%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ALG063+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n006.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 : Wed Aug 30 16:36:07 EDT 2023

% Result   : Theorem 11.02s 2.20s
% Output   : Proof 17.98s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG063+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Aug 28 02:54:36 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.22/0.61  ________       _____
% 0.22/0.61  ___  __ \_________(_)________________________________
% 0.22/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.22/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.22/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61  
% 0.22/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61  (2023-06-19)
% 0.22/0.61  
% 0.22/0.61  (c) Philipp Rümmer, 2009-2023
% 0.22/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61                Amanda Stjerna.
% 0.22/0.61  Free software under BSD-3-Clause.
% 0.22/0.61  
% 0.22/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61  
% 0.22/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.62  Running up to 7 provers in parallel.
% 0.22/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.24/1.42  Prover 4: Preprocessing ...
% 5.24/1.43  Prover 1: Preprocessing ...
% 5.24/1.49  Prover 0: Preprocessing ...
% 5.24/1.49  Prover 2: Preprocessing ...
% 5.24/1.49  Prover 3: Preprocessing ...
% 5.24/1.49  Prover 5: Preprocessing ...
% 5.24/1.49  Prover 6: Preprocessing ...
% 9.15/1.97  Prover 2: Constructing countermodel ...
% 9.15/1.97  Prover 1: Constructing countermodel ...
% 9.15/1.97  Prover 3: Constructing countermodel ...
% 9.15/1.97  Prover 4: Constructing countermodel ...
% 9.15/1.98  Prover 0: Constructing countermodel ...
% 9.75/2.01  Prover 6: Constructing countermodel ...
% 11.02/2.20  Prover 3: proved (1556ms)
% 11.02/2.20  
% 11.02/2.20  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.02/2.20  
% 11.02/2.20  Prover 2: stopped
% 11.02/2.20  Prover 0: stopped
% 11.02/2.20  Prover 6: stopped
% 11.02/2.21  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.02/2.21  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.02/2.21  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.02/2.21  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.97/2.47  Prover 8: Preprocessing ...
% 12.97/2.49  Prover 10: Preprocessing ...
% 13.65/2.53  Prover 11: Preprocessing ...
% 13.65/2.54  Prover 7: Preprocessing ...
% 13.65/2.57  Prover 5: Constructing countermodel ...
% 14.10/2.61  Prover 5: stopped
% 14.10/2.61  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.10/2.65  Prover 8: Constructing countermodel ...
% 14.95/2.72  Prover 13: Preprocessing ...
% 15.22/2.80  Prover 10: Constructing countermodel ...
% 15.22/2.81  Prover 11: Constructing countermodel ...
% 15.22/2.82  Prover 7: Constructing countermodel ...
% 15.22/2.96  Prover 13: Constructing countermodel ...
% 15.22/2.96  Prover 4: Found proof (size 650)
% 15.22/2.96  Prover 4: proved (2320ms)
% 15.22/2.96  Prover 8: stopped
% 15.22/2.96  Prover 11: stopped
% 15.22/2.96  Prover 13: stopped
% 15.22/2.96  Prover 10: stopped
% 15.22/2.96  Prover 7: stopped
% 15.22/2.97  Prover 1: Found proof (size 650)
% 15.22/2.97  Prover 1: proved (2331ms)
% 16.25/2.97  
% 16.25/2.97  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.25/2.97  
% 16.25/3.01  % SZS output start Proof for theBenchmark
% 16.25/3.01  Assumptions after simplification:
% 16.25/3.01  ---------------------------------
% 16.25/3.01  
% 16.25/3.01    (ax1)
% 17.14/3.06    $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ?
% 17.14/3.06    [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i]
% 17.14/3.06    :  ? [v8: $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ?
% 17.14/3.06    [v13: $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ?
% 17.14/3.06    [v18: $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ?
% 17.14/3.06    [v23: $i] :  ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) =
% 17.14/3.06      v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) =
% 17.14/3.06      v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) =
% 17.14/3.06      v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) =
% 17.14/3.06      v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6
% 17.14/3.06      & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 17.14/3.06      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) &
% 17.14/3.06      $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 17.14/3.06      $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 17.14/3.06      $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 |
% 17.14/3.06        v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 =
% 17.14/3.06        e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) &
% 17.14/3.06      (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 =
% 17.14/3.06        e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 |
% 17.14/3.06        v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 =
% 17.14/3.06        e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 |
% 17.14/3.06        v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 =
% 17.14/3.06        e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 |
% 17.14/3.06        v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12
% 17.14/3.06        = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 |
% 17.14/3.06        v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 =
% 17.14/3.06        e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 =
% 17.14/3.06        e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2
% 17.14/3.06        | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) &
% 17.14/3.06      (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4
% 17.14/3.06        = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 =
% 17.14/3.06        e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 =
% 17.14/3.06        e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1
% 17.14/3.06        | v0 = e0))
% 17.14/3.06  
% 17.14/3.06    (ax3)
% 17.14/3.07    $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ?
% 17.14/3.07    [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i]
% 17.14/3.07    :  ? [v8: $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ?
% 17.14/3.07    [v13: $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ?
% 17.14/3.07    [v18: $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ?
% 17.14/3.07    [v23: $i] :  ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) =
% 17.14/3.07      v20 & op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) =
% 17.14/3.07      v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2, e4) =
% 17.14/3.07      v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13 & op(e2, e0) =
% 17.14/3.07      v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) = v10 & op(e1, e1) =
% 17.14/3.07      v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 17.14/3.07      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) &
% 17.14/3.07      $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 17.14/3.07      $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 17.14/3.07      $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 |
% 17.14/3.07        v20 = e4 | v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 =
% 17.14/3.07        e4 | v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) &
% 17.14/3.07      (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 | v23 = e2
% 17.14/3.07        | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 | v18 = e2 | v12 =
% 17.14/3.07        e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 | v15 = e1 | v8 = e1) &
% 17.14/3.07      (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 | v4 = e1) & (v24 = e0 | v23 = e0
% 17.14/3.07        | v20 = e0 | v15 = e0 | v8 = e0) & (v24 = e0 | v22 = e0 | v18 = e0 | v12 =
% 17.14/3.07        e0 | v4 = e0) & (v23 = e4 | v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) &
% 17.14/3.07      (v23 = e3 | v21 = e3 | v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2
% 17.14/3.07        | v17 = e2 | v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 =
% 17.14/3.07        e1 | v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) &
% 17.14/3.07      (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 | v21 = e3
% 17.14/3.07        | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 | v19 = e2 | v14 =
% 17.14/3.07        e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 | v14 = e1 | v7 = e1) &
% 17.14/3.07      (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 | v7 = e0) & (v20 = e4 | v19 = e4
% 17.14/3.07        | v16 = e4 | v10 = e4 | v2 = e4) & (v20 = e3 | v19 = e3 | v16 = e3 | v10 =
% 17.14/3.07        e3 | v2 = e3) & (v20 = e2 | v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) &
% 17.14/3.07      (v20 = e1 | v19 = e1 | v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0
% 17.14/3.07        | v16 = e0 | v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 =
% 17.14/3.07        e4 | v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) &
% 17.14/3.07      (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 | v17 = e1
% 17.14/3.07        | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 | v16 = e0 | v13 =
% 17.14/3.07        e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 | v9 = e4 | v1 = e4) &
% 17.14/3.07      (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1 = e3) & (v15 = e2 | v14 = e2
% 17.14/3.07        | v13 = e2 | v9 = e2 | v1 = e2) & (v15 = e1 | v14 = e1 | v13 = e1 | v9 =
% 17.14/3.07        e1 | v1 = e1) & (v15 = e0 | v14 = e0 | v13 = e0 | v9 = e0 | v1 = e0) &
% 17.14/3.08      (v12 = e4 | v11 = e4 | v10 = e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3
% 17.14/3.08        | v10 = e3 | v9 = e3 | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 =
% 17.14/3.08        e2 | v5 = e2) & (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) &
% 17.14/3.08      (v12 = e0 | v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 |
% 17.14/3.08        v6 = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3 | v0
% 17.14/3.08        = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) & (v8 = e1 | v7
% 17.14/3.08        = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 = e4 | v2 = e4 | v1 =
% 17.14/3.08        e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v4 =
% 17.14/3.08        e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3 = e1 | v2 = e1
% 17.14/3.08        | v1 = e1 | v0 = e1) & (v0 = e0 | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0)
% 17.14/3.08          & (v4 = e0 | v3 = e0 | v2 = e0 | v1 = e0))))
% 17.14/3.08  
% 17.14/3.08    (ax4)
% 17.14/3.08    $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ?
% 17.14/3.08    [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i]
% 17.14/3.08    :  ? [v8: $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ?
% 17.14/3.08    [v13: $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ?
% 17.14/3.08    [v18: $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ?
% 17.14/3.08    [v23: $i] :  ? [v24: $i] : ( ~ (v24 = v23) &  ~ (v24 = v22) &  ~ (v24 = v21) &
% 17.14/3.08       ~ (v24 = v20) &  ~ (v24 = v19) &  ~ (v24 = v14) &  ~ (v24 = v9) &  ~ (v24 =
% 17.14/3.08        v4) &  ~ (v23 = v22) &  ~ (v23 = v21) &  ~ (v23 = v20) &  ~ (v23 = v18) & 
% 17.14/3.08      ~ (v23 = v13) &  ~ (v23 = v8) &  ~ (v23 = v3) &  ~ (v22 = v21) &  ~ (v22 =
% 17.14/3.08        v20) &  ~ (v22 = v17) &  ~ (v22 = v12) &  ~ (v22 = v7) &  ~ (v22 = v2) & 
% 17.14/3.08      ~ (v21 = v20) &  ~ (v21 = v16) &  ~ (v21 = v11) &  ~ (v21 = v6) &  ~ (v21 =
% 17.14/3.08        v1) &  ~ (v20 = v15) &  ~ (v20 = v10) &  ~ (v20 = v5) &  ~ (v20 = v0) &  ~
% 17.14/3.08      (v19 = v18) &  ~ (v19 = v17) &  ~ (v19 = v16) &  ~ (v19 = v15) &  ~ (v19 =
% 17.14/3.08        v14) &  ~ (v19 = v9) &  ~ (v19 = v4) &  ~ (v18 = v17) &  ~ (v18 = v16) & 
% 17.14/3.08      ~ (v18 = v15) &  ~ (v18 = v13) &  ~ (v18 = v8) &  ~ (v18 = v3) &  ~ (v17 =
% 17.14/3.08        v16) &  ~ (v17 = v15) &  ~ (v17 = v12) &  ~ (v17 = v7) &  ~ (v17 = v2) & 
% 17.14/3.08      ~ (v16 = v15) &  ~ (v16 = v11) &  ~ (v16 = v6) &  ~ (v16 = v1) &  ~ (v15 =
% 17.14/3.08        v10) &  ~ (v15 = v5) &  ~ (v15 = v0) &  ~ (v14 = v13) &  ~ (v14 = v12) & 
% 17.14/3.08      ~ (v14 = v11) &  ~ (v14 = v10) &  ~ (v14 = v9) &  ~ (v14 = v4) &  ~ (v13 =
% 17.14/3.08        v12) &  ~ (v13 = v11) &  ~ (v13 = v10) &  ~ (v13 = v8) &  ~ (v13 = v3) & 
% 17.14/3.08      ~ (v12 = v11) &  ~ (v12 = v10) &  ~ (v12 = v7) &  ~ (v12 = v2) &  ~ (v11 =
% 17.14/3.08        v10) &  ~ (v11 = v6) &  ~ (v11 = v1) &  ~ (v10 = v5) &  ~ (v10 = v0) &  ~
% 17.14/3.08      (v9 = v8) &  ~ (v9 = v7) &  ~ (v9 = v6) &  ~ (v9 = v5) &  ~ (v9 = v4) &  ~
% 17.14/3.08      (v8 = v7) &  ~ (v8 = v6) &  ~ (v8 = v5) &  ~ (v8 = v3) &  ~ (v7 = v6) &  ~
% 17.14/3.08      (v7 = v5) &  ~ (v7 = v2) &  ~ (v6 = v5) &  ~ (v6 = v1) &  ~ (v5 = v0) &  ~
% 17.14/3.08      (v4 = v3) &  ~ (v4 = v2) &  ~ (v4 = v1) &  ~ (v4 = v0) &  ~ (v3 = v2) &  ~
% 17.14/3.08      (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 = v0) &  ~ (v1 = v0) &
% 17.14/3.08      op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 &
% 17.14/3.08      op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 &
% 17.14/3.08      op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 &
% 17.14/3.08      op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 &
% 17.14/3.08      op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 &
% 17.14/3.08      op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 &
% 17.14/3.08      op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19)
% 17.14/3.08      & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 17.14/3.08      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 17.14/3.08      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.14/3.08  
% 17.14/3.08    (ax5)
% 17.14/3.08     ~ (e4 = e3) &  ~ (e4 = e2) &  ~ (e4 = e1) &  ~ (e4 = e0) &  ~ (e3 = e2) &  ~
% 17.14/3.08    (e3 = e1) &  ~ (e3 = e0) &  ~ (e2 = e1) &  ~ (e2 = e0) &  ~ (e1 = e0) & $i(e4)
% 17.14/3.08    & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 17.14/3.08  
% 17.14/3.08    (ax6)
% 17.14/3.08    op(e4, e4) = e2 & op(e2, e2) = e3 & op(e1, e2) = e0 & op(e1, e1) = e4 & $i(e4)
% 17.14/3.08    & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 17.14/3.08  
% 17.14/3.08    (co1)
% 17.45/3.09    $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ?
% 17.45/3.09    [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i]
% 17.45/3.09    :  ? [v8: $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ?
% 17.45/3.09    [v13: $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ?
% 17.45/3.09    [v18: $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ?
% 17.45/3.09    [v23: $i] :  ? [v24: $i] : (op(e4, e4) = v4 & op(e4, e3) = v24 & op(e4, e2) =
% 17.45/3.09      v23 & op(e4, e1) = v22 & op(e4, e0) = v21 & op(e3, e4) = v20 & op(e3, e3) =
% 17.45/3.09      v3 & op(e3, e2) = v19 & op(e3, e1) = v18 & op(e3, e0) = v17 & op(e2, e4) =
% 17.45/3.09      v16 & op(e2, e3) = v15 & op(e2, e2) = v2 & op(e2, e1) = v14 & op(e2, e0) =
% 17.45/3.09      v13 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2) = v10 & op(e1, e1) =
% 17.45/3.09      v1 & op(e1, e0) = v9 & op(e0, e4) = v8 & op(e0, e3) = v7 & op(e0, e2) = v6 &
% 17.45/3.09      op(e0, e1) = v5 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) &
% 17.45/3.09      $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 17.45/3.09      $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 17.45/3.09      $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v4 = e4 | v3 = e4 |
% 17.45/3.09        v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 | v1 = e3 | v0
% 17.45/3.09        = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v4 = e1 | v3
% 17.45/3.09        = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v4 = e0 | v3 = e0 | v2 = e0 | v1 =
% 17.45/3.09        e0 | v0 = e0) & ((v4 = e3 & v3 = e4 &  ~ (v24 = e4)) | (v4 = e3 & v3 = e4
% 17.45/3.09          &  ~ (v20 = e3)) | (v4 = e2 & v2 = e4 &  ~ (v23 = e4)) | (v4 = e2 & v2 =
% 17.45/3.09          e4 &  ~ (v16 = e2)) | (v4 = e1 & v1 = e4 &  ~ (v22 = e4)) | (v4 = e1 &
% 17.45/3.09          v1 = e4 &  ~ (v12 = e1)) | (v4 = e0 & v0 = e4 &  ~ (v21 = e4)) | (v4 =
% 17.45/3.09          e0 & v0 = e4 &  ~ (v8 = e0)) | (v3 = e2 & v2 = e3 &  ~ (v19 = e3)) | (v3
% 17.45/3.09          = e2 & v2 = e3 &  ~ (v15 = e2)) | (v3 = e1 & v1 = e3 &  ~ (v18 = e3)) |
% 17.45/3.09        (v3 = e1 & v1 = e3 &  ~ (v11 = e1)) | (v3 = e0 & v0 = e3 &  ~ (v17 = e3))
% 17.45/3.09        | (v3 = e0 & v0 = e3 &  ~ (v7 = e0)) | (v2 = e1 & v1 = e2 &  ~ (v14 = e2))
% 17.45/3.09        | (v2 = e1 & v1 = e2 &  ~ (v10 = e1)) | (v2 = e0 & v0 = e2 &  ~ (v13 =
% 17.45/3.09            e2)) | (v2 = e0 & v0 = e2 &  ~ (v6 = e0)) | (v1 = e0 & v0 = e1 &  ~
% 17.45/3.09          (v9 = e1)) | (v1 = e0 & v0 = e1 &  ~ (v5 = e0))))
% 17.45/3.09  
% 17.45/3.09    (function-axioms)
% 17.45/3.09     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (op(v3,
% 17.45/3.09          v2) = v1) |  ~ (op(v3, v2) = v0))
% 17.45/3.09  
% 17.45/3.09  Further assumptions not needed in the proof:
% 17.45/3.09  --------------------------------------------
% 17.45/3.09  ax2
% 17.45/3.09  
% 17.45/3.09  Those formulas are unsatisfiable:
% 17.45/3.09  ---------------------------------
% 17.45/3.09  
% 17.45/3.09  Begin of proof
% 17.45/3.09  | 
% 17.45/3.09  | ALPHA: (ax1) implies:
% 17.45/3.10  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 17.45/3.10  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 17.45/3.10  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 17.45/3.10  |         ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ? [v19:
% 17.45/3.10  |          $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i] :  ?
% 17.45/3.10  |        [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 &
% 17.45/3.10  |          op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) =
% 17.45/3.10  |          v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2,
% 17.45/3.10  |            e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11
% 17.45/3.10  |          & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) =
% 17.45/3.10  |          v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3)
% 17.45/3.10  |          = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24)
% 17.45/3.10  |          & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17)
% 17.45/3.10  |          & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10)
% 17.45/3.10  |          & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 17.45/3.10  |          $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1
% 17.45/3.10  |            | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 =
% 17.45/3.10  |            e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21
% 17.45/3.10  |            = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20
% 17.45/3.10  |            = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19
% 17.45/3.10  |            = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18
% 17.45/3.10  |            = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17
% 17.45/3.10  |            = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) &
% 17.45/3.10  |          (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 |
% 17.45/3.10  |            v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 |
% 17.45/3.10  |            v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 |
% 17.45/3.10  |            v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 |
% 17.45/3.10  |            v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0)
% 17.45/3.10  |          & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 =
% 17.45/3.10  |            e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 |
% 17.45/3.10  |            v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 =
% 17.45/3.10  |            e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4
% 17.45/3.10  |            | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3
% 17.45/3.10  |            = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1
% 17.45/3.10  |            | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) &
% 17.45/3.10  |          (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 17.45/3.10  | 
% 17.45/3.10  | ALPHA: (ax3) implies:
% 17.45/3.11  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 17.45/3.11  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 17.45/3.11  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 17.45/3.11  |         ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ? [v19:
% 17.45/3.11  |          $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i] :  ?
% 17.45/3.11  |        [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v20 &
% 17.45/3.11  |          op(e4, e1) = v15 & op(e4, e0) = v8 & op(e3, e4) = v22 & op(e3, e3) =
% 17.45/3.11  |          v21 & op(e3, e2) = v19 & op(e3, e1) = v14 & op(e3, e0) = v7 & op(e2,
% 17.45/3.11  |            e4) = v18 & op(e2, e3) = v17 & op(e2, e2) = v16 & op(e2, e1) = v13
% 17.45/3.11  |          & op(e2, e0) = v6 & op(e1, e4) = v12 & op(e1, e3) = v11 & op(e1, e2)
% 17.45/3.11  |          = v10 & op(e1, e1) = v9 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0,
% 17.45/3.11  |            e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 &
% 17.45/3.11  |          $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) &
% 17.45/3.11  |          $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) &
% 17.45/3.11  |          $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 17.45/3.11  |          $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v23 = e4 | v20 = e4 |
% 17.45/3.11  |            v15 = e4 | v8 = e4) & (v24 = e4 | v22 = e4 | v18 = e4 | v12 = e4 |
% 17.45/3.11  |            v4 = e4) & (v24 = e3 | v23 = e3 | v20 = e3 | v15 = e3 | v8 = e3) &
% 17.45/3.11  |          (v24 = e3 | v22 = e3 | v18 = e3 | v12 = e3 | v4 = e3) & (v24 = e2 |
% 17.45/3.11  |            v23 = e2 | v20 = e2 | v15 = e2 | v8 = e2) & (v24 = e2 | v22 = e2 |
% 17.45/3.11  |            v18 = e2 | v12 = e2 | v4 = e2) & (v24 = e1 | v23 = e1 | v20 = e1 |
% 17.45/3.11  |            v15 = e1 | v8 = e1) & (v24 = e1 | v22 = e1 | v18 = e1 | v12 = e1 |
% 17.45/3.11  |            v4 = e1) & (v24 = e0 | v23 = e0 | v20 = e0 | v15 = e0 | v8 = e0) &
% 17.45/3.11  |          (v24 = e0 | v22 = e0 | v18 = e0 | v12 = e0 | v4 = e0) & (v23 = e4 |
% 17.45/3.11  |            v21 = e4 | v17 = e4 | v11 = e4 | v3 = e4) & (v23 = e3 | v21 = e3 |
% 17.45/3.11  |            v17 = e3 | v11 = e3 | v3 = e3) & (v23 = e2 | v21 = e2 | v17 = e2 |
% 17.45/3.11  |            v11 = e2 | v3 = e2) & (v23 = e1 | v21 = e1 | v17 = e1 | v11 = e1 |
% 17.45/3.11  |            v3 = e1) & (v23 = e0 | v21 = e0 | v17 = e0 | v11 = e0 | v3 = e0) &
% 17.45/3.11  |          (v22 = e4 | v21 = e4 | v19 = e4 | v14 = e4 | v7 = e4) & (v22 = e3 |
% 17.45/3.11  |            v21 = e3 | v19 = e3 | v14 = e3 | v7 = e3) & (v22 = e2 | v21 = e2 |
% 17.45/3.11  |            v19 = e2 | v14 = e2 | v7 = e2) & (v22 = e1 | v21 = e1 | v19 = e1 |
% 17.45/3.11  |            v14 = e1 | v7 = e1) & (v22 = e0 | v21 = e0 | v19 = e0 | v14 = e0 |
% 17.45/3.11  |            v7 = e0) & (v20 = e4 | v19 = e4 | v16 = e4 | v10 = e4 | v2 = e4) &
% 17.45/3.11  |          (v20 = e3 | v19 = e3 | v16 = e3 | v10 = e3 | v2 = e3) & (v20 = e2 |
% 17.45/3.11  |            v19 = e2 | v16 = e2 | v10 = e2 | v2 = e2) & (v20 = e1 | v19 = e1 |
% 17.45/3.11  |            v16 = e1 | v10 = e1 | v2 = e1) & (v20 = e0 | v19 = e0 | v16 = e0 |
% 17.45/3.11  |            v10 = e0 | v2 = e0) & (v18 = e4 | v17 = e4 | v16 = e4 | v13 = e4 |
% 17.45/3.11  |            v6 = e4) & (v18 = e3 | v17 = e3 | v16 = e3 | v13 = e3 | v6 = e3) &
% 17.45/3.11  |          (v18 = e2 | v17 = e2 | v16 = e2 | v13 = e2 | v6 = e2) & (v18 = e1 |
% 17.45/3.11  |            v17 = e1 | v16 = e1 | v13 = e1 | v6 = e1) & (v18 = e0 | v17 = e0 |
% 17.45/3.11  |            v16 = e0 | v13 = e0 | v6 = e0) & (v15 = e4 | v14 = e4 | v13 = e4 |
% 17.45/3.11  |            v9 = e4 | v1 = e4) & (v15 = e3 | v14 = e3 | v13 = e3 | v9 = e3 | v1
% 17.45/3.11  |            = e3) & (v15 = e2 | v14 = e2 | v13 = e2 | v9 = e2 | v1 = e2) & (v15
% 17.45/3.11  |            = e1 | v14 = e1 | v13 = e1 | v9 = e1 | v1 = e1) & (v15 = e0 | v14 =
% 17.45/3.11  |            e0 | v13 = e0 | v9 = e0 | v1 = e0) & (v12 = e4 | v11 = e4 | v10 =
% 17.45/3.11  |            e4 | v9 = e4 | v5 = e4) & (v12 = e3 | v11 = e3 | v10 = e3 | v9 = e3
% 17.45/3.11  |            | v5 = e3) & (v12 = e2 | v11 = e2 | v10 = e2 | v9 = e2 | v5 = e2) &
% 17.45/3.11  |          (v12 = e1 | v11 = e1 | v10 = e1 | v9 = e1 | v5 = e1) & (v12 = e0 |
% 17.45/3.11  |            v11 = e0 | v10 = e0 | v9 = e0 | v5 = e0) & (v8 = e4 | v7 = e4 | v6
% 17.45/3.11  |            = e4 | v5 = e4 | v0 = e4) & (v8 = e3 | v7 = e3 | v6 = e3 | v5 = e3
% 17.45/3.11  |            | v0 = e3) & (v8 = e2 | v7 = e2 | v6 = e2 | v5 = e2 | v0 = e2) &
% 17.45/3.11  |          (v8 = e1 | v7 = e1 | v6 = e1 | v5 = e1 | v0 = e1) & (v4 = e4 | v3 =
% 17.45/3.11  |            e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3 |
% 17.45/3.11  |            v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0 =
% 17.45/3.11  |            e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v0 = e0
% 17.45/3.11  |            | ((v8 = e0 | v7 = e0 | v6 = e0 | v5 = e0) & (v4 = e0 | v3 = e0 |
% 17.45/3.11  |                v2 = e0 | v1 = e0))))
% 17.45/3.11  | 
% 17.45/3.11  | ALPHA: (ax4) implies:
% 17.45/3.12  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 17.45/3.12  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 17.45/3.12  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 17.45/3.12  |         ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ? [v19:
% 17.45/3.12  |          $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i] :  ?
% 17.45/3.12  |        [v24: $i] : ( ~ (v24 = v23) &  ~ (v24 = v22) &  ~ (v24 = v21) &  ~ (v24
% 17.45/3.12  |            = v20) &  ~ (v24 = v19) &  ~ (v24 = v14) &  ~ (v24 = v9) &  ~ (v24
% 17.45/3.12  |            = v4) &  ~ (v23 = v22) &  ~ (v23 = v21) &  ~ (v23 = v20) &  ~ (v23
% 17.45/3.12  |            = v18) &  ~ (v23 = v13) &  ~ (v23 = v8) &  ~ (v23 = v3) &  ~ (v22 =
% 17.45/3.12  |            v21) &  ~ (v22 = v20) &  ~ (v22 = v17) &  ~ (v22 = v12) &  ~ (v22 =
% 17.45/3.12  |            v7) &  ~ (v22 = v2) &  ~ (v21 = v20) &  ~ (v21 = v16) &  ~ (v21 =
% 17.45/3.12  |            v11) &  ~ (v21 = v6) &  ~ (v21 = v1) &  ~ (v20 = v15) &  ~ (v20 =
% 17.45/3.12  |            v10) &  ~ (v20 = v5) &  ~ (v20 = v0) &  ~ (v19 = v18) &  ~ (v19 =
% 17.45/3.12  |            v17) &  ~ (v19 = v16) &  ~ (v19 = v15) &  ~ (v19 = v14) &  ~ (v19 =
% 17.45/3.12  |            v9) &  ~ (v19 = v4) &  ~ (v18 = v17) &  ~ (v18 = v16) &  ~ (v18 =
% 17.45/3.12  |            v15) &  ~ (v18 = v13) &  ~ (v18 = v8) &  ~ (v18 = v3) &  ~ (v17 =
% 17.45/3.12  |            v16) &  ~ (v17 = v15) &  ~ (v17 = v12) &  ~ (v17 = v7) &  ~ (v17 =
% 17.45/3.12  |            v2) &  ~ (v16 = v15) &  ~ (v16 = v11) &  ~ (v16 = v6) &  ~ (v16 =
% 17.45/3.12  |            v1) &  ~ (v15 = v10) &  ~ (v15 = v5) &  ~ (v15 = v0) &  ~ (v14 =
% 17.45/3.12  |            v13) &  ~ (v14 = v12) &  ~ (v14 = v11) &  ~ (v14 = v10) &  ~ (v14 =
% 17.45/3.12  |            v9) &  ~ (v14 = v4) &  ~ (v13 = v12) &  ~ (v13 = v11) &  ~ (v13 =
% 17.45/3.12  |            v10) &  ~ (v13 = v8) &  ~ (v13 = v3) &  ~ (v12 = v11) &  ~ (v12 =
% 17.45/3.12  |            v10) &  ~ (v12 = v7) &  ~ (v12 = v2) &  ~ (v11 = v10) &  ~ (v11 =
% 17.45/3.12  |            v6) &  ~ (v11 = v1) &  ~ (v10 = v5) &  ~ (v10 = v0) &  ~ (v9 = v8)
% 17.45/3.12  |          &  ~ (v9 = v7) &  ~ (v9 = v6) &  ~ (v9 = v5) &  ~ (v9 = v4) &  ~ (v8
% 17.45/3.12  |            = v7) &  ~ (v8 = v6) &  ~ (v8 = v5) &  ~ (v8 = v3) &  ~ (v7 = v6) &
% 17.45/3.12  |           ~ (v7 = v5) &  ~ (v7 = v2) &  ~ (v6 = v5) &  ~ (v6 = v1) &  ~ (v5 =
% 17.45/3.12  |            v0) &  ~ (v4 = v3) &  ~ (v4 = v2) &  ~ (v4 = v1) &  ~ (v4 = v0) & 
% 17.45/3.12  |          ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 =
% 17.45/3.12  |            v0) &  ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4,
% 17.45/3.12  |            e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) = v23 &
% 17.45/3.12  |          op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & op(e3, e0) =
% 17.45/3.12  |          v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = v12 & op(e2,
% 17.45/3.12  |            e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, e3) = v16 &
% 17.45/3.12  |          op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & op(e0, e4) =
% 17.45/3.12  |          v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & op(e0,
% 17.45/3.12  |            e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) &
% 17.45/3.12  |          $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) &
% 17.45/3.12  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 17.45/3.12  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.45/3.12  | 
% 17.45/3.12  | ALPHA: (ax5) implies:
% 17.45/3.12  |   (4)   ~ (e1 = e0)
% 17.45/3.12  |   (5)   ~ (e2 = e0)
% 17.45/3.12  |   (6)   ~ (e2 = e1)
% 17.45/3.12  |   (7)   ~ (e3 = e1)
% 17.45/3.12  |   (8)   ~ (e3 = e2)
% 17.45/3.12  |   (9)   ~ (e4 = e1)
% 17.45/3.12  |   (10)   ~ (e4 = e3)
% 17.45/3.12  | 
% 17.45/3.12  | ALPHA: (ax6) implies:
% 17.45/3.12  |   (11)  op(e1, e1) = e4
% 17.45/3.12  |   (12)  op(e1, e2) = e0
% 17.45/3.12  |   (13)  op(e2, e2) = e3
% 17.45/3.12  |   (14)  op(e4, e4) = e2
% 17.45/3.12  | 
% 17.45/3.12  | ALPHA: (co1) implies:
% 17.45/3.12  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 17.45/3.12  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 17.45/3.12  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 17.45/3.12  |           $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ?
% 17.45/3.12  |         [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i]
% 17.45/3.12  |         :  ? [v24: $i] : (op(e4, e4) = v4 & op(e4, e3) = v24 & op(e4, e2) =
% 17.45/3.12  |           v23 & op(e4, e1) = v22 & op(e4, e0) = v21 & op(e3, e4) = v20 &
% 17.45/3.12  |           op(e3, e3) = v3 & op(e3, e2) = v19 & op(e3, e1) = v18 & op(e3, e0) =
% 17.45/3.12  |           v17 & op(e2, e4) = v16 & op(e2, e3) = v15 & op(e2, e2) = v2 & op(e2,
% 17.45/3.12  |             e1) = v14 & op(e2, e0) = v13 & op(e1, e4) = v12 & op(e1, e3) = v11
% 17.45/3.12  |           & op(e1, e2) = v10 & op(e1, e1) = v1 & op(e1, e0) = v9 & op(e0, e4)
% 17.45/3.12  |           = v8 & op(e0, e3) = v7 & op(e0, e2) = v6 & op(e0, e1) = v5 & op(e0,
% 17.45/3.12  |             e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) &
% 17.45/3.12  |           $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13)
% 17.45/3.12  |           & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 17.45/3.12  |           $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v4 = e4 | v3
% 17.45/3.12  |             = e4 | v2 = e4 | v1 = e4 | v0 = e4) & (v4 = e3 | v3 = e3 | v2 = e3
% 17.45/3.12  |             | v1 = e3 | v0 = e3) & (v4 = e2 | v3 = e2 | v2 = e2 | v1 = e2 | v0
% 17.45/3.12  |             = e2) & (v4 = e1 | v3 = e1 | v2 = e1 | v1 = e1 | v0 = e1) & (v4 =
% 17.45/3.12  |             e0 | v3 = e0 | v2 = e0 | v1 = e0 | v0 = e0) & ((v4 = e3 & v3 = e4
% 17.45/3.12  |               &  ~ (v24 = e4)) | (v4 = e3 & v3 = e4 &  ~ (v20 = e3)) | (v4 =
% 17.45/3.12  |               e2 & v2 = e4 &  ~ (v23 = e4)) | (v4 = e2 & v2 = e4 &  ~ (v16 =
% 17.45/3.12  |                 e2)) | (v4 = e1 & v1 = e4 &  ~ (v22 = e4)) | (v4 = e1 & v1 =
% 17.45/3.12  |               e4 &  ~ (v12 = e1)) | (v4 = e0 & v0 = e4 &  ~ (v21 = e4)) | (v4
% 17.45/3.12  |               = e0 & v0 = e4 &  ~ (v8 = e0)) | (v3 = e2 & v2 = e3 &  ~ (v19 =
% 17.45/3.12  |                 e3)) | (v3 = e2 & v2 = e3 &  ~ (v15 = e2)) | (v3 = e1 & v1 =
% 17.45/3.12  |               e3 &  ~ (v18 = e3)) | (v3 = e1 & v1 = e3 &  ~ (v11 = e1)) | (v3
% 17.45/3.12  |               = e0 & v0 = e3 &  ~ (v17 = e3)) | (v3 = e0 & v0 = e3 &  ~ (v7 =
% 17.45/3.12  |                 e0)) | (v2 = e1 & v1 = e2 &  ~ (v14 = e2)) | (v2 = e1 & v1 =
% 17.45/3.12  |               e2 &  ~ (v10 = e1)) | (v2 = e0 & v0 = e2 &  ~ (v13 = e2)) | (v2
% 17.45/3.12  |               = e0 & v0 = e2 &  ~ (v6 = e0)) | (v1 = e0 & v0 = e1 &  ~ (v9 =
% 17.45/3.12  |                 e1)) | (v1 = e0 & v0 = e1 &  ~ (v5 = e0))))
% 17.45/3.13  | 
% 17.45/3.13  | DELTA: instantiating (15) with fresh symbols all_4_0, all_4_1, all_4_2,
% 17.45/3.13  |        all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9,
% 17.45/3.13  |        all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16,
% 17.45/3.13  |        all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23,
% 17.45/3.13  |        all_4_24 gives:
% 17.45/3.13  |   (16)  op(e4, e4) = all_4_20 & op(e4, e3) = all_4_0 & op(e4, e2) = all_4_1 &
% 17.45/3.13  |         op(e4, e1) = all_4_2 & op(e4, e0) = all_4_3 & op(e3, e4) = all_4_4 &
% 17.45/3.13  |         op(e3, e3) = all_4_21 & op(e3, e2) = all_4_5 & op(e3, e1) = all_4_6 &
% 17.45/3.13  |         op(e3, e0) = all_4_7 & op(e2, e4) = all_4_8 & op(e2, e3) = all_4_9 &
% 17.45/3.13  |         op(e2, e2) = all_4_22 & op(e2, e1) = all_4_10 & op(e2, e0) = all_4_11
% 17.45/3.13  |         & op(e1, e4) = all_4_12 & op(e1, e3) = all_4_13 & op(e1, e2) =
% 17.45/3.13  |         all_4_14 & op(e1, e1) = all_4_23 & op(e1, e0) = all_4_15 & op(e0, e4)
% 17.45/3.13  |         = all_4_16 & op(e0, e3) = all_4_17 & op(e0, e2) = all_4_18 & op(e0,
% 17.45/3.13  |           e1) = all_4_19 & op(e0, e0) = all_4_24 & $i(all_4_0) & $i(all_4_1) &
% 17.45/3.13  |         $i(all_4_2) & $i(all_4_3) & $i(all_4_4) & $i(all_4_5) & $i(all_4_6) &
% 17.45/3.13  |         $i(all_4_7) & $i(all_4_8) & $i(all_4_9) & $i(all_4_10) & $i(all_4_11)
% 17.45/3.13  |         & $i(all_4_12) & $i(all_4_13) & $i(all_4_14) & $i(all_4_15) &
% 17.45/3.13  |         $i(all_4_16) & $i(all_4_17) & $i(all_4_18) & $i(all_4_19) &
% 17.45/3.13  |         $i(all_4_20) & $i(all_4_21) & $i(all_4_22) & $i(all_4_23) &
% 17.45/3.13  |         $i(all_4_24) & (all_4_20 = e4 | all_4_21 = e4 | all_4_22 = e4 |
% 17.45/3.13  |           all_4_23 = e4 | all_4_24 = e4) & (all_4_20 = e3 | all_4_21 = e3 |
% 17.45/3.13  |           all_4_22 = e3 | all_4_23 = e3 | all_4_24 = e3) & (all_4_20 = e2 |
% 17.45/3.13  |           all_4_21 = e2 | all_4_22 = e2 | all_4_23 = e2 | all_4_24 = e2) &
% 17.45/3.13  |         (all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 |
% 17.45/3.13  |           all_4_24 = e1) & (all_4_20 = e0 | all_4_21 = e0 | all_4_22 = e0 |
% 17.45/3.13  |           all_4_23 = e0 | all_4_24 = e0) & ((all_4_20 = e3 & all_4_21 = e4 & 
% 17.45/3.13  |             ~ (all_4_0 = e4)) | (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_4 =
% 17.45/3.13  |               e3)) | (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_1 = e4)) |
% 17.45/3.13  |           (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2)) | (all_4_20 = e1
% 17.45/3.13  |             & all_4_23 = e4 &  ~ (all_4_2 = e4)) | (all_4_20 = e1 & all_4_23 =
% 17.45/3.13  |             e4 &  ~ (all_4_12 = e1)) | (all_4_20 = e0 & all_4_24 = e4 &  ~
% 17.45/3.13  |             (all_4_3 = e4)) | (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 =
% 17.45/3.13  |               e0)) | (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) |
% 17.45/3.13  |           (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2)) | (all_4_21 = e1
% 17.45/3.13  |             & all_4_23 = e3 &  ~ (all_4_6 = e3)) | (all_4_21 = e1 & all_4_23 =
% 17.45/3.13  |             e3 &  ~ (all_4_13 = e1)) | (all_4_21 = e0 & all_4_24 = e3 &  ~
% 17.45/3.13  |             (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 =
% 17.45/3.13  |               e0)) | (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2)) |
% 17.45/3.13  |           (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 = e1)) | (all_4_22 =
% 17.45/3.13  |             e0 & all_4_24 = e2 &  ~ (all_4_11 = e2)) | (all_4_22 = e0 &
% 17.45/3.13  |             all_4_24 = e2 &  ~ (all_4_18 = e0)) | (all_4_23 = e0 & all_4_24 =
% 17.45/3.13  |             e1 &  ~ (all_4_15 = e1)) | (all_4_23 = e0 & all_4_24 = e1 &  ~
% 17.45/3.13  |             (all_4_19 = e0)))
% 17.45/3.13  | 
% 17.45/3.13  | ALPHA: (16) implies:
% 17.45/3.13  |   (17)  op(e0, e0) = all_4_24
% 17.45/3.13  |   (18)  op(e1, e1) = all_4_23
% 17.45/3.13  |   (19)  op(e1, e2) = all_4_14
% 17.45/3.13  |   (20)  op(e2, e2) = all_4_22
% 17.45/3.13  |   (21)  op(e4, e4) = all_4_20
% 17.45/3.13  |   (22)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) | (all_4_20 = e3 &
% 17.45/3.13  |           all_4_21 = e4 &  ~ (all_4_4 = e3)) | (all_4_20 = e2 & all_4_22 = e4
% 17.45/3.13  |           &  ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8
% 17.45/3.13  |             = e2)) | (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4)) |
% 17.45/3.13  |         (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12 = e1)) | (all_4_20 = e0
% 17.45/3.13  |           & all_4_24 = e4 &  ~ (all_4_3 = e4)) | (all_4_20 = e0 & all_4_24 =
% 17.45/3.13  |           e4 &  ~ (all_4_16 = e0)) | (all_4_21 = e2 & all_4_22 = e3 &  ~
% 17.45/3.13  |           (all_4_5 = e3)) | (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 =
% 17.45/3.13  |             e2)) | (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)) |
% 17.45/3.13  |         (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_13 = e1)) | (all_4_21 = e0
% 17.45/3.13  |           & all_4_24 = e3 &  ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 =
% 17.45/3.13  |           e3 &  ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 &  ~
% 17.45/3.13  |           (all_4_10 = e2)) | (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 =
% 17.45/3.13  |             e1)) | (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2)) |
% 17.45/3.13  |         (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 = e0)) | (all_4_23 = e0
% 17.45/3.13  |           & all_4_24 = e1 &  ~ (all_4_15 = e1)) | (all_4_23 = e0 & all_4_24 =
% 17.45/3.13  |           e1 &  ~ (all_4_19 = e0))
% 17.45/3.13  |   (23)  all_4_20 = e0 | all_4_21 = e0 | all_4_22 = e0 | all_4_23 = e0 |
% 17.45/3.13  |         all_4_24 = e0
% 17.45/3.13  |   (24)  all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 |
% 17.45/3.13  |         all_4_24 = e1
% 17.45/3.13  | 
% 17.45/3.13  | DELTA: instantiating (3) with fresh symbols all_6_0, all_6_1, all_6_2,
% 17.45/3.13  |        all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9,
% 17.45/3.13  |        all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15, all_6_16,
% 17.45/3.13  |        all_6_17, all_6_18, all_6_19, all_6_20, all_6_21, all_6_22, all_6_23,
% 17.45/3.13  |        all_6_24 gives:
% 17.45/3.13  |   (25)   ~ (all_6_0 = all_6_1) &  ~ (all_6_0 = all_6_2) &  ~ (all_6_0 =
% 17.45/3.13  |           all_6_3) &  ~ (all_6_0 = all_6_4) &  ~ (all_6_0 = all_6_5) &  ~
% 17.45/3.13  |         (all_6_0 = all_6_10) &  ~ (all_6_0 = all_6_15) &  ~ (all_6_0 =
% 17.45/3.13  |           all_6_20) &  ~ (all_6_1 = all_6_2) &  ~ (all_6_1 = all_6_3) &  ~
% 17.45/3.13  |         (all_6_1 = all_6_4) &  ~ (all_6_1 = all_6_6) &  ~ (all_6_1 = all_6_11)
% 17.45/3.13  |         &  ~ (all_6_1 = all_6_16) &  ~ (all_6_1 = all_6_21) &  ~ (all_6_2 =
% 17.45/3.13  |           all_6_3) &  ~ (all_6_2 = all_6_4) &  ~ (all_6_2 = all_6_7) &  ~
% 17.45/3.13  |         (all_6_2 = all_6_12) &  ~ (all_6_2 = all_6_17) &  ~ (all_6_2 =
% 17.45/3.13  |           all_6_22) &  ~ (all_6_3 = all_6_4) &  ~ (all_6_3 = all_6_8) &  ~
% 17.45/3.13  |         (all_6_3 = all_6_13) &  ~ (all_6_3 = all_6_18) &  ~ (all_6_3 =
% 17.45/3.14  |           all_6_23) &  ~ (all_6_4 = all_6_9) &  ~ (all_6_4 = all_6_14) &  ~
% 17.45/3.14  |         (all_6_4 = all_6_19) &  ~ (all_6_4 = all_6_24) &  ~ (all_6_5 =
% 17.45/3.14  |           all_6_6) &  ~ (all_6_5 = all_6_7) &  ~ (all_6_5 = all_6_8) &  ~
% 17.45/3.14  |         (all_6_5 = all_6_9) &  ~ (all_6_5 = all_6_10) &  ~ (all_6_5 =
% 17.45/3.14  |           all_6_15) &  ~ (all_6_5 = all_6_20) &  ~ (all_6_6 = all_6_7) &  ~
% 17.45/3.14  |         (all_6_6 = all_6_8) &  ~ (all_6_6 = all_6_9) &  ~ (all_6_6 = all_6_11)
% 17.45/3.14  |         &  ~ (all_6_6 = all_6_16) &  ~ (all_6_6 = all_6_21) &  ~ (all_6_7 =
% 17.45/3.14  |           all_6_8) &  ~ (all_6_7 = all_6_9) &  ~ (all_6_7 = all_6_12) &  ~
% 17.45/3.14  |         (all_6_7 = all_6_17) &  ~ (all_6_7 = all_6_22) &  ~ (all_6_8 =
% 17.45/3.14  |           all_6_9) &  ~ (all_6_8 = all_6_13) &  ~ (all_6_8 = all_6_18) &  ~
% 17.45/3.14  |         (all_6_8 = all_6_23) &  ~ (all_6_9 = all_6_14) &  ~ (all_6_9 =
% 17.45/3.14  |           all_6_19) &  ~ (all_6_9 = all_6_24) &  ~ (all_6_10 = all_6_11) &  ~
% 17.45/3.14  |         (all_6_10 = all_6_12) &  ~ (all_6_10 = all_6_13) &  ~ (all_6_10 =
% 17.45/3.14  |           all_6_14) &  ~ (all_6_10 = all_6_15) &  ~ (all_6_10 = all_6_20) &  ~
% 17.45/3.14  |         (all_6_11 = all_6_12) &  ~ (all_6_11 = all_6_13) &  ~ (all_6_11 =
% 17.45/3.14  |           all_6_14) &  ~ (all_6_11 = all_6_16) &  ~ (all_6_11 = all_6_21) &  ~
% 17.45/3.14  |         (all_6_12 = all_6_13) &  ~ (all_6_12 = all_6_14) &  ~ (all_6_12 =
% 17.45/3.14  |           all_6_17) &  ~ (all_6_12 = all_6_22) &  ~ (all_6_13 = all_6_14) &  ~
% 17.45/3.14  |         (all_6_13 = all_6_18) &  ~ (all_6_13 = all_6_23) &  ~ (all_6_14 =
% 17.45/3.14  |           all_6_19) &  ~ (all_6_14 = all_6_24) &  ~ (all_6_15 = all_6_16) &  ~
% 17.45/3.14  |         (all_6_15 = all_6_17) &  ~ (all_6_15 = all_6_18) &  ~ (all_6_15 =
% 17.45/3.14  |           all_6_19) &  ~ (all_6_15 = all_6_20) &  ~ (all_6_16 = all_6_17) &  ~
% 17.45/3.14  |         (all_6_16 = all_6_18) &  ~ (all_6_16 = all_6_19) &  ~ (all_6_16 =
% 17.45/3.14  |           all_6_21) &  ~ (all_6_17 = all_6_18) &  ~ (all_6_17 = all_6_19) &  ~
% 17.45/3.14  |         (all_6_17 = all_6_22) &  ~ (all_6_18 = all_6_19) &  ~ (all_6_18 =
% 17.45/3.14  |           all_6_23) &  ~ (all_6_19 = all_6_24) &  ~ (all_6_20 = all_6_21) &  ~
% 17.45/3.14  |         (all_6_20 = all_6_22) &  ~ (all_6_20 = all_6_23) &  ~ (all_6_20 =
% 17.45/3.14  |           all_6_24) &  ~ (all_6_21 = all_6_22) &  ~ (all_6_21 = all_6_23) &  ~
% 17.45/3.14  |         (all_6_21 = all_6_24) &  ~ (all_6_22 = all_6_23) &  ~ (all_6_22 =
% 17.45/3.14  |           all_6_24) &  ~ (all_6_23 = all_6_24) & op(e4, e4) = all_6_0 & op(e4,
% 17.45/3.14  |           e3) = all_6_5 & op(e4, e2) = all_6_10 & op(e4, e1) = all_6_15 &
% 17.45/3.14  |         op(e4, e0) = all_6_20 & op(e3, e4) = all_6_1 & op(e3, e3) = all_6_6 &
% 17.45/3.14  |         op(e3, e2) = all_6_11 & op(e3, e1) = all_6_16 & op(e3, e0) = all_6_21
% 17.45/3.14  |         & op(e2, e4) = all_6_2 & op(e2, e3) = all_6_7 & op(e2, e2) = all_6_12
% 17.45/3.14  |         & op(e2, e1) = all_6_17 & op(e2, e0) = all_6_22 & op(e1, e4) = all_6_3
% 17.45/3.14  |         & op(e1, e3) = all_6_8 & op(e1, e2) = all_6_13 & op(e1, e1) = all_6_18
% 17.45/3.14  |         & op(e1, e0) = all_6_23 & op(e0, e4) = all_6_4 & op(e0, e3) = all_6_9
% 17.45/3.14  |         & op(e0, e2) = all_6_14 & op(e0, e1) = all_6_19 & op(e0, e0) =
% 17.45/3.14  |         all_6_24 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & $i(all_6_3) &
% 17.45/3.14  |         $i(all_6_4) & $i(all_6_5) & $i(all_6_6) & $i(all_6_7) & $i(all_6_8) &
% 17.45/3.14  |         $i(all_6_9) & $i(all_6_10) & $i(all_6_11) & $i(all_6_12) &
% 17.45/3.14  |         $i(all_6_13) & $i(all_6_14) & $i(all_6_15) & $i(all_6_16) &
% 17.45/3.14  |         $i(all_6_17) & $i(all_6_18) & $i(all_6_19) & $i(all_6_20) &
% 17.45/3.14  |         $i(all_6_21) & $i(all_6_22) & $i(all_6_23) & $i(all_6_24)
% 17.45/3.14  | 
% 17.45/3.14  | ALPHA: (25) implies:
% 17.45/3.14  |   (26)   ~ (all_6_13 = all_6_18)
% 17.45/3.14  |   (27)   ~ (all_6_12 = all_6_13)
% 17.45/3.14  |   (28)  op(e1, e1) = all_6_18
% 17.45/3.14  |   (29)  op(e1, e2) = all_6_13
% 17.45/3.14  |   (30)  op(e2, e2) = all_6_12
% 17.45/3.14  |   (31)  op(e4, e4) = all_6_0
% 17.45/3.14  | 
% 17.45/3.14  | DELTA: instantiating (1) with fresh symbols all_8_0, all_8_1, all_8_2,
% 17.45/3.14  |        all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9,
% 17.45/3.14  |        all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15, all_8_16,
% 17.45/3.14  |        all_8_17, all_8_18, all_8_19, all_8_20, all_8_21, all_8_22, all_8_23,
% 17.45/3.14  |        all_8_24 gives:
% 17.45/3.14  |   (32)  op(e4, e4) = all_8_0 & op(e4, e3) = all_8_1 & op(e4, e2) = all_8_2 &
% 17.45/3.14  |         op(e4, e1) = all_8_3 & op(e4, e0) = all_8_4 & op(e3, e4) = all_8_5 &
% 17.45/3.14  |         op(e3, e3) = all_8_6 & op(e3, e2) = all_8_7 & op(e3, e1) = all_8_8 &
% 17.45/3.14  |         op(e3, e0) = all_8_9 & op(e2, e4) = all_8_10 & op(e2, e3) = all_8_11 &
% 17.45/3.14  |         op(e2, e2) = all_8_12 & op(e2, e1) = all_8_13 & op(e2, e0) = all_8_14
% 17.45/3.14  |         & op(e1, e4) = all_8_15 & op(e1, e3) = all_8_16 & op(e1, e2) =
% 17.45/3.14  |         all_8_17 & op(e1, e1) = all_8_18 & op(e1, e0) = all_8_19 & op(e0, e4)
% 17.45/3.14  |         = all_8_20 & op(e0, e3) = all_8_21 & op(e0, e2) = all_8_22 & op(e0,
% 17.45/3.14  |           e1) = all_8_23 & op(e0, e0) = all_8_24 & $i(all_8_0) & $i(all_8_1) &
% 17.45/3.14  |         $i(all_8_2) & $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6) &
% 17.45/3.14  |         $i(all_8_7) & $i(all_8_8) & $i(all_8_9) & $i(all_8_10) & $i(all_8_11)
% 17.45/3.14  |         & $i(all_8_12) & $i(all_8_13) & $i(all_8_14) & $i(all_8_15) &
% 17.45/3.14  |         $i(all_8_16) & $i(all_8_17) & $i(all_8_18) & $i(all_8_19) &
% 17.45/3.14  |         $i(all_8_20) & $i(all_8_21) & $i(all_8_22) & $i(all_8_23) &
% 17.45/3.14  |         $i(all_8_24) & (all_8_0 = e4 | all_8_0 = e3 | all_8_0 = e2 | all_8_0 =
% 17.45/3.14  |           e1 | all_8_0 = e0) & (all_8_1 = e4 | all_8_1 = e3 | all_8_1 = e2 |
% 17.45/3.14  |           all_8_1 = e1 | all_8_1 = e0) & (all_8_2 = e4 | all_8_2 = e3 |
% 17.45/3.14  |           all_8_2 = e2 | all_8_2 = e1 | all_8_2 = e0) & (all_8_3 = e4 |
% 17.45/3.14  |           all_8_3 = e3 | all_8_3 = e2 | all_8_3 = e1 | all_8_3 = e0) &
% 17.45/3.14  |         (all_8_4 = e4 | all_8_4 = e3 | all_8_4 = e2 | all_8_4 = e1 | all_8_4 =
% 17.45/3.14  |           e0) & (all_8_5 = e4 | all_8_5 = e3 | all_8_5 = e2 | all_8_5 = e1 |
% 17.45/3.14  |           all_8_5 = e0) & (all_8_6 = e4 | all_8_6 = e3 | all_8_6 = e2 |
% 17.45/3.14  |           all_8_6 = e1 | all_8_6 = e0) & (all_8_7 = e4 | all_8_7 = e3 |
% 17.45/3.14  |           all_8_7 = e2 | all_8_7 = e1 | all_8_7 = e0) & (all_8_8 = e4 |
% 17.45/3.14  |           all_8_8 = e3 | all_8_8 = e2 | all_8_8 = e1 | all_8_8 = e0) &
% 17.45/3.14  |         (all_8_9 = e4 | all_8_9 = e3 | all_8_9 = e2 | all_8_9 = e1 | all_8_9 =
% 17.45/3.14  |           e0) & (all_8_10 = e4 | all_8_10 = e3 | all_8_10 = e2 | all_8_10 = e1
% 17.45/3.14  |           | all_8_10 = e0) & (all_8_11 = e4 | all_8_11 = e3 | all_8_11 = e2 |
% 17.45/3.14  |           all_8_11 = e1 | all_8_11 = e0) & (all_8_12 = e4 | all_8_12 = e3 |
% 17.45/3.14  |           all_8_12 = e2 | all_8_12 = e1 | all_8_12 = e0) & (all_8_13 = e4 |
% 17.45/3.14  |           all_8_13 = e3 | all_8_13 = e2 | all_8_13 = e1 | all_8_13 = e0) &
% 17.45/3.14  |         (all_8_14 = e4 | all_8_14 = e3 | all_8_14 = e2 | all_8_14 = e1 |
% 17.45/3.14  |           all_8_14 = e0) & (all_8_15 = e4 | all_8_15 = e3 | all_8_15 = e2 |
% 17.45/3.14  |           all_8_15 = e1 | all_8_15 = e0) & (all_8_16 = e4 | all_8_16 = e3 |
% 17.45/3.14  |           all_8_16 = e2 | all_8_16 = e1 | all_8_16 = e0) & (all_8_17 = e4 |
% 17.45/3.14  |           all_8_17 = e3 | all_8_17 = e2 | all_8_17 = e1 | all_8_17 = e0) &
% 17.45/3.14  |         (all_8_18 = e4 | all_8_18 = e3 | all_8_18 = e2 | all_8_18 = e1 |
% 17.45/3.14  |           all_8_18 = e0) & (all_8_19 = e4 | all_8_19 = e3 | all_8_19 = e2 |
% 17.45/3.14  |           all_8_19 = e1 | all_8_19 = e0) & (all_8_20 = e4 | all_8_20 = e3 |
% 17.45/3.14  |           all_8_20 = e2 | all_8_20 = e1 | all_8_20 = e0) & (all_8_21 = e4 |
% 17.45/3.14  |           all_8_21 = e3 | all_8_21 = e2 | all_8_21 = e1 | all_8_21 = e0) &
% 17.45/3.14  |         (all_8_22 = e4 | all_8_22 = e3 | all_8_22 = e2 | all_8_22 = e1 |
% 17.45/3.14  |           all_8_22 = e0) & (all_8_23 = e4 | all_8_23 = e3 | all_8_23 = e2 |
% 17.45/3.14  |           all_8_23 = e1 | all_8_23 = e0) & (all_8_24 = e4 | all_8_24 = e3 |
% 17.45/3.14  |           all_8_24 = e2 | all_8_24 = e1 | all_8_24 = e0)
% 17.45/3.14  | 
% 17.45/3.14  | ALPHA: (32) implies:
% 17.45/3.14  |   (33)  op(e1, e1) = all_8_18
% 17.45/3.14  |   (34)  op(e1, e2) = all_8_17
% 17.45/3.14  |   (35)  op(e2, e2) = all_8_12
% 17.45/3.14  |   (36)  op(e4, e4) = all_8_0
% 17.45/3.14  | 
% 17.45/3.14  | DELTA: instantiating (2) with fresh symbols all_10_0, all_10_1, all_10_2,
% 17.45/3.14  |        all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, all_10_9,
% 17.45/3.14  |        all_10_10, all_10_11, all_10_12, all_10_13, all_10_14, all_10_15,
% 17.45/3.14  |        all_10_16, all_10_17, all_10_18, all_10_19, all_10_20, all_10_21,
% 17.45/3.14  |        all_10_22, all_10_23, all_10_24 gives:
% 17.45/3.15  |   (37)  op(e4, e4) = all_10_0 & op(e4, e3) = all_10_1 & op(e4, e2) = all_10_4
% 17.45/3.15  |         & op(e4, e1) = all_10_9 & op(e4, e0) = all_10_16 & op(e3, e4) =
% 17.45/3.15  |         all_10_2 & op(e3, e3) = all_10_3 & op(e3, e2) = all_10_5 & op(e3, e1)
% 17.45/3.15  |         = all_10_10 & op(e3, e0) = all_10_17 & op(e2, e4) = all_10_6 & op(e2,
% 17.45/3.15  |           e3) = all_10_7 & op(e2, e2) = all_10_8 & op(e2, e1) = all_10_11 &
% 17.45/3.15  |         op(e2, e0) = all_10_18 & op(e1, e4) = all_10_12 & op(e1, e3) =
% 17.45/3.15  |         all_10_13 & op(e1, e2) = all_10_14 & op(e1, e1) = all_10_15 & op(e1,
% 17.45/3.15  |           e0) = all_10_19 & op(e0, e4) = all_10_20 & op(e0, e3) = all_10_21 &
% 17.45/3.15  |         op(e0, e2) = all_10_22 & op(e0, e1) = all_10_23 & op(e0, e0) =
% 17.45/3.15  |         all_10_24 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & $i(all_10_3)
% 17.45/3.15  |         & $i(all_10_4) & $i(all_10_5) & $i(all_10_6) & $i(all_10_7) &
% 17.45/3.15  |         $i(all_10_8) & $i(all_10_9) & $i(all_10_10) & $i(all_10_11) &
% 17.45/3.15  |         $i(all_10_12) & $i(all_10_13) & $i(all_10_14) & $i(all_10_15) &
% 17.45/3.15  |         $i(all_10_16) & $i(all_10_17) & $i(all_10_18) & $i(all_10_19) &
% 17.45/3.15  |         $i(all_10_20) & $i(all_10_21) & $i(all_10_22) & $i(all_10_23) &
% 17.45/3.15  |         $i(all_10_24) & (all_10_0 = e4 | all_10_1 = e4 | all_10_4 = e4 |
% 17.45/3.15  |           all_10_9 = e4 | all_10_16 = e4) & (all_10_0 = e4 | all_10_2 = e4 |
% 17.45/3.15  |           all_10_6 = e4 | all_10_12 = e4 | all_10_20 = e4) & (all_10_0 = e3 |
% 17.45/3.15  |           all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3 | all_10_16 = e3) &
% 17.45/3.15  |         (all_10_0 = e3 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3 |
% 17.45/3.15  |           all_10_20 = e3) & (all_10_0 = e2 | all_10_1 = e2 | all_10_4 = e2 |
% 17.45/3.15  |           all_10_9 = e2 | all_10_16 = e2) & (all_10_0 = e2 | all_10_2 = e2 |
% 17.45/3.15  |           all_10_6 = e2 | all_10_12 = e2 | all_10_20 = e2) & (all_10_0 = e1 |
% 17.45/3.15  |           all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1 | all_10_16 = e1) &
% 17.45/3.15  |         (all_10_0 = e1 | all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1 |
% 17.45/3.15  |           all_10_20 = e1) & (all_10_0 = e0 | all_10_1 = e0 | all_10_4 = e0 |
% 17.45/3.15  |           all_10_9 = e0 | all_10_16 = e0) & (all_10_0 = e0 | all_10_2 = e0 |
% 17.45/3.15  |           all_10_6 = e0 | all_10_12 = e0 | all_10_20 = e0) & (all_10_1 = e4 |
% 17.45/3.15  |           all_10_3 = e4 | all_10_7 = e4 | all_10_13 = e4 | all_10_21 = e4) &
% 17.45/3.15  |         (all_10_1 = e3 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3 |
% 17.45/3.15  |           all_10_21 = e3) & (all_10_1 = e2 | all_10_3 = e2 | all_10_7 = e2 |
% 17.45/3.15  |           all_10_13 = e2 | all_10_21 = e2) & (all_10_1 = e1 | all_10_3 = e1 |
% 17.45/3.15  |           all_10_7 = e1 | all_10_13 = e1 | all_10_21 = e1) & (all_10_1 = e0 |
% 17.45/3.15  |           all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0 | all_10_21 = e0) &
% 17.45/3.15  |         (all_10_2 = e4 | all_10_3 = e4 | all_10_5 = e4 | all_10_10 = e4 |
% 17.45/3.15  |           all_10_17 = e4) & (all_10_2 = e3 | all_10_3 = e3 | all_10_5 = e3 |
% 17.45/3.15  |           all_10_10 = e3 | all_10_17 = e3) & (all_10_2 = e2 | all_10_3 = e2 |
% 17.45/3.15  |           all_10_5 = e2 | all_10_10 = e2 | all_10_17 = e2) & (all_10_2 = e1 |
% 17.45/3.15  |           all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1 | all_10_17 = e1) &
% 17.45/3.15  |         (all_10_2 = e0 | all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0 |
% 17.45/3.15  |           all_10_17 = e0) & (all_10_4 = e4 | all_10_5 = e4 | all_10_8 = e4 |
% 17.45/3.15  |           all_10_14 = e4 | all_10_22 = e4) & (all_10_4 = e3 | all_10_5 = e3 |
% 17.45/3.15  |           all_10_8 = e3 | all_10_14 = e3 | all_10_22 = e3) & (all_10_4 = e2 |
% 17.45/3.15  |           all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2 | all_10_22 = e2) &
% 17.45/3.15  |         (all_10_4 = e1 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1 |
% 17.45/3.15  |           all_10_22 = e1) & (all_10_4 = e0 | all_10_5 = e0 | all_10_8 = e0 |
% 17.45/3.15  |           all_10_14 = e0 | all_10_22 = e0) & (all_10_6 = e4 | all_10_7 = e4 |
% 17.45/3.15  |           all_10_8 = e4 | all_10_11 = e4 | all_10_18 = e4) & (all_10_6 = e3 |
% 17.45/3.15  |           all_10_7 = e3 | all_10_8 = e3 | all_10_11 = e3 | all_10_18 = e3) &
% 17.45/3.15  |         (all_10_6 = e2 | all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2 |
% 17.45/3.15  |           all_10_18 = e2) & (all_10_6 = e1 | all_10_7 = e1 | all_10_8 = e1 |
% 17.45/3.15  |           all_10_11 = e1 | all_10_18 = e1) & (all_10_6 = e0 | all_10_7 = e0 |
% 17.45/3.15  |           all_10_8 = e0 | all_10_11 = e0 | all_10_18 = e0) & (all_10_9 = e4 |
% 17.45/3.15  |           all_10_10 = e4 | all_10_11 = e4 | all_10_15 = e4 | all_10_23 = e4) &
% 17.45/3.15  |         (all_10_9 = e3 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3 |
% 17.45/3.15  |           all_10_23 = e3) & (all_10_9 = e2 | all_10_10 = e2 | all_10_11 = e2 |
% 17.45/3.15  |           all_10_15 = e2 | all_10_23 = e2) & (all_10_9 = e1 | all_10_10 = e1 |
% 17.45/3.15  |           all_10_11 = e1 | all_10_15 = e1 | all_10_23 = e1) & (all_10_9 = e0 |
% 17.45/3.15  |           all_10_10 = e0 | all_10_11 = e0 | all_10_15 = e0 | all_10_23 = e0) &
% 17.45/3.15  |         (all_10_12 = e4 | all_10_13 = e4 | all_10_14 = e4 | all_10_15 = e4 |
% 17.45/3.15  |           all_10_19 = e4) & (all_10_12 = e3 | all_10_13 = e3 | all_10_14 = e3
% 17.45/3.15  |           | all_10_15 = e3 | all_10_19 = e3) & (all_10_12 = e2 | all_10_13 =
% 17.45/3.15  |           e2 | all_10_14 = e2 | all_10_15 = e2 | all_10_19 = e2) & (all_10_12
% 17.45/3.15  |           = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1 | all_10_19
% 17.45/3.15  |           = e1) & (all_10_12 = e0 | all_10_13 = e0 | all_10_14 = e0 |
% 17.45/3.15  |           all_10_15 = e0 | all_10_19 = e0) & (all_10_16 = e4 | all_10_17 = e4
% 17.45/3.15  |           | all_10_18 = e4 | all_10_19 = e4 | all_10_24 = e4) & (all_10_16 =
% 17.45/3.15  |           e3 | all_10_17 = e3 | all_10_18 = e3 | all_10_19 = e3 | all_10_24 =
% 17.45/3.15  |           e3) & (all_10_16 = e2 | all_10_17 = e2 | all_10_18 = e2 | all_10_19
% 17.45/3.15  |           = e2 | all_10_24 = e2) & (all_10_16 = e1 | all_10_17 = e1 |
% 17.45/3.15  |           all_10_18 = e1 | all_10_19 = e1 | all_10_24 = e1) & (all_10_20 = e4
% 17.45/3.15  |           | all_10_21 = e4 | all_10_22 = e4 | all_10_23 = e4 | all_10_24 = e4)
% 17.45/3.15  |         & (all_10_20 = e3 | all_10_21 = e3 | all_10_22 = e3 | all_10_23 = e3 |
% 17.45/3.15  |           all_10_24 = e3) & (all_10_20 = e2 | all_10_21 = e2 | all_10_22 = e2
% 17.45/3.15  |           | all_10_23 = e2 | all_10_24 = e2) & (all_10_20 = e1 | all_10_21 =
% 17.45/3.15  |           e1 | all_10_22 = e1 | all_10_23 = e1 | all_10_24 = e1) & (all_10_24
% 17.45/3.15  |           = e0 | ((all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 |
% 17.45/3.15  |               all_10_19 = e0) & (all_10_20 = e0 | all_10_21 = e0 | all_10_22 =
% 17.45/3.15  |               e0 | all_10_23 = e0)))
% 17.45/3.15  | 
% 17.45/3.15  | ALPHA: (37) implies:
% 17.45/3.15  |   (38)  op(e0, e0) = all_10_24
% 17.45/3.15  |   (39)  op(e1, e1) = all_10_15
% 17.45/3.15  |   (40)  op(e1, e2) = all_10_14
% 17.45/3.15  |   (41)  op(e2, e2) = all_10_8
% 17.45/3.15  |   (42)  op(e4, e4) = all_10_0
% 17.45/3.15  |   (43)  all_10_24 = e0 | ((all_10_16 = e0 | all_10_17 = e0 | all_10_18 = e0 |
% 17.45/3.15  |             all_10_19 = e0) & (all_10_20 = e0 | all_10_21 = e0 | all_10_22 =
% 17.45/3.15  |             e0 | all_10_23 = e0))
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_4_24, all_10_24, e0, e0,
% 17.45/3.15  |              simplifying with (17), (38) gives:
% 17.45/3.15  |   (44)  all_10_24 = all_4_24
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_4_23, all_8_18, e1, e1,
% 17.45/3.15  |              simplifying with (18), (33) gives:
% 17.45/3.15  |   (45)  all_8_18 = all_4_23
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with e4, all_8_18, e1, e1,
% 17.45/3.15  |              simplifying with (11), (33) gives:
% 17.45/3.15  |   (46)  all_8_18 = e4
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_8_18, all_10_15, e1, e1,
% 17.45/3.15  |              simplifying with (33), (39) gives:
% 17.45/3.15  |   (47)  all_10_15 = all_8_18
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_6_18, all_10_15, e1, e1,
% 17.45/3.15  |              simplifying with (28), (39) gives:
% 17.45/3.15  |   (48)  all_10_15 = all_6_18
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_6_13, all_8_17, e2, e1,
% 17.45/3.15  |              simplifying with (29), (34) gives:
% 17.45/3.15  |   (49)  all_8_17 = all_6_13
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_4_14, all_8_17, e2, e1,
% 17.45/3.15  |              simplifying with (19), (34) gives:
% 17.45/3.15  |   (50)  all_8_17 = all_4_14
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_6_13, all_10_14, e2, e1,
% 17.45/3.15  |              simplifying with (29), (40) gives:
% 17.45/3.15  |   (51)  all_10_14 = all_6_13
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with e0, all_10_14, e2, e1,
% 17.45/3.15  |              simplifying with (12), (40) gives:
% 17.45/3.15  |   (52)  all_10_14 = e0
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_4_22, all_6_12, e2, e2,
% 17.45/3.15  |              simplifying with (20), (30) gives:
% 17.45/3.15  |   (53)  all_6_12 = all_4_22
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_6_12, all_8_12, e2, e2,
% 17.45/3.15  |              simplifying with (30), (35) gives:
% 17.45/3.15  |   (54)  all_8_12 = all_6_12
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_8_12, all_10_8, e2, e2,
% 17.45/3.15  |              simplifying with (35), (41) gives:
% 17.45/3.15  |   (55)  all_10_8 = all_8_12
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with e3, all_10_8, e2, e2,
% 17.45/3.15  |              simplifying with (13), (41) gives:
% 17.45/3.15  |   (56)  all_10_8 = e3
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_4_20, all_6_0, e4, e4,
% 17.45/3.15  |              simplifying with (21), (31) gives:
% 17.45/3.15  |   (57)  all_6_0 = all_4_20
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_6_0, all_8_0, e4, e4,
% 17.45/3.15  |              simplifying with (31), (36) gives:
% 17.45/3.15  |   (58)  all_8_0 = all_6_0
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with all_8_0, all_10_0, e4, e4,
% 17.45/3.15  |              simplifying with (36), (42) gives:
% 17.45/3.15  |   (59)  all_10_0 = all_8_0
% 17.45/3.15  | 
% 17.45/3.15  | GROUND_INST: instantiating (function-axioms) with e2, all_10_0, e4, e4,
% 17.45/3.15  |              simplifying with (14), (42) gives:
% 17.45/3.15  |   (60)  all_10_0 = e2
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (59), (60) imply:
% 17.45/3.15  |   (61)  all_8_0 = e2
% 17.45/3.15  | 
% 17.45/3.15  | SIMP: (61) implies:
% 17.45/3.15  |   (62)  all_8_0 = e2
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (55), (56) imply:
% 17.45/3.15  |   (63)  all_8_12 = e3
% 17.45/3.15  | 
% 17.45/3.15  | SIMP: (63) implies:
% 17.45/3.15  |   (64)  all_8_12 = e3
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (51), (52) imply:
% 17.45/3.15  |   (65)  all_6_13 = e0
% 17.45/3.15  | 
% 17.45/3.15  | SIMP: (65) implies:
% 17.45/3.15  |   (66)  all_6_13 = e0
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (47), (48) imply:
% 17.45/3.15  |   (67)  all_8_18 = all_6_18
% 17.45/3.15  | 
% 17.45/3.15  | SIMP: (67) implies:
% 17.45/3.15  |   (68)  all_8_18 = all_6_18
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (58), (62) imply:
% 17.45/3.15  |   (69)  all_6_0 = e2
% 17.45/3.15  | 
% 17.45/3.15  | SIMP: (69) implies:
% 17.45/3.15  |   (70)  all_6_0 = e2
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (54), (64) imply:
% 17.45/3.15  |   (71)  all_6_12 = e3
% 17.45/3.15  | 
% 17.45/3.15  | SIMP: (71) implies:
% 17.45/3.15  |   (72)  all_6_12 = e3
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (49), (50) imply:
% 17.45/3.15  |   (73)  all_6_13 = all_4_14
% 17.45/3.15  | 
% 17.45/3.15  | SIMP: (73) implies:
% 17.45/3.15  |   (74)  all_6_13 = all_4_14
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (46), (68) imply:
% 17.45/3.15  |   (75)  all_6_18 = e4
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (45), (68) imply:
% 17.45/3.15  |   (76)  all_6_18 = all_4_23
% 17.45/3.15  | 
% 17.45/3.15  | COMBINE_EQS: (57), (70) imply:
% 17.45/3.16  |   (77)  all_4_20 = e2
% 17.45/3.16  | 
% 17.45/3.16  | SIMP: (77) implies:
% 17.45/3.16  |   (78)  all_4_20 = e2
% 17.45/3.16  | 
% 17.45/3.16  | COMBINE_EQS: (53), (72) imply:
% 17.45/3.16  |   (79)  all_4_22 = e3
% 17.45/3.16  | 
% 17.45/3.16  | COMBINE_EQS: (66), (74) imply:
% 17.45/3.16  |   (80)  all_4_14 = e0
% 17.45/3.16  | 
% 17.45/3.16  | COMBINE_EQS: (75), (76) imply:
% 17.45/3.16  |   (81)  all_4_23 = e4
% 17.45/3.16  | 
% 17.45/3.16  | SIMP: (81) implies:
% 17.45/3.16  |   (82)  all_4_23 = e4
% 17.45/3.16  | 
% 17.45/3.16  | REDUCE: (27), (66), (72) imply:
% 17.45/3.16  |   (83)   ~ (e3 = e0)
% 17.45/3.16  | 
% 17.45/3.16  | REDUCE: (26), (66), (75) imply:
% 17.45/3.16  |   (84)   ~ (e4 = e0)
% 17.45/3.16  | 
% 17.45/3.16  | SIMP: (84) implies:
% 17.45/3.16  |   (85)   ~ (e4 = e0)
% 17.45/3.16  | 
% 17.45/3.16  | BETA: splitting (43) gives:
% 17.45/3.16  | 
% 17.45/3.16  | Case 1:
% 17.45/3.16  | | 
% 17.45/3.16  | |   (86)  all_10_24 = e0
% 17.45/3.16  | | 
% 17.45/3.16  | | COMBINE_EQS: (44), (86) imply:
% 17.45/3.16  | |   (87)  all_4_24 = e0
% 17.45/3.16  | | 
% 17.45/3.16  | | SIMP: (87) implies:
% 17.45/3.16  | |   (88)  all_4_24 = e0
% 17.45/3.16  | | 
% 17.45/3.16  | | BETA: splitting (22) gives:
% 17.45/3.16  | | 
% 17.45/3.16  | | Case 1:
% 17.45/3.16  | | | 
% 17.45/3.16  | | |   (89)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) | (all_4_20 =
% 17.45/3.16  | | |           e3 & all_4_21 = e4 &  ~ (all_4_4 = e3)) | (all_4_20 = e2 &
% 17.45/3.16  | | |           all_4_22 = e4 &  ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 =
% 17.45/3.16  | | |           e4 &  ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 &  ~
% 17.45/3.16  | | |           (all_4_2 = e4)) | (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12
% 17.45/3.16  | | |             = e1)) | (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_3 = e4)) |
% 17.45/3.16  | | |         (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 = e0)) | (all_4_21 =
% 17.45/3.16  | | |           e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) | (all_4_21 = e2 &
% 17.45/3.16  | | |           all_4_22 = e3 &  ~ (all_4_9 = e2))
% 17.45/3.16  | | | 
% 17.45/3.16  | | | BETA: splitting (89) gives:
% 17.45/3.16  | | | 
% 17.45/3.16  | | | Case 1:
% 17.45/3.16  | | | | 
% 17.45/3.16  | | | |   (90)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) | (all_4_20
% 17.45/3.16  | | | |           = e3 & all_4_21 = e4 &  ~ (all_4_4 = e3)) | (all_4_20 = e2 &
% 17.45/3.16  | | | |           all_4_22 = e4 &  ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22
% 17.45/3.16  | | | |           = e4 &  ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 & 
% 17.45/3.16  | | | |           ~ (all_4_2 = e4))
% 17.45/3.16  | | | | 
% 17.45/3.16  | | | | BETA: splitting (90) gives:
% 17.45/3.16  | | | | 
% 17.45/3.16  | | | | Case 1:
% 17.45/3.16  | | | | | 
% 17.45/3.16  | | | | |   (91)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) |
% 17.45/3.16  | | | | |         (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_4 = e3))
% 17.45/3.16  | | | | | 
% 17.45/3.16  | | | | | REF_CLOSE: (8), (78), (91) are inconsistent by sub-proof #14.
% 17.45/3.16  | | | | | 
% 17.77/3.16  | | | | Case 2:
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | |   (92)  (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_1 = e4)) |
% 17.77/3.16  | | | | |         (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2)) |
% 17.77/3.16  | | | | |         (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4))
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | | BETA: splitting (92) gives:
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | | Case 1:
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | |   (93)  all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_1 = e4)
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | | ALPHA: (93) implies:
% 17.77/3.16  | | | | | |   (94)  all_4_22 = e4
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | | REF_CLOSE: (10), (79), (94) are inconsistent by sub-proof #13.
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | Case 2:
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | |   (95)  (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2)) |
% 17.77/3.16  | | | | | |         (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4))
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | | BETA: splitting (95) gives:
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | | Case 1:
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | |   (96)  all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2)
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | | ALPHA: (96) implies:
% 17.77/3.16  | | | | | | |   (97)  all_4_22 = e4
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | | REF_CLOSE: (10), (79), (97) are inconsistent by sub-proof #13.
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | Case 2:
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | |   (98)  all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4)
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | | REF_CLOSE: (6), (78), (98) are inconsistent by sub-proof #12.
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | End of split
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | End of split
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | End of split
% 17.77/3.16  | | | | 
% 17.77/3.16  | | | Case 2:
% 17.77/3.16  | | | | 
% 17.77/3.16  | | | |   (99)  (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12 = e1)) | (all_4_20
% 17.77/3.16  | | | |           = e0 & all_4_24 = e4 &  ~ (all_4_3 = e4)) | (all_4_20 = e0 &
% 17.77/3.16  | | | |           all_4_24 = e4 &  ~ (all_4_16 = e0)) | (all_4_21 = e2 &
% 17.77/3.16  | | | |           all_4_22 = e3 &  ~ (all_4_5 = e3)) | (all_4_21 = e2 & all_4_22
% 17.77/3.16  | | | |           = e3 &  ~ (all_4_9 = e2))
% 17.77/3.16  | | | | 
% 17.77/3.16  | | | | BETA: splitting (99) gives:
% 17.77/3.16  | | | | 
% 17.77/3.16  | | | | Case 1:
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | |   (100)  (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12 = e1)) |
% 17.77/3.16  | | | | |          (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_3 = e4))
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | | REF_CLOSE: (5), (6), (78), (100) are inconsistent by sub-proof #11.
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | Case 2:
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | |   (101)  (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 = e0)) |
% 17.77/3.16  | | | | |          (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) |
% 17.77/3.16  | | | | |          (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2))
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | | BETA: splitting (101) gives:
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | | Case 1:
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | |   (102)  all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 = e0)
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | | REF_CLOSE: (5), (78), (102) are inconsistent by sub-proof #10.
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | Case 2:
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | |   (103)  (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) |
% 17.77/3.16  | | | | | |          (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2))
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | | BETA: splitting (103) gives:
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | | Case 1:
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | |   (104)  all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | | ALPHA: (104) implies:
% 17.77/3.16  | | | | | | |   (105)  all_4_21 = e2
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | | REF_CLOSE: (4), (6), (7), (9), (24), (78), (79), (82), (88), (105)
% 17.77/3.16  | | | | | | |            are inconsistent by sub-proof #7.
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | Case 2:
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | |   (106)  all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2)
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | | ALPHA: (106) implies:
% 17.77/3.16  | | | | | | |   (107)  all_4_21 = e2
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | | REF_CLOSE: (4), (6), (7), (9), (24), (78), (79), (82), (88), (107)
% 17.77/3.16  | | | | | | |            are inconsistent by sub-proof #7.
% 17.77/3.16  | | | | | | | 
% 17.77/3.16  | | | | | | End of split
% 17.77/3.16  | | | | | | 
% 17.77/3.16  | | | | | End of split
% 17.77/3.16  | | | | | 
% 17.77/3.16  | | | | End of split
% 17.77/3.16  | | | | 
% 17.77/3.16  | | | End of split
% 17.77/3.16  | | | 
% 17.77/3.16  | | Case 2:
% 17.77/3.16  | | | 
% 17.77/3.17  | | |   (108)  (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)) | (all_4_21 =
% 17.77/3.17  | | |            e1 & all_4_23 = e3 &  ~ (all_4_13 = e1)) | (all_4_21 = e0 &
% 17.77/3.17  | | |            all_4_24 = e3 &  ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24
% 17.77/3.17  | | |            = e3 &  ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 & 
% 17.77/3.17  | | |            ~ (all_4_10 = e2)) | (all_4_22 = e1 & all_4_23 = e2 &  ~
% 17.77/3.17  | | |            (all_4_14 = e1)) | (all_4_22 = e0 & all_4_24 = e2 &  ~
% 17.77/3.17  | | |            (all_4_11 = e2)) | (all_4_22 = e0 & all_4_24 = e2 &  ~
% 17.77/3.17  | | |            (all_4_18 = e0)) | (all_4_23 = e0 & all_4_24 = e1 &  ~
% 17.77/3.17  | | |            (all_4_15 = e1)) | (all_4_23 = e0 & all_4_24 = e1 &  ~
% 17.77/3.17  | | |            (all_4_19 = e0))
% 17.77/3.17  | | | 
% 17.77/3.17  | | | BETA: splitting (108) gives:
% 17.77/3.17  | | | 
% 17.77/3.17  | | | Case 1:
% 17.77/3.17  | | | | 
% 17.77/3.17  | | | |   (109)  (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)) | (all_4_21
% 17.77/3.17  | | | |            = e1 & all_4_23 = e3 &  ~ (all_4_13 = e1)) | (all_4_21 = e0 &
% 17.77/3.17  | | | |            all_4_24 = e3 &  ~ (all_4_7 = e3)) | (all_4_21 = e0 &
% 17.77/3.17  | | | |            all_4_24 = e3 &  ~ (all_4_17 = e0)) | (all_4_22 = e1 &
% 17.77/3.17  | | | |            all_4_23 = e2 &  ~ (all_4_10 = e2))
% 17.77/3.17  | | | | 
% 17.77/3.17  | | | | BETA: splitting (109) gives:
% 17.77/3.17  | | | | 
% 17.77/3.17  | | | | Case 1:
% 17.77/3.17  | | | | | 
% 17.77/3.17  | | | | |   (110)  (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)) |
% 17.77/3.17  | | | | |          (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_13 = e1))
% 17.77/3.17  | | | | | 
% 17.77/3.17  | | | | | BETA: splitting (110) gives:
% 17.77/3.17  | | | | | 
% 17.77/3.17  | | | | | Case 1:
% 17.77/3.17  | | | | | | 
% 17.77/3.17  | | | | | |   (111)  all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | ALPHA: (111) implies:
% 17.80/3.17  | | | | | |   (112)  all_4_23 = e3
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | REF_CLOSE: (10), (82), (112) are inconsistent by sub-proof #6.
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | Case 2:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | |   (113)  all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_13 = e1)
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | ALPHA: (113) implies:
% 17.80/3.17  | | | | | |   (114)  all_4_23 = e3
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | REF_CLOSE: (10), (82), (114) are inconsistent by sub-proof #6.
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | End of split
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | Case 2:
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | |   (115)  (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_7 = e3)) |
% 17.80/3.17  | | | | |          (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 = e0)) |
% 17.80/3.17  | | | | |          (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2))
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | | BETA: splitting (115) gives:
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | | Case 1:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | |   (116)  all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_7 = e3)
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | ALPHA: (116) implies:
% 17.80/3.17  | | | | | |   (117)  all_4_21 = e0
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (22), (24), (78),
% 17.80/3.17  | | | | | |            (79), (82), (83), (85), (117) are inconsistent by
% 17.80/3.17  | | | | | |            sub-proof #3.
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | Case 2:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | |   (118)  (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 = e0)) |
% 17.80/3.17  | | | | | |          (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2))
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | BETA: splitting (118) gives:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | Case 1:
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | |   (119)  all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 = e0)
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | ALPHA: (119) implies:
% 17.80/3.17  | | | | | | |   (120)  all_4_21 = e0
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (22), (24), (78),
% 17.80/3.17  | | | | | | |            (79), (82), (83), (85), (120) are inconsistent by
% 17.80/3.17  | | | | | | |            sub-proof #3.
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | Case 2:
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | |   (121)  all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2)
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | ALPHA: (121) implies:
% 17.80/3.17  | | | | | | |   (122)  all_4_22 = e1
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | REF_CLOSE: (7), (79), (122) are inconsistent by sub-proof #2.
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | End of split
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | End of split
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | End of split
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | Case 2:
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | |   (123)  (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 = e1)) |
% 17.80/3.17  | | | |          (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2)) |
% 17.80/3.17  | | | |          (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 = e0)) |
% 17.80/3.17  | | | |          (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)) |
% 17.80/3.17  | | | |          (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | | BETA: splitting (123) gives:
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | | Case 1:
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | |   (124)  (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 = e1)) |
% 17.80/3.17  | | | | |          (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2))
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | | BETA: splitting (124) gives:
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | | Case 1:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | |   (125)  all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 = e1)
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | ALPHA: (125) implies:
% 17.80/3.17  | | | | | |   (126)  all_4_22 = e1
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | REF_CLOSE: (7), (79), (126) are inconsistent by sub-proof #2.
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | Case 2:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | |   (127)  all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2)
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | ALPHA: (127) implies:
% 17.80/3.17  | | | | | |   (128)  all_4_24 = e2
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | COMBINE_EQS: (88), (128) imply:
% 17.80/3.17  | | | | | |   (129)  e2 = e0
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | REDUCE: (5), (129) imply:
% 17.80/3.17  | | | | | |   (130)  $false
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | CLOSE: (130) is inconsistent.
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | End of split
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | Case 2:
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | |   (131)  (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 = e0)) |
% 17.80/3.17  | | | | |          (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)) |
% 17.80/3.17  | | | | |          (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | | BETA: splitting (131) gives:
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | | Case 1:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | |   (132)  all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 = e0)
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | ALPHA: (132) implies:
% 17.80/3.17  | | | | | |   (133)  all_4_24 = e2
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | COMBINE_EQS: (88), (133) imply:
% 17.80/3.17  | | | | | |   (134)  e2 = e0
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | REDUCE: (5), (134) imply:
% 17.80/3.17  | | | | | |   (135)  $false
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | CLOSE: (135) is inconsistent.
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | Case 2:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | |   (136)  (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)) |
% 17.80/3.17  | | | | | |          (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | BETA: splitting (136) gives:
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | | Case 1:
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | |   (137)  all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | ALPHA: (137) implies:
% 17.80/3.17  | | | | | | |   (138)  all_4_24 = e1
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | REF_CLOSE: (4), (88), (138) are inconsistent by sub-proof #1.
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | Case 2:
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | |   (139)  all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0)
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | ALPHA: (139) implies:
% 17.80/3.17  | | | | | | |   (140)  all_4_24 = e1
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | | REF_CLOSE: (4), (88), (140) are inconsistent by sub-proof #1.
% 17.80/3.17  | | | | | | | 
% 17.80/3.17  | | | | | | End of split
% 17.80/3.17  | | | | | | 
% 17.80/3.17  | | | | | End of split
% 17.80/3.17  | | | | | 
% 17.80/3.17  | | | | End of split
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | End of split
% 17.80/3.17  | | | 
% 17.80/3.17  | | End of split
% 17.80/3.17  | | 
% 17.80/3.17  | Case 2:
% 17.80/3.17  | | 
% 17.80/3.17  | |   (141)   ~ (all_10_24 = e0)
% 17.80/3.17  | | 
% 17.80/3.17  | | REDUCE: (44), (141) imply:
% 17.80/3.17  | |   (142)   ~ (all_4_24 = e0)
% 17.80/3.17  | | 
% 17.80/3.17  | | BETA: splitting (23) gives:
% 17.80/3.17  | | 
% 17.80/3.17  | | Case 1:
% 17.80/3.17  | | | 
% 17.80/3.17  | | |   (143)  all_4_20 = e0
% 17.80/3.17  | | | 
% 17.80/3.17  | | | COMBINE_EQS: (78), (143) imply:
% 17.80/3.17  | | |   (144)  e2 = e0
% 17.80/3.17  | | | 
% 17.80/3.17  | | | SIMP: (144) implies:
% 17.80/3.17  | | |   (145)  e2 = e0
% 17.80/3.17  | | | 
% 17.80/3.17  | | | REDUCE: (5), (145) imply:
% 17.80/3.17  | | |   (146)  $false
% 17.80/3.17  | | | 
% 17.80/3.17  | | | CLOSE: (146) is inconsistent.
% 17.80/3.17  | | | 
% 17.80/3.17  | | Case 2:
% 17.80/3.17  | | | 
% 17.80/3.17  | | |   (147)   ~ (all_4_20 = e0)
% 17.80/3.17  | | |   (148)  all_4_21 = e0 | all_4_22 = e0 | all_4_23 = e0 | all_4_24 = e0
% 17.80/3.17  | | | 
% 17.80/3.17  | | | BETA: splitting (148) gives:
% 17.80/3.17  | | | 
% 17.80/3.17  | | | Case 1:
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | |   (149)  all_4_21 = e0
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (22), (24), (78), (79),
% 17.80/3.17  | | | |            (82), (83), (85), (149) are inconsistent by sub-proof #3.
% 17.80/3.17  | | | | 
% 17.80/3.17  | | | Case 2:
% 17.80/3.17  | | | | 
% 17.80/3.18  | | | |   (150)  all_4_22 = e0 | all_4_23 = e0 | all_4_24 = e0
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | | BETA: splitting (150) gives:
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | | Case 1:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | |   (151)  all_4_22 = e0
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | COMBINE_EQS: (79), (151) imply:
% 17.80/3.18  | | | | |   (152)  e3 = e0
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | SIMP: (152) implies:
% 17.80/3.18  | | | | |   (153)  e3 = e0
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | REDUCE: (83), (153) imply:
% 17.80/3.18  | | | | |   (154)  $false
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | CLOSE: (154) is inconsistent.
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | Case 2:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | |   (155)  all_4_23 = e0 | all_4_24 = e0
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | BETA: splitting (155) gives:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | Case 1:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | |   (156)  all_4_23 = e0
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | COMBINE_EQS: (82), (156) imply:
% 17.80/3.18  | | | | | |   (157)  e4 = e0
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | SIMP: (157) implies:
% 17.80/3.18  | | | | | |   (158)  e4 = e0
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | REDUCE: (85), (158) imply:
% 17.80/3.18  | | | | | |   (159)  $false
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | CLOSE: (159) is inconsistent.
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | Case 2:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | |   (160)  all_4_24 = e0
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | REDUCE: (142), (160) imply:
% 17.80/3.18  | | | | | |   (161)  $false
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | CLOSE: (161) is inconsistent.
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | End of split
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | End of split
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | End of split
% 17.80/3.18  | | | 
% 17.80/3.18  | | End of split
% 17.80/3.18  | | 
% 17.80/3.18  | End of split
% 17.80/3.18  | 
% 17.80/3.18  End of proof
% 17.80/3.18  
% 17.80/3.18  Sub-proof #1 shows that the following formulas are inconsistent:
% 17.80/3.18  ----------------------------------------------------------------
% 17.80/3.18    (1)  all_4_24 = e1
% 17.80/3.18    (2)  all_4_24 = e0
% 17.80/3.18    (3)   ~ (e1 = e0)
% 17.80/3.18  
% 17.80/3.18  Begin of proof
% 17.80/3.18  | 
% 17.80/3.18  | COMBINE_EQS: (1), (2) imply:
% 17.80/3.18  |   (4)  e1 = e0
% 17.80/3.18  | 
% 17.80/3.18  | SIMP: (4) implies:
% 17.80/3.18  |   (5)  e1 = e0
% 17.80/3.18  | 
% 17.80/3.18  | REDUCE: (3), (5) imply:
% 17.80/3.18  |   (6)  $false
% 17.80/3.18  | 
% 17.80/3.18  | CLOSE: (6) is inconsistent.
% 17.80/3.18  | 
% 17.80/3.18  End of proof
% 17.80/3.18  
% 17.80/3.18  Sub-proof #2 shows that the following formulas are inconsistent:
% 17.80/3.18  ----------------------------------------------------------------
% 17.80/3.18    (1)  all_4_22 = e3
% 17.80/3.18    (2)  all_4_22 = e1
% 17.80/3.18    (3)   ~ (e3 = e1)
% 17.80/3.18  
% 17.80/3.18  Begin of proof
% 17.80/3.18  | 
% 17.80/3.18  | COMBINE_EQS: (1), (2) imply:
% 17.80/3.18  |   (4)  e3 = e1
% 17.80/3.18  | 
% 17.80/3.18  | SIMP: (4) implies:
% 17.80/3.18  |   (5)  e3 = e1
% 17.80/3.18  | 
% 17.80/3.18  | REDUCE: (3), (5) imply:
% 17.80/3.18  |   (6)  $false
% 17.80/3.18  | 
% 17.80/3.18  | CLOSE: (6) is inconsistent.
% 17.80/3.18  | 
% 17.80/3.18  End of proof
% 17.80/3.18  
% 17.80/3.18  Sub-proof #3 shows that the following formulas are inconsistent:
% 17.80/3.18  ----------------------------------------------------------------
% 17.80/3.18    (1)   ~ (e4 = e3)
% 17.80/3.18    (2)   ~ (e3 = e2)
% 17.80/3.18    (3)   ~ (e4 = e1)
% 17.80/3.18    (4)  all_4_20 = e2
% 17.80/3.18    (5)   ~ (e4 = e0)
% 17.80/3.18    (6)  all_4_21 = e0
% 17.80/3.18    (7)   ~ (e3 = e0)
% 17.80/3.18    (8)  all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24
% 17.80/3.18         = e1
% 17.80/3.18    (9)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) | (all_4_20 = e3 &
% 17.80/3.18           all_4_21 = e4 &  ~ (all_4_4 = e3)) | (all_4_20 = e2 & all_4_22 = e4 & 
% 17.80/3.18           ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2))
% 17.80/3.18         | (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4)) | (all_4_20 = e1 &
% 17.80/3.18           all_4_23 = e4 &  ~ (all_4_12 = e1)) | (all_4_20 = e0 & all_4_24 = e4 & 
% 17.80/3.18           ~ (all_4_3 = e4)) | (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 =
% 17.80/3.18             e0)) | (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) |
% 17.80/3.18         (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2)) | (all_4_21 = e1 &
% 17.80/3.18           all_4_23 = e3 &  ~ (all_4_6 = e3)) | (all_4_21 = e1 & all_4_23 = e3 & 
% 17.80/3.18           ~ (all_4_13 = e1)) | (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_7 =
% 17.80/3.18             e3)) | (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 = e0)) |
% 17.80/3.18         (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2)) | (all_4_22 = e1 &
% 17.80/3.18           all_4_23 = e2 &  ~ (all_4_14 = e1)) | (all_4_22 = e0 & all_4_24 = e2 & 
% 17.80/3.18           ~ (all_4_11 = e2)) | (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 =
% 17.80/3.18             e0)) | (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)) |
% 17.80/3.18         (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.18    (10)   ~ (e2 = e0)
% 17.80/3.18    (11)   ~ (e2 = e1)
% 17.80/3.18    (12)   ~ (e3 = e1)
% 17.80/3.18    (13)   ~ (e1 = e0)
% 17.80/3.18    (14)  all_4_22 = e3
% 17.80/3.18    (15)  all_4_23 = e4
% 17.80/3.18  
% 17.80/3.18  Begin of proof
% 17.80/3.18  | 
% 17.80/3.18  | BETA: splitting (8) gives:
% 17.80/3.18  | 
% 17.80/3.18  | Case 1:
% 17.80/3.18  | | 
% 17.80/3.18  | |   (16)  all_4_20 = e1
% 17.80/3.18  | | 
% 17.80/3.18  | | REF_CLOSE: (4), (11), (16) are inconsistent by sub-proof #9.
% 17.80/3.18  | | 
% 17.80/3.18  | Case 2:
% 17.80/3.18  | | 
% 17.80/3.18  | |   (17)   ~ (all_4_20 = e1)
% 17.80/3.18  | |   (18)  all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1
% 17.80/3.18  | | 
% 17.80/3.18  | | BETA: splitting (9) gives:
% 17.80/3.18  | | 
% 17.80/3.18  | | Case 1:
% 17.80/3.18  | | | 
% 17.80/3.18  | | |   (19)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) | (all_4_20 =
% 17.80/3.18  | | |           e3 & all_4_21 = e4 &  ~ (all_4_4 = e3)) | (all_4_20 = e2 &
% 17.80/3.18  | | |           all_4_22 = e4 &  ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22 =
% 17.80/3.18  | | |           e4 &  ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 &  ~
% 17.80/3.18  | | |           (all_4_2 = e4)) | (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12
% 17.80/3.18  | | |             = e1)) | (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_3 = e4)) |
% 17.80/3.18  | | |         (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 = e0)) | (all_4_21 =
% 17.80/3.18  | | |           e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) | (all_4_21 = e2 &
% 17.80/3.18  | | |           all_4_22 = e3 &  ~ (all_4_9 = e2))
% 17.80/3.18  | | | 
% 17.80/3.18  | | | BETA: splitting (19) gives:
% 17.80/3.18  | | | 
% 17.80/3.18  | | | Case 1:
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | |   (20)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) | (all_4_20
% 17.80/3.18  | | | |           = e3 & all_4_21 = e4 &  ~ (all_4_4 = e3)) | (all_4_20 = e2 &
% 17.80/3.18  | | | |           all_4_22 = e4 &  ~ (all_4_1 = e4)) | (all_4_20 = e2 & all_4_22
% 17.80/3.18  | | | |           = e4 &  ~ (all_4_8 = e2)) | (all_4_20 = e1 & all_4_23 = e4 & 
% 17.80/3.18  | | | |           ~ (all_4_2 = e4))
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | | BETA: splitting (20) gives:
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | | Case 1:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | |   (21)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) |
% 17.80/3.18  | | | | |         (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_4 = e3))
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | REF_CLOSE: (2), (4), (21) are inconsistent by sub-proof #14.
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | Case 2:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | |   (22)  (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_1 = e4)) |
% 17.80/3.18  | | | | |         (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2)) |
% 17.80/3.18  | | | | |         (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4))
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | BETA: splitting (22) gives:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | Case 1:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | |   (23)  all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_1 = e4)
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | ALPHA: (23) implies:
% 17.80/3.18  | | | | | |   (24)  all_4_22 = e4
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | COMBINE_EQS: (14), (24) imply:
% 17.80/3.18  | | | | | |   (25)  e4 = e3
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | REDUCE: (1), (25) imply:
% 17.80/3.18  | | | | | |   (26)  $false
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | CLOSE: (26) is inconsistent.
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | Case 2:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | |   (27)  (all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2)) |
% 17.80/3.18  | | | | | |         (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4))
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | BETA: splitting (27) gives:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | Case 1:
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | |   (28)  all_4_20 = e2 & all_4_22 = e4 &  ~ (all_4_8 = e2)
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | ALPHA: (28) implies:
% 17.80/3.18  | | | | | | |   (29)  all_4_22 = e4
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | COMBINE_EQS: (14), (29) imply:
% 17.80/3.18  | | | | | | |   (30)  e4 = e3
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | REDUCE: (1), (30) imply:
% 17.80/3.18  | | | | | | |   (31)  $false
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | CLOSE: (31) is inconsistent.
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | Case 2:
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | |   (32)  all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4)
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | REF_CLOSE: (4), (11), (32) are inconsistent by sub-proof #12.
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | End of split
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | End of split
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | End of split
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | Case 2:
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | |   (33)  (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12 = e1)) | (all_4_20
% 17.80/3.18  | | | |           = e0 & all_4_24 = e4 &  ~ (all_4_3 = e4)) | (all_4_20 = e0 &
% 17.80/3.18  | | | |           all_4_24 = e4 &  ~ (all_4_16 = e0)) | (all_4_21 = e2 &
% 17.80/3.18  | | | |           all_4_22 = e3 &  ~ (all_4_5 = e3)) | (all_4_21 = e2 & all_4_22
% 17.80/3.18  | | | |           = e3 &  ~ (all_4_9 = e2))
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | | BETA: splitting (33) gives:
% 17.80/3.18  | | | | 
% 17.80/3.18  | | | | Case 1:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | |   (34)  (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12 = e1)) |
% 17.80/3.18  | | | | |         (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_3 = e4))
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | REF_CLOSE: (4), (10), (11), (34) are inconsistent by sub-proof #11.
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | Case 2:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | |   (35)  (all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 = e0)) |
% 17.80/3.18  | | | | |         (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) |
% 17.80/3.18  | | | | |         (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2))
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | BETA: splitting (35) gives:
% 17.80/3.18  | | | | | 
% 17.80/3.18  | | | | | Case 1:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | |   (36)  all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 = e0)
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | REF_CLOSE: (4), (10), (36) are inconsistent by sub-proof #10.
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | Case 2:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | |   (37)  (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)) |
% 17.80/3.18  | | | | | |         (all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2))
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | BETA: splitting (37) gives:
% 17.80/3.18  | | | | | | 
% 17.80/3.18  | | | | | | Case 1:
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | |   (38)  all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_5 = e3)
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | ALPHA: (38) implies:
% 17.80/3.18  | | | | | | |   (39)  all_4_21 = e2
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | COMBINE_EQS: (6), (39) imply:
% 17.80/3.18  | | | | | | |   (40)  e2 = e0
% 17.80/3.18  | | | | | | | 
% 17.80/3.18  | | | | | | | REDUCE: (10), (40) imply:
% 17.80/3.19  | | | | | | |   (41)  $false
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | CLOSE: (41) is inconsistent.
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | Case 2:
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | |   (42)  all_4_21 = e2 & all_4_22 = e3 &  ~ (all_4_9 = e2)
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | ALPHA: (42) implies:
% 17.80/3.19  | | | | | | |   (43)  all_4_21 = e2
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | COMBINE_EQS: (6), (43) imply:
% 17.80/3.19  | | | | | | |   (44)  e2 = e0
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | REDUCE: (10), (44) imply:
% 17.80/3.19  | | | | | | |   (45)  $false
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | CLOSE: (45) is inconsistent.
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | End of split
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | End of split
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | End of split
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | End of split
% 17.80/3.19  | | | 
% 17.80/3.19  | | Case 2:
% 17.80/3.19  | | | 
% 17.80/3.19  | | |   (46)  (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)) | (all_4_21 =
% 17.80/3.19  | | |           e1 & all_4_23 = e3 &  ~ (all_4_13 = e1)) | (all_4_21 = e0 &
% 17.80/3.19  | | |           all_4_24 = e3 &  ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24 =
% 17.80/3.19  | | |           e3 &  ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 &  ~
% 17.80/3.19  | | |           (all_4_10 = e2)) | (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14
% 17.80/3.19  | | |             = e1)) | (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2))
% 17.80/3.19  | | |         | (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 = e0)) | (all_4_23
% 17.80/3.19  | | |           = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)) | (all_4_23 = e0 &
% 17.80/3.19  | | |           all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.19  | | | 
% 17.80/3.19  | | | BETA: splitting (46) gives:
% 17.80/3.19  | | | 
% 17.80/3.19  | | | Case 1:
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | |   (47)  (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)) | (all_4_21
% 17.80/3.19  | | | |           = e1 & all_4_23 = e3 &  ~ (all_4_13 = e1)) | (all_4_21 = e0 &
% 17.80/3.19  | | | |           all_4_24 = e3 &  ~ (all_4_7 = e3)) | (all_4_21 = e0 & all_4_24
% 17.80/3.19  | | | |           = e3 &  ~ (all_4_17 = e0)) | (all_4_22 = e1 & all_4_23 = e2 & 
% 17.80/3.19  | | | |           ~ (all_4_10 = e2))
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | | BETA: splitting (47) gives:
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | | Case 1:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | |   (48)  (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)) |
% 17.80/3.19  | | | | |         (all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_13 = e1))
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | BETA: splitting (48) gives:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | Case 1:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (49)  all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_6 = e3)
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | ALPHA: (49) implies:
% 17.80/3.19  | | | | | |   (50)  all_4_21 = e1
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | COMBINE_EQS: (6), (50) imply:
% 17.80/3.19  | | | | | |   (51)  e1 = e0
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | REDUCE: (13), (51) imply:
% 17.80/3.19  | | | | | |   (52)  $false
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | CLOSE: (52) is inconsistent.
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | Case 2:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (53)  all_4_21 = e1 & all_4_23 = e3 &  ~ (all_4_13 = e1)
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | ALPHA: (53) implies:
% 17.80/3.19  | | | | | |   (54)  all_4_21 = e1
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | COMBINE_EQS: (6), (54) imply:
% 17.80/3.19  | | | | | |   (55)  e1 = e0
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | REDUCE: (13), (55) imply:
% 17.80/3.19  | | | | | |   (56)  $false
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | CLOSE: (56) is inconsistent.
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | End of split
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | Case 2:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | |   (57)  (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_7 = e3)) |
% 17.80/3.19  | | | | |         (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 = e0)) |
% 17.80/3.19  | | | | |         (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2))
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | BETA: splitting (57) gives:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | Case 1:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (58)  all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_7 = e3)
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | ALPHA: (58) implies:
% 17.80/3.19  | | | | | |   (59)  all_4_24 = e3
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | REF_CLOSE: (3), (6), (12), (13), (14), (15), (18), (59) are
% 17.80/3.19  | | | | | |            inconsistent by sub-proof #5.
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | Case 2:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (60)  (all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 = e0)) |
% 17.80/3.19  | | | | | |         (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2))
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | BETA: splitting (60) gives:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | Case 1:
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | |   (61)  all_4_21 = e0 & all_4_24 = e3 &  ~ (all_4_17 = e0)
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | ALPHA: (61) implies:
% 17.80/3.19  | | | | | | |   (62)  all_4_24 = e3
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | REF_CLOSE: (3), (6), (12), (13), (14), (15), (18), (62) are
% 17.80/3.19  | | | | | | |            inconsistent by sub-proof #5.
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | Case 2:
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | |   (63)  all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_10 = e2)
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | ALPHA: (63) implies:
% 17.80/3.19  | | | | | | |   (64)  all_4_22 = e1
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | COMBINE_EQS: (14), (64) imply:
% 17.80/3.19  | | | | | | |   (65)  e3 = e1
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | REDUCE: (12), (65) imply:
% 17.80/3.19  | | | | | | |   (66)  $false
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | CLOSE: (66) is inconsistent.
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | End of split
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | End of split
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | End of split
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | Case 2:
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | |   (67)  (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 = e1)) | (all_4_22
% 17.80/3.19  | | | |           = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2)) | (all_4_22 = e0 &
% 17.80/3.19  | | | |           all_4_24 = e2 &  ~ (all_4_18 = e0)) | (all_4_23 = e0 &
% 17.80/3.19  | | | |           all_4_24 = e1 &  ~ (all_4_15 = e1)) | (all_4_23 = e0 &
% 17.80/3.19  | | | |           all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | | BETA: splitting (67) gives:
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | | Case 1:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | |   (68)  (all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 = e1)) |
% 17.80/3.19  | | | | |         (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2))
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | BETA: splitting (68) gives:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | Case 1:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (69)  all_4_22 = e1 & all_4_23 = e2 &  ~ (all_4_14 = e1)
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | ALPHA: (69) implies:
% 17.80/3.19  | | | | | |   (70)  all_4_22 = e1
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | COMBINE_EQS: (14), (70) imply:
% 17.80/3.19  | | | | | |   (71)  e3 = e1
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | REDUCE: (12), (71) imply:
% 17.80/3.19  | | | | | |   (72)  $false
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | CLOSE: (72) is inconsistent.
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | Case 2:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (73)  all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_11 = e2)
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | ALPHA: (73) implies:
% 17.80/3.19  | | | | | |   (74)  all_4_22 = e0
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | COMBINE_EQS: (14), (74) imply:
% 17.80/3.19  | | | | | |   (75)  e3 = e0
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | REDUCE: (7), (75) imply:
% 17.80/3.19  | | | | | |   (76)  $false
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | CLOSE: (76) is inconsistent.
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | End of split
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | Case 2:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | |   (77)  (all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 = e0)) |
% 17.80/3.19  | | | | |         (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)) |
% 17.80/3.19  | | | | |         (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | BETA: splitting (77) gives:
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | | Case 1:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (78)  all_4_22 = e0 & all_4_24 = e2 &  ~ (all_4_18 = e0)
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | ALPHA: (78) implies:
% 17.80/3.19  | | | | | |   (79)  all_4_22 = e0
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | COMBINE_EQS: (14), (79) imply:
% 17.80/3.19  | | | | | |   (80)  e3 = e0
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | REDUCE: (7), (80) imply:
% 17.80/3.19  | | | | | |   (81)  $false
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | CLOSE: (81) is inconsistent.
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | Case 2:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | |   (82)  (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)) |
% 17.80/3.19  | | | | | |         (all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0))
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | BETA: splitting (82) gives:
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | | Case 1:
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | |   (83)  all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_15 = e1)
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | ALPHA: (83) implies:
% 17.80/3.19  | | | | | | |   (84)  all_4_23 = e0
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | REF_CLOSE: (5), (15), (84) are inconsistent by sub-proof #4.
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | Case 2:
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | |   (85)  all_4_23 = e0 & all_4_24 = e1 &  ~ (all_4_19 = e0)
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | ALPHA: (85) implies:
% 17.80/3.19  | | | | | | |   (86)  all_4_23 = e0
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | | REF_CLOSE: (5), (15), (86) are inconsistent by sub-proof #4.
% 17.80/3.19  | | | | | | | 
% 17.80/3.19  | | | | | | End of split
% 17.80/3.19  | | | | | | 
% 17.80/3.19  | | | | | End of split
% 17.80/3.19  | | | | | 
% 17.80/3.19  | | | | End of split
% 17.80/3.19  | | | | 
% 17.80/3.19  | | | End of split
% 17.80/3.19  | | | 
% 17.80/3.19  | | End of split
% 17.80/3.19  | | 
% 17.80/3.19  | End of split
% 17.80/3.19  | 
% 17.80/3.19  End of proof
% 17.80/3.19  
% 17.80/3.19  Sub-proof #4 shows that the following formulas are inconsistent:
% 17.80/3.19  ----------------------------------------------------------------
% 17.80/3.19    (1)  all_4_23 = e4
% 17.80/3.19    (2)  all_4_23 = e0
% 17.80/3.19    (3)   ~ (e4 = e0)
% 17.80/3.19  
% 17.80/3.19  Begin of proof
% 17.80/3.19  | 
% 17.80/3.19  | COMBINE_EQS: (1), (2) imply:
% 17.80/3.19  |   (4)  e4 = e0
% 17.80/3.19  | 
% 17.80/3.19  | SIMP: (4) implies:
% 17.80/3.19  |   (5)  e4 = e0
% 17.80/3.19  | 
% 17.80/3.19  | REDUCE: (3), (5) imply:
% 17.80/3.19  |   (6)  $false
% 17.80/3.19  | 
% 17.80/3.19  | CLOSE: (6) is inconsistent.
% 17.80/3.19  | 
% 17.80/3.19  End of proof
% 17.80/3.19  
% 17.80/3.19  Sub-proof #5 shows that the following formulas are inconsistent:
% 17.80/3.19  ----------------------------------------------------------------
% 17.80/3.19    (1)   ~ (e4 = e1)
% 17.80/3.19    (2)  all_4_21 = e0
% 17.80/3.19    (3)  all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1
% 17.80/3.19    (4)  all_4_24 = e3
% 17.80/3.19    (5)   ~ (e3 = e1)
% 17.80/3.19    (6)   ~ (e1 = e0)
% 17.80/3.19    (7)  all_4_22 = e3
% 17.80/3.19    (8)  all_4_23 = e4
% 17.80/3.19  
% 17.80/3.19  Begin of proof
% 17.80/3.19  | 
% 17.80/3.19  | BETA: splitting (3) gives:
% 17.80/3.19  | 
% 17.80/3.19  | Case 1:
% 17.80/3.19  | | 
% 17.80/3.19  | |   (9)  all_4_21 = e1
% 17.80/3.19  | | 
% 17.80/3.19  | | COMBINE_EQS: (2), (9) imply:
% 17.80/3.19  | |   (10)  e1 = e0
% 17.80/3.19  | | 
% 17.80/3.19  | | REDUCE: (6), (10) imply:
% 17.80/3.19  | |   (11)  $false
% 17.80/3.19  | | 
% 17.80/3.19  | | CLOSE: (11) is inconsistent.
% 17.80/3.19  | | 
% 17.80/3.19  | Case 2:
% 17.80/3.19  | | 
% 17.80/3.19  | |   (12)  all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1
% 17.80/3.19  | | 
% 17.80/3.19  | | BETA: splitting (12) gives:
% 17.80/3.19  | | 
% 17.80/3.19  | | Case 1:
% 17.80/3.19  | | | 
% 17.80/3.19  | | |   (13)  all_4_22 = e1
% 17.80/3.19  | | | 
% 17.80/3.19  | | | COMBINE_EQS: (7), (13) imply:
% 17.80/3.19  | | |   (14)  e3 = e1
% 17.80/3.19  | | | 
% 17.80/3.19  | | | REDUCE: (5), (14) imply:
% 17.80/3.19  | | |   (15)  $false
% 17.80/3.19  | | | 
% 17.80/3.19  | | | CLOSE: (15) is inconsistent.
% 17.80/3.19  | | | 
% 17.80/3.19  | | Case 2:
% 17.80/3.19  | | | 
% 17.80/3.19  | | |   (16)   ~ (all_4_22 = e1)
% 17.80/3.19  | | |   (17)  all_4_23 = e1 | all_4_24 = e1
% 17.80/3.19  | | | 
% 17.80/3.19  | | | BETA: splitting (17) gives:
% 17.80/3.19  | | | 
% 17.80/3.19  | | | Case 1:
% 17.80/3.19  | | | | 
% 17.80/3.20  | | | |   (18)  all_4_23 = e1
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | REF_CLOSE: (1), (8), (18) are inconsistent by sub-proof #8.
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | Case 2:
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | |   (19)  all_4_24 = e1
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | COMBINE_EQS: (4), (19) imply:
% 17.80/3.20  | | | |   (20)  e3 = e1
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | SIMP: (20) implies:
% 17.80/3.20  | | | |   (21)  e3 = e1
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | REDUCE: (5), (21) imply:
% 17.80/3.20  | | | |   (22)  $false
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | CLOSE: (22) is inconsistent.
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | End of split
% 17.80/3.20  | | | 
% 17.80/3.20  | | End of split
% 17.80/3.20  | | 
% 17.80/3.20  | End of split
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #6 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  all_4_23 = e4
% 17.80/3.20    (2)  all_4_23 = e3
% 17.80/3.20    (3)   ~ (e4 = e3)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | COMBINE_EQS: (1), (2) imply:
% 17.80/3.20  |   (4)  e4 = e3
% 17.80/3.20  | 
% 17.80/3.20  | SIMP: (4) implies:
% 17.80/3.20  |   (5)  e4 = e3
% 17.80/3.20  | 
% 17.80/3.20  | REDUCE: (3), (5) imply:
% 17.80/3.20  |   (6)  $false
% 17.80/3.20  | 
% 17.80/3.20  | CLOSE: (6) is inconsistent.
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #7 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)   ~ (e4 = e1)
% 17.80/3.20    (2)  all_4_21 = e2
% 17.80/3.20    (3)  all_4_20 = e2
% 17.80/3.20    (4)  all_4_24 = e0
% 17.80/3.20    (5)  all_4_20 = e1 | all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24
% 17.80/3.20         = e1
% 17.80/3.20    (6)   ~ (e2 = e1)
% 17.80/3.20    (7)   ~ (e3 = e1)
% 17.80/3.20    (8)   ~ (e1 = e0)
% 17.80/3.20    (9)  all_4_22 = e3
% 17.80/3.20    (10)  all_4_23 = e4
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | BETA: splitting (5) gives:
% 17.80/3.20  | 
% 17.80/3.20  | Case 1:
% 17.80/3.20  | | 
% 17.80/3.20  | |   (11)  all_4_20 = e1
% 17.80/3.20  | | 
% 17.80/3.20  | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #9.
% 17.80/3.20  | | 
% 17.80/3.20  | Case 2:
% 17.80/3.20  | | 
% 17.80/3.20  | |   (12)   ~ (all_4_20 = e1)
% 17.80/3.20  | |   (13)  all_4_21 = e1 | all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1
% 17.80/3.20  | | 
% 17.80/3.20  | | BETA: splitting (13) gives:
% 17.80/3.20  | | 
% 17.80/3.20  | | Case 1:
% 17.80/3.20  | | | 
% 17.80/3.20  | | |   (14)  all_4_21 = e1
% 17.80/3.20  | | | 
% 17.80/3.20  | | | COMBINE_EQS: (2), (14) imply:
% 17.80/3.20  | | |   (15)  e2 = e1
% 17.80/3.20  | | | 
% 17.80/3.20  | | | SIMP: (15) implies:
% 17.80/3.20  | | |   (16)  e2 = e1
% 17.80/3.20  | | | 
% 17.80/3.20  | | | REDUCE: (6), (16) imply:
% 17.80/3.20  | | |   (17)  $false
% 17.80/3.20  | | | 
% 17.80/3.20  | | | CLOSE: (17) is inconsistent.
% 17.80/3.20  | | | 
% 17.80/3.20  | | Case 2:
% 17.80/3.20  | | | 
% 17.80/3.20  | | |   (18)  all_4_22 = e1 | all_4_23 = e1 | all_4_24 = e1
% 17.80/3.20  | | | 
% 17.80/3.20  | | | BETA: splitting (18) gives:
% 17.80/3.20  | | | 
% 17.80/3.20  | | | Case 1:
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | |   (19)  all_4_22 = e1
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | COMBINE_EQS: (9), (19) imply:
% 17.80/3.20  | | | |   (20)  e3 = e1
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | REDUCE: (7), (20) imply:
% 17.80/3.20  | | | |   (21)  $false
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | CLOSE: (21) is inconsistent.
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | Case 2:
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | |   (22)  all_4_23 = e1 | all_4_24 = e1
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | BETA: splitting (22) gives:
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | | Case 1:
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | |   (23)  all_4_23 = e1
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | | REF_CLOSE: (1), (10), (23) are inconsistent by sub-proof #8.
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | Case 2:
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | |   (24)  all_4_24 = e1
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | | COMBINE_EQS: (4), (24) imply:
% 17.80/3.20  | | | | |   (25)  e1 = e0
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | | REDUCE: (8), (25) imply:
% 17.80/3.20  | | | | |   (26)  $false
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | | CLOSE: (26) is inconsistent.
% 17.80/3.20  | | | | | 
% 17.80/3.20  | | | | End of split
% 17.80/3.20  | | | | 
% 17.80/3.20  | | | End of split
% 17.80/3.20  | | | 
% 17.80/3.20  | | End of split
% 17.80/3.20  | | 
% 17.80/3.20  | End of split
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #8 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  all_4_23 = e4
% 17.80/3.20    (2)  all_4_23 = e1
% 17.80/3.20    (3)   ~ (e4 = e1)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | COMBINE_EQS: (1), (2) imply:
% 17.80/3.20  |   (4)  e4 = e1
% 17.80/3.20  | 
% 17.80/3.20  | SIMP: (4) implies:
% 17.80/3.20  |   (5)  e4 = e1
% 17.80/3.20  | 
% 17.80/3.20  | REDUCE: (3), (5) imply:
% 17.80/3.20  |   (6)  $false
% 17.80/3.20  | 
% 17.80/3.20  | CLOSE: (6) is inconsistent.
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #9 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  all_4_20 = e2
% 17.80/3.20    (2)  all_4_20 = e1
% 17.80/3.20    (3)   ~ (e2 = e1)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | COMBINE_EQS: (1), (2) imply:
% 17.80/3.20  |   (4)  e2 = e1
% 17.80/3.20  | 
% 17.80/3.20  | SIMP: (4) implies:
% 17.80/3.20  |   (5)  e2 = e1
% 17.80/3.20  | 
% 17.80/3.20  | REDUCE: (3), (5) imply:
% 17.80/3.20  |   (6)  $false
% 17.80/3.20  | 
% 17.80/3.20  | CLOSE: (6) is inconsistent.
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #10 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_16 = e0)
% 17.80/3.20    (2)  all_4_20 = e2
% 17.80/3.20    (3)   ~ (e2 = e0)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | ALPHA: (1) implies:
% 17.80/3.20  |   (4)  all_4_20 = e0
% 17.80/3.20  | 
% 17.80/3.20  | COMBINE_EQS: (2), (4) imply:
% 17.80/3.20  |   (5)  e2 = e0
% 17.80/3.20  | 
% 17.80/3.20  | REDUCE: (3), (5) imply:
% 17.80/3.20  |   (6)  $false
% 17.80/3.20  | 
% 17.80/3.20  | CLOSE: (6) is inconsistent.
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #11 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  (all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12 = e1)) | (all_4_20 = e0 &
% 17.80/3.20           all_4_24 = e4 &  ~ (all_4_3 = e4))
% 17.80/3.20    (2)  all_4_20 = e2
% 17.80/3.20    (3)   ~ (e2 = e1)
% 17.80/3.20    (4)   ~ (e2 = e0)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | BETA: splitting (1) gives:
% 17.80/3.20  | 
% 17.80/3.20  | Case 1:
% 17.80/3.20  | | 
% 17.80/3.20  | |   (5)  all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_12 = e1)
% 17.80/3.20  | | 
% 17.80/3.20  | | ALPHA: (5) implies:
% 17.80/3.20  | |   (6)  all_4_20 = e1
% 17.80/3.20  | | 
% 17.80/3.20  | | COMBINE_EQS: (2), (6) imply:
% 17.80/3.20  | |   (7)  e2 = e1
% 17.80/3.20  | | 
% 17.80/3.20  | | REDUCE: (3), (7) imply:
% 17.80/3.20  | |   (8)  $false
% 17.80/3.20  | | 
% 17.80/3.20  | | CLOSE: (8) is inconsistent.
% 17.80/3.20  | | 
% 17.80/3.20  | Case 2:
% 17.80/3.20  | | 
% 17.80/3.20  | |   (9)  all_4_20 = e0 & all_4_24 = e4 &  ~ (all_4_3 = e4)
% 17.80/3.20  | | 
% 17.80/3.20  | | ALPHA: (9) implies:
% 17.80/3.20  | |   (10)  all_4_20 = e0
% 17.80/3.20  | | 
% 17.80/3.20  | | COMBINE_EQS: (2), (10) imply:
% 17.80/3.20  | |   (11)  e2 = e0
% 17.80/3.20  | | 
% 17.80/3.20  | | REDUCE: (4), (11) imply:
% 17.80/3.20  | |   (12)  $false
% 17.80/3.20  | | 
% 17.80/3.20  | | CLOSE: (12) is inconsistent.
% 17.80/3.20  | | 
% 17.80/3.20  | End of split
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #12 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  all_4_20 = e1 & all_4_23 = e4 &  ~ (all_4_2 = e4)
% 17.80/3.20    (2)  all_4_20 = e2
% 17.80/3.20    (3)   ~ (e2 = e1)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | ALPHA: (1) implies:
% 17.80/3.20  |   (4)  all_4_20 = e1
% 17.80/3.20  | 
% 17.80/3.20  | COMBINE_EQS: (2), (4) imply:
% 17.80/3.20  |   (5)  e2 = e1
% 17.80/3.20  | 
% 17.80/3.20  | REDUCE: (3), (5) imply:
% 17.80/3.20  |   (6)  $false
% 17.80/3.20  | 
% 17.80/3.20  | CLOSE: (6) is inconsistent.
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #13 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  all_4_22 = e4
% 17.80/3.20    (2)  all_4_22 = e3
% 17.80/3.20    (3)   ~ (e4 = e3)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | COMBINE_EQS: (1), (2) imply:
% 17.80/3.20  |   (4)  e4 = e3
% 17.80/3.20  | 
% 17.80/3.20  | SIMP: (4) implies:
% 17.80/3.20  |   (5)  e4 = e3
% 17.80/3.20  | 
% 17.80/3.20  | REDUCE: (3), (5) imply:
% 17.80/3.20  |   (6)  $false
% 17.80/3.20  | 
% 17.80/3.20  | CLOSE: (6) is inconsistent.
% 17.80/3.20  | 
% 17.80/3.20  End of proof
% 17.80/3.20  
% 17.80/3.20  Sub-proof #14 shows that the following formulas are inconsistent:
% 17.80/3.20  ----------------------------------------------------------------
% 17.80/3.20    (1)  (all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)) | (all_4_20 = e3 &
% 17.80/3.20           all_4_21 = e4 &  ~ (all_4_4 = e3))
% 17.80/3.20    (2)  all_4_20 = e2
% 17.80/3.20    (3)   ~ (e3 = e2)
% 17.80/3.20  
% 17.80/3.20  Begin of proof
% 17.80/3.20  | 
% 17.80/3.20  | BETA: splitting (1) gives:
% 17.80/3.20  | 
% 17.80/3.20  | Case 1:
% 17.80/3.20  | | 
% 17.80/3.20  | |   (4)  all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_0 = e4)
% 17.80/3.20  | | 
% 17.80/3.20  | | ALPHA: (4) implies:
% 17.80/3.20  | |   (5)  all_4_20 = e3
% 17.80/3.20  | | 
% 17.80/3.20  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #15.
% 17.80/3.20  | | 
% 17.80/3.20  | Case 2:
% 17.80/3.20  | | 
% 17.98/3.20  | |   (6)  all_4_20 = e3 & all_4_21 = e4 &  ~ (all_4_4 = e3)
% 17.98/3.20  | | 
% 17.98/3.20  | | ALPHA: (6) implies:
% 17.98/3.20  | |   (7)  all_4_20 = e3
% 17.98/3.20  | | 
% 17.98/3.20  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #15.
% 17.98/3.20  | | 
% 17.98/3.20  | End of split
% 17.98/3.20  | 
% 17.98/3.20  End of proof
% 17.98/3.20  
% 17.98/3.20  Sub-proof #15 shows that the following formulas are inconsistent:
% 17.98/3.20  ----------------------------------------------------------------
% 17.98/3.20    (1)  all_4_20 = e3
% 17.98/3.20    (2)  all_4_20 = e2
% 17.98/3.20    (3)   ~ (e3 = e2)
% 17.98/3.20  
% 17.98/3.20  Begin of proof
% 17.98/3.20  | 
% 17.98/3.20  | COMBINE_EQS: (1), (2) imply:
% 17.98/3.20  |   (4)  e3 = e2
% 17.98/3.20  | 
% 17.98/3.20  | SIMP: (4) implies:
% 17.98/3.20  |   (5)  e3 = e2
% 17.98/3.20  | 
% 17.98/3.20  | REDUCE: (3), (5) imply:
% 17.98/3.20  |   (6)  $false
% 17.98/3.20  | 
% 17.98/3.20  | CLOSE: (6) is inconsistent.
% 17.98/3.20  | 
% 17.98/3.20  End of proof
% 17.98/3.20  % SZS output end Proof for theBenchmark
% 17.98/3.20  
% 17.98/3.20  2591ms
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