDUCE: (3), (168) imply:
% 248.40/41.99  | | | | | | | |   (169)   ~ leq(n3, n5)
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | PRED_UNIFY: (151), (169) imply:
% 248.40/41.99  | | | | | | | |   (170)  $false
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | CLOSE: (170) is inconsistent.
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | |   (171)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/41.99  | | | | | | | |              n3, n1) = all_74_13 & $i(all_74_13))
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | BETA: splitting (171) gives:
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 1:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (172)   ~ leq(n1, all_74_21)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | REDUCE: (3), (172) imply:
% 248.40/41.99  | | | | | | | | |   (173)   ~ leq(n1, n5)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | PRED_UNIFY: (165), (173) imply:
% 248.40/41.99  | | | | | | | | |   (174)  $false
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | CLOSE: (174) is inconsistent.
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | Case 2:
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | |   (175)  a_select3(pminus_ds1_filter, n3, n1) = all_74_13 &
% 248.40/41.99  | | | | | | | | |          $i(all_74_13)
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | ALPHA: (175) implies:
% 248.40/41.99  | | | | | | | | |   (176)  a_select3(pminus_ds1_filter, n3, n1) = all_74_13
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | | REF_CLOSE: (21), (25), (163), (176) are inconsistent by
% 248.40/41.99  | | | | | | | | |            sub-proof #19.
% 248.40/41.99  | | | | | | | | | 
% 248.40/41.99  | | | | | | | | End of split
% 248.40/41.99  | | | | | | | | 
% 248.40/41.99  | | | | | | | End of split
% 248.40/41.99  | | | | | | | 
% 248.40/41.99  | | | | | | End of split
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | Case 2:
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | |   (177)  all_74_15 = n2
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (150), (177) imply:
% 248.40/41.99  | | | | | |   (178)  a_select3(pminus_ds1_filter, n2, n3) = all_74_13
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (149), (177) imply:
% 248.40/41.99  | | | | | |   (179)  a_select3(pminus_ds1_filter, n3, n2) = all_74_12
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (6), (177) imply:
% 248.40/41.99  | | | | | |   (180)  leq(n2, n5)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | REDUCE: (17), (177) imply:
% 248.40/41.99  | | | | | |   (181)  leq(n0, n2)
% 248.40/41.99  | | | | | | 
% 248.40/41.99  | | | | | | GROUND_INST: instantiating (1) with n2, n3, all_74_13, simplifying
% 248.40/41.99  | | | | | |              with (7), (22), (152), (178), (181) gives:
% 248.40/42.00  | | | | | |   (182)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.00  | | | | | |          (a_select3(pminus_ds1_filter, n3, n2) = all_74_13 &
% 248.40/42.00  | | | | | |            $i(all_74_13))
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | BETA: splitting (182) gives:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | Case 1:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (183)   ~ leq(n3, all_74_21)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | REDUCE: (3), (183) imply:
% 248.40/42.00  | | | | | | |   (184)   ~ leq(n3, n5)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | PRED_UNIFY: (151), (184) imply:
% 248.40/42.00  | | | | | | |   (185)  $false
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | CLOSE: (185) is inconsistent.
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | Case 2:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (186)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n3,
% 248.40/42.00  | | | | | | |              n2) = all_74_13 & $i(all_74_13))
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | BETA: splitting (186) gives:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | Case 1:
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | |   (187)   ~ leq(n2, all_74_21)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | REDUCE: (3), (187) imply:
% 248.40/42.00  | | | | | | | |   (188)   ~ leq(n2, n5)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | PRED_UNIFY: (180), (188) imply:
% 248.40/42.00  | | | | | | | |   (189)  $false
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | CLOSE: (189) is inconsistent.
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | Case 2:
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | |   (190)  a_select3(pminus_ds1_filter, n3, n2) = all_74_13 &
% 248.40/42.00  | | | | | | | |          $i(all_74_13)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | ALPHA: (190) implies:
% 248.40/42.00  | | | | | | | |   (191)  a_select3(pminus_ds1_filter, n3, n2) = all_74_13
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | GROUND_INST: instantiating (25) with all_74_13, all_74_12, n2,
% 248.40/42.00  | | | | | | | |              n3, pminus_ds1_filter, simplifying with (179),
% 248.40/42.00  | | | | | | | |              (191) gives:
% 248.40/42.00  | | | | | | | |   (192)  all_74_12 = all_74_13
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | REDUCE: (21), (192) imply:
% 248.40/42.00  | | | | | | | |   (193)  $false
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | CLOSE: (193) is inconsistent.
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | End of split
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | End of split
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | End of split
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | Case 2:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | |   (194)  all_74_15 = n3
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (150), (194) imply:
% 248.40/42.00  | | | | |   (195)  a_select3(pminus_ds1_filter, n3, n3) = all_74_13
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (149), (194) imply:
% 248.40/42.00  | | | | |   (196)  a_select3(pminus_ds1_filter, n3, n3) = all_74_12
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | GROUND_INST: instantiating (25) with all_74_13, all_74_12, n3, n3,
% 248.40/42.00  | | | | |              pminus_ds1_filter, simplifying with (195), (196) gives:
% 248.40/42.00  | | | | |   (197)  all_74_12 = all_74_13
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (21), (197) imply:
% 248.40/42.00  | | | | |   (198)  $false
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | CLOSE: (198) is inconsistent.
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | End of split
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | End of split
% 248.40/42.00  | | | 
% 248.40/42.00  | | Case 2:
% 248.40/42.00  | | | 
% 248.40/42.00  | | |   (199)  all_74_15 = n4
% 248.40/42.00  | | | 
% 248.40/42.00  | | | REDUCE: (19), (199) imply:
% 248.40/42.00  | | |   (200)  a_select3(pminus_ds1_filter, all_74_14, n4) = all_74_12
% 248.40/42.00  | | | 
% 248.40/42.00  | | | REDUCE: (10), (199) imply:
% 248.40/42.00  | | |   (201)  a_select3(pminus_ds1_filter, n4, all_74_14) = all_74_13
% 248.40/42.00  | | | 
% 248.40/42.00  | | | REDUCE: (6), (199) imply:
% 248.40/42.00  | | |   (202)  leq(n4, n5)
% 248.40/42.00  | | | 
% 248.40/42.00  | | | REDUCE: (17), (199) imply:
% 248.40/42.00  | | |   (203)  leq(n0, n4)
% 248.40/42.00  | | | 
% 248.40/42.00  | | | BETA: splitting (28) gives:
% 248.40/42.00  | | | 
% 248.40/42.00  | | | Case 1:
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | |   (204)  gt(n3, all_74_14)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | GROUND_INST: instantiating (15) with all_74_14, n3, n2, simplifying with
% 248.40/42.00  | | | |              (7), (9), (13), (204) gives:
% 248.40/42.00  | | | |   (205)  leq(all_74_14, n2)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | GROUND_INST: instantiating (23) with all_74_14, n2, simplifying with
% 248.40/42.00  | | | |              (9), (22), (205) gives:
% 248.40/42.00  | | | |   (206)  all_74_14 = n2 | gt(n2, all_74_14)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | BETA: splitting (206) gives:
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | Case 1:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | |   (207)  gt(n2, all_74_14)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | GROUND_INST: instantiating (15) with all_74_14, n2, n1, simplifying
% 248.40/42.00  | | | | |              with (9), (11), (22), (207) gives:
% 248.40/42.00  | | | | |   (208)  leq(all_74_14, n1)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | GROUND_INST: instantiating (2) with all_74_14, simplifying with (5),
% 248.40/42.00  | | | | |              (9), (208) gives:
% 248.40/42.00  | | | | |   (209)  all_74_14 = n1 | all_74_14 = n0
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | BETA: splitting (209) gives:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | Case 1:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (210)  all_74_14 = n0
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (20), (210) imply:
% 248.40/42.00  | | | | | |   (211)  $false
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | CLOSE: (211) is inconsistent.
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | Case 2:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (212)  all_74_14 = n1
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (200), (212) imply:
% 248.40/42.00  | | | | | |   (213)  a_select3(pminus_ds1_filter, n1, n4) = all_74_12
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (201), (212) imply:
% 248.40/42.00  | | | | | |   (214)  a_select3(pminus_ds1_filter, n4, n1) = all_74_13
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (9), (212) imply:
% 248.40/42.00  | | | | | |   (215)  $i(n1)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (24), (212) imply:
% 248.40/42.00  | | | | | |   (216)  leq(n1, n5)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (5), (212) imply:
% 248.40/42.00  | | | | | |   (217)  leq(n0, n1)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | GROUND_INST: instantiating (1) with n1, n4, all_74_12, simplifying
% 248.40/42.00  | | | | | |              with (16), (203), (213), (215), (217) gives:
% 248.40/42.00  | | | | | |   (218)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.00  | | | | | |          (a_select3(pminus_ds1_filter, n4, n1) = all_74_12 &
% 248.40/42.00  | | | | | |            $i(all_74_12))
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | BETA: splitting (218) gives:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | Case 1:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (219)   ~ leq(n4, all_74_21)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | REDUCE: (3), (219) imply:
% 248.40/42.00  | | | | | | |   (220)   ~ leq(n4, n5)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | PRED_UNIFY: (202), (220) imply:
% 248.40/42.00  | | | | | | |   (221)  $false
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | CLOSE: (221) is inconsistent.
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | Case 2:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (222)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.00  | | | | | | |              n1) = all_74_12 & $i(all_74_12))
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | BETA: splitting (222) gives:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | Case 1:
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | |   (223)   ~ leq(n1, all_74_21)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | REDUCE: (3), (223) imply:
% 248.40/42.00  | | | | | | | |   (224)   ~ leq(n1, n5)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | PRED_UNIFY: (216), (224) imply:
% 248.40/42.00  | | | | | | | |   (225)  $false
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | CLOSE: (225) is inconsistent.
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | Case 2:
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | |   (226)  a_select3(pminus_ds1_filter, n4, n1) = all_74_12 &
% 248.40/42.00  | | | | | | | |          $i(all_74_12)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | ALPHA: (226) implies:
% 248.40/42.00  | | | | | | | |   (227)  a_select3(pminus_ds1_filter, n4, n1) = all_74_12
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | REF_CLOSE: (21), (25), (214), (227) are inconsistent by
% 248.40/42.00  | | | | | | | |            sub-proof #18.
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | End of split
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | End of split
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | End of split
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | Case 2:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | |   (228)  all_74_14 = n2
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (200), (228) imply:
% 248.40/42.00  | | | | |   (229)  a_select3(pminus_ds1_filter, n2, n4) = all_74_12
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (201), (228) imply:
% 248.40/42.00  | | | | |   (230)  a_select3(pminus_ds1_filter, n4, n2) = all_74_13
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (24), (228) imply:
% 248.40/42.00  | | | | |   (231)  leq(n2, n5)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (5), (228) imply:
% 248.40/42.00  | | | | |   (232)  leq(n0, n2)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | GROUND_INST: instantiating (1) with n2, n4, all_74_12, simplifying
% 248.40/42.00  | | | | |              with (16), (22), (203), (229), (232) gives:
% 248.40/42.00  | | | | |   (233)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.00  | | | | |          (a_select3(pminus_ds1_filter, n4, n2) = all_74_12 &
% 248.40/42.00  | | | | |            $i(all_74_12))
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | BETA: splitting (233) gives:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | Case 1:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (234)   ~ leq(n4, all_74_21)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (3), (234) imply:
% 248.40/42.00  | | | | | |   (235)   ~ leq(n4, n5)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | PRED_UNIFY: (202), (235) imply:
% 248.40/42.00  | | | | | |   (236)  $false
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | CLOSE: (236) is inconsistent.
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | Case 2:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (237)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.00  | | | | | |              n2) = all_74_12 & $i(all_74_12))
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | BETA: splitting (237) gives:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | Case 1:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (238)   ~ leq(n2, all_74_21)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | REDUCE: (3), (238) imply:
% 248.40/42.00  | | | | | | |   (239)   ~ leq(n2, n5)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | PRED_UNIFY: (231), (239) imply:
% 248.40/42.00  | | | | | | |   (240)  $false
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | CLOSE: (240) is inconsistent.
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | Case 2:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (241)  a_select3(pminus_ds1_filter, n4, n2) = all_74_12 &
% 248.40/42.00  | | | | | | |          $i(all_74_12)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | ALPHA: (241) implies:
% 248.40/42.00  | | | | | | |   (242)  a_select3(pminus_ds1_filter, n4, n2) = all_74_12
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | GROUND_INST: instantiating (25) with all_74_12, all_74_13, n2, n4,
% 248.40/42.00  | | | | | | |              pminus_ds1_filter, simplifying with (230), (242)
% 248.40/42.00  | | | | | | |              gives:
% 248.40/42.00  | | | | | | |   (243)  all_74_12 = all_74_13
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | REDUCE: (21), (243) imply:
% 248.40/42.00  | | | | | | |   (244)  $false
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | CLOSE: (244) is inconsistent.
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | End of split
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | End of split
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | End of split
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | Case 2:
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | |   (245)  all_74_14 = n3
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | REDUCE: (200), (245) imply:
% 248.40/42.00  | | | |   (246)  a_select3(pminus_ds1_filter, n3, n4) = all_74_12
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | REDUCE: (201), (245) imply:
% 248.40/42.00  | | | |   (247)  a_select3(pminus_ds1_filter, n4, n3) = all_74_13
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | REDUCE: (24), (245) imply:
% 248.40/42.00  | | | |   (248)  leq(n3, n5)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | REDUCE: (5), (245) imply:
% 248.40/42.00  | | | |   (249)  leq(n0, n3)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | GROUND_INST: instantiating (1) with n3, n4, all_74_12, simplifying with
% 248.40/42.00  | | | |              (7), (16), (203), (246), (249) gives:
% 248.40/42.00  | | | |   (250)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.40/42.00  | | | |          (a_select3(pminus_ds1_filter, n4, n3) = all_74_12 &
% 248.40/42.00  | | | |            $i(all_74_12))
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | BETA: splitting (250) gives:
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | Case 1:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | |   (251)   ~ leq(n4, all_74_21)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (3), (251) imply:
% 248.40/42.00  | | | | |   (252)   ~ leq(n4, n5)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | PRED_UNIFY: (202), (252) imply:
% 248.40/42.00  | | | | |   (253)  $false
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | CLOSE: (253) is inconsistent.
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | Case 2:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | |   (254)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n4, n3)
% 248.40/42.00  | | | | |            = all_74_12 & $i(all_74_12))
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | BETA: splitting (254) gives:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | Case 1:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (255)   ~ leq(n3, all_74_21)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (3), (255) imply:
% 248.40/42.00  | | | | | |   (256)   ~ leq(n3, n5)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | PRED_UNIFY: (248), (256) imply:
% 248.40/42.00  | | | | | |   (257)  $false
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | CLOSE: (257) is inconsistent.
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | Case 2:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (258)  a_select3(pminus_ds1_filter, n4, n3) = all_74_12 &
% 248.40/42.00  | | | | | |          $i(all_74_12)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | ALPHA: (258) implies:
% 248.40/42.00  | | | | | |   (259)  a_select3(pminus_ds1_filter, n4, n3) = all_74_12
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REF_CLOSE: (21), (25), (247), (259) are inconsistent by sub-proof
% 248.40/42.00  | | | | | |            #17.
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | End of split
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | End of split
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | End of split
% 248.40/42.00  | | | 
% 248.40/42.00  | | End of split
% 248.40/42.00  | | 
% 248.40/42.00  | Case 2:
% 248.40/42.00  | | 
% 248.40/42.00  | |   (260)  all_74_14 = n4
% 248.40/42.00  | | 
% 248.40/42.00  | | REDUCE: (19), (260) imply:
% 248.40/42.00  | |   (261)  a_select3(pminus_ds1_filter, n4, all_74_15) = all_74_12
% 248.40/42.00  | | 
% 248.40/42.00  | | REDUCE: (10), (260) imply:
% 248.40/42.00  | |   (262)  a_select3(pminus_ds1_filter, all_74_15, n4) = all_74_13
% 248.40/42.00  | | 
% 248.40/42.00  | | REDUCE: (24), (260) imply:
% 248.40/42.00  | |   (263)  leq(n4, n5)
% 248.40/42.00  | | 
% 248.40/42.00  | | REDUCE: (5), (260) imply:
% 248.40/42.00  | |   (264)  leq(n0, n4)
% 248.40/42.00  | | 
% 248.40/42.00  | | BETA: splitting (14) gives:
% 248.40/42.00  | | 
% 248.40/42.00  | | Case 1:
% 248.40/42.00  | | | 
% 248.40/42.00  | | |   (265)  gt(n4, all_74_15)
% 248.40/42.00  | | | 
% 248.40/42.00  | | | GROUND_INST: instantiating (15) with all_74_15, n4, n3, simplifying with
% 248.40/42.00  | | |              (12), (16), (18), (265) gives:
% 248.40/42.00  | | |   (266)  leq(all_74_15, n3)
% 248.40/42.00  | | | 
% 248.40/42.00  | | | GROUND_INST: instantiating (23) with all_74_15, n3, simplifying with (7),
% 248.40/42.00  | | |              (18), (266) gives:
% 248.40/42.00  | | |   (267)  all_74_15 = n3 | gt(n3, all_74_15)
% 248.40/42.00  | | | 
% 248.40/42.00  | | | BETA: splitting (267) gives:
% 248.40/42.00  | | | 
% 248.40/42.00  | | | Case 1:
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | |   (268)  gt(n3, all_74_15)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | GROUND_INST: instantiating (15) with all_74_15, n3, n2, simplifying with
% 248.40/42.00  | | | |              (7), (13), (18), (268) gives:
% 248.40/42.00  | | | |   (269)  leq(all_74_15, n2)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | GROUND_INST: instantiating (23) with all_74_15, n2, simplifying with
% 248.40/42.00  | | | |              (18), (22), (269) gives:
% 248.40/42.00  | | | |   (270)  all_74_15 = n2 | gt(n2, all_74_15)
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | BETA: splitting (270) gives:
% 248.40/42.00  | | | | 
% 248.40/42.00  | | | | Case 1:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | |   (271)  gt(n2, all_74_15)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | GROUND_INST: instantiating (15) with all_74_15, n2, n1, simplifying
% 248.40/42.00  | | | | |              with (11), (18), (22), (271) gives:
% 248.40/42.00  | | | | |   (272)  leq(all_74_15, n1)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | GROUND_INST: instantiating (2) with all_74_15, simplifying with (17),
% 248.40/42.00  | | | | |              (18), (272) gives:
% 248.40/42.00  | | | | |   (273)  all_74_15 = n1 | all_74_15 = n0
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | BETA: splitting (273) gives:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | Case 1:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (274)  all_74_15 = n0
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (4), (274) imply:
% 248.40/42.00  | | | | | |   (275)  $false
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | CLOSE: (275) is inconsistent.
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | Case 2:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (276)  all_74_15 = n1
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (262), (276) imply:
% 248.40/42.00  | | | | | |   (277)  a_select3(pminus_ds1_filter, n1, n4) = all_74_13
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (261), (276) imply:
% 248.40/42.00  | | | | | |   (278)  a_select3(pminus_ds1_filter, n4, n1) = all_74_12
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (18), (276) imply:
% 248.40/42.00  | | | | | |   (279)  $i(n1)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (6), (276) imply:
% 248.40/42.00  | | | | | |   (280)  leq(n1, n5)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (17), (276) imply:
% 248.40/42.00  | | | | | |   (281)  leq(n0, n1)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | GROUND_INST: instantiating (1) with n1, n4, all_74_13, simplifying
% 248.40/42.00  | | | | | |              with (16), (264), (277), (279), (281) gives:
% 248.40/42.00  | | | | | |   (282)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.00  | | | | | |          (a_select3(pminus_ds1_filter, n4, n1) = all_74_13 &
% 248.40/42.00  | | | | | |            $i(all_74_13))
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | BETA: splitting (282) gives:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | Case 1:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (283)   ~ leq(n4, all_74_21)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | REDUCE: (3), (283) imply:
% 248.40/42.00  | | | | | | |   (284)   ~ leq(n4, n5)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | PRED_UNIFY: (263), (284) imply:
% 248.40/42.00  | | | | | | |   (285)  $false
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | CLOSE: (285) is inconsistent.
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | Case 2:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (286)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.00  | | | | | | |              n1) = all_74_13 & $i(all_74_13))
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | BETA: splitting (286) gives:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | Case 1:
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | |   (287)   ~ leq(n1, all_74_21)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | REDUCE: (3), (287) imply:
% 248.40/42.00  | | | | | | | |   (288)   ~ leq(n1, n5)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | PRED_UNIFY: (280), (288) imply:
% 248.40/42.00  | | | | | | | |   (289)  $false
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | CLOSE: (289) is inconsistent.
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | Case 2:
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | |   (290)  a_select3(pminus_ds1_filter, n4, n1) = all_74_13 &
% 248.40/42.00  | | | | | | | |          $i(all_74_13)
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | ALPHA: (290) implies:
% 248.40/42.00  | | | | | | | |   (291)  a_select3(pminus_ds1_filter, n4, n1) = all_74_13
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | | REF_CLOSE: (21), (25), (278), (291) are inconsistent by
% 248.40/42.00  | | | | | | | |            sub-proof #18.
% 248.40/42.00  | | | | | | | | 
% 248.40/42.00  | | | | | | | End of split
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | End of split
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | End of split
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | Case 2:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | |   (292)  all_74_15 = n2
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (262), (292) imply:
% 248.40/42.00  | | | | |   (293)  a_select3(pminus_ds1_filter, n2, n4) = all_74_13
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (261), (292) imply:
% 248.40/42.00  | | | | |   (294)  a_select3(pminus_ds1_filter, n4, n2) = all_74_12
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (6), (292) imply:
% 248.40/42.00  | | | | |   (295)  leq(n2, n5)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | REDUCE: (17), (292) imply:
% 248.40/42.00  | | | | |   (296)  leq(n0, n2)
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | GROUND_INST: instantiating (1) with n2, n4, all_74_13, simplifying
% 248.40/42.00  | | | | |              with (16), (22), (264), (293), (296) gives:
% 248.40/42.00  | | | | |   (297)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.00  | | | | |          (a_select3(pminus_ds1_filter, n4, n2) = all_74_13 &
% 248.40/42.00  | | | | |            $i(all_74_13))
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | BETA: splitting (297) gives:
% 248.40/42.00  | | | | | 
% 248.40/42.00  | | | | | Case 1:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (298)   ~ leq(n4, all_74_21)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | REDUCE: (3), (298) imply:
% 248.40/42.00  | | | | | |   (299)   ~ leq(n4, n5)
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | PRED_UNIFY: (263), (299) imply:
% 248.40/42.00  | | | | | |   (300)  $false
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | CLOSE: (300) is inconsistent.
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | Case 2:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | |   (301)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.00  | | | | | |              n2) = all_74_13 & $i(all_74_13))
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | BETA: splitting (301) gives:
% 248.40/42.00  | | | | | | 
% 248.40/42.00  | | | | | | Case 1:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (302)   ~ leq(n2, all_74_21)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | REDUCE: (3), (302) imply:
% 248.40/42.00  | | | | | | |   (303)   ~ leq(n2, n5)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | PRED_UNIFY: (295), (303) imply:
% 248.40/42.00  | | | | | | |   (304)  $false
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | CLOSE: (304) is inconsistent.
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | Case 2:
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | |   (305)  a_select3(pminus_ds1_filter, n4, n2) = all_74_13 &
% 248.40/42.00  | | | | | | |          $i(all_74_13)
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | ALPHA: (305) implies:
% 248.40/42.00  | | | | | | |   (306)  a_select3(pminus_ds1_filter, n4, n2) = all_74_13
% 248.40/42.00  | | | | | | | 
% 248.40/42.00  | | | | | | | GROUND_INST: instantiating (25) with all_74_12, all_74_13, n2, n4,
% 248.40/42.00  | | | | | | |              pminus_ds1_filter, simplifying with (294), (306)
% 248.40/42.00  | | | | | | |              gives:
% 248.40/42.00  | | | | | | |   (307)  all_74_12 = all_74_13
% 248.40/42.00  | | | | | | | 
% 248.40/42.01  | | | | | | | REDUCE: (21), (307) imply:
% 248.40/42.01  | | | | | | |   (308)  $false
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | | CLOSE: (308) is inconsistent.
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | End of split
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | End of split
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | End of split
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | Case 2:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | |   (309)  all_74_15 = n3
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (262), (309) imply:
% 248.40/42.01  | | | |   (310)  a_select3(pminus_ds1_filter, n3, n4) = all_74_13
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (261), (309) imply:
% 248.40/42.01  | | | |   (311)  a_select3(pminus_ds1_filter, n4, n3) = all_74_12
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (6), (309) imply:
% 248.40/42.01  | | | |   (312)  leq(n3, n5)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (17), (309) imply:
% 248.40/42.01  | | | |   (313)  leq(n0, n3)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | GROUND_INST: instantiating (1) with n3, n4, all_74_13, simplifying with
% 248.40/42.01  | | | |              (7), (16), (264), (310), (313) gives:
% 248.40/42.01  | | | |   (314)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.40/42.01  | | | |          (a_select3(pminus_ds1_filter, n4, n3) = all_74_13 &
% 248.40/42.01  | | | |            $i(all_74_13))
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | BETA: splitting (314) gives:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | Case 1:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (315)   ~ leq(n4, all_74_21)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (3), (315) imply:
% 248.40/42.01  | | | | |   (316)   ~ leq(n4, n5)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | PRED_UNIFY: (263), (316) imply:
% 248.40/42.01  | | | | |   (317)  $false
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | CLOSE: (317) is inconsistent.
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | Case 2:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (318)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n4, n3)
% 248.40/42.01  | | | | |            = all_74_13 & $i(all_74_13))
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | BETA: splitting (318) gives:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | Case 1:
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | |   (319)   ~ leq(n3, all_74_21)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | REDUCE: (3), (319) imply:
% 248.40/42.01  | | | | | |   (320)   ~ leq(n3, n5)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | PRED_UNIFY: (312), (320) imply:
% 248.40/42.01  | | | | | |   (321)  $false
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | CLOSE: (321) is inconsistent.
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | Case 2:
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | |   (322)  a_select3(pminus_ds1_filter, n4, n3) = all_74_13 &
% 248.40/42.01  | | | | | |          $i(all_74_13)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | ALPHA: (322) implies:
% 248.40/42.01  | | | | | |   (323)  a_select3(pminus_ds1_filter, n4, n3) = all_74_13
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | REF_CLOSE: (21), (25), (311), (323) are inconsistent by sub-proof
% 248.40/42.01  | | | | | |            #17.
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | End of split
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | End of split
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | End of split
% 248.40/42.01  | | | 
% 248.40/42.01  | | Case 2:
% 248.40/42.01  | | | 
% 248.40/42.01  | | |   (324)  all_74_15 = n4
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (262), (324) imply:
% 248.40/42.01  | | |   (325)  a_select3(pminus_ds1_filter, n4, n4) = all_74_13
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (261), (324) imply:
% 248.40/42.01  | | |   (326)  a_select3(pminus_ds1_filter, n4, n4) = all_74_12
% 248.40/42.01  | | | 
% 248.40/42.01  | | | GROUND_INST: instantiating (25) with all_74_13, all_74_12, n4, n4,
% 248.40/42.01  | | |              pminus_ds1_filter, simplifying with (325), (326) gives:
% 248.40/42.01  | | |   (327)  all_74_12 = all_74_13
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (21), (327) imply:
% 248.40/42.01  | | |   (328)  $false
% 248.40/42.01  | | | 
% 248.40/42.01  | | | CLOSE: (328) is inconsistent.
% 248.40/42.01  | | | 
% 248.40/42.01  | | End of split
% 248.40/42.01  | | 
% 248.40/42.01  | End of split
% 248.40/42.01  | 
% 248.40/42.01  End of proof
% 248.40/42.01  
% 248.40/42.01  Sub-proof #17 shows that the following formulas are inconsistent:
% 248.40/42.01  ----------------------------------------------------------------
% 248.40/42.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.01           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.01             v0))
% 248.40/42.01    (2)  a_select3(pminus_ds1_filter, n4, n3) = all_74_12
% 248.40/42.01    (3)  a_select3(pminus_ds1_filter, n4, n3) = all_74_13
% 248.40/42.01    (4)   ~ (all_74_12 = all_74_13)
% 248.40/42.01  
% 248.40/42.01  Begin of proof
% 248.40/42.01  | 
% 248.40/42.01  | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n3, n4,
% 248.40/42.01  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.01  |   (5)  all_74_12 = all_74_13
% 248.40/42.01  | 
% 248.40/42.01  | REDUCE: (4), (5) imply:
% 248.40/42.01  |   (6)  $false
% 248.40/42.01  | 
% 248.40/42.01  | CLOSE: (6) is inconsistent.
% 248.40/42.01  | 
% 248.40/42.01  End of proof
% 248.40/42.01  
% 248.40/42.01  Sub-proof #18 shows that the following formulas are inconsistent:
% 248.40/42.01  ----------------------------------------------------------------
% 248.40/42.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.01           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.01             v0))
% 248.40/42.01    (2)  a_select3(pminus_ds1_filter, n4, n1) = all_74_12
% 248.40/42.01    (3)  a_select3(pminus_ds1_filter, n4, n1) = all_74_13
% 248.40/42.01    (4)   ~ (all_74_12 = all_74_13)
% 248.40/42.01  
% 248.40/42.01  Begin of proof
% 248.40/42.01  | 
% 248.40/42.01  | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n1, n4,
% 248.40/42.01  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.01  |   (5)  all_74_12 = all_74_13
% 248.40/42.01  | 
% 248.40/42.01  | REDUCE: (4), (5) imply:
% 248.40/42.01  |   (6)  $false
% 248.40/42.01  | 
% 248.40/42.01  | CLOSE: (6) is inconsistent.
% 248.40/42.01  | 
% 248.40/42.01  End of proof
% 248.40/42.01  
% 248.40/42.01  Sub-proof #19 shows that the following formulas are inconsistent:
% 248.40/42.01  ----------------------------------------------------------------
% 248.40/42.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.01           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.01             v0))
% 248.40/42.01    (2)  a_select3(pminus_ds1_filter, n3, n1) = all_74_12
% 248.40/42.01    (3)  a_select3(pminus_ds1_filter, n3, n1) = all_74_13
% 248.40/42.01    (4)   ~ (all_74_12 = all_74_13)
% 248.40/42.01  
% 248.40/42.01  Begin of proof
% 248.40/42.01  | 
% 248.40/42.01  | GROUND_INST: instantiating (1) with all_74_13, all_74_12, n1, n3,
% 248.40/42.01  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.01  |   (5)  all_74_12 = all_74_13
% 248.40/42.01  | 
% 248.40/42.01  | REDUCE: (4), (5) imply:
% 248.40/42.01  |   (6)  $false
% 248.40/42.01  | 
% 248.40/42.01  | CLOSE: (6) is inconsistent.
% 248.40/42.01  | 
% 248.40/42.01  End of proof
% 248.40/42.01  
% 248.40/42.01  Sub-proof #20 shows that the following formulas are inconsistent:
% 248.40/42.01  ----------------------------------------------------------------
% 248.40/42.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.01           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.01             v0))
% 248.40/42.01    (2)  a_select3(pminus_ds1_filter, n2, n1) = all_74_12
% 248.40/42.01    (3)  a_select3(pminus_ds1_filter, n2, n1) = all_74_13
% 248.40/42.01    (4)   ~ (all_74_12 = all_74_13)
% 248.40/42.01  
% 248.40/42.01  Begin of proof
% 248.40/42.01  | 
% 248.40/42.01  | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n1, n2,
% 248.40/42.01  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.01  |   (5)  all_74_12 = all_74_13
% 248.40/42.01  | 
% 248.40/42.01  | REDUCE: (4), (5) imply:
% 248.40/42.01  |   (6)  $false
% 248.40/42.01  | 
% 248.40/42.01  | CLOSE: (6) is inconsistent.
% 248.40/42.01  | 
% 248.40/42.01  End of proof
% 248.40/42.01  
% 248.40/42.01  Sub-proof #21 shows that the following formulas are inconsistent:
% 248.40/42.01  ----------------------------------------------------------------
% 248.40/42.01    (1)  $i(n0)
% 248.40/42.01    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.40/42.01           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.40/42.01           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.40/42.01           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.01    (3)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.01           leq(n0, v0))
% 248.40/42.01    (4)  leq(n0, n5)
% 248.40/42.01    (5)  all_74_21 = n5
% 248.40/42.01    (6)  leq(n0, all_74_14)
% 248.40/42.01    (7)  $i(n3)
% 248.40/42.01    (8)  all_74_14 = n4 | gt(n4, all_74_14)
% 248.40/42.01    (9)  $i(all_74_14)
% 248.40/42.01    (10)  pred(n2) = n1
% 248.40/42.01    (11)  pred(n4) = n3
% 248.40/42.01    (12)  pred(n3) = n2
% 248.40/42.01    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/42.01            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/42.01    (14)  $i(n4)
% 248.40/42.01    (15)   ~ (all_74_14 = n0)
% 248.40/42.01    (16)   ~ (all_74_12 = all_74_13)
% 248.40/42.01    (17)  $i(n2)
% 248.40/42.01    (18)  leq(n0, n0)
% 248.40/42.01    (19)  a_select3(pminus_ds1_filter, n0, all_74_14) = all_74_13
% 248.40/42.01    (20)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.40/42.01            leq(v0, v1) | gt(v1, v0))
% 248.40/42.01    (21)  a_select3(pminus_ds1_filter, all_74_14, n0) = all_74_12
% 248.40/42.01    (22)  leq(all_74_14, n5)
% 248.40/42.01    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.01          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.01              v0))
% 248.40/42.01  
% 248.40/42.01  Begin of proof
% 248.40/42.01  | 
% 248.40/42.01  | BETA: splitting (8) gives:
% 248.40/42.01  | 
% 248.40/42.01  | Case 1:
% 248.40/42.01  | | 
% 248.40/42.01  | |   (24)  gt(n4, all_74_14)
% 248.40/42.01  | | 
% 248.40/42.01  | | GROUND_INST: instantiating (13) with all_74_14, n4, n3, simplifying with
% 248.40/42.01  | |              (9), (11), (14), (24) gives:
% 248.40/42.01  | |   (25)  leq(all_74_14, n3)
% 248.40/42.01  | | 
% 248.40/42.01  | | GROUND_INST: instantiating (20) with all_74_14, n3, simplifying with (7),
% 248.40/42.01  | |              (9), (25) gives:
% 248.40/42.01  | |   (26)  all_74_14 = n3 | gt(n3, all_74_14)
% 248.40/42.01  | | 
% 248.40/42.01  | | BETA: splitting (26) gives:
% 248.40/42.01  | | 
% 248.40/42.01  | | Case 1:
% 248.40/42.01  | | | 
% 248.40/42.01  | | |   (27)  gt(n3, all_74_14)
% 248.40/42.01  | | | 
% 248.40/42.01  | | | GROUND_INST: instantiating (13) with all_74_14, n3, n2, simplifying with
% 248.40/42.01  | | |              (7), (9), (12), (27) gives:
% 248.40/42.01  | | |   (28)  leq(all_74_14, n2)
% 248.40/42.01  | | | 
% 248.40/42.01  | | | GROUND_INST: instantiating (20) with all_74_14, n2, simplifying with (9),
% 248.40/42.01  | | |              (17), (28) gives:
% 248.40/42.01  | | |   (29)  all_74_14 = n2 | gt(n2, all_74_14)
% 248.40/42.01  | | | 
% 248.40/42.01  | | | BETA: splitting (29) gives:
% 248.40/42.01  | | | 
% 248.40/42.01  | | | Case 1:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | |   (30)  gt(n2, all_74_14)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | GROUND_INST: instantiating (13) with all_74_14, n2, n1, simplifying with
% 248.40/42.01  | | | |              (9), (10), (17), (30) gives:
% 248.40/42.01  | | | |   (31)  leq(all_74_14, n1)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | GROUND_INST: instantiating (3) with all_74_14, simplifying with (6),
% 248.40/42.01  | | | |              (9), (31) gives:
% 248.40/42.01  | | | |   (32)  all_74_14 = n1 | all_74_14 = n0
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | BETA: splitting (32) gives:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | Case 1:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (33)  all_74_14 = n0
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (15), (33) imply:
% 248.40/42.01  | | | | |   (34)  $false
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | CLOSE: (34) is inconsistent.
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | Case 2:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (35)  all_74_14 = n1
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (21), (35) imply:
% 248.40/42.01  | | | | |   (36)  a_select3(pminus_ds1_filter, n1, n0) = all_74_12
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (19), (35) imply:
% 248.40/42.01  | | | | |   (37)  a_select3(pminus_ds1_filter, n0, n1) = all_74_13
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (9), (35) imply:
% 248.40/42.01  | | | | |   (38)  $i(n1)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (22), (35) imply:
% 248.40/42.01  | | | | |   (39)  leq(n1, n5)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (6), (35) imply:
% 248.40/42.01  | | | | |   (40)  leq(n0, n1)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | GROUND_INST: instantiating (2) with n0, n1, all_74_13, simplifying
% 248.40/42.01  | | | | |              with (1), (18), (37), (38), (40) gives:
% 248.40/42.01  | | | | |   (41)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.01  | | | | |         (a_select3(pminus_ds1_filter, n1, n0) = all_74_13 &
% 248.40/42.01  | | | | |           $i(all_74_13))
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | BETA: splitting (41) gives:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | Case 1:
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | |   (42)   ~ leq(n0, all_74_21)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | REDUCE: (5), (42) imply:
% 248.40/42.01  | | | | | |   (43)   ~ leq(n0, n5)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | PRED_UNIFY: (4), (43) imply:
% 248.40/42.01  | | | | | |   (44)  $false
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | CLOSE: (44) is inconsistent.
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | Case 2:
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n1,
% 248.40/42.01  | | | | | |             n0) = all_74_13 & $i(all_74_13))
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | BETA: splitting (45) gives:
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | Case 1:
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | | REDUCE: (5), (46) imply:
% 248.40/42.01  | | | | | | |   (47)   ~ leq(n1, n5)
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 248.40/42.01  | | | | | | |   (48)  $false
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | | CLOSE: (48) is inconsistent.
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | Case 2:
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | |   (49)  a_select3(pminus_ds1_filter, n1, n0) = all_74_13 &
% 248.40/42.01  | | | | | | |         $i(all_74_13)
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | | ALPHA: (49) implies:
% 248.40/42.01  | | | | | | |   (50)  a_select3(pminus_ds1_filter, n1, n0) = all_74_13
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | | REF_CLOSE: (16), (23), (36), (50) are inconsistent by sub-proof
% 248.40/42.01  | | | | | | |            #25.
% 248.40/42.01  | | | | | | | 
% 248.40/42.01  | | | | | | End of split
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | End of split
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | End of split
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | Case 2:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | |   (51)  all_74_14 = n2
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (21), (51) imply:
% 248.40/42.01  | | | |   (52)  a_select3(pminus_ds1_filter, n2, n0) = all_74_12
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (19), (51) imply:
% 248.40/42.01  | | | |   (53)  a_select3(pminus_ds1_filter, n0, n2) = all_74_13
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (22), (51) imply:
% 248.40/42.01  | | | |   (54)  leq(n2, n5)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (6), (51) imply:
% 248.40/42.01  | | | |   (55)  leq(n0, n2)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | GROUND_INST: instantiating (2) with n0, n2, all_74_13, simplifying with
% 248.40/42.01  | | | |              (1), (17), (18), (53), (55) gives:
% 248.40/42.01  | | | |   (56)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.01  | | | |         (a_select3(pminus_ds1_filter, n2, n0) = all_74_13 &
% 248.40/42.01  | | | |           $i(all_74_13))
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | BETA: splitting (56) gives:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | Case 1:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (57)   ~ leq(n0, all_74_21)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (5), (57) imply:
% 248.40/42.01  | | | | |   (58)   ~ leq(n0, n5)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | PRED_UNIFY: (4), (58) imply:
% 248.40/42.01  | | | | |   (59)  $false
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | CLOSE: (59) is inconsistent.
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | Case 2:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (60)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n2, n0)
% 248.40/42.01  | | | | |           = all_74_13 & $i(all_74_13))
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | BETA: splitting (60) gives:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | Case 1:
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | |   (61)   ~ leq(n2, all_74_21)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | REDUCE: (5), (61) imply:
% 248.40/42.01  | | | | | |   (62)   ~ leq(n2, n5)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | PRED_UNIFY: (54), (62) imply:
% 248.40/42.01  | | | | | |   (63)  $false
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | CLOSE: (63) is inconsistent.
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | Case 2:
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | |   (64)  a_select3(pminus_ds1_filter, n2, n0) = all_74_13 &
% 248.40/42.01  | | | | | |         $i(all_74_13)
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | ALPHA: (64) implies:
% 248.40/42.01  | | | | | |   (65)  a_select3(pminus_ds1_filter, n2, n0) = all_74_13
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | GROUND_INST: instantiating (23) with all_74_12, all_74_13, n0, n2,
% 248.40/42.01  | | | | | |              pminus_ds1_filter, simplifying with (52), (65) gives:
% 248.40/42.01  | | | | | |   (66)  all_74_12 = all_74_13
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | REDUCE: (16), (66) imply:
% 248.40/42.01  | | | | | |   (67)  $false
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | | CLOSE: (67) is inconsistent.
% 248.40/42.01  | | | | | | 
% 248.40/42.01  | | | | | End of split
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | End of split
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | End of split
% 248.40/42.01  | | | 
% 248.40/42.01  | | Case 2:
% 248.40/42.01  | | | 
% 248.40/42.01  | | |   (68)  all_74_14 = n3
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (21), (68) imply:
% 248.40/42.01  | | |   (69)  a_select3(pminus_ds1_filter, n3, n0) = all_74_12
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (19), (68) imply:
% 248.40/42.01  | | |   (70)  a_select3(pminus_ds1_filter, n0, n3) = all_74_13
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (22), (68) imply:
% 248.40/42.01  | | |   (71)  leq(n3, n5)
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (6), (68) imply:
% 248.40/42.01  | | |   (72)  leq(n0, n3)
% 248.40/42.01  | | | 
% 248.40/42.01  | | | GROUND_INST: instantiating (2) with n0, n3, all_74_13, simplifying with
% 248.40/42.01  | | |              (1), (7), (18), (70), (72) gives:
% 248.40/42.01  | | |   (73)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.01  | | |         (a_select3(pminus_ds1_filter, n3, n0) = all_74_13 & $i(all_74_13))
% 248.40/42.01  | | | 
% 248.40/42.01  | | | BETA: splitting (73) gives:
% 248.40/42.01  | | | 
% 248.40/42.01  | | | Case 1:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | |   (74)   ~ leq(n0, all_74_21)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | REDUCE: (5), (74) imply:
% 248.40/42.01  | | | |   (75)   ~ leq(n0, n5)
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | PRED_UNIFY: (4), (75) imply:
% 248.40/42.01  | | | |   (76)  $false
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | CLOSE: (76) is inconsistent.
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | Case 2:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | |   (77)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n3, n0) =
% 248.40/42.01  | | | |           all_74_13 & $i(all_74_13))
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | BETA: splitting (77) gives:
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | | Case 1:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (78)   ~ leq(n3, all_74_21)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REDUCE: (5), (78) imply:
% 248.40/42.01  | | | | |   (79)   ~ leq(n3, n5)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | PRED_UNIFY: (71), (79) imply:
% 248.40/42.01  | | | | |   (80)  $false
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | CLOSE: (80) is inconsistent.
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | Case 2:
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | |   (81)  a_select3(pminus_ds1_filter, n3, n0) = all_74_13 &
% 248.40/42.01  | | | | |         $i(all_74_13)
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | ALPHA: (81) implies:
% 248.40/42.01  | | | | |   (82)  a_select3(pminus_ds1_filter, n3, n0) = all_74_13
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | | REF_CLOSE: (16), (23), (69), (82) are inconsistent by sub-proof #24.
% 248.40/42.01  | | | | | 
% 248.40/42.01  | | | | End of split
% 248.40/42.01  | | | | 
% 248.40/42.01  | | | End of split
% 248.40/42.01  | | | 
% 248.40/42.01  | | End of split
% 248.40/42.01  | | 
% 248.40/42.01  | Case 2:
% 248.40/42.01  | | 
% 248.40/42.01  | |   (83)  all_74_14 = n4
% 248.40/42.01  | | 
% 248.40/42.01  | | REDUCE: (21), (83) imply:
% 248.40/42.01  | |   (84)  a_select3(pminus_ds1_filter, n4, n0) = all_74_12
% 248.40/42.01  | | 
% 248.40/42.01  | | REDUCE: (19), (83) imply:
% 248.40/42.01  | |   (85)  a_select3(pminus_ds1_filter, n0, n4) = all_74_13
% 248.40/42.01  | | 
% 248.40/42.01  | | REDUCE: (22), (83) imply:
% 248.40/42.01  | |   (86)  leq(n4, n5)
% 248.40/42.01  | | 
% 248.40/42.01  | | REDUCE: (6), (83) imply:
% 248.40/42.01  | |   (87)  leq(n0, n4)
% 248.40/42.01  | | 
% 248.40/42.01  | | GROUND_INST: instantiating (2) with n0, n4, all_74_13, simplifying with (1),
% 248.40/42.01  | |              (14), (18), (85), (87) gives:
% 248.40/42.01  | |   (88)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.01  | |         (a_select3(pminus_ds1_filter, n4, n0) = all_74_13 & $i(all_74_13))
% 248.40/42.01  | | 
% 248.40/42.01  | | BETA: splitting (88) gives:
% 248.40/42.01  | | 
% 248.40/42.01  | | Case 1:
% 248.40/42.01  | | | 
% 248.40/42.01  | | |   (89)   ~ leq(n0, all_74_21)
% 248.40/42.01  | | | 
% 248.40/42.01  | | | REDUCE: (5), (89) imply:
% 248.40/42.01  | | |   (90)   ~ leq(n0, n5)
% 248.40/42.01  | | | 
% 248.40/42.02  | | | PRED_UNIFY: (4), (90) imply:
% 248.40/42.02  | | |   (91)  $false
% 248.40/42.02  | | | 
% 248.40/42.02  | | | CLOSE: (91) is inconsistent.
% 248.40/42.02  | | | 
% 248.40/42.02  | | Case 2:
% 248.40/42.02  | | | 
% 248.40/42.02  | | |   (92)   ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n4, n0) =
% 248.40/42.02  | | |           all_74_13 & $i(all_74_13))
% 248.40/42.02  | | | 
% 248.40/42.02  | | | BETA: splitting (92) gives:
% 248.40/42.02  | | | 
% 248.40/42.02  | | | Case 1:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (93)   ~ leq(n4, all_74_21)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REDUCE: (5), (93) imply:
% 248.40/42.02  | | | |   (94)   ~ leq(n4, n5)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | PRED_UNIFY: (86), (94) imply:
% 248.40/42.02  | | | |   (95)  $false
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | CLOSE: (95) is inconsistent.
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | Case 2:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (96)  a_select3(pminus_ds1_filter, n4, n0) = all_74_13 & $i(all_74_13)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | ALPHA: (96) implies:
% 248.40/42.02  | | | |   (97)  a_select3(pminus_ds1_filter, n4, n0) = all_74_13
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REF_CLOSE: (16), (23), (84), (97) are inconsistent by sub-proof #23.
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | End of split
% 248.40/42.02  | | | 
% 248.40/42.02  | | End of split
% 248.40/42.02  | | 
% 248.40/42.02  | End of split
% 248.40/42.02  | 
% 248.40/42.02  End of proof
% 248.40/42.02  
% 248.40/42.02  Sub-proof #22 shows that the following formulas are inconsistent:
% 248.40/42.02  ----------------------------------------------------------------
% 248.40/42.02    (1)  $i(n0)
% 248.40/42.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.40/42.02           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.40/42.02           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.40/42.02           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.02    (3)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.02           leq(n0, v0))
% 248.40/42.02    (4)  leq(n0, n5)
% 248.40/42.02    (5)  all_74_21 = n5
% 248.40/42.02    (6)   ~ (all_74_15 = n0)
% 248.40/42.02    (7)  leq(all_74_15, n5)
% 248.40/42.02    (8)  $i(n3)
% 248.40/42.02    (9)  pred(n2) = n1
% 248.40/42.02    (10)  pred(n4) = n3
% 248.40/42.02    (11)  pred(n3) = n2
% 248.40/42.02    (12)  all_74_15 = n4 | gt(n4, all_74_15)
% 248.40/42.02    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/42.02            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/42.02    (14)  a_select3(pminus_ds1_filter, all_74_15, n0) = all_74_13
% 248.40/42.02    (15)  $i(n4)
% 248.40/42.02    (16)  leq(n0, all_74_15)
% 248.40/42.02    (17)  $i(all_74_15)
% 248.40/42.02    (18)  a_select3(pminus_ds1_filter, n0, all_74_15) = all_74_12
% 248.40/42.02    (19)   ~ (all_74_12 = all_74_13)
% 248.40/42.02    (20)  $i(n2)
% 248.40/42.02    (21)  leq(n0, n0)
% 248.40/42.02    (22)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.40/42.02            leq(v0, v1) | gt(v1, v0))
% 248.40/42.02    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.02          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.02              v0))
% 248.40/42.02  
% 248.40/42.02  Begin of proof
% 248.40/42.02  | 
% 248.40/42.02  | BETA: splitting (12) gives:
% 248.40/42.02  | 
% 248.40/42.02  | Case 1:
% 248.40/42.02  | | 
% 248.40/42.02  | |   (24)  gt(n4, all_74_15)
% 248.40/42.02  | | 
% 248.40/42.02  | | GROUND_INST: instantiating (13) with all_74_15, n4, n3, simplifying with
% 248.40/42.02  | |              (10), (15), (17), (24) gives:
% 248.40/42.02  | |   (25)  leq(all_74_15, n3)
% 248.40/42.02  | | 
% 248.40/42.02  | | GROUND_INST: instantiating (22) with all_74_15, n3, simplifying with (8),
% 248.40/42.02  | |              (17), (25) gives:
% 248.40/42.02  | |   (26)  all_74_15 = n3 | gt(n3, all_74_15)
% 248.40/42.02  | | 
% 248.40/42.02  | | BETA: splitting (26) gives:
% 248.40/42.02  | | 
% 248.40/42.02  | | Case 1:
% 248.40/42.02  | | | 
% 248.40/42.02  | | |   (27)  gt(n3, all_74_15)
% 248.40/42.02  | | | 
% 248.40/42.02  | | | GROUND_INST: instantiating (13) with all_74_15, n3, n2, simplifying with
% 248.40/42.02  | | |              (8), (11), (17), (27) gives:
% 248.40/42.02  | | |   (28)  leq(all_74_15, n2)
% 248.40/42.02  | | | 
% 248.40/42.02  | | | GROUND_INST: instantiating (22) with all_74_15, n2, simplifying with (17),
% 248.40/42.02  | | |              (20), (28) gives:
% 248.40/42.02  | | |   (29)  all_74_15 = n2 | gt(n2, all_74_15)
% 248.40/42.02  | | | 
% 248.40/42.02  | | | BETA: splitting (29) gives:
% 248.40/42.02  | | | 
% 248.40/42.02  | | | Case 1:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (30)  gt(n2, all_74_15)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | GROUND_INST: instantiating (13) with all_74_15, n2, n1, simplifying with
% 248.40/42.02  | | | |              (9), (17), (20), (30) gives:
% 248.40/42.02  | | | |   (31)  leq(all_74_15, n1)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | GROUND_INST: instantiating (3) with all_74_15, simplifying with (16),
% 248.40/42.02  | | | |              (17), (31) gives:
% 248.40/42.02  | | | |   (32)  all_74_15 = n1 | all_74_15 = n0
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | BETA: splitting (32) gives:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | Case 1:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | |   (33)  all_74_15 = n0
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (6), (33) imply:
% 248.40/42.02  | | | | |   (34)  $false
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | CLOSE: (34) is inconsistent.
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | Case 2:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | |   (35)  all_74_15 = n1
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (14), (35) imply:
% 248.40/42.02  | | | | |   (36)  a_select3(pminus_ds1_filter, n1, n0) = all_74_13
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (18), (35) imply:
% 248.40/42.02  | | | | |   (37)  a_select3(pminus_ds1_filter, n0, n1) = all_74_12
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (17), (35) imply:
% 248.40/42.02  | | | | |   (38)  $i(n1)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (7), (35) imply:
% 248.40/42.02  | | | | |   (39)  leq(n1, n5)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (16), (35) imply:
% 248.40/42.02  | | | | |   (40)  leq(n0, n1)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | GROUND_INST: instantiating (2) with n0, n1, all_74_12, simplifying
% 248.40/42.02  | | | | |              with (1), (21), (37), (38), (40) gives:
% 248.40/42.02  | | | | |   (41)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.02  | | | | |         (a_select3(pminus_ds1_filter, n1, n0) = all_74_12 &
% 248.40/42.02  | | | | |           $i(all_74_12))
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | BETA: splitting (41) gives:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | Case 1:
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | |   (42)   ~ leq(n0, all_74_21)
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | REDUCE: (5), (42) imply:
% 248.40/42.02  | | | | | |   (43)   ~ leq(n0, n5)
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | PRED_UNIFY: (4), (43) imply:
% 248.40/42.02  | | | | | |   (44)  $false
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | CLOSE: (44) is inconsistent.
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | Case 2:
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n1,
% 248.40/42.02  | | | | | |             n0) = all_74_12 & $i(all_74_12))
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | BETA: splitting (45) gives:
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | Case 1:
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | | REDUCE: (5), (46) imply:
% 248.40/42.02  | | | | | | |   (47)   ~ leq(n1, n5)
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 248.40/42.02  | | | | | | |   (48)  $false
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | | CLOSE: (48) is inconsistent.
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | Case 2:
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | |   (49)  a_select3(pminus_ds1_filter, n1, n0) = all_74_12 &
% 248.40/42.02  | | | | | | |         $i(all_74_12)
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | | ALPHA: (49) implies:
% 248.40/42.02  | | | | | | |   (50)  a_select3(pminus_ds1_filter, n1, n0) = all_74_12
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | | REF_CLOSE: (19), (23), (36), (50) are inconsistent by sub-proof
% 248.40/42.02  | | | | | | |            #25.
% 248.40/42.02  | | | | | | | 
% 248.40/42.02  | | | | | | End of split
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | End of split
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | End of split
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | Case 2:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (51)  all_74_15 = n2
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REDUCE: (14), (51) imply:
% 248.40/42.02  | | | |   (52)  a_select3(pminus_ds1_filter, n2, n0) = all_74_13
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REDUCE: (18), (51) imply:
% 248.40/42.02  | | | |   (53)  a_select3(pminus_ds1_filter, n0, n2) = all_74_12
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REDUCE: (7), (51) imply:
% 248.40/42.02  | | | |   (54)  leq(n2, n5)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REDUCE: (16), (51) imply:
% 248.40/42.02  | | | |   (55)  leq(n0, n2)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | GROUND_INST: instantiating (2) with n0, n2, all_74_12, simplifying with
% 248.40/42.02  | | | |              (1), (20), (21), (53), (55) gives:
% 248.40/42.02  | | | |   (56)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.02  | | | |         (a_select3(pminus_ds1_filter, n2, n0) = all_74_12 &
% 248.40/42.02  | | | |           $i(all_74_12))
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | BETA: splitting (56) gives:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | Case 1:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | |   (57)   ~ leq(n0, all_74_21)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (5), (57) imply:
% 248.40/42.02  | | | | |   (58)   ~ leq(n0, n5)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | PRED_UNIFY: (4), (58) imply:
% 248.40/42.02  | | | | |   (59)  $false
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | CLOSE: (59) is inconsistent.
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | Case 2:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | |   (60)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n2, n0)
% 248.40/42.02  | | | | |           = all_74_12 & $i(all_74_12))
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | BETA: splitting (60) gives:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | Case 1:
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | |   (61)   ~ leq(n2, all_74_21)
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | REDUCE: (5), (61) imply:
% 248.40/42.02  | | | | | |   (62)   ~ leq(n2, n5)
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | PRED_UNIFY: (54), (62) imply:
% 248.40/42.02  | | | | | |   (63)  $false
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | CLOSE: (63) is inconsistent.
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | Case 2:
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | |   (64)  a_select3(pminus_ds1_filter, n2, n0) = all_74_12 &
% 248.40/42.02  | | | | | |         $i(all_74_12)
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | ALPHA: (64) implies:
% 248.40/42.02  | | | | | |   (65)  a_select3(pminus_ds1_filter, n2, n0) = all_74_12
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | GROUND_INST: instantiating (23) with all_74_12, all_74_13, n0, n2,
% 248.40/42.02  | | | | | |              pminus_ds1_filter, simplifying with (52), (65) gives:
% 248.40/42.02  | | | | | |   (66)  all_74_12 = all_74_13
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | REDUCE: (19), (66) imply:
% 248.40/42.02  | | | | | |   (67)  $false
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | | CLOSE: (67) is inconsistent.
% 248.40/42.02  | | | | | | 
% 248.40/42.02  | | | | | End of split
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | End of split
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | End of split
% 248.40/42.02  | | | 
% 248.40/42.02  | | Case 2:
% 248.40/42.02  | | | 
% 248.40/42.02  | | |   (68)  all_74_15 = n3
% 248.40/42.02  | | | 
% 248.40/42.02  | | | REDUCE: (14), (68) imply:
% 248.40/42.02  | | |   (69)  a_select3(pminus_ds1_filter, n3, n0) = all_74_13
% 248.40/42.02  | | | 
% 248.40/42.02  | | | REDUCE: (18), (68) imply:
% 248.40/42.02  | | |   (70)  a_select3(pminus_ds1_filter, n0, n3) = all_74_12
% 248.40/42.02  | | | 
% 248.40/42.02  | | | REDUCE: (7), (68) imply:
% 248.40/42.02  | | |   (71)  leq(n3, n5)
% 248.40/42.02  | | | 
% 248.40/42.02  | | | REDUCE: (16), (68) imply:
% 248.40/42.02  | | |   (72)  leq(n0, n3)
% 248.40/42.02  | | | 
% 248.40/42.02  | | | GROUND_INST: instantiating (2) with n0, n3, all_74_12, simplifying with
% 248.40/42.02  | | |              (1), (8), (21), (70), (72) gives:
% 248.40/42.02  | | |   (73)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.02  | | |         (a_select3(pminus_ds1_filter, n3, n0) = all_74_12 & $i(all_74_12))
% 248.40/42.02  | | | 
% 248.40/42.02  | | | BETA: splitting (73) gives:
% 248.40/42.02  | | | 
% 248.40/42.02  | | | Case 1:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (74)   ~ leq(n0, all_74_21)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REDUCE: (5), (74) imply:
% 248.40/42.02  | | | |   (75)   ~ leq(n0, n5)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | PRED_UNIFY: (4), (75) imply:
% 248.40/42.02  | | | |   (76)  $false
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | CLOSE: (76) is inconsistent.
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | Case 2:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (77)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n3, n0) =
% 248.40/42.02  | | | |           all_74_12 & $i(all_74_12))
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | BETA: splitting (77) gives:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | Case 1:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | |   (78)   ~ leq(n3, all_74_21)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REDUCE: (5), (78) imply:
% 248.40/42.02  | | | | |   (79)   ~ leq(n3, n5)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | PRED_UNIFY: (71), (79) imply:
% 248.40/42.02  | | | | |   (80)  $false
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | CLOSE: (80) is inconsistent.
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | Case 2:
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | |   (81)  a_select3(pminus_ds1_filter, n3, n0) = all_74_12 &
% 248.40/42.02  | | | | |         $i(all_74_12)
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | ALPHA: (81) implies:
% 248.40/42.02  | | | | |   (82)  a_select3(pminus_ds1_filter, n3, n0) = all_74_12
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | | REF_CLOSE: (19), (23), (69), (82) are inconsistent by sub-proof #24.
% 248.40/42.02  | | | | | 
% 248.40/42.02  | | | | End of split
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | End of split
% 248.40/42.02  | | | 
% 248.40/42.02  | | End of split
% 248.40/42.02  | | 
% 248.40/42.02  | Case 2:
% 248.40/42.02  | | 
% 248.40/42.02  | |   (83)  all_74_15 = n4
% 248.40/42.02  | | 
% 248.40/42.02  | | REDUCE: (14), (83) imply:
% 248.40/42.02  | |   (84)  a_select3(pminus_ds1_filter, n4, n0) = all_74_13
% 248.40/42.02  | | 
% 248.40/42.02  | | REDUCE: (18), (83) imply:
% 248.40/42.02  | |   (85)  a_select3(pminus_ds1_filter, n0, n4) = all_74_12
% 248.40/42.02  | | 
% 248.40/42.02  | | REDUCE: (7), (83) imply:
% 248.40/42.02  | |   (86)  leq(n4, n5)
% 248.40/42.02  | | 
% 248.40/42.02  | | REDUCE: (16), (83) imply:
% 248.40/42.02  | |   (87)  leq(n0, n4)
% 248.40/42.02  | | 
% 248.40/42.02  | | GROUND_INST: instantiating (2) with n0, n4, all_74_12, simplifying with (1),
% 248.40/42.02  | |              (15), (21), (85), (87) gives:
% 248.40/42.02  | |   (88)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.02  | |         (a_select3(pminus_ds1_filter, n4, n0) = all_74_12 & $i(all_74_12))
% 248.40/42.02  | | 
% 248.40/42.02  | | BETA: splitting (88) gives:
% 248.40/42.02  | | 
% 248.40/42.02  | | Case 1:
% 248.40/42.02  | | | 
% 248.40/42.02  | | |   (89)   ~ leq(n0, all_74_21)
% 248.40/42.02  | | | 
% 248.40/42.02  | | | REDUCE: (5), (89) imply:
% 248.40/42.02  | | |   (90)   ~ leq(n0, n5)
% 248.40/42.02  | | | 
% 248.40/42.02  | | | PRED_UNIFY: (4), (90) imply:
% 248.40/42.02  | | |   (91)  $false
% 248.40/42.02  | | | 
% 248.40/42.02  | | | CLOSE: (91) is inconsistent.
% 248.40/42.02  | | | 
% 248.40/42.02  | | Case 2:
% 248.40/42.02  | | | 
% 248.40/42.02  | | |   (92)   ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n4, n0) =
% 248.40/42.02  | | |           all_74_12 & $i(all_74_12))
% 248.40/42.02  | | | 
% 248.40/42.02  | | | BETA: splitting (92) gives:
% 248.40/42.02  | | | 
% 248.40/42.02  | | | Case 1:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (93)   ~ leq(n4, all_74_21)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REDUCE: (5), (93) imply:
% 248.40/42.02  | | | |   (94)   ~ leq(n4, n5)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | PRED_UNIFY: (86), (94) imply:
% 248.40/42.02  | | | |   (95)  $false
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | CLOSE: (95) is inconsistent.
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | Case 2:
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | |   (96)  a_select3(pminus_ds1_filter, n4, n0) = all_74_12 & $i(all_74_12)
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | ALPHA: (96) implies:
% 248.40/42.02  | | | |   (97)  a_select3(pminus_ds1_filter, n4, n0) = all_74_12
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | | REF_CLOSE: (19), (23), (84), (97) are inconsistent by sub-proof #23.
% 248.40/42.02  | | | | 
% 248.40/42.02  | | | End of split
% 248.40/42.02  | | | 
% 248.40/42.02  | | End of split
% 248.40/42.02  | | 
% 248.40/42.02  | End of split
% 248.40/42.02  | 
% 248.40/42.02  End of proof
% 248.40/42.02  
% 248.40/42.02  Sub-proof #23 shows that the following formulas are inconsistent:
% 248.40/42.02  ----------------------------------------------------------------
% 248.40/42.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.02           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.02             v0))
% 248.40/42.02    (2)  a_select3(pminus_ds1_filter, n4, n0) = all_74_12
% 248.40/42.02    (3)  a_select3(pminus_ds1_filter, n4, n0) = all_74_13
% 248.40/42.02    (4)   ~ (all_74_12 = all_74_13)
% 248.40/42.02  
% 248.40/42.02  Begin of proof
% 248.40/42.02  | 
% 248.40/42.02  | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n0, n4,
% 248.40/42.02  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.02  |   (5)  all_74_12 = all_74_13
% 248.40/42.02  | 
% 248.40/42.02  | REDUCE: (4), (5) imply:
% 248.40/42.02  |   (6)  $false
% 248.40/42.02  | 
% 248.40/42.02  | CLOSE: (6) is inconsistent.
% 248.40/42.02  | 
% 248.40/42.02  End of proof
% 248.40/42.02  
% 248.40/42.02  Sub-proof #24 shows that the following formulas are inconsistent:
% 248.40/42.02  ----------------------------------------------------------------
% 248.40/42.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.02           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.02             v0))
% 248.40/42.02    (2)  a_select3(pminus_ds1_filter, n3, n0) = all_74_12
% 248.40/42.02    (3)  a_select3(pminus_ds1_filter, n3, n0) = all_74_13
% 248.40/42.02    (4)   ~ (all_74_12 = all_74_13)
% 248.40/42.02  
% 248.40/42.02  Begin of proof
% 248.40/42.02  | 
% 248.40/42.02  | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n0, n3,
% 248.40/42.02  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.02  |   (5)  all_74_12 = all_74_13
% 248.40/42.02  | 
% 248.40/42.02  | REDUCE: (4), (5) imply:
% 248.40/42.02  |   (6)  $false
% 248.40/42.02  | 
% 248.40/42.02  | CLOSE: (6) is inconsistent.
% 248.40/42.02  | 
% 248.40/42.02  End of proof
% 248.40/42.02  
% 248.40/42.02  Sub-proof #25 shows that the following formulas are inconsistent:
% 248.40/42.02  ----------------------------------------------------------------
% 248.40/42.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.02           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.02             v0))
% 248.40/42.02    (2)  a_select3(pminus_ds1_filter, n1, n0) = all_74_12
% 248.40/42.02    (3)  a_select3(pminus_ds1_filter, n1, n0) = all_74_13
% 248.40/42.02    (4)   ~ (all_74_12 = all_74_13)
% 248.40/42.02  
% 248.40/42.02  Begin of proof
% 248.40/42.02  | 
% 248.40/42.02  | GROUND_INST: instantiating (1) with all_74_12, all_74_13, n0, n1,
% 248.40/42.02  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.02  |   (5)  all_74_12 = all_74_13
% 248.40/42.02  | 
% 248.40/42.02  | REDUCE: (4), (5) imply:
% 248.40/42.02  |   (6)  $false
% 248.40/42.02  | 
% 248.40/42.02  | CLOSE: (6) is inconsistent.
% 248.40/42.02  | 
% 248.40/42.02  End of proof
% 248.40/42.02  
% 248.40/42.02  Sub-proof #26 shows that the following formulas are inconsistent:
% 248.40/42.02  ----------------------------------------------------------------
% 248.40/42.02    (1)  a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8
% 248.40/42.02    (2)  leq(n0, all_74_10)
% 248.40/42.02    (3)  a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9
% 248.40/42.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.40/42.02           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.40/42.02           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.40/42.02           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.02    (5)   ~ gt(n0, n0)
% 248.40/42.02    (6)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.02           leq(n0, v0))
% 248.40/42.02    (7)  all_74_21 = n5
% 248.40/42.02    (8)  $i(all_74_11)
% 248.40/42.02    (9)  pred(n5) = n4
% 248.40/42.02    (10)  $i(n3)
% 248.40/42.02    (11)  $i(all_74_10)
% 248.40/42.02    (12)  all_74_10 = n5 | all_74_10 = n4 | all_74_10 = n3 | all_74_10 = n2 |
% 248.40/42.02          all_74_10 = n1 | all_74_10 = n0
% 248.40/42.02    (13)  leq(n0, all_74_11)
% 248.40/42.02    (14)  pred(n2) = n1
% 248.40/42.03    (15)  pred(n4) = n3
% 248.40/42.03    (16)  pred(n3) = n2
% 248.40/42.03    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/42.03            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/42.03    (18)  $i(n4)
% 248.40/42.03    (19)  leq(all_74_11, n5)
% 248.40/42.03    (20)  all_74_11 = n5 | all_74_11 = n4 | all_74_11 = n3 | all_74_11 = n2 |
% 248.40/42.03          all_74_11 = n1 | all_74_11 = n0
% 248.40/42.03    (21)  leq(all_74_10, n5)
% 248.40/42.03    (22)  $i(n2)
% 248.40/42.03    (23)  $i(n5)
% 248.40/42.03    (24)   ~ (all_74_8 = all_74_9)
% 248.40/42.03    (25)  gt(all_74_10, n0)
% 248.40/42.03    (26)  all_74_11 = n0 | gt(all_74_11, n0)
% 248.40/42.03    (27)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.40/42.03            leq(v0, v1) | gt(v1, v0))
% 248.40/42.03    (28)  all_74_10 = n5 | gt(n5, all_74_10)
% 248.40/42.03    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.03          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.03              v0))
% 248.40/42.03    (30)  all_74_11 = n5 | gt(n5, all_74_11)
% 248.40/42.03  
% 248.40/42.03  Begin of proof
% 248.40/42.03  | 
% 248.40/42.03  | BETA: splitting (26) gives:
% 248.40/42.03  | 
% 248.40/42.03  | Case 1:
% 248.40/42.03  | | 
% 248.40/42.03  | |   (31)  gt(all_74_11, n0)
% 248.40/42.03  | | 
% 248.40/42.03  | | BETA: splitting (28) gives:
% 248.40/42.03  | | 
% 248.40/42.03  | | Case 1:
% 248.40/42.03  | | | 
% 248.40/42.03  | | |   (32)  gt(n5, all_74_10)
% 248.40/42.03  | | | 
% 248.40/42.03  | | | GROUND_INST: instantiating (17) with all_74_10, n5, n4, simplifying with
% 248.40/42.03  | | |              (9), (11), (23), (32) gives:
% 248.40/42.03  | | |   (33)  leq(all_74_10, n4)
% 248.40/42.03  | | | 
% 248.40/42.03  | | | BETA: splitting (30) gives:
% 248.40/42.03  | | | 
% 248.40/42.03  | | | Case 1:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | |   (34)  gt(n5, all_74_11)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | GROUND_INST: instantiating (17) with all_74_11, n5, n4, simplifying with
% 248.40/42.03  | | | |              (8), (9), (23), (34) gives:
% 248.40/42.03  | | | |   (35)  leq(all_74_11, n4)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | GROUND_INST: instantiating (27) with all_74_10, n4, simplifying with
% 248.40/42.03  | | | |              (11), (18), (33) gives:
% 248.40/42.03  | | | |   (36)  all_74_10 = n4 | gt(n4, all_74_10)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | GROUND_INST: instantiating (27) with all_74_11, n4, simplifying with
% 248.40/42.03  | | | |              (8), (18), (35) gives:
% 248.40/42.03  | | | |   (37)  all_74_11 = n4 | gt(n4, all_74_11)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | BETA: splitting (20) gives:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | Case 1:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | |   (38)  all_74_11 = n0
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | REDUCE: (31), (38) imply:
% 248.40/42.03  | | | | |   (39)  gt(n0, n0)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | PRED_UNIFY: (5), (39) imply:
% 248.40/42.03  | | | | |   (40)  $false
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | CLOSE: (40) is inconsistent.
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | Case 2:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | |   (41)   ~ (all_74_11 = n0)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | BETA: splitting (12) gives:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | Case 1:
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | |   (42)  all_74_10 = n0
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | REDUCE: (25), (42) imply:
% 248.40/42.03  | | | | | |   (43)  gt(n0, n0)
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | PRED_UNIFY: (5), (43) imply:
% 248.40/42.03  | | | | | |   (44)  $false
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | CLOSE: (44) is inconsistent.
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | Case 2:
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | |   (45)   ~ (all_74_10 = n0)
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (13),
% 248.40/42.03  | | | | | |            (14), (15), (16), (17), (18), (19), (21), (22), (24),
% 248.40/42.03  | | | | | |            (27), (29), (36), (37), (41), (45) are inconsistent by
% 248.40/42.03  | | | | | |            sub-proof #34.
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | End of split
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | End of split
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | Case 2:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | |   (46)  all_74_11 = n5
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (1), (46) imply:
% 248.40/42.03  | | | |   (47)  a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (3), (46) imply:
% 248.40/42.03  | | | |   (48)  a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (19), (46) imply:
% 248.40/42.03  | | | |   (49)  leq(n5, n5)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (13), (46) imply:
% 248.40/42.03  | | | |   (50)  leq(n0, n5)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | GROUND_INST: instantiating (27) with all_74_10, n4, simplifying with
% 248.40/42.03  | | | |              (11), (18), (33) gives:
% 248.40/42.03  | | | |   (51)  all_74_10 = n4 | gt(n4, all_74_10)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | BETA: splitting (12) gives:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | Case 1:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | |   (52)  all_74_10 = n0
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | REDUCE: (25), (52) imply:
% 248.40/42.03  | | | | |   (53)  gt(n0, n0)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | PRED_UNIFY: (5), (53) imply:
% 248.40/42.03  | | | | |   (54)  $false
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | CLOSE: (54) is inconsistent.
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | Case 2:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | |   (55)   ~ (all_74_10 = n0)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | REF_CLOSE: (2), (4), (6), (7), (10), (11), (14), (15), (16), (17),
% 248.40/42.03  | | | | |            (18), (21), (22), (23), (24), (27), (29), (47), (48), (49),
% 248.40/42.03  | | | | |            (50), (51), (55) are inconsistent by sub-proof #31.
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | End of split
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | End of split
% 248.40/42.03  | | | 
% 248.40/42.03  | | Case 2:
% 248.40/42.03  | | | 
% 248.40/42.03  | | |   (56)  all_74_10 = n5
% 248.40/42.03  | | | 
% 248.40/42.03  | | | REDUCE: (1), (56) imply:
% 248.40/42.03  | | |   (57)  a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8
% 248.40/42.03  | | | 
% 248.40/42.03  | | | REDUCE: (3), (56) imply:
% 248.40/42.03  | | |   (58)  a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9
% 248.40/42.03  | | | 
% 248.40/42.03  | | | REDUCE: (21), (56) imply:
% 248.40/42.03  | | |   (59)  leq(n5, n5)
% 248.40/42.03  | | | 
% 248.40/42.03  | | | REDUCE: (2), (56) imply:
% 248.40/42.03  | | |   (60)  leq(n0, n5)
% 248.40/42.03  | | | 
% 248.40/42.03  | | | BETA: splitting (30) gives:
% 248.40/42.03  | | | 
% 248.40/42.03  | | | Case 1:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | |   (61)  gt(n5, all_74_11)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | GROUND_INST: instantiating (17) with all_74_11, n5, n4, simplifying with
% 248.40/42.03  | | | |              (8), (9), (23), (61) gives:
% 248.40/42.03  | | | |   (62)  leq(all_74_11, n4)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | GROUND_INST: instantiating (27) with all_74_11, n4, simplifying with
% 248.40/42.03  | | | |              (8), (18), (62) gives:
% 248.40/42.03  | | | |   (63)  all_74_11 = n4 | gt(n4, all_74_11)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | BETA: splitting (20) gives:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | Case 1:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | |   (64)  all_74_11 = n0
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | REDUCE: (31), (64) imply:
% 248.40/42.03  | | | | |   (65)  gt(n0, n0)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | PRED_UNIFY: (5), (65) imply:
% 248.40/42.03  | | | | |   (66)  $false
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | CLOSE: (66) is inconsistent.
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | Case 2:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | |   (67)   ~ (all_74_11 = n0)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | REF_CLOSE: (4), (6), (7), (8), (10), (13), (14), (15), (16), (17),
% 248.40/42.03  | | | | |            (18), (19), (22), (23), (24), (27), (29), (57), (58), (59),
% 248.40/42.03  | | | | |            (60), (63), (67) are inconsistent by sub-proof #30.
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | End of split
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | Case 2:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | |   (68)  all_74_11 = n5
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (58), (68) imply:
% 248.40/42.03  | | | |   (69)  a_select3(pminus_ds1_filter, n5, n5) = all_74_9
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (57), (68) imply:
% 248.40/42.03  | | | |   (70)  a_select3(pminus_ds1_filter, n5, n5) = all_74_8
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | GROUND_INST: instantiating (29) with all_74_9, all_74_8, n5, n5,
% 248.40/42.03  | | | |              pminus_ds1_filter, simplifying with (69), (70) gives:
% 248.40/42.03  | | | |   (71)  all_74_8 = all_74_9
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (24), (71) imply:
% 248.40/42.03  | | | |   (72)  $false
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | CLOSE: (72) is inconsistent.
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | End of split
% 248.40/42.03  | | | 
% 248.40/42.03  | | End of split
% 248.40/42.03  | | 
% 248.40/42.03  | Case 2:
% 248.40/42.03  | | 
% 248.40/42.03  | |   (73)  all_74_11 = n0
% 248.40/42.03  | |   (74)   ~ gt(all_74_11, n0)
% 248.40/42.03  | | 
% 248.40/42.03  | | REDUCE: (1), (73) imply:
% 248.40/42.03  | |   (75)  a_select3(pminus_ds1_filter, all_74_10, n0) = all_74_8
% 248.40/42.03  | | 
% 248.40/42.03  | | REDUCE: (3), (73) imply:
% 248.40/42.03  | |   (76)  a_select3(pminus_ds1_filter, n0, all_74_10) = all_74_9
% 248.40/42.03  | | 
% 248.40/42.03  | | REDUCE: (8), (73) imply:
% 248.40/42.03  | |   (77)  $i(n0)
% 248.40/42.03  | | 
% 248.40/42.03  | | REDUCE: (19), (73) imply:
% 248.40/42.03  | |   (78)  leq(n0, n5)
% 248.40/42.03  | | 
% 248.40/42.03  | | REDUCE: (13), (73) imply:
% 248.40/42.03  | |   (79)  leq(n0, n0)
% 248.40/42.03  | | 
% 248.40/42.03  | | BETA: splitting (28) gives:
% 248.40/42.03  | | 
% 248.40/42.03  | | Case 1:
% 248.40/42.03  | | | 
% 248.40/42.03  | | |   (80)  gt(n5, all_74_10)
% 248.40/42.03  | | | 
% 248.40/42.03  | | | GROUND_INST: instantiating (17) with all_74_10, n5, n4, simplifying with
% 248.40/42.03  | | |              (9), (11), (23), (80) gives:
% 248.40/42.03  | | |   (81)  leq(all_74_10, n4)
% 248.40/42.03  | | | 
% 248.40/42.03  | | | GROUND_INST: instantiating (27) with all_74_10, n4, simplifying with (11),
% 248.40/42.03  | | |              (18), (81) gives:
% 248.40/42.03  | | |   (82)  all_74_10 = n4 | gt(n4, all_74_10)
% 248.40/42.03  | | | 
% 248.40/42.03  | | | BETA: splitting (12) gives:
% 248.40/42.03  | | | 
% 248.40/42.03  | | | Case 1:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | |   (83)  all_74_10 = n0
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | REDUCE: (25), (83) imply:
% 248.40/42.03  | | | |   (84)  gt(n0, n0)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | PRED_UNIFY: (5), (84) imply:
% 248.40/42.03  | | | |   (85)  $false
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | CLOSE: (85) is inconsistent.
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | Case 2:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | |   (86)   ~ (all_74_10 = n0)
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | BETA: splitting (82) gives:
% 248.40/42.03  | | | | 
% 248.40/42.03  | | | | Case 1:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | |   (87)  gt(n4, all_74_10)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | GROUND_INST: instantiating (17) with all_74_10, n4, n3, simplifying
% 248.40/42.03  | | | | |              with (11), (15), (18), (87) gives:
% 248.40/42.03  | | | | |   (88)  leq(all_74_10, n3)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | GROUND_INST: instantiating (27) with all_74_10, n3, simplifying with
% 248.40/42.03  | | | | |              (10), (11), (88) gives:
% 248.40/42.03  | | | | |   (89)  all_74_10 = n3 | gt(n3, all_74_10)
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | BETA: splitting (89) gives:
% 248.40/42.03  | | | | | 
% 248.40/42.03  | | | | | Case 1:
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | |   (90)  gt(n3, all_74_10)
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | GROUND_INST: instantiating (17) with all_74_10, n3, n2, simplifying
% 248.40/42.03  | | | | | |              with (10), (11), (16), (90) gives:
% 248.40/42.03  | | | | | |   (91)  leq(all_74_10, n2)
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | GROUND_INST: instantiating (27) with all_74_10, n2, simplifying with
% 248.40/42.03  | | | | | |              (11), (22), (91) gives:
% 248.40/42.03  | | | | | |   (92)  all_74_10 = n2 | gt(n2, all_74_10)
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | BETA: splitting (92) gives:
% 248.40/42.03  | | | | | | 
% 248.40/42.03  | | | | | | Case 1:
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | |   (93)  gt(n2, all_74_10)
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | GROUND_INST: instantiating (17) with all_74_10, n2, n1,
% 248.40/42.03  | | | | | | |              simplifying with (11), (14), (22), (93) gives:
% 248.40/42.03  | | | | | | |   (94)  leq(all_74_10, n1)
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | GROUND_INST: instantiating (6) with all_74_10, simplifying with
% 248.40/42.03  | | | | | | |              (2), (11), (94) gives:
% 248.40/42.03  | | | | | | |   (95)  all_74_10 = n1 | all_74_10 = n0
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | BETA: splitting (95) gives:
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | Case 1:
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | |   (96)  all_74_10 = n0
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | REDUCE: (86), (96) imply:
% 248.40/42.03  | | | | | | | |   (97)  $false
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | CLOSE: (97) is inconsistent.
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | Case 2:
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | |   (98)  all_74_10 = n1
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | REDUCE: (75), (98) imply:
% 248.40/42.03  | | | | | | | |   (99)  a_select3(pminus_ds1_filter, n1, n0) = all_74_8
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | REDUCE: (76), (98) imply:
% 248.40/42.03  | | | | | | | |   (100)  a_select3(pminus_ds1_filter, n0, n1) = all_74_9
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | REDUCE: (11), (98) imply:
% 248.40/42.03  | | | | | | | |   (101)  $i(n1)
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | REDUCE: (21), (98) imply:
% 248.40/42.03  | | | | | | | |   (102)  leq(n1, n5)
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | REDUCE: (2), (98) imply:
% 248.40/42.03  | | | | | | | |   (103)  leq(n0, n1)
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | GROUND_INST: instantiating (4) with n0, n1, all_74_9,
% 248.40/42.03  | | | | | | | |              simplifying with (77), (79), (100), (101), (103)
% 248.40/42.03  | | | | | | | |              gives:
% 248.40/42.03  | | | | | | | |   (104)   ~ leq(n1, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.03  | | | | | | | |          (a_select3(pminus_ds1_filter, n1, n0) = all_74_9 &
% 248.40/42.03  | | | | | | | |            $i(all_74_9))
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | BETA: splitting (104) gives:
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | Case 1:
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | |   (105)   ~ leq(n0, all_74_21)
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | REDUCE: (7), (105) imply:
% 248.40/42.03  | | | | | | | | |   (106)   ~ leq(n0, n5)
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | PRED_UNIFY: (78), (106) imply:
% 248.40/42.03  | | | | | | | | |   (107)  $false
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | CLOSE: (107) is inconsistent.
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | Case 2:
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | |   (108)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/42.03  | | | | | | | | |              n1, n0) = all_74_9 & $i(all_74_9))
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | BETA: splitting (108) gives:
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | Case 1:
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | |   (109)   ~ leq(n1, all_74_21)
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | | REDUCE: (7), (109) imply:
% 248.40/42.03  | | | | | | | | | |   (110)   ~ leq(n1, n5)
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | | PRED_UNIFY: (102), (110) imply:
% 248.40/42.03  | | | | | | | | | |   (111)  $false
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | | CLOSE: (111) is inconsistent.
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | Case 2:
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | |   (112)  a_select3(pminus_ds1_filter, n1, n0) = all_74_9 &
% 248.40/42.03  | | | | | | | | | |          $i(all_74_9)
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | | ALPHA: (112) implies:
% 248.40/42.03  | | | | | | | | | |   (113)  a_select3(pminus_ds1_filter, n1, n0) = all_74_9
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | | GROUND_INST: instantiating (29) with all_74_9, all_74_8, n0,
% 248.40/42.03  | | | | | | | | | |              n1, pminus_ds1_filter, simplifying with (99),
% 248.40/42.03  | | | | | | | | | |              (113) gives:
% 248.40/42.03  | | | | | | | | | |   (114)  all_74_8 = all_74_9
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | | REDUCE: (24), (114) imply:
% 248.40/42.03  | | | | | | | | | |   (115)  $false
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | | CLOSE: (115) is inconsistent.
% 248.40/42.03  | | | | | | | | | | 
% 248.40/42.03  | | | | | | | | | End of split
% 248.40/42.03  | | | | | | | | | 
% 248.40/42.03  | | | | | | | | End of split
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | End of split
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | Case 2:
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | |   (116)  all_74_10 = n2
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | REDUCE: (75), (116) imply:
% 248.40/42.03  | | | | | | |   (117)  a_select3(pminus_ds1_filter, n2, n0) = all_74_8
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | REDUCE: (76), (116) imply:
% 248.40/42.03  | | | | | | |   (118)  a_select3(pminus_ds1_filter, n0, n2) = all_74_9
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | REDUCE: (21), (116) imply:
% 248.40/42.03  | | | | | | |   (119)  leq(n2, n5)
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | REDUCE: (2), (116) imply:
% 248.40/42.03  | | | | | | |   (120)  leq(n0, n2)
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | GROUND_INST: instantiating (4) with n0, n2, all_74_9, simplifying
% 248.40/42.03  | | | | | | |              with (22), (77), (79), (118), (120) gives:
% 248.40/42.03  | | | | | | |   (121)   ~ leq(n2, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.03  | | | | | | |          (a_select3(pminus_ds1_filter, n2, n0) = all_74_9 &
% 248.40/42.03  | | | | | | |            $i(all_74_9))
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | BETA: splitting (121) gives:
% 248.40/42.03  | | | | | | | 
% 248.40/42.03  | | | | | | | Case 1:
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | |   (122)   ~ leq(n0, all_74_21)
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | REDUCE: (7), (122) imply:
% 248.40/42.03  | | | | | | | |   (123)   ~ leq(n0, n5)
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | PRED_UNIFY: (78), (123) imply:
% 248.40/42.03  | | | | | | | |   (124)  $false
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | | CLOSE: (124) is inconsistent.
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | Case 2:
% 248.40/42.03  | | | | | | | | 
% 248.40/42.03  | | | | | | | |   (125)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/42.04  | | | | | | | |              n2, n0) = all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | | BETA: splitting (125) gives:
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | | Case 1:
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | |   (126)   ~ leq(n2, all_74_21)
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | | REDUCE: (7), (126) imply:
% 248.40/42.04  | | | | | | | | |   (127)   ~ leq(n2, n5)
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | | PRED_UNIFY: (119), (127) imply:
% 248.40/42.04  | | | | | | | | |   (128)  $false
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | | CLOSE: (128) is inconsistent.
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | Case 2:
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | |   (129)  a_select3(pminus_ds1_filter, n2, n0) = all_74_9 &
% 248.40/42.04  | | | | | | | | |          $i(all_74_9)
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | | ALPHA: (129) implies:
% 248.40/42.04  | | | | | | | | |   (130)  a_select3(pminus_ds1_filter, n2, n0) = all_74_9
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | | GROUND_INST: instantiating (29) with all_74_9, all_74_8, n0,
% 248.40/42.04  | | | | | | | | |              n2, pminus_ds1_filter, simplifying with (117),
% 248.40/42.04  | | | | | | | | |              (130) gives:
% 248.40/42.04  | | | | | | | | |   (131)  all_74_8 = all_74_9
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | | REDUCE: (24), (131) imply:
% 248.40/42.04  | | | | | | | | |   (132)  $false
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | | CLOSE: (132) is inconsistent.
% 248.40/42.04  | | | | | | | | | 
% 248.40/42.04  | | | | | | | | End of split
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | End of split
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | End of split
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | Case 2:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | |   (133)  all_74_10 = n3
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | REDUCE: (75), (133) imply:
% 248.40/42.04  | | | | | |   (134)  a_select3(pminus_ds1_filter, n3, n0) = all_74_8
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | REDUCE: (76), (133) imply:
% 248.40/42.04  | | | | | |   (135)  a_select3(pminus_ds1_filter, n0, n3) = all_74_9
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | REDUCE: (21), (133) imply:
% 248.40/42.04  | | | | | |   (136)  leq(n3, n5)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | REDUCE: (2), (133) imply:
% 248.40/42.04  | | | | | |   (137)  leq(n0, n3)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | GROUND_INST: instantiating (4) with n0, n3, all_74_9, simplifying
% 248.40/42.04  | | | | | |              with (10), (77), (79), (135), (137) gives:
% 248.40/42.04  | | | | | |   (138)   ~ leq(n3, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.04  | | | | | |          (a_select3(pminus_ds1_filter, n3, n0) = all_74_9 &
% 248.40/42.04  | | | | | |            $i(all_74_9))
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | BETA: splitting (138) gives:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | Case 1:
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | |   (139)   ~ leq(n0, all_74_21)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | REDUCE: (7), (139) imply:
% 248.40/42.04  | | | | | | |   (140)   ~ leq(n0, n5)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | PRED_UNIFY: (78), (140) imply:
% 248.40/42.04  | | | | | | |   (141)  $false
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | CLOSE: (141) is inconsistent.
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | Case 2:
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | |   (142)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n3,
% 248.40/42.04  | | | | | | |              n0) = all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | BETA: splitting (142) gives:
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | Case 1:
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | |   (143)   ~ leq(n3, all_74_21)
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | | REDUCE: (7), (143) imply:
% 248.40/42.04  | | | | | | | |   (144)   ~ leq(n3, n5)
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | | PRED_UNIFY: (136), (144) imply:
% 248.40/42.04  | | | | | | | |   (145)  $false
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | | CLOSE: (145) is inconsistent.
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | Case 2:
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | |   (146)  a_select3(pminus_ds1_filter, n3, n0) = all_74_9 &
% 248.40/42.04  | | | | | | | |          $i(all_74_9)
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | | ALPHA: (146) implies:
% 248.40/42.04  | | | | | | | |   (147)  a_select3(pminus_ds1_filter, n3, n0) = all_74_9
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | | REF_CLOSE: (24), (29), (134), (147) are inconsistent by
% 248.40/42.04  | | | | | | | |            sub-proof #29.
% 248.40/42.04  | | | | | | | | 
% 248.40/42.04  | | | | | | | End of split
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | End of split
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | End of split
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | Case 2:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | |   (148)  all_74_10 = n4
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (75), (148) imply:
% 248.40/42.04  | | | | |   (149)  a_select3(pminus_ds1_filter, n4, n0) = all_74_8
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (76), (148) imply:
% 248.40/42.04  | | | | |   (150)  a_select3(pminus_ds1_filter, n0, n4) = all_74_9
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (21), (148) imply:
% 248.40/42.04  | | | | |   (151)  leq(n4, n5)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (2), (148) imply:
% 248.40/42.04  | | | | |   (152)  leq(n0, n4)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | GROUND_INST: instantiating (4) with n0, n4, all_74_9, simplifying with
% 248.40/42.04  | | | | |              (18), (77), (79), (150), (152) gives:
% 248.40/42.04  | | | | |   (153)   ~ leq(n4, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.04  | | | | |          (a_select3(pminus_ds1_filter, n4, n0) = all_74_9 &
% 248.40/42.04  | | | | |            $i(all_74_9))
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | BETA: splitting (153) gives:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | Case 1:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | |   (154)   ~ leq(n0, all_74_21)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | REDUCE: (7), (154) imply:
% 248.40/42.04  | | | | | |   (155)   ~ leq(n0, n5)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | PRED_UNIFY: (78), (155) imply:
% 248.40/42.04  | | | | | |   (156)  $false
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | CLOSE: (156) is inconsistent.
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | Case 2:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | |   (157)   ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.04  | | | | | |              n0) = all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | BETA: splitting (157) gives:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | Case 1:
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | |   (158)   ~ leq(n4, all_74_21)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | REDUCE: (7), (158) imply:
% 248.40/42.04  | | | | | | |   (159)   ~ leq(n4, n5)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | PRED_UNIFY: (151), (159) imply:
% 248.40/42.04  | | | | | | |   (160)  $false
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | CLOSE: (160) is inconsistent.
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | Case 2:
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | |   (161)  a_select3(pminus_ds1_filter, n4, n0) = all_74_9 &
% 248.40/42.04  | | | | | | |          $i(all_74_9)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | ALPHA: (161) implies:
% 248.40/42.04  | | | | | | |   (162)  a_select3(pminus_ds1_filter, n4, n0) = all_74_9
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | REF_CLOSE: (24), (29), (149), (162) are inconsistent by sub-proof
% 248.40/42.04  | | | | | | |            #28.
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | End of split
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | End of split
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | End of split
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | End of split
% 248.40/42.04  | | | 
% 248.40/42.04  | | Case 2:
% 248.40/42.04  | | | 
% 248.40/42.04  | | |   (163)  all_74_10 = n5
% 248.40/42.04  | | | 
% 248.40/42.04  | | | REDUCE: (75), (163) imply:
% 248.40/42.04  | | |   (164)  a_select3(pminus_ds1_filter, n5, n0) = all_74_8
% 248.40/42.04  | | | 
% 248.40/42.04  | | | REDUCE: (76), (163) imply:
% 248.40/42.04  | | |   (165)  a_select3(pminus_ds1_filter, n0, n5) = all_74_9
% 248.40/42.04  | | | 
% 248.40/42.04  | | | REDUCE: (21), (163) imply:
% 248.40/42.04  | | |   (166)  leq(n5, n5)
% 248.40/42.04  | | | 
% 248.40/42.04  | | | GROUND_INST: instantiating (4) with n0, n5, all_74_9, simplifying with
% 248.40/42.04  | | |              (23), (77), (78), (79), (165) gives:
% 248.40/42.04  | | |   (167)   ~ leq(n5, all_74_21) |  ~ leq(n0, all_74_21) |
% 248.40/42.04  | | |          (a_select3(pminus_ds1_filter, n5, n0) = all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | 
% 248.40/42.04  | | | BETA: splitting (167) gives:
% 248.40/42.04  | | | 
% 248.40/42.04  | | | Case 1:
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | |   (168)   ~ leq(n0, all_74_21)
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | REDUCE: (7), (168) imply:
% 248.40/42.04  | | | |   (169)   ~ leq(n0, n5)
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | PRED_UNIFY: (78), (169) imply:
% 248.40/42.04  | | | |   (170)  $false
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | CLOSE: (170) is inconsistent.
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | Case 2:
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | |   (171)   ~ leq(n5, all_74_21) | (a_select3(pminus_ds1_filter, n5, n0) =
% 248.40/42.04  | | | |            all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | BETA: splitting (171) gives:
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | Case 1:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | |   (172)   ~ leq(n5, all_74_21)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (7), (172) imply:
% 248.40/42.04  | | | | |   (173)   ~ leq(n5, n5)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | PRED_UNIFY: (166), (173) imply:
% 248.40/42.04  | | | | |   (174)  $false
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | CLOSE: (174) is inconsistent.
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | Case 2:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | |   (175)  a_select3(pminus_ds1_filter, n5, n0) = all_74_9 &
% 248.40/42.04  | | | | |          $i(all_74_9)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | ALPHA: (175) implies:
% 248.40/42.04  | | | | |   (176)  a_select3(pminus_ds1_filter, n5, n0) = all_74_9
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REF_CLOSE: (24), (29), (164), (176) are inconsistent by sub-proof #27.
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | End of split
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | End of split
% 248.40/42.04  | | | 
% 248.40/42.04  | | End of split
% 248.40/42.04  | | 
% 248.40/42.04  | End of split
% 248.40/42.04  | 
% 248.40/42.04  End of proof
% 248.40/42.04  
% 248.40/42.04  Sub-proof #27 shows that the following formulas are inconsistent:
% 248.40/42.04  ----------------------------------------------------------------
% 248.40/42.04    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.04           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.04             v0))
% 248.40/42.04    (2)  a_select3(pminus_ds1_filter, n5, n0) = all_74_8
% 248.40/42.04    (3)  a_select3(pminus_ds1_filter, n5, n0) = all_74_9
% 248.40/42.04    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.04  
% 248.40/42.04  Begin of proof
% 248.40/42.04  | 
% 248.40/42.04  | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n0, n5,
% 248.40/42.04  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.04  |   (5)  all_74_8 = all_74_9
% 248.40/42.04  | 
% 248.40/42.04  | REDUCE: (4), (5) imply:
% 248.40/42.04  |   (6)  $false
% 248.40/42.04  | 
% 248.40/42.04  | CLOSE: (6) is inconsistent.
% 248.40/42.04  | 
% 248.40/42.04  End of proof
% 248.40/42.04  
% 248.40/42.04  Sub-proof #28 shows that the following formulas are inconsistent:
% 248.40/42.04  ----------------------------------------------------------------
% 248.40/42.04    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.04           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.04             v0))
% 248.40/42.04    (2)  a_select3(pminus_ds1_filter, n4, n0) = all_74_8
% 248.40/42.04    (3)  a_select3(pminus_ds1_filter, n4, n0) = all_74_9
% 248.40/42.04    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.04  
% 248.40/42.04  Begin of proof
% 248.40/42.04  | 
% 248.40/42.04  | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n0, n4,
% 248.40/42.04  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.04  |   (5)  all_74_8 = all_74_9
% 248.40/42.04  | 
% 248.40/42.04  | REDUCE: (4), (5) imply:
% 248.40/42.04  |   (6)  $false
% 248.40/42.04  | 
% 248.40/42.04  | CLOSE: (6) is inconsistent.
% 248.40/42.04  | 
% 248.40/42.04  End of proof
% 248.40/42.04  
% 248.40/42.04  Sub-proof #29 shows that the following formulas are inconsistent:
% 248.40/42.04  ----------------------------------------------------------------
% 248.40/42.04    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.04           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.04             v0))
% 248.40/42.04    (2)  a_select3(pminus_ds1_filter, n3, n0) = all_74_8
% 248.40/42.04    (3)  a_select3(pminus_ds1_filter, n3, n0) = all_74_9
% 248.40/42.04    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.04  
% 248.40/42.04  Begin of proof
% 248.40/42.04  | 
% 248.40/42.04  | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n0, n3,
% 248.40/42.04  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.04  |   (5)  all_74_8 = all_74_9
% 248.40/42.04  | 
% 248.40/42.04  | REDUCE: (4), (5) imply:
% 248.40/42.04  |   (6)  $false
% 248.40/42.04  | 
% 248.40/42.04  | CLOSE: (6) is inconsistent.
% 248.40/42.04  | 
% 248.40/42.04  End of proof
% 248.40/42.04  
% 248.40/42.04  Sub-proof #30 shows that the following formulas are inconsistent:
% 248.40/42.04  ----------------------------------------------------------------
% 248.40/42.04    (1)  all_74_11 = n4 | gt(n4, all_74_11)
% 248.40/42.04    (2)  a_select3(pminus_ds1_filter, all_74_11, n5) = all_74_9
% 248.40/42.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.40/42.04           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.40/42.04           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.40/42.04           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.04    (4)   ~ (all_74_11 = n0)
% 248.40/42.04    (5)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.04           leq(n0, v0))
% 248.40/42.04    (6)  leq(n0, n5)
% 248.40/42.04    (7)  all_74_21 = n5
% 248.40/42.04    (8)  $i(all_74_11)
% 248.40/42.04    (9)  $i(n3)
% 248.40/42.04    (10)  leq(n0, all_74_11)
% 248.40/42.04    (11)  pred(n2) = n1
% 248.40/42.04    (12)  pred(n4) = n3
% 248.40/42.04    (13)  pred(n3) = n2
% 248.40/42.04    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/42.04            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/42.04    (15)  $i(n4)
% 248.40/42.04    (16)  leq(all_74_11, n5)
% 248.40/42.04    (17)  leq(n5, n5)
% 248.40/42.04    (18)  $i(n2)
% 248.40/42.04    (19)  a_select3(pminus_ds1_filter, n5, all_74_11) = all_74_8
% 248.40/42.04    (20)  $i(n5)
% 248.40/42.04    (21)   ~ (all_74_8 = all_74_9)
% 248.40/42.04    (22)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.40/42.04            leq(v0, v1) | gt(v1, v0))
% 248.40/42.04    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.04          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.04              v0))
% 248.40/42.04  
% 248.40/42.04  Begin of proof
% 248.40/42.04  | 
% 248.40/42.04  | BETA: splitting (1) gives:
% 248.40/42.04  | 
% 248.40/42.04  | Case 1:
% 248.40/42.04  | | 
% 248.40/42.04  | |   (24)  gt(n4, all_74_11)
% 248.40/42.04  | | 
% 248.40/42.04  | | GROUND_INST: instantiating (14) with all_74_11, n4, n3, simplifying with
% 248.40/42.04  | |              (8), (12), (15), (24) gives:
% 248.40/42.04  | |   (25)  leq(all_74_11, n3)
% 248.40/42.04  | | 
% 248.40/42.04  | | GROUND_INST: instantiating (22) with all_74_11, n3, simplifying with (8),
% 248.40/42.04  | |              (9), (25) gives:
% 248.40/42.04  | |   (26)  all_74_11 = n3 | gt(n3, all_74_11)
% 248.40/42.04  | | 
% 248.40/42.04  | | BETA: splitting (26) gives:
% 248.40/42.04  | | 
% 248.40/42.04  | | Case 1:
% 248.40/42.04  | | | 
% 248.40/42.04  | | |   (27)  gt(n3, all_74_11)
% 248.40/42.04  | | | 
% 248.40/42.04  | | | GROUND_INST: instantiating (14) with all_74_11, n3, n2, simplifying with
% 248.40/42.04  | | |              (8), (9), (13), (27) gives:
% 248.40/42.04  | | |   (28)  leq(all_74_11, n2)
% 248.40/42.04  | | | 
% 248.40/42.04  | | | GROUND_INST: instantiating (22) with all_74_11, n2, simplifying with (8),
% 248.40/42.04  | | |              (18), (28) gives:
% 248.40/42.04  | | |   (29)  all_74_11 = n2 | gt(n2, all_74_11)
% 248.40/42.04  | | | 
% 248.40/42.04  | | | BETA: splitting (29) gives:
% 248.40/42.04  | | | 
% 248.40/42.04  | | | Case 1:
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | |   (30)  gt(n2, all_74_11)
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | GROUND_INST: instantiating (14) with all_74_11, n2, n1, simplifying with
% 248.40/42.04  | | | |              (8), (11), (18), (30) gives:
% 248.40/42.04  | | | |   (31)  leq(all_74_11, n1)
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | GROUND_INST: instantiating (5) with all_74_11, simplifying with (8),
% 248.40/42.04  | | | |              (10), (31) gives:
% 248.40/42.04  | | | |   (32)  all_74_11 = n1 | all_74_11 = n0
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | BETA: splitting (32) gives:
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | Case 1:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | |   (33)  all_74_11 = n0
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (4), (33) imply:
% 248.40/42.04  | | | | |   (34)  $false
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | CLOSE: (34) is inconsistent.
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | Case 2:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | |   (35)  all_74_11 = n1
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (2), (35) imply:
% 248.40/42.04  | | | | |   (36)  a_select3(pminus_ds1_filter, n1, n5) = all_74_9
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (19), (35) imply:
% 248.40/42.04  | | | | |   (37)  a_select3(pminus_ds1_filter, n5, n1) = all_74_8
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (8), (35) imply:
% 248.40/42.04  | | | | |   (38)  $i(n1)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (16), (35) imply:
% 248.40/42.04  | | | | |   (39)  leq(n1, n5)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (10), (35) imply:
% 248.40/42.04  | | | | |   (40)  leq(n0, n1)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | GROUND_INST: instantiating (3) with n1, n5, all_74_9, simplifying with
% 248.40/42.04  | | | | |              (6), (20), (36), (38), (40) gives:
% 248.40/42.04  | | | | |   (41)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.04  | | | | |         (a_select3(pminus_ds1_filter, n5, n1) = all_74_9 &
% 248.40/42.04  | | | | |           $i(all_74_9))
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | BETA: splitting (41) gives:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | Case 1:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | |   (42)   ~ leq(n5, all_74_21)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | REDUCE: (7), (42) imply:
% 248.40/42.04  | | | | | |   (43)   ~ leq(n5, n5)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | PRED_UNIFY: (17), (43) imply:
% 248.40/42.04  | | | | | |   (44)  $false
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | CLOSE: (44) is inconsistent.
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | Case 2:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n5,
% 248.40/42.04  | | | | | |             n1) = all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | BETA: splitting (45) gives:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | Case 1:
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | REDUCE: (7), (46) imply:
% 248.40/42.04  | | | | | | |   (47)   ~ leq(n1, n5)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 248.40/42.04  | | | | | | |   (48)  $false
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | CLOSE: (48) is inconsistent.
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | Case 2:
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | |   (49)  a_select3(pminus_ds1_filter, n5, n1) = all_74_9 &
% 248.40/42.04  | | | | | | |         $i(all_74_9)
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | ALPHA: (49) implies:
% 248.40/42.04  | | | | | | |   (50)  a_select3(pminus_ds1_filter, n5, n1) = all_74_9
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | GROUND_INST: instantiating (23) with all_74_8, all_74_9, n1, n5,
% 248.40/42.04  | | | | | | |              pminus_ds1_filter, simplifying with (37), (50) gives:
% 248.40/42.04  | | | | | | |   (51)  all_74_8 = all_74_9
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | REDUCE: (21), (51) imply:
% 248.40/42.04  | | | | | | |   (52)  $false
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | | CLOSE: (52) is inconsistent.
% 248.40/42.04  | | | | | | | 
% 248.40/42.04  | | | | | | End of split
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | End of split
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | End of split
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | Case 2:
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | |   (53)  all_74_11 = n2
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | REDUCE: (2), (53) imply:
% 248.40/42.04  | | | |   (54)  a_select3(pminus_ds1_filter, n2, n5) = all_74_9
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | REDUCE: (19), (53) imply:
% 248.40/42.04  | | | |   (55)  a_select3(pminus_ds1_filter, n5, n2) = all_74_8
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | REDUCE: (16), (53) imply:
% 248.40/42.04  | | | |   (56)  leq(n2, n5)
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | REDUCE: (10), (53) imply:
% 248.40/42.04  | | | |   (57)  leq(n0, n2)
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | GROUND_INST: instantiating (3) with n2, n5, all_74_9, simplifying with
% 248.40/42.04  | | | |              (6), (18), (20), (54), (57) gives:
% 248.40/42.04  | | | |   (58)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.04  | | | |         (a_select3(pminus_ds1_filter, n5, n2) = all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | BETA: splitting (58) gives:
% 248.40/42.04  | | | | 
% 248.40/42.04  | | | | Case 1:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | |   (59)   ~ leq(n5, all_74_21)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | REDUCE: (7), (59) imply:
% 248.40/42.04  | | | | |   (60)   ~ leq(n5, n5)
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | PRED_UNIFY: (17), (60) imply:
% 248.40/42.04  | | | | |   (61)  $false
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | CLOSE: (61) is inconsistent.
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | Case 2:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | |   (62)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n5, n2)
% 248.40/42.04  | | | | |           = all_74_9 & $i(all_74_9))
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | BETA: splitting (62) gives:
% 248.40/42.04  | | | | | 
% 248.40/42.04  | | | | | Case 1:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | |   (63)   ~ leq(n2, all_74_21)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | REDUCE: (7), (63) imply:
% 248.40/42.04  | | | | | |   (64)   ~ leq(n2, n5)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | PRED_UNIFY: (56), (64) imply:
% 248.40/42.04  | | | | | |   (65)  $false
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | CLOSE: (65) is inconsistent.
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | Case 2:
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | |   (66)  a_select3(pminus_ds1_filter, n5, n2) = all_74_9 &
% 248.40/42.04  | | | | | |         $i(all_74_9)
% 248.40/42.04  | | | | | | 
% 248.40/42.04  | | | | | | ALPHA: (66) implies:
% 248.40/42.05  | | | | | |   (67)  a_select3(pminus_ds1_filter, n5, n2) = all_74_9
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | GROUND_INST: instantiating (23) with all_74_8, all_74_9, n2, n5,
% 248.40/42.05  | | | | | |              pminus_ds1_filter, simplifying with (55), (67) gives:
% 248.40/42.05  | | | | | |   (68)  all_74_8 = all_74_9
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | REDUCE: (21), (68) imply:
% 248.40/42.05  | | | | | |   (69)  $false
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | CLOSE: (69) is inconsistent.
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | End of split
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | End of split
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | End of split
% 248.40/42.05  | | | 
% 248.40/42.05  | | Case 2:
% 248.40/42.05  | | | 
% 248.40/42.05  | | |   (70)  all_74_11 = n3
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (2), (70) imply:
% 248.40/42.05  | | |   (71)  a_select3(pminus_ds1_filter, n3, n5) = all_74_9
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (19), (70) imply:
% 248.40/42.05  | | |   (72)  a_select3(pminus_ds1_filter, n5, n3) = all_74_8
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (16), (70) imply:
% 248.40/42.05  | | |   (73)  leq(n3, n5)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (10), (70) imply:
% 248.40/42.05  | | |   (74)  leq(n0, n3)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | GROUND_INST: instantiating (3) with n3, n5, all_74_9, simplifying with
% 248.40/42.05  | | |              (6), (9), (20), (71), (74) gives:
% 248.40/42.05  | | |   (75)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.40/42.05  | | |         (a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9))
% 248.40/42.05  | | | 
% 248.40/42.05  | | | BETA: splitting (75) gives:
% 248.40/42.05  | | | 
% 248.40/42.05  | | | Case 1:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (76)   ~ leq(n5, all_74_21)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (7), (76) imply:
% 248.40/42.05  | | | |   (77)   ~ leq(n5, n5)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | PRED_UNIFY: (17), (77) imply:
% 248.40/42.05  | | | |   (78)  $false
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | CLOSE: (78) is inconsistent.
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | Case 2:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (79)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n5, n3) =
% 248.40/42.05  | | | |           all_74_9 & $i(all_74_9))
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | BETA: splitting (79) gives:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | Case 1:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (80)   ~ leq(n3, all_74_21)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (7), (80) imply:
% 248.40/42.05  | | | | |   (81)   ~ leq(n3, n5)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | PRED_UNIFY: (73), (81) imply:
% 248.40/42.05  | | | | |   (82)  $false
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | CLOSE: (82) is inconsistent.
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | Case 2:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (83)  a_select3(pminus_ds1_filter, n5, n3) = all_74_9 & $i(all_74_9)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | ALPHA: (83) implies:
% 248.40/42.05  | | | | |   (84)  a_select3(pminus_ds1_filter, n5, n3) = all_74_9
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REF_CLOSE: (21), (23), (72), (84) are inconsistent by sub-proof #33.
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | End of split
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | End of split
% 248.40/42.05  | | | 
% 248.40/42.05  | | End of split
% 248.40/42.05  | | 
% 248.40/42.05  | Case 2:
% 248.40/42.05  | | 
% 248.40/42.05  | |   (85)  all_74_11 = n4
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (2), (85) imply:
% 248.40/42.05  | |   (86)  a_select3(pminus_ds1_filter, n4, n5) = all_74_9
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (19), (85) imply:
% 248.40/42.05  | |   (87)  a_select3(pminus_ds1_filter, n5, n4) = all_74_8
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (16), (85) imply:
% 248.40/42.05  | |   (88)  leq(n4, n5)
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (10), (85) imply:
% 248.40/42.05  | |   (89)  leq(n0, n4)
% 248.40/42.05  | | 
% 248.40/42.05  | | GROUND_INST: instantiating (3) with n4, n5, all_74_9, simplifying with (6),
% 248.40/42.05  | |              (15), (20), (86), (89) gives:
% 248.40/42.05  | |   (90)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 248.40/42.05  | |         (a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9))
% 248.40/42.05  | | 
% 248.40/42.05  | | BETA: splitting (90) gives:
% 248.40/42.05  | | 
% 248.40/42.05  | | Case 1:
% 248.40/42.05  | | | 
% 248.40/42.05  | | |   (91)   ~ leq(n5, all_74_21)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (7), (91) imply:
% 248.40/42.05  | | |   (92)   ~ leq(n5, n5)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | PRED_UNIFY: (17), (92) imply:
% 248.40/42.05  | | |   (93)  $false
% 248.40/42.05  | | | 
% 248.40/42.05  | | | CLOSE: (93) is inconsistent.
% 248.40/42.05  | | | 
% 248.40/42.05  | | Case 2:
% 248.40/42.05  | | | 
% 248.40/42.05  | | |   (94)   ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n5, n4) =
% 248.40/42.05  | | |           all_74_9 & $i(all_74_9))
% 248.40/42.05  | | | 
% 248.40/42.05  | | | BETA: splitting (94) gives:
% 248.40/42.05  | | | 
% 248.40/42.05  | | | Case 1:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (95)   ~ leq(n4, all_74_21)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (7), (95) imply:
% 248.40/42.05  | | | |   (96)   ~ leq(n4, n5)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | PRED_UNIFY: (88), (96) imply:
% 248.40/42.05  | | | |   (97)  $false
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | CLOSE: (97) is inconsistent.
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | Case 2:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (98)  a_select3(pminus_ds1_filter, n5, n4) = all_74_9 & $i(all_74_9)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | ALPHA: (98) implies:
% 248.40/42.05  | | | |   (99)  a_select3(pminus_ds1_filter, n5, n4) = all_74_9
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REF_CLOSE: (21), (23), (87), (99) are inconsistent by sub-proof #32.
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | End of split
% 248.40/42.05  | | | 
% 248.40/42.05  | | End of split
% 248.40/42.05  | | 
% 248.40/42.05  | End of split
% 248.40/42.05  | 
% 248.40/42.05  End of proof
% 248.40/42.05  
% 248.40/42.05  Sub-proof #31 shows that the following formulas are inconsistent:
% 248.40/42.05  ----------------------------------------------------------------
% 248.40/42.05    (1)  leq(n0, all_74_10)
% 248.40/42.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.40/42.05           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.40/42.05           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.40/42.05           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.05    (3)   ~ (all_74_10 = n0)
% 248.40/42.05    (4)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.05           leq(n0, v0))
% 248.40/42.05    (5)  leq(n0, n5)
% 248.40/42.05    (6)  all_74_21 = n5
% 248.40/42.05    (7)  $i(n3)
% 248.40/42.05    (8)  a_select3(pminus_ds1_filter, all_74_10, n5) = all_74_8
% 248.40/42.05    (9)  $i(all_74_10)
% 248.40/42.05    (10)  a_select3(pminus_ds1_filter, n5, all_74_10) = all_74_9
% 248.40/42.05    (11)  pred(n2) = n1
% 248.40/42.05    (12)  pred(n4) = n3
% 248.40/42.05    (13)  pred(n3) = n2
% 248.40/42.05    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/42.05            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/42.05    (15)  $i(n4)
% 248.40/42.05    (16)  leq(all_74_10, n5)
% 248.40/42.05    (17)  leq(n5, n5)
% 248.40/42.05    (18)  $i(n2)
% 248.40/42.05    (19)  $i(n5)
% 248.40/42.05    (20)   ~ (all_74_8 = all_74_9)
% 248.40/42.05    (21)  all_74_10 = n4 | gt(n4, all_74_10)
% 248.40/42.05    (22)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.40/42.05            leq(v0, v1) | gt(v1, v0))
% 248.40/42.05    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.05          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.05              v0))
% 248.40/42.05  
% 248.40/42.05  Begin of proof
% 248.40/42.05  | 
% 248.40/42.05  | BETA: splitting (21) gives:
% 248.40/42.05  | 
% 248.40/42.05  | Case 1:
% 248.40/42.05  | | 
% 248.40/42.05  | |   (24)  gt(n4, all_74_10)
% 248.40/42.05  | | 
% 248.40/42.05  | | GROUND_INST: instantiating (14) with all_74_10, n4, n3, simplifying with
% 248.40/42.05  | |              (9), (12), (15), (24) gives:
% 248.40/42.05  | |   (25)  leq(all_74_10, n3)
% 248.40/42.05  | | 
% 248.40/42.05  | | GROUND_INST: instantiating (22) with all_74_10, n3, simplifying with (7),
% 248.40/42.05  | |              (9), (25) gives:
% 248.40/42.05  | |   (26)  all_74_10 = n3 | gt(n3, all_74_10)
% 248.40/42.05  | | 
% 248.40/42.05  | | BETA: splitting (26) gives:
% 248.40/42.05  | | 
% 248.40/42.05  | | Case 1:
% 248.40/42.05  | | | 
% 248.40/42.05  | | |   (27)  gt(n3, all_74_10)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | GROUND_INST: instantiating (14) with all_74_10, n3, n2, simplifying with
% 248.40/42.05  | | |              (7), (9), (13), (27) gives:
% 248.40/42.05  | | |   (28)  leq(all_74_10, n2)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | GROUND_INST: instantiating (22) with all_74_10, n2, simplifying with (9),
% 248.40/42.05  | | |              (18), (28) gives:
% 248.40/42.05  | | |   (29)  all_74_10 = n2 | gt(n2, all_74_10)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | BETA: splitting (29) gives:
% 248.40/42.05  | | | 
% 248.40/42.05  | | | Case 1:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (30)  gt(n2, all_74_10)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | GROUND_INST: instantiating (14) with all_74_10, n2, n1, simplifying with
% 248.40/42.05  | | | |              (9), (11), (18), (30) gives:
% 248.40/42.05  | | | |   (31)  leq(all_74_10, n1)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | GROUND_INST: instantiating (4) with all_74_10, simplifying with (1),
% 248.40/42.05  | | | |              (9), (31) gives:
% 248.40/42.05  | | | |   (32)  all_74_10 = n1 | all_74_10 = n0
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | BETA: splitting (32) gives:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | Case 1:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (33)  all_74_10 = n0
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (3), (33) imply:
% 248.40/42.05  | | | | |   (34)  $false
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | CLOSE: (34) is inconsistent.
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | Case 2:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (35)  all_74_10 = n1
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (8), (35) imply:
% 248.40/42.05  | | | | |   (36)  a_select3(pminus_ds1_filter, n1, n5) = all_74_8
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (10), (35) imply:
% 248.40/42.05  | | | | |   (37)  a_select3(pminus_ds1_filter, n5, n1) = all_74_9
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (9), (35) imply:
% 248.40/42.05  | | | | |   (38)  $i(n1)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (16), (35) imply:
% 248.40/42.05  | | | | |   (39)  leq(n1, n5)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (1), (35) imply:
% 248.40/42.05  | | | | |   (40)  leq(n0, n1)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | GROUND_INST: instantiating (2) with n1, n5, all_74_8, simplifying with
% 248.40/42.05  | | | | |              (5), (19), (36), (38), (40) gives:
% 248.40/42.05  | | | | |   (41)   ~ leq(n5, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.05  | | | | |         (a_select3(pminus_ds1_filter, n5, n1) = all_74_8 &
% 248.40/42.05  | | | | |           $i(all_74_8))
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | BETA: splitting (41) gives:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | Case 1:
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | |   (42)   ~ leq(n5, all_74_21)
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | REDUCE: (6), (42) imply:
% 248.40/42.05  | | | | | |   (43)   ~ leq(n5, n5)
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | PRED_UNIFY: (17), (43) imply:
% 248.40/42.05  | | | | | |   (44)  $false
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | CLOSE: (44) is inconsistent.
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | Case 2:
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | |   (45)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n5,
% 248.40/42.05  | | | | | |             n1) = all_74_8 & $i(all_74_8))
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | BETA: splitting (45) gives:
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | Case 1:
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | |   (46)   ~ leq(n1, all_74_21)
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | | REDUCE: (6), (46) imply:
% 248.40/42.05  | | | | | | |   (47)   ~ leq(n1, n5)
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | | PRED_UNIFY: (39), (47) imply:
% 248.40/42.05  | | | | | | |   (48)  $false
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | | CLOSE: (48) is inconsistent.
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | Case 2:
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | |   (49)  a_select3(pminus_ds1_filter, n5, n1) = all_74_8 &
% 248.40/42.05  | | | | | | |         $i(all_74_8)
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | | ALPHA: (49) implies:
% 248.40/42.05  | | | | | | |   (50)  a_select3(pminus_ds1_filter, n5, n1) = all_74_8
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | | GROUND_INST: instantiating (23) with all_74_8, all_74_9, n1, n5,
% 248.40/42.05  | | | | | | |              pminus_ds1_filter, simplifying with (37), (50) gives:
% 248.40/42.05  | | | | | | |   (51)  all_74_8 = all_74_9
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | | REDUCE: (20), (51) imply:
% 248.40/42.05  | | | | | | |   (52)  $false
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | | CLOSE: (52) is inconsistent.
% 248.40/42.05  | | | | | | | 
% 248.40/42.05  | | | | | | End of split
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | End of split
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | End of split
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | Case 2:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (53)  all_74_10 = n2
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (8), (53) imply:
% 248.40/42.05  | | | |   (54)  a_select3(pminus_ds1_filter, n2, n5) = all_74_8
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (10), (53) imply:
% 248.40/42.05  | | | |   (55)  a_select3(pminus_ds1_filter, n5, n2) = all_74_9
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (16), (53) imply:
% 248.40/42.05  | | | |   (56)  leq(n2, n5)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (1), (53) imply:
% 248.40/42.05  | | | |   (57)  leq(n0, n2)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | GROUND_INST: instantiating (2) with n2, n5, all_74_8, simplifying with
% 248.40/42.05  | | | |              (5), (18), (19), (54), (57) gives:
% 248.40/42.05  | | | |   (58)   ~ leq(n5, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.05  | | | |         (a_select3(pminus_ds1_filter, n5, n2) = all_74_8 & $i(all_74_8))
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | BETA: splitting (58) gives:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | Case 1:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (59)   ~ leq(n5, all_74_21)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (6), (59) imply:
% 248.40/42.05  | | | | |   (60)   ~ leq(n5, n5)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | PRED_UNIFY: (17), (60) imply:
% 248.40/42.05  | | | | |   (61)  $false
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | CLOSE: (61) is inconsistent.
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | Case 2:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (62)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n5, n2)
% 248.40/42.05  | | | | |           = all_74_8 & $i(all_74_8))
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | BETA: splitting (62) gives:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | Case 1:
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | |   (63)   ~ leq(n2, all_74_21)
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | REDUCE: (6), (63) imply:
% 248.40/42.05  | | | | | |   (64)   ~ leq(n2, n5)
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | PRED_UNIFY: (56), (64) imply:
% 248.40/42.05  | | | | | |   (65)  $false
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | CLOSE: (65) is inconsistent.
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | Case 2:
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | |   (66)  a_select3(pminus_ds1_filter, n5, n2) = all_74_8 &
% 248.40/42.05  | | | | | |         $i(all_74_8)
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | ALPHA: (66) implies:
% 248.40/42.05  | | | | | |   (67)  a_select3(pminus_ds1_filter, n5, n2) = all_74_8
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | GROUND_INST: instantiating (23) with all_74_8, all_74_9, n2, n5,
% 248.40/42.05  | | | | | |              pminus_ds1_filter, simplifying with (55), (67) gives:
% 248.40/42.05  | | | | | |   (68)  all_74_8 = all_74_9
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | REDUCE: (20), (68) imply:
% 248.40/42.05  | | | | | |   (69)  $false
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | | CLOSE: (69) is inconsistent.
% 248.40/42.05  | | | | | | 
% 248.40/42.05  | | | | | End of split
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | End of split
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | End of split
% 248.40/42.05  | | | 
% 248.40/42.05  | | Case 2:
% 248.40/42.05  | | | 
% 248.40/42.05  | | |   (70)  all_74_10 = n3
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (8), (70) imply:
% 248.40/42.05  | | |   (71)  a_select3(pminus_ds1_filter, n3, n5) = all_74_8
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (10), (70) imply:
% 248.40/42.05  | | |   (72)  a_select3(pminus_ds1_filter, n5, n3) = all_74_9
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (16), (70) imply:
% 248.40/42.05  | | |   (73)  leq(n3, n5)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (1), (70) imply:
% 248.40/42.05  | | |   (74)  leq(n0, n3)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | GROUND_INST: instantiating (2) with n3, n5, all_74_8, simplifying with
% 248.40/42.05  | | |              (5), (7), (19), (71), (74) gives:
% 248.40/42.05  | | |   (75)   ~ leq(n5, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.40/42.05  | | |         (a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & $i(all_74_8))
% 248.40/42.05  | | | 
% 248.40/42.05  | | | BETA: splitting (75) gives:
% 248.40/42.05  | | | 
% 248.40/42.05  | | | Case 1:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (76)   ~ leq(n5, all_74_21)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (6), (76) imply:
% 248.40/42.05  | | | |   (77)   ~ leq(n5, n5)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | PRED_UNIFY: (17), (77) imply:
% 248.40/42.05  | | | |   (78)  $false
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | CLOSE: (78) is inconsistent.
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | Case 2:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (79)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n5, n3) =
% 248.40/42.05  | | | |           all_74_8 & $i(all_74_8))
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | BETA: splitting (79) gives:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | Case 1:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (80)   ~ leq(n3, all_74_21)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REDUCE: (6), (80) imply:
% 248.40/42.05  | | | | |   (81)   ~ leq(n3, n5)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | PRED_UNIFY: (73), (81) imply:
% 248.40/42.05  | | | | |   (82)  $false
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | CLOSE: (82) is inconsistent.
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | Case 2:
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | |   (83)  a_select3(pminus_ds1_filter, n5, n3) = all_74_8 & $i(all_74_8)
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | ALPHA: (83) implies:
% 248.40/42.05  | | | | |   (84)  a_select3(pminus_ds1_filter, n5, n3) = all_74_8
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | | REF_CLOSE: (20), (23), (72), (84) are inconsistent by sub-proof #33.
% 248.40/42.05  | | | | | 
% 248.40/42.05  | | | | End of split
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | End of split
% 248.40/42.05  | | | 
% 248.40/42.05  | | End of split
% 248.40/42.05  | | 
% 248.40/42.05  | Case 2:
% 248.40/42.05  | | 
% 248.40/42.05  | |   (85)  all_74_10 = n4
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (8), (85) imply:
% 248.40/42.05  | |   (86)  a_select3(pminus_ds1_filter, n4, n5) = all_74_8
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (10), (85) imply:
% 248.40/42.05  | |   (87)  a_select3(pminus_ds1_filter, n5, n4) = all_74_9
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (16), (85) imply:
% 248.40/42.05  | |   (88)  leq(n4, n5)
% 248.40/42.05  | | 
% 248.40/42.05  | | REDUCE: (1), (85) imply:
% 248.40/42.05  | |   (89)  leq(n0, n4)
% 248.40/42.05  | | 
% 248.40/42.05  | | GROUND_INST: instantiating (2) with n4, n5, all_74_8, simplifying with (5),
% 248.40/42.05  | |              (15), (19), (86), (89) gives:
% 248.40/42.05  | |   (90)   ~ leq(n5, all_74_21) |  ~ leq(n4, all_74_21) |
% 248.40/42.05  | |         (a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8))
% 248.40/42.05  | | 
% 248.40/42.05  | | BETA: splitting (90) gives:
% 248.40/42.05  | | 
% 248.40/42.05  | | Case 1:
% 248.40/42.05  | | | 
% 248.40/42.05  | | |   (91)   ~ leq(n5, all_74_21)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | REDUCE: (6), (91) imply:
% 248.40/42.05  | | |   (92)   ~ leq(n5, n5)
% 248.40/42.05  | | | 
% 248.40/42.05  | | | PRED_UNIFY: (17), (92) imply:
% 248.40/42.05  | | |   (93)  $false
% 248.40/42.05  | | | 
% 248.40/42.05  | | | CLOSE: (93) is inconsistent.
% 248.40/42.05  | | | 
% 248.40/42.05  | | Case 2:
% 248.40/42.05  | | | 
% 248.40/42.05  | | |   (94)   ~ leq(n4, all_74_21) | (a_select3(pminus_ds1_filter, n5, n4) =
% 248.40/42.05  | | |           all_74_8 & $i(all_74_8))
% 248.40/42.05  | | | 
% 248.40/42.05  | | | BETA: splitting (94) gives:
% 248.40/42.05  | | | 
% 248.40/42.05  | | | Case 1:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (95)   ~ leq(n4, all_74_21)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REDUCE: (6), (95) imply:
% 248.40/42.05  | | | |   (96)   ~ leq(n4, n5)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | PRED_UNIFY: (88), (96) imply:
% 248.40/42.05  | | | |   (97)  $false
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | CLOSE: (97) is inconsistent.
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | Case 2:
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | |   (98)  a_select3(pminus_ds1_filter, n5, n4) = all_74_8 & $i(all_74_8)
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | ALPHA: (98) implies:
% 248.40/42.05  | | | |   (99)  a_select3(pminus_ds1_filter, n5, n4) = all_74_8
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | | REF_CLOSE: (20), (23), (87), (99) are inconsistent by sub-proof #32.
% 248.40/42.05  | | | | 
% 248.40/42.05  | | | End of split
% 248.40/42.05  | | | 
% 248.40/42.05  | | End of split
% 248.40/42.05  | | 
% 248.40/42.05  | End of split
% 248.40/42.05  | 
% 248.40/42.05  End of proof
% 248.40/42.05  
% 248.40/42.05  Sub-proof #32 shows that the following formulas are inconsistent:
% 248.40/42.05  ----------------------------------------------------------------
% 248.40/42.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.05           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.05             v0))
% 248.40/42.06    (2)  a_select3(pminus_ds1_filter, n5, n4) = all_74_8
% 248.40/42.06    (3)  a_select3(pminus_ds1_filter, n5, n4) = all_74_9
% 248.40/42.06    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.06  
% 248.40/42.06  Begin of proof
% 248.40/42.06  | 
% 248.40/42.06  | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n4, n5,
% 248.40/42.06  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.06  |   (5)  all_74_8 = all_74_9
% 248.40/42.06  | 
% 248.40/42.06  | REDUCE: (4), (5) imply:
% 248.40/42.06  |   (6)  $false
% 248.40/42.06  | 
% 248.40/42.06  | CLOSE: (6) is inconsistent.
% 248.40/42.06  | 
% 248.40/42.06  End of proof
% 248.40/42.06  
% 248.40/42.06  Sub-proof #33 shows that the following formulas are inconsistent:
% 248.40/42.06  ----------------------------------------------------------------
% 248.40/42.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.06           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.06             v0))
% 248.40/42.06    (2)  a_select3(pminus_ds1_filter, n5, n3) = all_74_8
% 248.40/42.06    (3)  a_select3(pminus_ds1_filter, n5, n3) = all_74_9
% 248.40/42.06    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.06  
% 248.40/42.06  Begin of proof
% 248.40/42.06  | 
% 248.40/42.06  | GROUND_INST: instantiating (1) with all_74_8, all_74_9, n3, n5,
% 248.40/42.06  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.06  |   (5)  all_74_8 = all_74_9
% 248.40/42.06  | 
% 248.40/42.06  | REDUCE: (4), (5) imply:
% 248.40/42.06  |   (6)  $false
% 248.40/42.06  | 
% 248.40/42.06  | CLOSE: (6) is inconsistent.
% 248.40/42.06  | 
% 248.40/42.06  End of proof
% 248.40/42.06  
% 248.40/42.06  Sub-proof #34 shows that the following formulas are inconsistent:
% 248.40/42.06  ----------------------------------------------------------------
% 248.40/42.06    (1)  all_74_11 = n4 | gt(n4, all_74_11)
% 248.40/42.06    (2)  a_select3(pminus_ds1_filter, all_74_10, all_74_11) = all_74_8
% 248.40/42.06    (3)  leq(n0, all_74_10)
% 248.40/42.06    (4)  a_select3(pminus_ds1_filter, all_74_11, all_74_10) = all_74_9
% 248.40/42.06    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 248.40/42.06           (a_select3(pminus_ds1_filter, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 248.40/42.06           ~ leq(v1, all_74_21) |  ~ leq(v0, all_74_21) |  ~ leq(n0, v1) |  ~
% 248.40/42.06           leq(n0, v0) | (a_select3(pminus_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.06    (6)   ~ (all_74_11 = n0)
% 248.40/42.06    (7)   ~ (all_74_10 = n0)
% 248.40/42.06    (8)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.06           leq(n0, v0))
% 248.40/42.06    (9)  all_74_21 = n5
% 248.40/42.06    (10)  $i(all_74_11)
% 248.40/42.06    (11)  $i(n3)
% 248.40/42.06    (12)  $i(all_74_10)
% 248.40/42.06    (13)  leq(n0, all_74_11)
% 248.40/42.06    (14)  pred(n2) = n1
% 248.40/42.06    (15)  pred(n4) = n3
% 248.40/42.06    (16)  pred(n3) = n2
% 248.40/42.06    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/42.06            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/42.06    (18)  $i(n4)
% 248.40/42.06    (19)  leq(all_74_11, n5)
% 248.40/42.06    (20)  leq(all_74_10, n5)
% 248.40/42.06    (21)  $i(n2)
% 248.40/42.06    (22)   ~ (all_74_8 = all_74_9)
% 248.40/42.06    (23)  all_74_10 = n4 | gt(n4, all_74_10)
% 248.40/42.06    (24)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 248.40/42.06            leq(v0, v1) | gt(v1, v0))
% 248.40/42.06    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.06          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.06              v0))
% 248.40/42.06  
% 248.40/42.06  Begin of proof
% 248.40/42.06  | 
% 248.40/42.06  | BETA: splitting (23) gives:
% 248.40/42.06  | 
% 248.40/42.06  | Case 1:
% 248.40/42.06  | | 
% 248.40/42.06  | |   (26)  gt(n4, all_74_10)
% 248.40/42.06  | | 
% 248.40/42.06  | | GROUND_INST: instantiating (17) with all_74_10, n4, n3, simplifying with
% 248.40/42.06  | |              (12), (15), (18), (26) gives:
% 248.40/42.06  | |   (27)  leq(all_74_10, n3)
% 248.40/42.06  | | 
% 248.40/42.06  | | GROUND_INST: instantiating (24) with all_74_10, n3, simplifying with (11),
% 248.40/42.06  | |              (12), (27) gives:
% 248.40/42.06  | |   (28)  all_74_10 = n3 | gt(n3, all_74_10)
% 248.40/42.06  | | 
% 248.40/42.06  | | BETA: splitting (1) gives:
% 248.40/42.06  | | 
% 248.40/42.06  | | Case 1:
% 248.40/42.06  | | | 
% 248.40/42.06  | | |   (29)  gt(n4, all_74_11)
% 248.40/42.06  | | | 
% 248.40/42.06  | | | GROUND_INST: instantiating (17) with all_74_11, n4, n3, simplifying with
% 248.40/42.06  | | |              (10), (15), (18), (29) gives:
% 248.40/42.06  | | |   (30)  leq(all_74_11, n3)
% 248.40/42.06  | | | 
% 248.40/42.06  | | | GROUND_INST: instantiating (24) with all_74_11, n3, simplifying with (10),
% 248.40/42.06  | | |              (11), (30) gives:
% 248.40/42.06  | | |   (31)  all_74_11 = n3 | gt(n3, all_74_11)
% 248.40/42.06  | | | 
% 248.40/42.06  | | | BETA: splitting (28) gives:
% 248.40/42.06  | | | 
% 248.40/42.06  | | | Case 1:
% 248.40/42.06  | | | | 
% 248.40/42.06  | | | |   (32)  gt(n3, all_74_10)
% 248.40/42.06  | | | | 
% 248.40/42.06  | | | | GROUND_INST: instantiating (17) with all_74_10, n3, n2, simplifying with
% 248.40/42.06  | | | |              (11), (12), (16), (32) gives:
% 248.40/42.06  | | | |   (33)  leq(all_74_10, n2)
% 248.40/42.06  | | | | 
% 248.40/42.06  | | | | GROUND_INST: instantiating (24) with all_74_10, n2, simplifying with
% 248.40/42.06  | | | |              (12), (21), (33) gives:
% 248.40/42.06  | | | |   (34)  all_74_10 = n2 | gt(n2, all_74_10)
% 248.40/42.06  | | | | 
% 248.40/42.06  | | | | BETA: splitting (31) gives:
% 248.40/42.06  | | | | 
% 248.40/42.06  | | | | Case 1:
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | |   (35)  gt(n3, all_74_11)
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | GROUND_INST: instantiating (17) with all_74_11, n3, n2, simplifying
% 248.40/42.06  | | | | |              with (10), (11), (16), (35) gives:
% 248.40/42.06  | | | | |   (36)  leq(all_74_11, n2)
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | GROUND_INST: instantiating (24) with all_74_11, n2, simplifying with
% 248.40/42.06  | | | | |              (10), (21), (36) gives:
% 248.40/42.06  | | | | |   (37)  all_74_11 = n2 | gt(n2, all_74_11)
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | BETA: splitting (34) gives:
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | Case 1:
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | |   (38)  gt(n2, all_74_10)
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | GROUND_INST: instantiating (17) with all_74_10, n2, n1, simplifying
% 248.40/42.06  | | | | | |              with (12), (14), (21), (38) gives:
% 248.40/42.06  | | | | | |   (39)  leq(all_74_10, n1)
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | GROUND_INST: instantiating (8) with all_74_10, simplifying with (3),
% 248.40/42.06  | | | | | |              (12), (39) gives:
% 248.40/42.06  | | | | | |   (40)  all_74_10 = n1 | all_74_10 = n0
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | BETA: splitting (40) gives:
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | Case 1:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | |   (41)  all_74_10 = n0
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (7), (41) imply:
% 248.40/42.06  | | | | | | |   (42)  $false
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | CLOSE: (42) is inconsistent.
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | Case 2:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | |   (43)  all_74_10 = n1
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (2), (43) imply:
% 248.40/42.06  | | | | | | |   (44)  a_select3(pminus_ds1_filter, n1, all_74_11) = all_74_8
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (4), (43) imply:
% 248.40/42.06  | | | | | | |   (45)  a_select3(pminus_ds1_filter, all_74_11, n1) = all_74_9
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (12), (43) imply:
% 248.40/42.06  | | | | | | |   (46)  $i(n1)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (20), (43) imply:
% 248.40/42.06  | | | | | | |   (47)  leq(n1, n5)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (3), (43) imply:
% 248.40/42.06  | | | | | | |   (48)  leq(n0, n1)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | BETA: splitting (37) gives:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | |   (49)  gt(n2, all_74_11)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | GROUND_INST: instantiating (17) with all_74_11, n2, n1,
% 248.40/42.06  | | | | | | | |              simplifying with (10), (14), (21), (49) gives:
% 248.40/42.06  | | | | | | | |   (50)  leq(all_74_11, n1)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | GROUND_INST: instantiating (8) with all_74_11, simplifying with
% 248.40/42.06  | | | | | | | |              (10), (13), (50) gives:
% 248.40/42.06  | | | | | | | |   (51)  all_74_11 = n1 | all_74_11 = n0
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | BETA: splitting (51) gives:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | |   (52)  all_74_11 = n0
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | REDUCE: (6), (52) imply:
% 248.40/42.06  | | | | | | | | |   (53)  $false
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | CLOSE: (53) is inconsistent.
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | |   (54)  all_74_11 = n1
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | REDUCE: (45), (54) imply:
% 248.40/42.06  | | | | | | | | |   (55)  a_select3(pminus_ds1_filter, n1, n1) = all_74_9
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | REDUCE: (44), (54) imply:
% 248.40/42.06  | | | | | | | | |   (56)  a_select3(pminus_ds1_filter, n1, n1) = all_74_8
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | GROUND_INST: instantiating (25) with all_74_9, all_74_8, n1,
% 248.40/42.06  | | | | | | | | |              n1, pminus_ds1_filter, simplifying with (55), (56)
% 248.40/42.06  | | | | | | | | |              gives:
% 248.40/42.06  | | | | | | | | |   (57)  all_74_8 = all_74_9
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | REDUCE: (22), (57) imply:
% 248.40/42.06  | | | | | | | | |   (58)  $false
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | CLOSE: (58) is inconsistent.
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | End of split
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | |   (59)  all_74_11 = n2
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (45), (59) imply:
% 248.40/42.06  | | | | | | | |   (60)  a_select3(pminus_ds1_filter, n2, n1) = all_74_9
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (44), (59) imply:
% 248.40/42.06  | | | | | | | |   (61)  a_select3(pminus_ds1_filter, n1, n2) = all_74_8
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (19), (59) imply:
% 248.40/42.06  | | | | | | | |   (62)  leq(n2, n5)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (13), (59) imply:
% 248.40/42.06  | | | | | | | |   (63)  leq(n0, n2)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | GROUND_INST: instantiating (5) with n1, n2, all_74_8,
% 248.40/42.06  | | | | | | | |              simplifying with (21), (46), (48), (61), (63)
% 248.40/42.06  | | | | | | | |              gives:
% 248.40/42.06  | | | | | | | |   (64)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.06  | | | | | | | |         (a_select3(pminus_ds1_filter, n2, n1) = all_74_8 &
% 248.40/42.06  | | | | | | | |           $i(all_74_8))
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | BETA: splitting (64) gives:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | |   (65)   ~ leq(n2, all_74_21)
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | REDUCE: (9), (65) imply:
% 248.40/42.06  | | | | | | | | |   (66)   ~ leq(n2, n5)
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | PRED_UNIFY: (62), (66) imply:
% 248.40/42.06  | | | | | | | | |   (67)  $false
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | CLOSE: (67) is inconsistent.
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | |   (68)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/42.06  | | | | | | | | |             n2, n1) = all_74_8 & $i(all_74_8))
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | BETA: splitting (68) gives:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | |   (69)   ~ leq(n1, all_74_21)
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | REDUCE: (9), (69) imply:
% 248.40/42.06  | | | | | | | | | |   (70)   ~ leq(n1, n5)
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | PRED_UNIFY: (47), (70) imply:
% 248.40/42.06  | | | | | | | | | |   (71)  $false
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | CLOSE: (71) is inconsistent.
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | |   (72)  a_select3(pminus_ds1_filter, n2, n1) = all_74_8 &
% 248.40/42.06  | | | | | | | | | |         $i(all_74_8)
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | ALPHA: (72) implies:
% 248.40/42.06  | | | | | | | | | |   (73)  a_select3(pminus_ds1_filter, n2, n1) = all_74_8
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | GROUND_INST: instantiating (25) with all_74_8, all_74_9, n1,
% 248.40/42.06  | | | | | | | | | |              n2, pminus_ds1_filter, simplifying with (60), (73)
% 248.40/42.06  | | | | | | | | | |              gives:
% 248.40/42.06  | | | | | | | | | |   (74)  all_74_8 = all_74_9
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | REDUCE: (22), (74) imply:
% 248.40/42.06  | | | | | | | | | |   (75)  $false
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | CLOSE: (75) is inconsistent.
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | End of split
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | End of split
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | End of split
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | End of split
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | Case 2:
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | |   (76)  all_74_10 = n2
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | REDUCE: (2), (76) imply:
% 248.40/42.06  | | | | | |   (77)  a_select3(pminus_ds1_filter, n2, all_74_11) = all_74_8
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | REDUCE: (4), (76) imply:
% 248.40/42.06  | | | | | |   (78)  a_select3(pminus_ds1_filter, all_74_11, n2) = all_74_9
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | REDUCE: (20), (76) imply:
% 248.40/42.06  | | | | | |   (79)  leq(n2, n5)
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | REDUCE: (3), (76) imply:
% 248.40/42.06  | | | | | |   (80)  leq(n0, n2)
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | BETA: splitting (37) gives:
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | Case 1:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | |   (81)  gt(n2, all_74_11)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | GROUND_INST: instantiating (17) with all_74_11, n2, n1,
% 248.40/42.06  | | | | | | |              simplifying with (10), (14), (21), (81) gives:
% 248.40/42.06  | | | | | | |   (82)  leq(all_74_11, n1)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | GROUND_INST: instantiating (8) with all_74_11, simplifying with
% 248.40/42.06  | | | | | | |              (10), (13), (82) gives:
% 248.40/42.06  | | | | | | |   (83)  all_74_11 = n1 | all_74_11 = n0
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | BETA: splitting (83) gives:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | |   (84)  all_74_11 = n0
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (6), (84) imply:
% 248.40/42.06  | | | | | | | |   (85)  $false
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | CLOSE: (85) is inconsistent.
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | |   (86)  all_74_11 = n1
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (78), (86) imply:
% 248.40/42.06  | | | | | | | |   (87)  a_select3(pminus_ds1_filter, n1, n2) = all_74_9
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (77), (86) imply:
% 248.40/42.06  | | | | | | | |   (88)  a_select3(pminus_ds1_filter, n2, n1) = all_74_8
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (10), (86) imply:
% 248.40/42.06  | | | | | | | |   (89)  $i(n1)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (19), (86) imply:
% 248.40/42.06  | | | | | | | |   (90)  leq(n1, n5)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (13), (86) imply:
% 248.40/42.06  | | | | | | | |   (91)  leq(n0, n1)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | GROUND_INST: instantiating (5) with n1, n2, all_74_9,
% 248.40/42.06  | | | | | | | |              simplifying with (21), (80), (87), (89), (91)
% 248.40/42.06  | | | | | | | |              gives:
% 248.40/42.06  | | | | | | | |   (92)   ~ leq(n2, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.06  | | | | | | | |         (a_select3(pminus_ds1_filter, n2, n1) = all_74_9 &
% 248.40/42.06  | | | | | | | |           $i(all_74_9))
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | BETA: splitting (92) gives:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | |   (93)   ~ leq(n2, all_74_21)
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | REDUCE: (9), (93) imply:
% 248.40/42.06  | | | | | | | | |   (94)   ~ leq(n2, n5)
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | PRED_UNIFY: (79), (94) imply:
% 248.40/42.06  | | | | | | | | |   (95)  $false
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | CLOSE: (95) is inconsistent.
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | |   (96)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/42.06  | | | | | | | | |             n2, n1) = all_74_9 & $i(all_74_9))
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | BETA: splitting (96) gives:
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | |   (97)   ~ leq(n1, all_74_21)
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | REDUCE: (9), (97) imply:
% 248.40/42.06  | | | | | | | | | |   (98)   ~ leq(n1, n5)
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | PRED_UNIFY: (90), (98) imply:
% 248.40/42.06  | | | | | | | | | |   (99)  $false
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | CLOSE: (99) is inconsistent.
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | |   (100)  a_select3(pminus_ds1_filter, n2, n1) = all_74_9 &
% 248.40/42.06  | | | | | | | | | |          $i(all_74_9)
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | ALPHA: (100) implies:
% 248.40/42.06  | | | | | | | | | |   (101)  a_select3(pminus_ds1_filter, n2, n1) = all_74_9
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | GROUND_INST: instantiating (25) with all_74_8, all_74_9, n1,
% 248.40/42.06  | | | | | | | | | |              n2, pminus_ds1_filter, simplifying with (88),
% 248.40/42.06  | | | | | | | | | |              (101) gives:
% 248.40/42.06  | | | | | | | | | |   (102)  all_74_8 = all_74_9
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | REDUCE: (22), (102) imply:
% 248.40/42.06  | | | | | | | | | |   (103)  $false
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | | CLOSE: (103) is inconsistent.
% 248.40/42.06  | | | | | | | | | | 
% 248.40/42.06  | | | | | | | | | End of split
% 248.40/42.06  | | | | | | | | | 
% 248.40/42.06  | | | | | | | | End of split
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | End of split
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | Case 2:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | |   (104)  all_74_11 = n2
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (78), (104) imply:
% 248.40/42.06  | | | | | | |   (105)  a_select3(pminus_ds1_filter, n2, n2) = all_74_9
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (77), (104) imply:
% 248.40/42.06  | | | | | | |   (106)  a_select3(pminus_ds1_filter, n2, n2) = all_74_8
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | GROUND_INST: instantiating (25) with all_74_9, all_74_8, n2, n2,
% 248.40/42.06  | | | | | | |              pminus_ds1_filter, simplifying with (105), (106)
% 248.40/42.06  | | | | | | |              gives:
% 248.40/42.06  | | | | | | |   (107)  all_74_8 = all_74_9
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (22), (107) imply:
% 248.40/42.06  | | | | | | |   (108)  $false
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | CLOSE: (108) is inconsistent.
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | End of split
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | End of split
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | Case 2:
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | |   (109)  all_74_11 = n3
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | REDUCE: (2), (109) imply:
% 248.40/42.06  | | | | |   (110)  a_select3(pminus_ds1_filter, all_74_10, n3) = all_74_8
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | REDUCE: (4), (109) imply:
% 248.40/42.06  | | | | |   (111)  a_select3(pminus_ds1_filter, n3, all_74_10) = all_74_9
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | REDUCE: (19), (109) imply:
% 248.40/42.06  | | | | |   (112)  leq(n3, n5)
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | REDUCE: (13), (109) imply:
% 248.40/42.06  | | | | |   (113)  leq(n0, n3)
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | BETA: splitting (34) gives:
% 248.40/42.06  | | | | | 
% 248.40/42.06  | | | | | Case 1:
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | |   (114)  gt(n2, all_74_10)
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | GROUND_INST: instantiating (17) with all_74_10, n2, n1, simplifying
% 248.40/42.06  | | | | | |              with (12), (14), (21), (114) gives:
% 248.40/42.06  | | | | | |   (115)  leq(all_74_10, n1)
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | GROUND_INST: instantiating (8) with all_74_10, simplifying with (3),
% 248.40/42.06  | | | | | |              (12), (115) gives:
% 248.40/42.06  | | | | | |   (116)  all_74_10 = n1 | all_74_10 = n0
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | BETA: splitting (116) gives:
% 248.40/42.06  | | | | | | 
% 248.40/42.06  | | | | | | Case 1:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | |   (117)  all_74_10 = n0
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (7), (117) imply:
% 248.40/42.06  | | | | | | |   (118)  $false
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | CLOSE: (118) is inconsistent.
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | Case 2:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | |   (119)  all_74_10 = n1
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (110), (119) imply:
% 248.40/42.06  | | | | | | |   (120)  a_select3(pminus_ds1_filter, n1, n3) = all_74_8
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (111), (119) imply:
% 248.40/42.06  | | | | | | |   (121)  a_select3(pminus_ds1_filter, n3, n1) = all_74_9
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (12), (119) imply:
% 248.40/42.06  | | | | | | |   (122)  $i(n1)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (20), (119) imply:
% 248.40/42.06  | | | | | | |   (123)  leq(n1, n5)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | REDUCE: (3), (119) imply:
% 248.40/42.06  | | | | | | |   (124)  leq(n0, n1)
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | GROUND_INST: instantiating (5) with n1, n3, all_74_8, simplifying
% 248.40/42.06  | | | | | | |              with (11), (113), (120), (122), (124) gives:
% 248.40/42.06  | | | | | | |   (125)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.06  | | | | | | |          (a_select3(pminus_ds1_filter, n3, n1) = all_74_8 &
% 248.40/42.06  | | | | | | |            $i(all_74_8))
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | BETA: splitting (125) gives:
% 248.40/42.06  | | | | | | | 
% 248.40/42.06  | | | | | | | Case 1:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | |   (126)   ~ leq(n3, all_74_21)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | REDUCE: (9), (126) imply:
% 248.40/42.06  | | | | | | | |   (127)   ~ leq(n3, n5)
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | PRED_UNIFY: (112), (127) imply:
% 248.40/42.06  | | | | | | | |   (128)  $false
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | | CLOSE: (128) is inconsistent.
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | Case 2:
% 248.40/42.06  | | | | | | | | 
% 248.40/42.06  | | | | | | | |   (129)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/42.07  | | | | | | | |              n3, n1) = all_74_8 & $i(all_74_8))
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | BETA: splitting (129) gives:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | Case 1:
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | |   (130)   ~ leq(n1, all_74_21)
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | REDUCE: (9), (130) imply:
% 248.40/42.07  | | | | | | | | |   (131)   ~ leq(n1, n5)
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | PRED_UNIFY: (123), (131) imply:
% 248.40/42.07  | | | | | | | | |   (132)  $false
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | CLOSE: (132) is inconsistent.
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | Case 2:
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | |   (133)  a_select3(pminus_ds1_filter, n3, n1) = all_74_8 &
% 248.40/42.07  | | | | | | | | |          $i(all_74_8)
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | ALPHA: (133) implies:
% 248.40/42.07  | | | | | | | | |   (134)  a_select3(pminus_ds1_filter, n3, n1) = all_74_8
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | REF_CLOSE: (22), (25), (121), (134) are inconsistent by
% 248.40/42.07  | | | | | | | | |            sub-proof #38.
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | End of split
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | End of split
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | End of split
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | Case 2:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (135)  all_74_10 = n2
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (110), (135) imply:
% 248.40/42.07  | | | | | |   (136)  a_select3(pminus_ds1_filter, n2, n3) = all_74_8
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (111), (135) imply:
% 248.40/42.07  | | | | | |   (137)  a_select3(pminus_ds1_filter, n3, n2) = all_74_9
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (20), (135) imply:
% 248.40/42.07  | | | | | |   (138)  leq(n2, n5)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (3), (135) imply:
% 248.40/42.07  | | | | | |   (139)  leq(n0, n2)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | GROUND_INST: instantiating (5) with n2, n3, all_74_8, simplifying
% 248.40/42.07  | | | | | |              with (11), (21), (113), (136), (139) gives:
% 248.40/42.07  | | | | | |   (140)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.07  | | | | | |          (a_select3(pminus_ds1_filter, n3, n2) = all_74_8 &
% 248.40/42.07  | | | | | |            $i(all_74_8))
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | BETA: splitting (140) gives:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | Case 1:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (141)   ~ leq(n3, all_74_21)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (9), (141) imply:
% 248.40/42.07  | | | | | | |   (142)   ~ leq(n3, n5)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | PRED_UNIFY: (112), (142) imply:
% 248.40/42.07  | | | | | | |   (143)  $false
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | CLOSE: (143) is inconsistent.
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | Case 2:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (144)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n3,
% 248.40/42.07  | | | | | | |              n2) = all_74_8 & $i(all_74_8))
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | BETA: splitting (144) gives:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | Case 1:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (145)   ~ leq(n2, all_74_21)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | REDUCE: (9), (145) imply:
% 248.40/42.07  | | | | | | | |   (146)   ~ leq(n2, n5)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | PRED_UNIFY: (138), (146) imply:
% 248.40/42.07  | | | | | | | |   (147)  $false
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | CLOSE: (147) is inconsistent.
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | Case 2:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (148)  a_select3(pminus_ds1_filter, n3, n2) = all_74_8 &
% 248.40/42.07  | | | | | | | |          $i(all_74_8)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | ALPHA: (148) implies:
% 248.40/42.07  | | | | | | | |   (149)  a_select3(pminus_ds1_filter, n3, n2) = all_74_8
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | REF_CLOSE: (22), (25), (137), (149) are inconsistent by
% 248.40/42.07  | | | | | | | |            sub-proof #37.
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | End of split
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | End of split
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | End of split
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | End of split
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | Case 2:
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | |   (150)  all_74_10 = n3
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (2), (150) imply:
% 248.40/42.07  | | | |   (151)  a_select3(pminus_ds1_filter, n3, all_74_11) = all_74_8
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (4), (150) imply:
% 248.40/42.07  | | | |   (152)  a_select3(pminus_ds1_filter, all_74_11, n3) = all_74_9
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (20), (150) imply:
% 248.40/42.07  | | | |   (153)  leq(n3, n5)
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (3), (150) imply:
% 248.40/42.07  | | | |   (154)  leq(n0, n3)
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | BETA: splitting (31) gives:
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | Case 1:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | |   (155)  gt(n3, all_74_11)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | GROUND_INST: instantiating (17) with all_74_11, n3, n2, simplifying
% 248.40/42.07  | | | | |              with (10), (11), (16), (155) gives:
% 248.40/42.07  | | | | |   (156)  leq(all_74_11, n2)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | GROUND_INST: instantiating (24) with all_74_11, n2, simplifying with
% 248.40/42.07  | | | | |              (10), (21), (156) gives:
% 248.40/42.07  | | | | |   (157)  all_74_11 = n2 | gt(n2, all_74_11)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | BETA: splitting (157) gives:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | Case 1:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (158)  gt(n2, all_74_11)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | GROUND_INST: instantiating (17) with all_74_11, n2, n1, simplifying
% 248.40/42.07  | | | | | |              with (10), (14), (21), (158) gives:
% 248.40/42.07  | | | | | |   (159)  leq(all_74_11, n1)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | GROUND_INST: instantiating (8) with all_74_11, simplifying with
% 248.40/42.07  | | | | | |              (10), (13), (159) gives:
% 248.40/42.07  | | | | | |   (160)  all_74_11 = n1 | all_74_11 = n0
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | BETA: splitting (160) gives:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | Case 1:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (161)  all_74_11 = n0
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (6), (161) imply:
% 248.40/42.07  | | | | | | |   (162)  $false
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | CLOSE: (162) is inconsistent.
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | Case 2:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (163)  all_74_11 = n1
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (152), (163) imply:
% 248.40/42.07  | | | | | | |   (164)  a_select3(pminus_ds1_filter, n1, n3) = all_74_9
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (151), (163) imply:
% 248.40/42.07  | | | | | | |   (165)  a_select3(pminus_ds1_filter, n3, n1) = all_74_8
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (10), (163) imply:
% 248.40/42.07  | | | | | | |   (166)  $i(n1)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (19), (163) imply:
% 248.40/42.07  | | | | | | |   (167)  leq(n1, n5)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (13), (163) imply:
% 248.40/42.07  | | | | | | |   (168)  leq(n0, n1)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | GROUND_INST: instantiating (5) with n1, n3, all_74_9, simplifying
% 248.40/42.07  | | | | | | |              with (11), (154), (164), (166), (168) gives:
% 248.40/42.07  | | | | | | |   (169)   ~ leq(n3, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.07  | | | | | | |          (a_select3(pminus_ds1_filter, n3, n1) = all_74_9 &
% 248.40/42.07  | | | | | | |            $i(all_74_9))
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | BETA: splitting (169) gives:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | Case 1:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (170)   ~ leq(n3, all_74_21)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | REDUCE: (9), (170) imply:
% 248.40/42.07  | | | | | | | |   (171)   ~ leq(n3, n5)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | PRED_UNIFY: (153), (171) imply:
% 248.40/42.07  | | | | | | | |   (172)  $false
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | CLOSE: (172) is inconsistent.
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | Case 2:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (173)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter,
% 248.40/42.07  | | | | | | | |              n3, n1) = all_74_9 & $i(all_74_9))
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | BETA: splitting (173) gives:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | Case 1:
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | |   (174)   ~ leq(n1, all_74_21)
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | REDUCE: (9), (174) imply:
% 248.40/42.07  | | | | | | | | |   (175)   ~ leq(n1, n5)
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | PRED_UNIFY: (167), (175) imply:
% 248.40/42.07  | | | | | | | | |   (176)  $false
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | CLOSE: (176) is inconsistent.
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | Case 2:
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | |   (177)  a_select3(pminus_ds1_filter, n3, n1) = all_74_9 &
% 248.40/42.07  | | | | | | | | |          $i(all_74_9)
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | ALPHA: (177) implies:
% 248.40/42.07  | | | | | | | | |   (178)  a_select3(pminus_ds1_filter, n3, n1) = all_74_9
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | | REF_CLOSE: (22), (25), (165), (178) are inconsistent by
% 248.40/42.07  | | | | | | | | |            sub-proof #38.
% 248.40/42.07  | | | | | | | | | 
% 248.40/42.07  | | | | | | | | End of split
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | End of split
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | End of split
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | Case 2:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (179)  all_74_11 = n2
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (152), (179) imply:
% 248.40/42.07  | | | | | |   (180)  a_select3(pminus_ds1_filter, n2, n3) = all_74_9
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (151), (179) imply:
% 248.40/42.07  | | | | | |   (181)  a_select3(pminus_ds1_filter, n3, n2) = all_74_8
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (19), (179) imply:
% 248.40/42.07  | | | | | |   (182)  leq(n2, n5)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (13), (179) imply:
% 248.40/42.07  | | | | | |   (183)  leq(n0, n2)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | GROUND_INST: instantiating (5) with n2, n3, all_74_9, simplifying
% 248.40/42.07  | | | | | |              with (11), (21), (154), (180), (183) gives:
% 248.40/42.07  | | | | | |   (184)   ~ leq(n3, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.07  | | | | | |          (a_select3(pminus_ds1_filter, n3, n2) = all_74_9 &
% 248.40/42.07  | | | | | |            $i(all_74_9))
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | BETA: splitting (184) gives:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | Case 1:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (185)   ~ leq(n3, all_74_21)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (9), (185) imply:
% 248.40/42.07  | | | | | | |   (186)   ~ leq(n3, n5)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | PRED_UNIFY: (153), (186) imply:
% 248.40/42.07  | | | | | | |   (187)  $false
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | CLOSE: (187) is inconsistent.
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | Case 2:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (188)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n3,
% 248.40/42.07  | | | | | | |              n2) = all_74_9 & $i(all_74_9))
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | BETA: splitting (188) gives:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | Case 1:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (189)   ~ leq(n2, all_74_21)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | REDUCE: (9), (189) imply:
% 248.40/42.07  | | | | | | | |   (190)   ~ leq(n2, n5)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | PRED_UNIFY: (182), (190) imply:
% 248.40/42.07  | | | | | | | |   (191)  $false
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | CLOSE: (191) is inconsistent.
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | Case 2:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (192)  a_select3(pminus_ds1_filter, n3, n2) = all_74_9 &
% 248.40/42.07  | | | | | | | |          $i(all_74_9)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | ALPHA: (192) implies:
% 248.40/42.07  | | | | | | | |   (193)  a_select3(pminus_ds1_filter, n3, n2) = all_74_9
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | REF_CLOSE: (22), (25), (181), (193) are inconsistent by
% 248.40/42.07  | | | | | | | |            sub-proof #37.
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | End of split
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | End of split
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | End of split
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | Case 2:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | |   (194)  all_74_11 = n3
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (152), (194) imply:
% 248.40/42.07  | | | | |   (195)  a_select3(pminus_ds1_filter, n3, n3) = all_74_9
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (151), (194) imply:
% 248.40/42.07  | | | | |   (196)  a_select3(pminus_ds1_filter, n3, n3) = all_74_8
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | GROUND_INST: instantiating (25) with all_74_9, all_74_8, n3, n3,
% 248.40/42.07  | | | | |              pminus_ds1_filter, simplifying with (195), (196) gives:
% 248.40/42.07  | | | | |   (197)  all_74_8 = all_74_9
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (22), (197) imply:
% 248.40/42.07  | | | | |   (198)  $false
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | CLOSE: (198) is inconsistent.
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | End of split
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | End of split
% 248.40/42.07  | | | 
% 248.40/42.07  | | Case 2:
% 248.40/42.07  | | | 
% 248.40/42.07  | | |   (199)  all_74_11 = n4
% 248.40/42.07  | | | 
% 248.40/42.07  | | | REDUCE: (2), (199) imply:
% 248.40/42.07  | | |   (200)  a_select3(pminus_ds1_filter, all_74_10, n4) = all_74_8
% 248.40/42.07  | | | 
% 248.40/42.07  | | | REDUCE: (4), (199) imply:
% 248.40/42.07  | | |   (201)  a_select3(pminus_ds1_filter, n4, all_74_10) = all_74_9
% 248.40/42.07  | | | 
% 248.40/42.07  | | | REDUCE: (19), (199) imply:
% 248.40/42.07  | | |   (202)  leq(n4, n5)
% 248.40/42.07  | | | 
% 248.40/42.07  | | | REDUCE: (13), (199) imply:
% 248.40/42.07  | | |   (203)  leq(n0, n4)
% 248.40/42.07  | | | 
% 248.40/42.07  | | | BETA: splitting (28) gives:
% 248.40/42.07  | | | 
% 248.40/42.07  | | | Case 1:
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | |   (204)  gt(n3, all_74_10)
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | GROUND_INST: instantiating (17) with all_74_10, n3, n2, simplifying with
% 248.40/42.07  | | | |              (11), (12), (16), (204) gives:
% 248.40/42.07  | | | |   (205)  leq(all_74_10, n2)
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | GROUND_INST: instantiating (24) with all_74_10, n2, simplifying with
% 248.40/42.07  | | | |              (12), (21), (205) gives:
% 248.40/42.07  | | | |   (206)  all_74_10 = n2 | gt(n2, all_74_10)
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | BETA: splitting (206) gives:
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | Case 1:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | |   (207)  gt(n2, all_74_10)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | GROUND_INST: instantiating (17) with all_74_10, n2, n1, simplifying
% 248.40/42.07  | | | | |              with (12), (14), (21), (207) gives:
% 248.40/42.07  | | | | |   (208)  leq(all_74_10, n1)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | GROUND_INST: instantiating (8) with all_74_10, simplifying with (3),
% 248.40/42.07  | | | | |              (12), (208) gives:
% 248.40/42.07  | | | | |   (209)  all_74_10 = n1 | all_74_10 = n0
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | BETA: splitting (209) gives:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | Case 1:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (210)  all_74_10 = n0
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (7), (210) imply:
% 248.40/42.07  | | | | | |   (211)  $false
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | CLOSE: (211) is inconsistent.
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | Case 2:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (212)  all_74_10 = n1
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (200), (212) imply:
% 248.40/42.07  | | | | | |   (213)  a_select3(pminus_ds1_filter, n1, n4) = all_74_8
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (201), (212) imply:
% 248.40/42.07  | | | | | |   (214)  a_select3(pminus_ds1_filter, n4, n1) = all_74_9
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (12), (212) imply:
% 248.40/42.07  | | | | | |   (215)  $i(n1)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (20), (212) imply:
% 248.40/42.07  | | | | | |   (216)  leq(n1, n5)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (3), (212) imply:
% 248.40/42.07  | | | | | |   (217)  leq(n0, n1)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | GROUND_INST: instantiating (5) with n1, n4, all_74_8, simplifying
% 248.40/42.07  | | | | | |              with (18), (203), (213), (215), (217) gives:
% 248.40/42.07  | | | | | |   (218)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.07  | | | | | |          (a_select3(pminus_ds1_filter, n4, n1) = all_74_8 &
% 248.40/42.07  | | | | | |            $i(all_74_8))
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | BETA: splitting (218) gives:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | Case 1:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (219)   ~ leq(n4, all_74_21)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (9), (219) imply:
% 248.40/42.07  | | | | | | |   (220)   ~ leq(n4, n5)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | PRED_UNIFY: (202), (220) imply:
% 248.40/42.07  | | | | | | |   (221)  $false
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | CLOSE: (221) is inconsistent.
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | Case 2:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (222)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.07  | | | | | | |              n1) = all_74_8 & $i(all_74_8))
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | BETA: splitting (222) gives:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | Case 1:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (223)   ~ leq(n1, all_74_21)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | REDUCE: (9), (223) imply:
% 248.40/42.07  | | | | | | | |   (224)   ~ leq(n1, n5)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | PRED_UNIFY: (216), (224) imply:
% 248.40/42.07  | | | | | | | |   (225)  $false
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | CLOSE: (225) is inconsistent.
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | Case 2:
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | |   (226)  a_select3(pminus_ds1_filter, n4, n1) = all_74_8 &
% 248.40/42.07  | | | | | | | |          $i(all_74_8)
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | ALPHA: (226) implies:
% 248.40/42.07  | | | | | | | |   (227)  a_select3(pminus_ds1_filter, n4, n1) = all_74_8
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | | REF_CLOSE: (22), (25), (214), (227) are inconsistent by
% 248.40/42.07  | | | | | | | |            sub-proof #36.
% 248.40/42.07  | | | | | | | | 
% 248.40/42.07  | | | | | | | End of split
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | End of split
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | End of split
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | Case 2:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | |   (228)  all_74_10 = n2
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (200), (228) imply:
% 248.40/42.07  | | | | |   (229)  a_select3(pminus_ds1_filter, n2, n4) = all_74_8
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (201), (228) imply:
% 248.40/42.07  | | | | |   (230)  a_select3(pminus_ds1_filter, n4, n2) = all_74_9
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (20), (228) imply:
% 248.40/42.07  | | | | |   (231)  leq(n2, n5)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (3), (228) imply:
% 248.40/42.07  | | | | |   (232)  leq(n0, n2)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | GROUND_INST: instantiating (5) with n2, n4, all_74_8, simplifying with
% 248.40/42.07  | | | | |              (18), (21), (203), (229), (232) gives:
% 248.40/42.07  | | | | |   (233)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.07  | | | | |          (a_select3(pminus_ds1_filter, n4, n2) = all_74_8 &
% 248.40/42.07  | | | | |            $i(all_74_8))
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | BETA: splitting (233) gives:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | Case 1:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (234)   ~ leq(n4, all_74_21)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (9), (234) imply:
% 248.40/42.07  | | | | | |   (235)   ~ leq(n4, n5)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | PRED_UNIFY: (202), (235) imply:
% 248.40/42.07  | | | | | |   (236)  $false
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | CLOSE: (236) is inconsistent.
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | Case 2:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (237)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.07  | | | | | |              n2) = all_74_8 & $i(all_74_8))
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | BETA: splitting (237) gives:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | Case 1:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (238)   ~ leq(n2, all_74_21)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (9), (238) imply:
% 248.40/42.07  | | | | | | |   (239)   ~ leq(n2, n5)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | PRED_UNIFY: (231), (239) imply:
% 248.40/42.07  | | | | | | |   (240)  $false
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | CLOSE: (240) is inconsistent.
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | Case 2:
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | |   (241)  a_select3(pminus_ds1_filter, n4, n2) = all_74_8 &
% 248.40/42.07  | | | | | | |          $i(all_74_8)
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | ALPHA: (241) implies:
% 248.40/42.07  | | | | | | |   (242)  a_select3(pminus_ds1_filter, n4, n2) = all_74_8
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | GROUND_INST: instantiating (25) with all_74_9, all_74_8, n2, n4,
% 248.40/42.07  | | | | | | |              pminus_ds1_filter, simplifying with (230), (242)
% 248.40/42.07  | | | | | | |              gives:
% 248.40/42.07  | | | | | | |   (243)  all_74_8 = all_74_9
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | REDUCE: (22), (243) imply:
% 248.40/42.07  | | | | | | |   (244)  $false
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | | CLOSE: (244) is inconsistent.
% 248.40/42.07  | | | | | | | 
% 248.40/42.07  | | | | | | End of split
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | End of split
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | End of split
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | Case 2:
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | |   (245)  all_74_10 = n3
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (200), (245) imply:
% 248.40/42.07  | | | |   (246)  a_select3(pminus_ds1_filter, n3, n4) = all_74_8
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (201), (245) imply:
% 248.40/42.07  | | | |   (247)  a_select3(pminus_ds1_filter, n4, n3) = all_74_9
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (20), (245) imply:
% 248.40/42.07  | | | |   (248)  leq(n3, n5)
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | REDUCE: (3), (245) imply:
% 248.40/42.07  | | | |   (249)  leq(n0, n3)
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | GROUND_INST: instantiating (5) with n3, n4, all_74_8, simplifying with
% 248.40/42.07  | | | |              (11), (18), (203), (246), (249) gives:
% 248.40/42.07  | | | |   (250)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.40/42.07  | | | |          (a_select3(pminus_ds1_filter, n4, n3) = all_74_8 &
% 248.40/42.07  | | | |            $i(all_74_8))
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | BETA: splitting (250) gives:
% 248.40/42.07  | | | | 
% 248.40/42.07  | | | | Case 1:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | |   (251)   ~ leq(n4, all_74_21)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | REDUCE: (9), (251) imply:
% 248.40/42.07  | | | | |   (252)   ~ leq(n4, n5)
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | PRED_UNIFY: (202), (252) imply:
% 248.40/42.07  | | | | |   (253)  $false
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | CLOSE: (253) is inconsistent.
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | Case 2:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | |   (254)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n4, n3)
% 248.40/42.07  | | | | |            = all_74_8 & $i(all_74_8))
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | BETA: splitting (254) gives:
% 248.40/42.07  | | | | | 
% 248.40/42.07  | | | | | Case 1:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (255)   ~ leq(n3, all_74_21)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | REDUCE: (9), (255) imply:
% 248.40/42.07  | | | | | |   (256)   ~ leq(n3, n5)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | PRED_UNIFY: (248), (256) imply:
% 248.40/42.07  | | | | | |   (257)  $false
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | CLOSE: (257) is inconsistent.
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | Case 2:
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | |   (258)  a_select3(pminus_ds1_filter, n4, n3) = all_74_8 &
% 248.40/42.07  | | | | | |          $i(all_74_8)
% 248.40/42.07  | | | | | | 
% 248.40/42.07  | | | | | | ALPHA: (258) implies:
% 248.40/42.08  | | | | | |   (259)  a_select3(pminus_ds1_filter, n4, n3) = all_74_8
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REF_CLOSE: (22), (25), (247), (259) are inconsistent by sub-proof
% 248.40/42.08  | | | | | |            #35.
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | End of split
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | End of split
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | End of split
% 248.40/42.08  | | | 
% 248.40/42.08  | | End of split
% 248.40/42.08  | | 
% 248.40/42.08  | Case 2:
% 248.40/42.08  | | 
% 248.40/42.08  | |   (260)  all_74_10 = n4
% 248.40/42.08  | | 
% 248.40/42.08  | | REDUCE: (2), (260) imply:
% 248.40/42.08  | |   (261)  a_select3(pminus_ds1_filter, n4, all_74_11) = all_74_8
% 248.40/42.08  | | 
% 248.40/42.08  | | REDUCE: (4), (260) imply:
% 248.40/42.08  | |   (262)  a_select3(pminus_ds1_filter, all_74_11, n4) = all_74_9
% 248.40/42.08  | | 
% 248.40/42.08  | | REDUCE: (20), (260) imply:
% 248.40/42.08  | |   (263)  leq(n4, n5)
% 248.40/42.08  | | 
% 248.40/42.08  | | REDUCE: (3), (260) imply:
% 248.40/42.08  | |   (264)  leq(n0, n4)
% 248.40/42.08  | | 
% 248.40/42.08  | | BETA: splitting (1) gives:
% 248.40/42.08  | | 
% 248.40/42.08  | | Case 1:
% 248.40/42.08  | | | 
% 248.40/42.08  | | |   (265)  gt(n4, all_74_11)
% 248.40/42.08  | | | 
% 248.40/42.08  | | | GROUND_INST: instantiating (17) with all_74_11, n4, n3, simplifying with
% 248.40/42.08  | | |              (10), (15), (18), (265) gives:
% 248.40/42.08  | | |   (266)  leq(all_74_11, n3)
% 248.40/42.08  | | | 
% 248.40/42.08  | | | GROUND_INST: instantiating (24) with all_74_11, n3, simplifying with (10),
% 248.40/42.08  | | |              (11), (266) gives:
% 248.40/42.08  | | |   (267)  all_74_11 = n3 | gt(n3, all_74_11)
% 248.40/42.08  | | | 
% 248.40/42.08  | | | BETA: splitting (267) gives:
% 248.40/42.08  | | | 
% 248.40/42.08  | | | Case 1:
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | |   (268)  gt(n3, all_74_11)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | GROUND_INST: instantiating (17) with all_74_11, n3, n2, simplifying with
% 248.40/42.08  | | | |              (10), (11), (16), (268) gives:
% 248.40/42.08  | | | |   (269)  leq(all_74_11, n2)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | GROUND_INST: instantiating (24) with all_74_11, n2, simplifying with
% 248.40/42.08  | | | |              (10), (21), (269) gives:
% 248.40/42.08  | | | |   (270)  all_74_11 = n2 | gt(n2, all_74_11)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | BETA: splitting (270) gives:
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | Case 1:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | |   (271)  gt(n2, all_74_11)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | GROUND_INST: instantiating (17) with all_74_11, n2, n1, simplifying
% 248.40/42.08  | | | | |              with (10), (14), (21), (271) gives:
% 248.40/42.08  | | | | |   (272)  leq(all_74_11, n1)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | GROUND_INST: instantiating (8) with all_74_11, simplifying with (10),
% 248.40/42.08  | | | | |              (13), (272) gives:
% 248.40/42.08  | | | | |   (273)  all_74_11 = n1 | all_74_11 = n0
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | BETA: splitting (273) gives:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | Case 1:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | |   (274)  all_74_11 = n0
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (6), (274) imply:
% 248.40/42.08  | | | | | |   (275)  $false
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | CLOSE: (275) is inconsistent.
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | Case 2:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | |   (276)  all_74_11 = n1
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (262), (276) imply:
% 248.40/42.08  | | | | | |   (277)  a_select3(pminus_ds1_filter, n1, n4) = all_74_9
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (261), (276) imply:
% 248.40/42.08  | | | | | |   (278)  a_select3(pminus_ds1_filter, n4, n1) = all_74_8
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (10), (276) imply:
% 248.40/42.08  | | | | | |   (279)  $i(n1)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (19), (276) imply:
% 248.40/42.08  | | | | | |   (280)  leq(n1, n5)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (13), (276) imply:
% 248.40/42.08  | | | | | |   (281)  leq(n0, n1)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | GROUND_INST: instantiating (5) with n1, n4, all_74_9, simplifying
% 248.40/42.08  | | | | | |              with (18), (264), (277), (279), (281) gives:
% 248.40/42.08  | | | | | |   (282)   ~ leq(n4, all_74_21) |  ~ leq(n1, all_74_21) |
% 248.40/42.08  | | | | | |          (a_select3(pminus_ds1_filter, n4, n1) = all_74_9 &
% 248.40/42.08  | | | | | |            $i(all_74_9))
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | BETA: splitting (282) gives:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | Case 1:
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | |   (283)   ~ leq(n4, all_74_21)
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | REDUCE: (9), (283) imply:
% 248.40/42.08  | | | | | | |   (284)   ~ leq(n4, n5)
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | PRED_UNIFY: (263), (284) imply:
% 248.40/42.08  | | | | | | |   (285)  $false
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | CLOSE: (285) is inconsistent.
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | Case 2:
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | |   (286)   ~ leq(n1, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.08  | | | | | | |              n1) = all_74_9 & $i(all_74_9))
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | BETA: splitting (286) gives:
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | Case 1:
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | |   (287)   ~ leq(n1, all_74_21)
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | | REDUCE: (9), (287) imply:
% 248.40/42.08  | | | | | | | |   (288)   ~ leq(n1, n5)
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | | PRED_UNIFY: (280), (288) imply:
% 248.40/42.08  | | | | | | | |   (289)  $false
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | | CLOSE: (289) is inconsistent.
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | Case 2:
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | |   (290)  a_select3(pminus_ds1_filter, n4, n1) = all_74_9 &
% 248.40/42.08  | | | | | | | |          $i(all_74_9)
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | | ALPHA: (290) implies:
% 248.40/42.08  | | | | | | | |   (291)  a_select3(pminus_ds1_filter, n4, n1) = all_74_9
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | | REF_CLOSE: (22), (25), (278), (291) are inconsistent by
% 248.40/42.08  | | | | | | | |            sub-proof #36.
% 248.40/42.08  | | | | | | | | 
% 248.40/42.08  | | | | | | | End of split
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | End of split
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | End of split
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | Case 2:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | |   (292)  all_74_11 = n2
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | REDUCE: (262), (292) imply:
% 248.40/42.08  | | | | |   (293)  a_select3(pminus_ds1_filter, n2, n4) = all_74_9
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | REDUCE: (261), (292) imply:
% 248.40/42.08  | | | | |   (294)  a_select3(pminus_ds1_filter, n4, n2) = all_74_8
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | REDUCE: (19), (292) imply:
% 248.40/42.08  | | | | |   (295)  leq(n2, n5)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | REDUCE: (13), (292) imply:
% 248.40/42.08  | | | | |   (296)  leq(n0, n2)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | GROUND_INST: instantiating (5) with n2, n4, all_74_9, simplifying with
% 248.40/42.08  | | | | |              (18), (21), (264), (293), (296) gives:
% 248.40/42.08  | | | | |   (297)   ~ leq(n4, all_74_21) |  ~ leq(n2, all_74_21) |
% 248.40/42.08  | | | | |          (a_select3(pminus_ds1_filter, n4, n2) = all_74_9 &
% 248.40/42.08  | | | | |            $i(all_74_9))
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | BETA: splitting (297) gives:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | Case 1:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | |   (298)   ~ leq(n4, all_74_21)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (9), (298) imply:
% 248.40/42.08  | | | | | |   (299)   ~ leq(n4, n5)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | PRED_UNIFY: (263), (299) imply:
% 248.40/42.08  | | | | | |   (300)  $false
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | CLOSE: (300) is inconsistent.
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | Case 2:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | |   (301)   ~ leq(n2, all_74_21) | (a_select3(pminus_ds1_filter, n4,
% 248.40/42.08  | | | | | |              n2) = all_74_9 & $i(all_74_9))
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | BETA: splitting (301) gives:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | Case 1:
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | |   (302)   ~ leq(n2, all_74_21)
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | REDUCE: (9), (302) imply:
% 248.40/42.08  | | | | | | |   (303)   ~ leq(n2, n5)
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | PRED_UNIFY: (295), (303) imply:
% 248.40/42.08  | | | | | | |   (304)  $false
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | CLOSE: (304) is inconsistent.
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | Case 2:
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | |   (305)  a_select3(pminus_ds1_filter, n4, n2) = all_74_9 &
% 248.40/42.08  | | | | | | |          $i(all_74_9)
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | ALPHA: (305) implies:
% 248.40/42.08  | | | | | | |   (306)  a_select3(pminus_ds1_filter, n4, n2) = all_74_9
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | GROUND_INST: instantiating (25) with all_74_9, all_74_8, n2, n4,
% 248.40/42.08  | | | | | | |              pminus_ds1_filter, simplifying with (294), (306)
% 248.40/42.08  | | | | | | |              gives:
% 248.40/42.08  | | | | | | |   (307)  all_74_8 = all_74_9
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | REDUCE: (22), (307) imply:
% 248.40/42.08  | | | | | | |   (308)  $false
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | | CLOSE: (308) is inconsistent.
% 248.40/42.08  | | | | | | | 
% 248.40/42.08  | | | | | | End of split
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | End of split
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | End of split
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | Case 2:
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | |   (309)  all_74_11 = n3
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | REDUCE: (262), (309) imply:
% 248.40/42.08  | | | |   (310)  a_select3(pminus_ds1_filter, n3, n4) = all_74_9
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | REDUCE: (261), (309) imply:
% 248.40/42.08  | | | |   (311)  a_select3(pminus_ds1_filter, n4, n3) = all_74_8
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | REDUCE: (19), (309) imply:
% 248.40/42.08  | | | |   (312)  leq(n3, n5)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | REDUCE: (13), (309) imply:
% 248.40/42.08  | | | |   (313)  leq(n0, n3)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | GROUND_INST: instantiating (5) with n3, n4, all_74_9, simplifying with
% 248.40/42.08  | | | |              (11), (18), (264), (310), (313) gives:
% 248.40/42.08  | | | |   (314)   ~ leq(n4, all_74_21) |  ~ leq(n3, all_74_21) |
% 248.40/42.08  | | | |          (a_select3(pminus_ds1_filter, n4, n3) = all_74_9 &
% 248.40/42.08  | | | |            $i(all_74_9))
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | BETA: splitting (314) gives:
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | Case 1:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | |   (315)   ~ leq(n4, all_74_21)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | REDUCE: (9), (315) imply:
% 248.40/42.08  | | | | |   (316)   ~ leq(n4, n5)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | PRED_UNIFY: (263), (316) imply:
% 248.40/42.08  | | | | |   (317)  $false
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | CLOSE: (317) is inconsistent.
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | Case 2:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | |   (318)   ~ leq(n3, all_74_21) | (a_select3(pminus_ds1_filter, n4, n3)
% 248.40/42.08  | | | | |            = all_74_9 & $i(all_74_9))
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | BETA: splitting (318) gives:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | Case 1:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | |   (319)   ~ leq(n3, all_74_21)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (9), (319) imply:
% 248.40/42.08  | | | | | |   (320)   ~ leq(n3, n5)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | PRED_UNIFY: (312), (320) imply:
% 248.40/42.08  | | | | | |   (321)  $false
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | CLOSE: (321) is inconsistent.
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | Case 2:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | |   (322)  a_select3(pminus_ds1_filter, n4, n3) = all_74_9 &
% 248.40/42.08  | | | | | |          $i(all_74_9)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | ALPHA: (322) implies:
% 248.40/42.08  | | | | | |   (323)  a_select3(pminus_ds1_filter, n4, n3) = all_74_9
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REF_CLOSE: (22), (25), (311), (323) are inconsistent by sub-proof
% 248.40/42.08  | | | | | |            #35.
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | End of split
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | End of split
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | End of split
% 248.40/42.08  | | | 
% 248.40/42.08  | | Case 2:
% 248.40/42.08  | | | 
% 248.40/42.08  | | |   (324)  all_74_11 = n4
% 248.40/42.08  | | | 
% 248.40/42.08  | | | REDUCE: (262), (324) imply:
% 248.40/42.08  | | |   (325)  a_select3(pminus_ds1_filter, n4, n4) = all_74_9
% 248.40/42.08  | | | 
% 248.40/42.08  | | | REDUCE: (261), (324) imply:
% 248.40/42.08  | | |   (326)  a_select3(pminus_ds1_filter, n4, n4) = all_74_8
% 248.40/42.08  | | | 
% 248.40/42.08  | | | GROUND_INST: instantiating (25) with all_74_9, all_74_8, n4, n4,
% 248.40/42.08  | | |              pminus_ds1_filter, simplifying with (325), (326) gives:
% 248.40/42.08  | | |   (327)  all_74_8 = all_74_9
% 248.40/42.08  | | | 
% 248.40/42.08  | | | REDUCE: (22), (327) imply:
% 248.40/42.08  | | |   (328)  $false
% 248.40/42.08  | | | 
% 248.40/42.08  | | | CLOSE: (328) is inconsistent.
% 248.40/42.08  | | | 
% 248.40/42.08  | | End of split
% 248.40/42.08  | | 
% 248.40/42.08  | End of split
% 248.40/42.08  | 
% 248.40/42.08  End of proof
% 248.40/42.08  
% 248.40/42.08  Sub-proof #35 shows that the following formulas are inconsistent:
% 248.40/42.08  ----------------------------------------------------------------
% 248.40/42.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.08           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.08             v0))
% 248.40/42.08    (2)  a_select3(pminus_ds1_filter, n4, n3) = all_74_8
% 248.40/42.08    (3)  a_select3(pminus_ds1_filter, n4, n3) = all_74_9
% 248.40/42.08    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.08  
% 248.40/42.08  Begin of proof
% 248.40/42.08  | 
% 248.40/42.08  | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n3, n4,
% 248.40/42.08  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.08  |   (5)  all_74_8 = all_74_9
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (4), (5) imply:
% 248.40/42.08  |   (6)  $false
% 248.40/42.08  | 
% 248.40/42.08  | CLOSE: (6) is inconsistent.
% 248.40/42.08  | 
% 248.40/42.08  End of proof
% 248.40/42.08  
% 248.40/42.08  Sub-proof #36 shows that the following formulas are inconsistent:
% 248.40/42.08  ----------------------------------------------------------------
% 248.40/42.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.08           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.08             v0))
% 248.40/42.08    (2)  a_select3(pminus_ds1_filter, n4, n1) = all_74_8
% 248.40/42.08    (3)  a_select3(pminus_ds1_filter, n4, n1) = all_74_9
% 248.40/42.08    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.08  
% 248.40/42.08  Begin of proof
% 248.40/42.08  | 
% 248.40/42.08  | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n1, n4,
% 248.40/42.08  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.08  |   (5)  all_74_8 = all_74_9
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (4), (5) imply:
% 248.40/42.08  |   (6)  $false
% 248.40/42.08  | 
% 248.40/42.08  | CLOSE: (6) is inconsistent.
% 248.40/42.08  | 
% 248.40/42.08  End of proof
% 248.40/42.08  
% 248.40/42.08  Sub-proof #37 shows that the following formulas are inconsistent:
% 248.40/42.08  ----------------------------------------------------------------
% 248.40/42.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.08           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.08             v0))
% 248.40/42.08    (2)  a_select3(pminus_ds1_filter, n3, n2) = all_74_8
% 248.40/42.08    (3)  a_select3(pminus_ds1_filter, n3, n2) = all_74_9
% 248.40/42.08    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.08  
% 248.40/42.08  Begin of proof
% 248.40/42.08  | 
% 248.40/42.08  | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n2, n3,
% 248.40/42.08  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.08  |   (5)  all_74_8 = all_74_9
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (4), (5) imply:
% 248.40/42.08  |   (6)  $false
% 248.40/42.08  | 
% 248.40/42.08  | CLOSE: (6) is inconsistent.
% 248.40/42.08  | 
% 248.40/42.08  End of proof
% 248.40/42.08  
% 248.40/42.08  Sub-proof #38 shows that the following formulas are inconsistent:
% 248.40/42.08  ----------------------------------------------------------------
% 248.40/42.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.08           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.08             v0))
% 248.40/42.08    (2)  a_select3(pminus_ds1_filter, n3, n1) = all_74_8
% 248.40/42.08    (3)  a_select3(pminus_ds1_filter, n3, n1) = all_74_9
% 248.40/42.08    (4)   ~ (all_74_8 = all_74_9)
% 248.40/42.08  
% 248.40/42.08  Begin of proof
% 248.40/42.08  | 
% 248.40/42.08  | GROUND_INST: instantiating (1) with all_74_9, all_74_8, n1, n3,
% 248.40/42.08  |              pminus_ds1_filter, simplifying with (2), (3) gives:
% 248.40/42.08  |   (5)  all_74_8 = all_74_9
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (4), (5) imply:
% 248.40/42.08  |   (6)  $false
% 248.40/42.08  | 
% 248.40/42.08  | CLOSE: (6) is inconsistent.
% 248.40/42.08  | 
% 248.40/42.08  End of proof
% 248.40/42.08  
% 248.40/42.08  Sub-proof #39 shows that the following formulas are inconsistent:
% 248.40/42.08  ----------------------------------------------------------------
% 248.40/42.08    (1)  $i(all_74_11)
% 248.40/42.08    (2)  all_74_11 = n0
% 248.40/42.08    (3)  gt(all_74_11, n0)
% 248.40/42.08    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.40/42.08  
% 248.40/42.08  Begin of proof
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (1), (2) imply:
% 248.40/42.08  |   (5)  $i(n0)
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (2), (3) imply:
% 248.40/42.08  |   (6)  gt(n0, n0)
% 248.40/42.08  | 
% 248.40/42.08  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.40/42.08  |   (7)  $false
% 248.40/42.08  | 
% 248.40/42.08  | CLOSE: (7) is inconsistent.
% 248.40/42.08  | 
% 248.40/42.08  End of proof
% 248.40/42.08  
% 248.40/42.08  Sub-proof #40 shows that the following formulas are inconsistent:
% 248.40/42.08  ----------------------------------------------------------------
% 248.40/42.08    (1)  $i(all_74_10)
% 248.40/42.08    (2)  all_74_10 = n0
% 248.40/42.08    (3)  gt(all_74_10, n0)
% 248.40/42.08    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.40/42.08  
% 248.40/42.08  Begin of proof
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (1), (2) imply:
% 248.40/42.08  |   (5)  $i(n0)
% 248.40/42.08  | 
% 248.40/42.08  | REDUCE: (2), (3) imply:
% 248.40/42.08  |   (6)  gt(n0, n0)
% 248.40/42.08  | 
% 248.40/42.08  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.40/42.08  |   (7)  $false
% 248.40/42.08  | 
% 248.40/42.08  | CLOSE: (7) is inconsistent.
% 248.40/42.08  | 
% 248.40/42.08  End of proof
% 248.40/42.08  
% 248.40/42.08  Sub-proof #41 shows that the following formulas are inconsistent:
% 248.40/42.08  ----------------------------------------------------------------
% 248.40/42.08    (1)  all_74_6 = n2 | gt(n2, all_74_6)
% 248.40/42.08    (2)  leq(all_74_6, n2)
% 248.40/42.08    (3)   ~ gt(n0, n0)
% 248.40/42.08    (4)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.08           leq(n0, v0))
% 248.40/42.08    (5)  gt(all_74_6, n0)
% 248.40/42.08    (6)  leq(n0, all_74_7)
% 248.40/42.08    (7)  $i(all_74_7)
% 248.40/42.08    (8)  a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5
% 248.40/42.08    (9)  all_74_20 = n2
% 248.40/42.08    (10)  pred(n2) = n1
% 248.40/42.08    (11)  $i(all_74_6)
% 248.40/42.08    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (pred(v1) = v2) |  ~
% 248.40/42.08            $i(v1) |  ~ $i(v0) |  ~ gt(v1, v0) | leq(v0, v2))
% 248.40/42.08    (13)  all_74_7 = n2 | gt(n2, all_74_7)
% 248.40/42.08    (14)   ~ (all_74_4 = all_74_5)
% 248.40/42.08    (15)  all_74_7 = n2 | all_74_7 = n1 | all_74_7 = n0
% 248.40/42.08    (16)  all_74_6 = n2 | all_74_6 = n1 | all_74_6 = n0
% 248.40/42.08    (17)  $i(n2)
% 248.40/42.08    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 248.40/42.08                v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_20) |  ~
% 248.40/42.08            leq(v0, all_74_20) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 248.40/42.08            (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.08    (19)  a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4
% 248.40/42.08    (20)  leq(all_74_7, n2)
% 248.40/42.08    (21)  all_74_7 = n0 | gt(all_74_7, n0)
% 248.40/42.08    (22)  leq(n0, all_74_6)
% 248.40/42.08    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.08          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.08              v0))
% 248.40/42.08  
% 248.40/42.08  Begin of proof
% 248.40/42.08  | 
% 248.40/42.08  | BETA: splitting (21) gives:
% 248.40/42.08  | 
% 248.40/42.08  | Case 1:
% 248.40/42.08  | | 
% 248.40/42.08  | |   (24)  gt(all_74_7, n0)
% 248.40/42.08  | | 
% 248.40/42.08  | | BETA: splitting (13) gives:
% 248.40/42.08  | | 
% 248.40/42.08  | | Case 1:
% 248.40/42.08  | | | 
% 248.40/42.08  | | |   (25)  gt(n2, all_74_7)
% 248.40/42.08  | | | 
% 248.40/42.08  | | | BETA: splitting (1) gives:
% 248.40/42.08  | | | 
% 248.40/42.08  | | | Case 1:
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | |   (26)  gt(n2, all_74_6)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | GROUND_INST: instantiating (12) with all_74_7, n2, n1, simplifying with
% 248.40/42.08  | | | |              (7), (10), (17), (25) gives:
% 248.40/42.08  | | | |   (27)  leq(all_74_7, n1)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | GROUND_INST: instantiating (12) with all_74_6, n2, n1, simplifying with
% 248.40/42.08  | | | |              (10), (11), (17), (26) gives:
% 248.40/42.08  | | | |   (28)  leq(all_74_6, n1)
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | BETA: splitting (16) gives:
% 248.40/42.08  | | | | 
% 248.40/42.08  | | | | Case 1:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | |   (29)  all_74_6 = n0
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | REDUCE: (5), (29) imply:
% 248.40/42.08  | | | | |   (30)  gt(n0, n0)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | PRED_UNIFY: (3), (30) imply:
% 248.40/42.08  | | | | |   (31)  $false
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | CLOSE: (31) is inconsistent.
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | Case 2:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | |   (32)   ~ (all_74_6 = n0)
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | BETA: splitting (15) gives:
% 248.40/42.08  | | | | | 
% 248.40/42.08  | | | | | Case 1:
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | |   (33)  all_74_7 = n0
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | REDUCE: (24), (33) imply:
% 248.40/42.08  | | | | | |   (34)  gt(n0, n0)
% 248.40/42.08  | | | | | | 
% 248.40/42.08  | | | | | | PRED_UNIFY: (3), (34) imply:
% 248.40/42.09  | | | | | |   (35)  $false
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | | CLOSE: (35) is inconsistent.
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | Case 2:
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | |   (36)   ~ (all_74_7 = n0)
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | | REF_CLOSE: (4), (6), (7), (8), (11), (14), (19), (22), (23), (27),
% 248.40/42.09  | | | | | |            (28), (32), (36) are inconsistent by sub-proof #47.
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | End of split
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | End of split
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | Case 2:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (37)  all_74_6 = n2
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (19), (37) imply:
% 248.40/42.09  | | | |   (38)  a_select3(r_ds1_filter, n2, all_74_7) = all_74_4
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (8), (37) imply:
% 248.40/42.09  | | | |   (39)  a_select3(r_ds1_filter, all_74_7, n2) = all_74_5
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (2), (37) imply:
% 248.40/42.09  | | | |   (40)  leq(n2, n2)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (22), (37) imply:
% 248.40/42.09  | | | |   (41)  leq(n0, n2)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | GROUND_INST: instantiating (12) with all_74_7, n2, n1, simplifying with
% 248.40/42.09  | | | |              (7), (10), (17), (25) gives:
% 248.40/42.09  | | | |   (42)  leq(all_74_7, n1)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | BETA: splitting (15) gives:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | Case 1:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (43)  all_74_7 = n0
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (24), (43) imply:
% 248.40/42.09  | | | | |   (44)  gt(n0, n0)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | PRED_UNIFY: (3), (44) imply:
% 248.40/42.09  | | | | |   (45)  $false
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | CLOSE: (45) is inconsistent.
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | Case 2:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (46)   ~ (all_74_7 = n0)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REF_CLOSE: (4), (6), (7), (9), (14), (17), (18), (20), (23), (38),
% 248.40/42.09  | | | | |            (39), (40), (41), (42), (46) are inconsistent by sub-proof
% 248.40/42.09  | | | | |            #46.
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | End of split
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | End of split
% 248.40/42.09  | | | 
% 248.40/42.09  | | Case 2:
% 248.40/42.09  | | | 
% 248.40/42.09  | | |   (47)  all_74_7 = n2
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (19), (47) imply:
% 248.40/42.09  | | |   (48)  a_select3(r_ds1_filter, all_74_6, n2) = all_74_4
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (8), (47) imply:
% 248.40/42.09  | | |   (49)  a_select3(r_ds1_filter, n2, all_74_6) = all_74_5
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (20), (47) imply:
% 248.40/42.09  | | |   (50)  leq(n2, n2)
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (6), (47) imply:
% 248.40/42.09  | | |   (51)  leq(n0, n2)
% 248.40/42.09  | | | 
% 248.40/42.09  | | | BETA: splitting (1) gives:
% 248.40/42.09  | | | 
% 248.40/42.09  | | | Case 1:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (52)  gt(n2, all_74_6)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | GROUND_INST: instantiating (12) with all_74_6, n2, n1, simplifying with
% 248.40/42.09  | | | |              (10), (11), (17), (52) gives:
% 248.40/42.09  | | | |   (53)  leq(all_74_6, n1)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | GROUND_INST: instantiating (4) with all_74_6, simplifying with (11),
% 248.40/42.09  | | | |              (22), (53) gives:
% 248.40/42.09  | | | |   (54)  all_74_6 = n1 | all_74_6 = n0
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | BETA: splitting (16) gives:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | Case 1:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (55)  all_74_6 = n0
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (5), (55) imply:
% 248.40/42.09  | | | | |   (56)  gt(n0, n0)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | PRED_UNIFY: (3), (56) imply:
% 248.40/42.09  | | | | |   (57)  $false
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | CLOSE: (57) is inconsistent.
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | Case 2:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (58)   ~ (all_74_6 = n0)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REF_CLOSE: (2), (9), (11), (14), (17), (18), (22), (23), (48), (49),
% 248.40/42.09  | | | | |            (50), (51), (54), (58) are inconsistent by sub-proof #45.
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | End of split
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | Case 2:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (59)  all_74_6 = n2
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REF_CLOSE: (14), (23), (48), (49), (59) are inconsistent by sub-proof
% 248.40/42.09  | | | |            #44.
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | End of split
% 248.40/42.09  | | | 
% 248.40/42.09  | | End of split
% 248.40/42.09  | | 
% 248.40/42.09  | Case 2:
% 248.40/42.09  | | 
% 248.40/42.09  | |   (60)  all_74_7 = n0
% 248.40/42.09  | |   (61)   ~ gt(all_74_7, n0)
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (19), (60) imply:
% 248.40/42.09  | |   (62)  a_select3(r_ds1_filter, all_74_6, n0) = all_74_4
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (8), (60) imply:
% 248.40/42.09  | |   (63)  a_select3(r_ds1_filter, n0, all_74_6) = all_74_5
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (7), (60) imply:
% 248.40/42.09  | |   (64)  $i(n0)
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (20), (60) imply:
% 248.40/42.09  | |   (65)  leq(n0, n2)
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (6), (60) imply:
% 248.40/42.09  | |   (66)  leq(n0, n0)
% 248.40/42.09  | | 
% 248.40/42.09  | | BETA: splitting (1) gives:
% 248.40/42.09  | | 
% 248.40/42.09  | | Case 1:
% 248.40/42.09  | | | 
% 248.40/42.09  | | |   (67)  gt(n2, all_74_6)
% 248.40/42.09  | | | 
% 248.40/42.09  | | | GROUND_INST: instantiating (12) with all_74_6, n2, n1, simplifying with
% 248.40/42.09  | | |              (10), (11), (17), (67) gives:
% 248.40/42.09  | | |   (68)  leq(all_74_6, n1)
% 248.40/42.09  | | | 
% 248.40/42.09  | | | GROUND_INST: instantiating (4) with all_74_6, simplifying with (11), (22),
% 248.40/42.09  | | |              (68) gives:
% 248.40/42.09  | | |   (69)  all_74_6 = n1 | all_74_6 = n0
% 248.40/42.09  | | | 
% 248.40/42.09  | | | BETA: splitting (16) gives:
% 248.40/42.09  | | | 
% 248.40/42.09  | | | Case 1:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (70)  all_74_6 = n0
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (5), (70) imply:
% 248.40/42.09  | | | |   (71)  gt(n0, n0)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | PRED_UNIFY: (3), (71) imply:
% 248.40/42.09  | | | |   (72)  $false
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | CLOSE: (72) is inconsistent.
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | Case 2:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (73)   ~ (all_74_6 = n0)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | BETA: splitting (69) gives:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | Case 1:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (74)  all_74_6 = n0
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (73), (74) imply:
% 248.40/42.09  | | | | |   (75)  $false
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | CLOSE: (75) is inconsistent.
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | Case 2:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (76)  all_74_6 = n1
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (62), (76) imply:
% 248.40/42.09  | | | | |   (77)  a_select3(r_ds1_filter, n1, n0) = all_74_4
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (63), (76) imply:
% 248.40/42.09  | | | | |   (78)  a_select3(r_ds1_filter, n0, n1) = all_74_5
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (11), (76) imply:
% 248.40/42.09  | | | | |   (79)  $i(n1)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (2), (76) imply:
% 248.40/42.09  | | | | |   (80)  leq(n1, n2)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (22), (76) imply:
% 248.40/42.09  | | | | |   (81)  leq(n0, n1)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | GROUND_INST: instantiating (18) with n0, n1, all_74_5, simplifying
% 248.40/42.09  | | | | |              with (64), (66), (78), (79), (81) gives:
% 248.40/42.09  | | | | |   (82)   ~ leq(n1, all_74_20) |  ~ leq(n0, all_74_20) |
% 248.40/42.09  | | | | |         (a_select3(r_ds1_filter, n1, n0) = all_74_5 & $i(all_74_5))
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | BETA: splitting (82) gives:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | Case 1:
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | |   (83)   ~ leq(n0, all_74_20)
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | | REDUCE: (9), (83) imply:
% 248.40/42.09  | | | | | |   (84)   ~ leq(n0, n2)
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | | PRED_UNIFY: (65), (84) imply:
% 248.40/42.09  | | | | | |   (85)  $false
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | | CLOSE: (85) is inconsistent.
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | Case 2:
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | |   (86)   ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter, n1, n0) =
% 248.40/42.09  | | | | | |           all_74_5 & $i(all_74_5))
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | | BETA: splitting (86) gives:
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | | Case 1:
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | |   (87)   ~ leq(n1, all_74_20)
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | | REDUCE: (9), (87) imply:
% 248.40/42.09  | | | | | | |   (88)   ~ leq(n1, n2)
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | | PRED_UNIFY: (80), (88) imply:
% 248.40/42.09  | | | | | | |   (89)  $false
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | | CLOSE: (89) is inconsistent.
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | Case 2:
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | |   (90)  a_select3(r_ds1_filter, n1, n0) = all_74_5 & $i(all_74_5)
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | | ALPHA: (90) implies:
% 248.40/42.09  | | | | | | |   (91)  a_select3(r_ds1_filter, n1, n0) = all_74_5
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | | REF_CLOSE: (14), (23), (77), (91) are inconsistent by sub-proof
% 248.40/42.09  | | | | | | |            #43.
% 248.40/42.09  | | | | | | | 
% 248.40/42.09  | | | | | | End of split
% 248.40/42.09  | | | | | | 
% 248.40/42.09  | | | | | End of split
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | End of split
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | End of split
% 248.40/42.09  | | | 
% 248.40/42.09  | | Case 2:
% 248.40/42.09  | | | 
% 248.40/42.09  | | |   (92)  all_74_6 = n2
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (62), (92) imply:
% 248.40/42.09  | | |   (93)  a_select3(r_ds1_filter, n2, n0) = all_74_4
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (63), (92) imply:
% 248.40/42.09  | | |   (94)  a_select3(r_ds1_filter, n0, n2) = all_74_5
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (2), (92) imply:
% 248.40/42.09  | | |   (95)  leq(n2, n2)
% 248.40/42.09  | | | 
% 248.40/42.09  | | | GROUND_INST: instantiating (18) with n0, n2, all_74_5, simplifying with
% 248.40/42.09  | | |              (17), (64), (65), (66), (94) gives:
% 248.40/42.09  | | |   (96)   ~ leq(n2, all_74_20) |  ~ leq(n0, all_74_20) |
% 248.40/42.09  | | |         (a_select3(r_ds1_filter, n2, n0) = all_74_5 & $i(all_74_5))
% 248.40/42.09  | | | 
% 248.40/42.09  | | | BETA: splitting (96) gives:
% 248.40/42.09  | | | 
% 248.40/42.09  | | | Case 1:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (97)   ~ leq(n0, all_74_20)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (9), (97) imply:
% 248.40/42.09  | | | |   (98)   ~ leq(n0, n2)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | PRED_UNIFY: (65), (98) imply:
% 248.40/42.09  | | | |   (99)  $false
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | CLOSE: (99) is inconsistent.
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | Case 2:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (100)   ~ leq(n2, all_74_20) | (a_select3(r_ds1_filter, n2, n0) =
% 248.40/42.09  | | | |            all_74_5 & $i(all_74_5))
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | BETA: splitting (100) gives:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | Case 1:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (101)   ~ leq(n2, all_74_20)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REDUCE: (9), (101) imply:
% 248.40/42.09  | | | | |   (102)   ~ leq(n2, n2)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | PRED_UNIFY: (95), (102) imply:
% 248.40/42.09  | | | | |   (103)  $false
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | CLOSE: (103) is inconsistent.
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | Case 2:
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | |   (104)  a_select3(r_ds1_filter, n2, n0) = all_74_5 & $i(all_74_5)
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | ALPHA: (104) implies:
% 248.40/42.09  | | | | |   (105)  a_select3(r_ds1_filter, n2, n0) = all_74_5
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | | REF_CLOSE: (14), (23), (93), (105) are inconsistent by sub-proof #42.
% 248.40/42.09  | | | | | 
% 248.40/42.09  | | | | End of split
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | End of split
% 248.40/42.09  | | | 
% 248.40/42.09  | | End of split
% 248.40/42.09  | | 
% 248.40/42.09  | End of split
% 248.40/42.09  | 
% 248.40/42.09  End of proof
% 248.40/42.09  
% 248.40/42.09  Sub-proof #42 shows that the following formulas are inconsistent:
% 248.40/42.09  ----------------------------------------------------------------
% 248.40/42.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.09           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.09             v0))
% 248.40/42.09    (2)  a_select3(r_ds1_filter, n2, n0) = all_74_4
% 248.40/42.09    (3)  a_select3(r_ds1_filter, n2, n0) = all_74_5
% 248.40/42.09    (4)   ~ (all_74_4 = all_74_5)
% 248.40/42.09  
% 248.40/42.09  Begin of proof
% 248.40/42.09  | 
% 248.40/42.09  | GROUND_INST: instantiating (1) with all_74_5, all_74_4, n0, n2, r_ds1_filter,
% 248.40/42.09  |              simplifying with (2), (3) gives:
% 248.40/42.09  |   (5)  all_74_4 = all_74_5
% 248.40/42.09  | 
% 248.40/42.09  | REDUCE: (4), (5) imply:
% 248.40/42.09  |   (6)  $false
% 248.40/42.09  | 
% 248.40/42.09  | CLOSE: (6) is inconsistent.
% 248.40/42.09  | 
% 248.40/42.09  End of proof
% 248.40/42.09  
% 248.40/42.09  Sub-proof #43 shows that the following formulas are inconsistent:
% 248.40/42.09  ----------------------------------------------------------------
% 248.40/42.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.09           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.09             v0))
% 248.40/42.09    (2)  a_select3(r_ds1_filter, n1, n0) = all_74_4
% 248.40/42.09    (3)  a_select3(r_ds1_filter, n1, n0) = all_74_5
% 248.40/42.09    (4)   ~ (all_74_4 = all_74_5)
% 248.40/42.09  
% 248.40/42.09  Begin of proof
% 248.40/42.09  | 
% 248.40/42.09  | GROUND_INST: instantiating (1) with all_74_5, all_74_4, n0, n1, r_ds1_filter,
% 248.40/42.09  |              simplifying with (2), (3) gives:
% 248.40/42.09  |   (5)  all_74_4 = all_74_5
% 248.40/42.09  | 
% 248.40/42.09  | REDUCE: (4), (5) imply:
% 248.40/42.09  |   (6)  $false
% 248.40/42.09  | 
% 248.40/42.09  | CLOSE: (6) is inconsistent.
% 248.40/42.09  | 
% 248.40/42.09  End of proof
% 248.40/42.09  
% 248.40/42.09  Sub-proof #44 shows that the following formulas are inconsistent:
% 248.40/42.09  ----------------------------------------------------------------
% 248.40/42.09    (1)  all_74_6 = n2
% 248.40/42.09    (2)  a_select3(r_ds1_filter, all_74_6, n2) = all_74_4
% 248.40/42.09    (3)   ~ (all_74_4 = all_74_5)
% 248.40/42.09    (4)  a_select3(r_ds1_filter, n2, all_74_6) = all_74_5
% 248.40/42.09    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.09           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.09             v0))
% 248.40/42.09  
% 248.40/42.09  Begin of proof
% 248.40/42.09  | 
% 248.40/42.09  | REDUCE: (1), (2) imply:
% 248.40/42.09  |   (6)  a_select3(r_ds1_filter, n2, n2) = all_74_4
% 248.40/42.09  | 
% 248.40/42.09  | REDUCE: (1), (4) imply:
% 248.40/42.09  |   (7)  a_select3(r_ds1_filter, n2, n2) = all_74_5
% 248.40/42.09  | 
% 248.40/42.09  | GROUND_INST: instantiating (5) with all_74_5, all_74_4, n2, n2, r_ds1_filter,
% 248.40/42.09  |              simplifying with (6), (7) gives:
% 248.40/42.09  |   (8)  all_74_4 = all_74_5
% 248.40/42.09  | 
% 248.40/42.09  | REDUCE: (3), (8) imply:
% 248.40/42.09  |   (9)  $false
% 248.40/42.09  | 
% 248.40/42.09  | CLOSE: (9) is inconsistent.
% 248.40/42.09  | 
% 248.40/42.09  End of proof
% 248.40/42.09  
% 248.40/42.09  Sub-proof #45 shows that the following formulas are inconsistent:
% 248.40/42.09  ----------------------------------------------------------------
% 248.40/42.09    (1)   ~ (all_74_6 = n0)
% 248.40/42.09    (2)  leq(all_74_6, n2)
% 248.40/42.09    (3)  all_74_6 = n1 | all_74_6 = n0
% 248.40/42.09    (4)  leq(n2, n2)
% 248.40/42.09    (5)  all_74_20 = n2
% 248.40/42.09    (6)  $i(all_74_6)
% 248.40/42.09    (7)  leq(n0, n2)
% 248.40/42.09    (8)  a_select3(r_ds1_filter, all_74_6, n2) = all_74_4
% 248.40/42.09    (9)   ~ (all_74_4 = all_74_5)
% 248.40/42.09    (10)  $i(n2)
% 248.40/42.09    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 248.40/42.09                v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_20) |  ~
% 248.40/42.09            leq(v0, all_74_20) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 248.40/42.09            (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.09    (12)  a_select3(r_ds1_filter, n2, all_74_6) = all_74_5
% 248.40/42.09    (13)  leq(n0, all_74_6)
% 248.40/42.09    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.09          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.09              v0))
% 248.40/42.09  
% 248.40/42.09  Begin of proof
% 248.40/42.09  | 
% 248.40/42.09  | BETA: splitting (3) gives:
% 248.40/42.09  | 
% 248.40/42.09  | Case 1:
% 248.40/42.09  | | 
% 248.40/42.09  | |   (15)  all_74_6 = n0
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (1), (15) imply:
% 248.40/42.09  | |   (16)  $false
% 248.40/42.09  | | 
% 248.40/42.09  | | CLOSE: (16) is inconsistent.
% 248.40/42.09  | | 
% 248.40/42.09  | Case 2:
% 248.40/42.09  | | 
% 248.40/42.09  | |   (17)  all_74_6 = n1
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (8), (17) imply:
% 248.40/42.09  | |   (18)  a_select3(r_ds1_filter, n1, n2) = all_74_4
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (12), (17) imply:
% 248.40/42.09  | |   (19)  a_select3(r_ds1_filter, n2, n1) = all_74_5
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (6), (17) imply:
% 248.40/42.09  | |   (20)  $i(n1)
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (2), (17) imply:
% 248.40/42.09  | |   (21)  leq(n1, n2)
% 248.40/42.09  | | 
% 248.40/42.09  | | REDUCE: (13), (17) imply:
% 248.40/42.09  | |   (22)  leq(n0, n1)
% 248.40/42.09  | | 
% 248.40/42.09  | | GROUND_INST: instantiating (11) with n1, n2, all_74_4, simplifying with (7),
% 248.40/42.09  | |              (10), (18), (20), (22) gives:
% 248.40/42.09  | |   (23)   ~ leq(n2, all_74_20) |  ~ leq(n1, all_74_20) |
% 248.40/42.09  | |         (a_select3(r_ds1_filter, n2, n1) = all_74_4 & $i(all_74_4))
% 248.40/42.09  | | 
% 248.40/42.09  | | BETA: splitting (23) gives:
% 248.40/42.09  | | 
% 248.40/42.09  | | Case 1:
% 248.40/42.09  | | | 
% 248.40/42.09  | | |   (24)   ~ leq(n2, all_74_20)
% 248.40/42.09  | | | 
% 248.40/42.09  | | | REDUCE: (5), (24) imply:
% 248.40/42.09  | | |   (25)   ~ leq(n2, n2)
% 248.40/42.09  | | | 
% 248.40/42.09  | | | PRED_UNIFY: (4), (25) imply:
% 248.40/42.09  | | |   (26)  $false
% 248.40/42.09  | | | 
% 248.40/42.09  | | | CLOSE: (26) is inconsistent.
% 248.40/42.09  | | | 
% 248.40/42.09  | | Case 2:
% 248.40/42.09  | | | 
% 248.40/42.09  | | |   (27)   ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter, n2, n1) =
% 248.40/42.09  | | |           all_74_4 & $i(all_74_4))
% 248.40/42.09  | | | 
% 248.40/42.09  | | | BETA: splitting (27) gives:
% 248.40/42.09  | | | 
% 248.40/42.09  | | | Case 1:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (28)   ~ leq(n1, all_74_20)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (5), (28) imply:
% 248.40/42.09  | | | |   (29)   ~ leq(n1, n2)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | PRED_UNIFY: (21), (29) imply:
% 248.40/42.09  | | | |   (30)  $false
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | CLOSE: (30) is inconsistent.
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | Case 2:
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | |   (31)  a_select3(r_ds1_filter, n2, n1) = all_74_4 & $i(all_74_4)
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | ALPHA: (31) implies:
% 248.40/42.09  | | | |   (32)  a_select3(r_ds1_filter, n2, n1) = all_74_4
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | GROUND_INST: instantiating (14) with all_74_5, all_74_4, n1, n2,
% 248.40/42.09  | | | |              r_ds1_filter, simplifying with (19), (32) gives:
% 248.40/42.09  | | | |   (33)  all_74_4 = all_74_5
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | REDUCE: (9), (33) imply:
% 248.40/42.09  | | | |   (34)  $false
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | | CLOSE: (34) is inconsistent.
% 248.40/42.09  | | | | 
% 248.40/42.09  | | | End of split
% 248.40/42.09  | | | 
% 248.40/42.09  | | End of split
% 248.40/42.09  | | 
% 248.40/42.09  | End of split
% 248.40/42.09  | 
% 248.40/42.09  End of proof
% 248.40/42.09  
% 248.40/42.09  Sub-proof #46 shows that the following formulas are inconsistent:
% 248.40/42.09  ----------------------------------------------------------------
% 248.40/42.09    (1)  a_select3(r_ds1_filter, n2, all_74_7) = all_74_4
% 248.40/42.09    (2)  leq(all_74_7, n1)
% 248.40/42.09    (3)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.09           leq(n0, v0))
% 248.40/42.09    (4)  leq(n0, all_74_7)
% 248.40/42.09    (5)  leq(n2, n2)
% 248.40/42.09    (6)  $i(all_74_7)
% 248.40/42.09    (7)  all_74_20 = n2
% 248.40/42.09    (8)  leq(n0, n2)
% 248.40/42.09    (9)   ~ (all_74_4 = all_74_5)
% 248.40/42.09    (10)  $i(n2)
% 248.40/42.09    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (a_select3(r_ds1_filter,
% 248.40/42.09                v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ leq(v1, all_74_20) |  ~
% 248.40/42.09            leq(v0, all_74_20) |  ~ leq(n0, v1) |  ~ leq(n0, v0) |
% 248.40/42.09            (a_select3(r_ds1_filter, v1, v0) = v2 & $i(v2)))
% 248.40/42.09    (12)  leq(all_74_7, n2)
% 248.40/42.09    (13)  a_select3(r_ds1_filter, all_74_7, n2) = all_74_5
% 248.40/42.09    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.09          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.09              v0))
% 248.40/42.10    (15)   ~ (all_74_7 = n0)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (3) with all_74_7, simplifying with (2), (4), (6)
% 248.40/42.10  |              gives:
% 248.40/42.10  |   (16)  all_74_7 = n1 | all_74_7 = n0
% 248.40/42.10  | 
% 248.40/42.10  | BETA: splitting (16) gives:
% 248.40/42.10  | 
% 248.40/42.10  | Case 1:
% 248.40/42.10  | | 
% 248.40/42.10  | |   (17)  all_74_7 = n0
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (15), (17) imply:
% 248.40/42.10  | |   (18)  $false
% 248.40/42.10  | | 
% 248.40/42.10  | | CLOSE: (18) is inconsistent.
% 248.40/42.10  | | 
% 248.40/42.10  | Case 2:
% 248.40/42.10  | | 
% 248.40/42.10  | |   (19)  all_74_7 = n1
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (13), (19) imply:
% 248.40/42.10  | |   (20)  a_select3(r_ds1_filter, n1, n2) = all_74_5
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (1), (19) imply:
% 248.40/42.10  | |   (21)  a_select3(r_ds1_filter, n2, n1) = all_74_4
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (6), (19) imply:
% 248.40/42.10  | |   (22)  $i(n1)
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (12), (19) imply:
% 248.40/42.10  | |   (23)  leq(n1, n2)
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (4), (19) imply:
% 248.40/42.10  | |   (24)  leq(n0, n1)
% 248.40/42.10  | | 
% 248.40/42.10  | | GROUND_INST: instantiating (11) with n1, n2, all_74_5, simplifying with (8),
% 248.40/42.10  | |              (10), (20), (22), (24) gives:
% 248.40/42.10  | |   (25)   ~ leq(n2, all_74_20) |  ~ leq(n1, all_74_20) |
% 248.40/42.10  | |         (a_select3(r_ds1_filter, n2, n1) = all_74_5 & $i(all_74_5))
% 248.40/42.10  | | 
% 248.40/42.10  | | BETA: splitting (25) gives:
% 248.40/42.10  | | 
% 248.40/42.10  | | Case 1:
% 248.40/42.10  | | | 
% 248.40/42.10  | | |   (26)   ~ leq(n2, all_74_20)
% 248.40/42.10  | | | 
% 248.40/42.10  | | | REDUCE: (7), (26) imply:
% 248.40/42.10  | | |   (27)   ~ leq(n2, n2)
% 248.40/42.10  | | | 
% 248.40/42.10  | | | PRED_UNIFY: (5), (27) imply:
% 248.40/42.10  | | |   (28)  $false
% 248.40/42.10  | | | 
% 248.40/42.10  | | | CLOSE: (28) is inconsistent.
% 248.40/42.10  | | | 
% 248.40/42.10  | | Case 2:
% 248.40/42.10  | | | 
% 248.40/42.10  | | |   (29)   ~ leq(n1, all_74_20) | (a_select3(r_ds1_filter, n2, n1) =
% 248.40/42.10  | | |           all_74_5 & $i(all_74_5))
% 248.40/42.10  | | | 
% 248.40/42.10  | | | BETA: splitting (29) gives:
% 248.40/42.10  | | | 
% 248.40/42.10  | | | Case 1:
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | |   (30)   ~ leq(n1, all_74_20)
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | | REDUCE: (7), (30) imply:
% 248.40/42.10  | | | |   (31)   ~ leq(n1, n2)
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | | PRED_UNIFY: (23), (31) imply:
% 248.40/42.10  | | | |   (32)  $false
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | | CLOSE: (32) is inconsistent.
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | Case 2:
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | |   (33)  a_select3(r_ds1_filter, n2, n1) = all_74_5 & $i(all_74_5)
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | | ALPHA: (33) implies:
% 248.40/42.10  | | | |   (34)  a_select3(r_ds1_filter, n2, n1) = all_74_5
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | | GROUND_INST: instantiating (14) with all_74_5, all_74_4, n1, n2,
% 248.40/42.10  | | | |              r_ds1_filter, simplifying with (21), (34) gives:
% 248.40/42.10  | | | |   (35)  all_74_4 = all_74_5
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | | REDUCE: (9), (35) imply:
% 248.40/42.10  | | | |   (36)  $false
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | | CLOSE: (36) is inconsistent.
% 248.40/42.10  | | | | 
% 248.40/42.10  | | | End of split
% 248.40/42.10  | | | 
% 248.40/42.10  | | End of split
% 248.40/42.10  | | 
% 248.40/42.10  | End of split
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #47 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ~ (all_74_6 = n0)
% 248.40/42.10    (2)  leq(all_74_7, n1)
% 248.40/42.10    (3)   ! [v0: $i] : (v0 = n1 | v0 = n0 |  ~ $i(v0) |  ~ leq(v0, n1) |  ~
% 248.40/42.10           leq(n0, v0))
% 248.40/42.10    (4)  leq(n0, all_74_7)
% 248.40/42.10    (5)  $i(all_74_7)
% 248.40/42.10    (6)  a_select3(r_ds1_filter, all_74_7, all_74_6) = all_74_5
% 248.40/42.10    (7)  $i(all_74_6)
% 248.40/42.10    (8)   ~ (all_74_4 = all_74_5)
% 248.40/42.10    (9)  a_select3(r_ds1_filter, all_74_6, all_74_7) = all_74_4
% 248.40/42.10    (10)  leq(n0, all_74_6)
% 248.40/42.10    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] :
% 248.40/42.10          (v1 = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10              v0))
% 248.40/42.10    (12)  leq(all_74_6, n1)
% 248.40/42.10    (13)   ~ (all_74_7 = n0)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (3) with all_74_7, simplifying with (2), (4), (5)
% 248.40/42.10  |              gives:
% 248.40/42.10  |   (14)  all_74_7 = n1 | all_74_7 = n0
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (3) with all_74_6, simplifying with (7), (10), (12)
% 248.40/42.10  |              gives:
% 248.40/42.10  |   (15)  all_74_6 = n1 | all_74_6 = n0
% 248.40/42.10  | 
% 248.40/42.10  | BETA: splitting (15) gives:
% 248.40/42.10  | 
% 248.40/42.10  | Case 1:
% 248.40/42.10  | | 
% 248.40/42.10  | |   (16)  all_74_6 = n0
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (1), (16) imply:
% 248.40/42.10  | |   (17)  $false
% 248.40/42.10  | | 
% 248.40/42.10  | | CLOSE: (17) is inconsistent.
% 248.40/42.10  | | 
% 248.40/42.10  | Case 2:
% 248.40/42.10  | | 
% 248.40/42.10  | |   (18)  all_74_6 = n1
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (9), (18) imply:
% 248.40/42.10  | |   (19)  a_select3(r_ds1_filter, n1, all_74_7) = all_74_4
% 248.40/42.10  | | 
% 248.40/42.10  | | REDUCE: (6), (18) imply:
% 248.40/42.10  | |   (20)  a_select3(r_ds1_filter, all_74_7, n1) = all_74_5
% 248.40/42.10  | | 
% 248.40/42.10  | | BETA: splitting (14) gives:
% 248.40/42.10  | | 
% 248.40/42.10  | | Case 1:
% 248.40/42.10  | | | 
% 248.40/42.10  | | |   (21)  all_74_7 = n0
% 248.40/42.10  | | | 
% 248.40/42.10  | | | REDUCE: (13), (21) imply:
% 248.40/42.10  | | |   (22)  $false
% 248.40/42.10  | | | 
% 248.40/42.10  | | | CLOSE: (22) is inconsistent.
% 248.40/42.10  | | | 
% 248.40/42.10  | | Case 2:
% 248.40/42.10  | | | 
% 248.40/42.10  | | |   (23)  all_74_7 = n1
% 248.40/42.10  | | | 
% 248.40/42.10  | | | REDUCE: (20), (23) imply:
% 248.40/42.10  | | |   (24)  a_select3(r_ds1_filter, n1, n1) = all_74_5
% 248.40/42.10  | | | 
% 248.40/42.10  | | | REDUCE: (19), (23) imply:
% 248.40/42.10  | | |   (25)  a_select3(r_ds1_filter, n1, n1) = all_74_4
% 248.40/42.10  | | | 
% 248.40/42.10  | | | GROUND_INST: instantiating (11) with all_74_5, all_74_4, n1, n1,
% 248.40/42.10  | | |              r_ds1_filter, simplifying with (24), (25) gives:
% 248.40/42.10  | | |   (26)  all_74_4 = all_74_5
% 248.40/42.10  | | | 
% 248.40/42.10  | | | REDUCE: (8), (26) imply:
% 248.40/42.10  | | |   (27)  $false
% 248.40/42.10  | | | 
% 248.40/42.10  | | | CLOSE: (27) is inconsistent.
% 248.40/42.10  | | | 
% 248.40/42.10  | | End of split
% 248.40/42.10  | | 
% 248.40/42.10  | End of split
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #48 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)  $i(all_74_7)
% 248.40/42.10    (2)  all_74_7 = n0
% 248.40/42.10    (3)  gt(all_74_7, n0)
% 248.40/42.10    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (1), (2) imply:
% 248.40/42.10  |   (5)  $i(n0)
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (2), (3) imply:
% 248.40/42.10  |   (6)  gt(n0, n0)
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.40/42.10  |   (7)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (7) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #49 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)  $i(all_74_6)
% 248.40/42.10    (2)  all_74_6 = n0
% 248.40/42.10    (3)  gt(all_74_6, n0)
% 248.40/42.10    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (1), (2) imply:
% 248.40/42.10  |   (5)  $i(n0)
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (2), (3) imply:
% 248.40/42.10  |   (6)  gt(n0, n0)
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.40/42.10  |   (7)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (7) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #50 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n5, n0) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n5, n0) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n0, n5, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #51 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n4, n0) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n4, n0) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n0, n4, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #52 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n1, n0) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n1, n0) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n0, n1, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #53 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n5, n4) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n5, n4) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n4, n5, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #54 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n5, n3) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n5, n3) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n3, n5, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #55 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n4, n3) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n4, n3) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n3, n4, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #56 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n4, n2) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n4, n2) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_0, all_74_1, n2, n4, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #57 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1
% 248.40/42.10           = v0 |  ~ (a_select3(v4, v3, v2) = v1) |  ~ (a_select3(v4, v3, v2) =
% 248.40/42.10             v0))
% 248.40/42.10    (2)  a_select3(q_ds1_filter, n3, n1) = all_74_0
% 248.40/42.10    (3)  a_select3(q_ds1_filter, n3, n1) = all_74_1
% 248.40/42.10    (4)   ~ (all_74_0 = all_74_1)
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (1) with all_74_1, all_74_0, n1, n3, q_ds1_filter,
% 248.40/42.10  |              simplifying with (2), (3) gives:
% 248.40/42.10  |   (5)  all_74_0 = all_74_1
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (4), (5) imply:
% 248.40/42.10  |   (6)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (6) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #58 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)  $i(all_74_3)
% 248.40/42.10    (2)  all_74_3 = n0
% 248.40/42.10    (3)  gt(all_74_3, n0)
% 248.40/42.10    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (1), (2) imply:
% 248.40/42.10  |   (5)  $i(n0)
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (2), (3) imply:
% 248.40/42.10  |   (6)  gt(n0, n0)
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.40/42.10  |   (7)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (7) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  
% 248.40/42.10  Sub-proof #59 shows that the following formulas are inconsistent:
% 248.40/42.10  ----------------------------------------------------------------
% 248.40/42.10    (1)  $i(all_74_2)
% 248.40/42.10    (2)  all_74_2 = n0
% 248.40/42.10    (3)  gt(all_74_2, n0)
% 248.40/42.10    (4)   ! [v0: $i] : ( ~ $i(v0) |  ~ gt(v0, v0))
% 248.40/42.10  
% 248.40/42.10  Begin of proof
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (1), (2) imply:
% 248.40/42.10  |   (5)  $i(n0)
% 248.40/42.10  | 
% 248.40/42.10  | REDUCE: (2), (3) imply:
% 248.40/42.10  |   (6)  gt(n0, n0)
% 248.40/42.10  | 
% 248.40/42.10  | GROUND_INST: instantiating (4) with n0, simplifying with (5), (6) gives:
% 248.40/42.10  |   (7)  $false
% 248.40/42.10  | 
% 248.40/42.10  | CLOSE: (7) is inconsistent.
% 248.40/42.10  | 
% 248.40/42.10  End of proof
% 248.40/42.10  % SZS output end Proof for theBenchmark
% 248.40/42.10  
% 248.40/42.10  41542ms
%------------------------------------------------------------------------------